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Altium Designer 20.2.6 Build 244 Crack

Altium Designer 20.2.6 Build 244 Crack

Altium Designer 20.2.6 Build 244 Crack

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Circuit Design: Know It All

Circuit Design The Newnes Know It All Series PIC Microcontrollers: Know It All Lucio Di Jasio, Tim Wilmshurst, Dogan .

Author: Darren Ashby


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Circuit Design

The Newnes Know It All Series PIC Microcontrollers: Know It All Lucio Di Jasio, Tim Wilmshurst, Dogan Ibrahim, John Morton, Martin Bates, Jack Smith, D.W. Smith, and Chuck Hellebuyck ISBN: 978-0-7506-8615-0 Embedded Software: Know It All Jean Labrosse, Jack Ganssle, Tammy Noergaard, Robert Oshana, Colin Walls, Keith Curtis, Jason Andrews, David J. Katz, Rick Gentile, Kamal Hyder, and Bob Perrin ISBN: 978-0-7506-8583-2 Embedded Hardware: Know It All Jack Ganssle, Tammy Noergaard, Fred Eady, Lewin Edwards, David J. Katz, Rick Gentile, Ken Arnold, Kamal Hyder, and Bob Perrin ISBN: 978-0-7506-8584-9 Wireless Networking: Know It All Praphul Chandra, Daniel M. Dobkin, Alan Bensky, Ron Olexa, David Lide, and Farid Dowla ISBN: 978-0-7506-8582-5 RF & Wireless Technologies: Know It All Bruce Fette, Roberto Aiello, Praphul Chandra, Daniel Dobkin, Alan Bensky, Douglas Miron, David Lide, Farid Dowla, and Ron Olexa ISBN: 978-0-7506-8581-8 Electrical Engineering: Know It All Clive Maxfield, Alan Bensky, John Bird, W. Bolton, Izzat Darwazeh, Walt Kester, M. A. Laughton, Andrew Leven, Luis Moura, Ron Schmitt, Keith Sueker, Mike Tooley, DF Warne, Tim Williams ISBN: 978-1-85617-528-9 Audio Engineering: Know It All Douglas Self, Richard Brice, Don Davis, Ben Duncan, John Linsley Hood, Morgan Jones, Eugene Patronis, Ian Sinclair, Andrew Singmin, John Watkinson ISBN: 978-1-85617-526-5 Circuit Design: Know It All Darren Ashby, Bonnie Baker, Stuart Ball, John Crowe, Barrie Hayes-Gill, Ian Grout, Ian Hickman, Walt Kester, Ron Mancini, Robert A. Pease, Mike Tooley, Tim Williams, Peter Wilson, Bob Zeidman ISBN: 978-1-85617-527-2 Test and Measurement: Know It All Jon Wilson, Stuart Ball, GMS de Silva,Tony Fischer-Cripps, Dogan Ibrahim, Kevin James, Walt Kester, M. A. Laughton, Chris Nadovich, Alex Porter, Edward Ramsden, Stephen Scheiber, Mike Tooley, D. F. Warne, Tim Williams ISBN: 978-1-85617-530-2 Mobile Wireless Security: Know It All Praphul Chandra, Alan Bensky, Tony Bradley, Chris Hurley, Steve Rackley, John Rittinghouse, James Ransome, Timothy Stapko, George Stefanek, Frank Thornton, Chris Lanthem, Jon Wilson ISBN: 978-1-85617-529-6 For more information on these and magix photostory deluxe 2019 review - Activators Patch Newnes titles visit: www.newnespress.com

Circuit Design Darren Ashby Bonnie Baker Stuart Ball J. Crowe Barrie Hayes-Gill Ian Hickman Walt Kester Ron Mancini Ian Grout Robert A. Pease Mike Tooley Tim Williams Peter Wilson Bob Zeidman

AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO

Newnes is an imprint of Elsevier

Newnes is an imprint of Elsevier 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA Linacre House, Jordan Hill, Oxford OX2 8DP, UK Copyright

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2008, Elsevier Inc. All rights reserved.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333, E-mail: [email protected] You may also complete your request online via the Elsevier homepage (http://elsevier.com), by selecting “Support & Contact” then “Copyright and Permission” and then “Obtaining Permissions.” Library of Congress Cataloging-in-Publication Data Application submitted British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ISBN: 978-1-85617-527-2 For information on all Newnes publications visit our Web site at www.elsevierdirect.com Printed in the United States of America 08 09 10 10 9 8 7 6 5 4 3

2

1

Contents About the Authors. xv Chapter 1: The Fundamentals . 1 1.1 Electrical Fundamentals.1 1.2 Passive Components . 36 1.3 DC Circuits. 87 1.4 Alternating Voltage and Current . 124 1.5 Circuit Simulation . 151 1.6 Intuitive Circuit Design . 166 1.7 Troubleshooting Basic . 177 References . 208

Chapter 2: The Semiconductor Diode.211 References . 215

Chapter 3: Understanding Diodes and Their Problems .217 3.1 Speed Demons . 219 3.2 Turn ’em off—turn ’em on. 220 3.3 Other Strange Things that Diodes Can Do to You. 222 3.4 Zener, Zener, Zener. 225 3.5 Diodes that Glow in the Dark, Efficiently. 228 3.6 Optoisolators . 228 3.7 Assault and Battery . 231 References . 232

Chapter 4: Bipolar Transistors .235 References . 247

Chapter 5: Field-Effect Transistors.249 References . 254

Chapter 6: Identifying and Avoiding Transistor Problems.255 6.1 6.2

More Beta—More Better? . 257 Field-Effect Transistors . 258

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Contents

6.3 Power Transistors may Hog Current . 261 6.4 Apply the 5-Second Rule . 264 6.5 Fabrication Structures make a Difference. 264 6.6 Power-Circuit Design Requires Expertise. 267 6.7 MOSFETs Avoid Secondary Breakdown . 269 References . 270

Chapter 7: Digital Circuit Fundamentals .271 7.1 Digital Technology. 273 References . 278

Chapter 8: Number Systems .279 8.1 8.2 8.3 8.4 8.5 8.6 8.7

Introduction. 279 Decimal–Unsigned Binary Conversion. 280 Signed Binary Numbers. 284 Gray Code . 289 Binary Coded Decimal . 290 Octal-Binary Conversion . 291 Hexadecimal-Binary Conversion. 294

Chapter 9: Binary Data Manipulation .301 9.1 Introduction. 301 9.2 Logical Operations . 302 9.3 Boolean Algebra . 303 9.4 Combinational Logic Gates . 306 9.5 Truth Tables. 308 References . 317

Chapter 10: Combinational Logic Design.319 10.1 Introduction. 319 10.2 NAND and NOR Logic . 332 10.3 Karnaugh Maps . 334 10.4 Don’t Care Conditions. 341 References . 341

Chapter 11: Sequential Logic Design .343 11.1 11.2 11.3 11.4 11.5 11.6

Introduction. 343 Level Sensitive Latches and Edge-triggered Flip-flops . 348 The D Latch and D-type Flip-Flop . 348 Counter Design . 354 State Machine Design. 366 Moore Versus Mealy State Machines. 377

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11.7 Shift Registers. 377 11.8 Digital Scan Path . 379 References . 382

Chapter 12: Memory.383 12.1 12.2 12.3

Introduction . 383 Random Access Memory . 385 Read-only Memory. 386

Chapter 13: Selecting a Design Route.389 13.1 13.2 13.3 13.4 13.5 13.6

Introduction . 389 Discrete Implementation . 391 Mask Programmable ASICs . 400 Field-Programmable Logic. 414 VHDL . 434 Choosing a Design Route . 436

Chapter 14: Designing with Logic ICs.441 14.1

Logic ICs . 441

Chapter 15: Interfacing.455 15.1 15.2 15.3 15.4 15.5 audacity full version crack download - Crack Key For U Mixing Analog and Digital . 455 Generating Digital Levels from Analog Inputs . 458 Protection Against Externally Applied Overvoltages . 461 Isolation . 462 Classic Data Interface Standards . 465 High-Performance Data Interface Standards . 471

Chapter 16: DSP and Digital Filters .477 16.1 Origins of Real-World Signals and Their Units of Measurement . 477 16.2 Reasons for Processing Real-World Signals . 478 16.3 Generation of Real-World Signals. 480 16.4 Methods and Technologies Available for Processing Real-World Signals 480 16.5 Analog Versus Digital Signal Processing . 481 16.6 A Practical Example . 482 16.7 Finite Impulse Response (FIR) Filters . 489 16.8 FIR Filter Implementation In DSP Hardware Using Circular Buffering . 494 16.9 Designing FIR Filters . 497 16.10 Infinite Impulse Response (IIR) Filters . 508 16.11 IIR Filter Design Techniques . 511 16.12 Multirate Filters. 514 16.13 Adaptive Filters . 519 References . 523

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Chapter 17: Dealing with High-Speed Logic .525 References on Dealing with High-Speed Logic . 532 Chapter 18: Bridging the Gap between Analog and Digital .533 18.1 Try to Measure Temperature Digitally . 536 18.2 Road Blocks Abound. 540 18.3 The Ultimate Key to Analog Success. 548 18.4 How Analog and Digital Design Differ . 549 18.5 Time and Its Inversion. 556 18.6 Organizing Your Toolbox . 556 18.7 Set Your Foundation and Move On, Out of The Box . 557 References . 558

Chapter 19: Op-Amps .559 19.1 The Magical Mysterious Op-Amp . 559 19.2 Understanding Op-Amp Parameters . 572 19.3 Modeling Op-Amps . 599 19.4 Finding the Perfect Op-Amp . 600 References . 618

Chapter 20: Analog-to-Digital Converters.619 20.1 20.2 20.3 20.4 20.5 20.6 20.7 20.8 20.9 20.10 20.11 20.12 20.13 20.14

ADCs . 621 Types of ADCs . 624 ADC Comparison . 633 Sample and Hold . 634 Real Parts. 636 Microprocessor Interfacing . 637 Clocked Interfaces . 643 Serial Interfaces. 644 Multichannel ADCs . 650 Internal Microcontroller ADCs. 650 Codecs . 652 Interrupt Rates. 652 Dual-Function Pins On Microcontrollers . 653 Design Checklist . 655

Chapter 21: Sensors.657 21.1 21.2 21.3 21.4 21.5

Instrumentation and Control Systems . 657 Transducers . 659 Sensors. 660 Switches. 667 Semiconductor Temperature Sensors . 672

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Contents 21.6 titanium backup pro key 1.3.2 apk - Free Activators 21.8 21.9 21.10 21.11 21.12 21.13

ix

Thermocouples . 672 Threshold Detection. 674 Outputs . 676 LED Indicators . 676 Driving High-Current Loads . 678 Audible Outputs . 678 Motors. 681 Driving Mains Connected Loads . 682

Chapter 22: Active Filters .685 22.1 Introduction . 685 22.2 Fundamentals of Low-Pass Filters. 686 22.3 Low-Pass Filter Design. 697 22.4 High-Pass Filter Design . 707 22.5 Band-Pass Filter Design. 714 22.6 Band-Rejection Filter Design . 724 22.7 All-Pass Filter Design. 729 22.8 Practical Design Hints . 734 22.9 Filter Coefficient Tables . 744 References . 752

Chapter 23: Radio-Frequency (RF) Circuits .753 23.1 Modulation of Radio Waves . 753 23.2 Low-Power RF Amplifiers. 759 23.3 Stability. 762 23.4 Linearity. 767 23.5 Noise and Dynamic Range . 771 23.6 Impedances and Gain . 773 23.7 Mixers. 778 23.8 Demodulators . 783 23.9 Oscillators . 787 References . 795

Chapter 24: Signal Sources.797 24.1 Voltage References. 797 24.2 NonsinusoidaI Waveform Generators . 800 24.3 Sine Wave Generators . 808 24.4 Voltage-Controlled Oscillators And Phase Detectors . 817 References . 828

Chapter 25: EDA Design Tools for Analog and RF .829 25.1 25.2

The Old Pencil and Paper Design Process. 835 Is Your Simulation Fundamentally Valid?. 838

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Contents 25.3 Macromodels: What Can They Do? . 843 25.4 VHDL-AMS. 849 References . 867

Chapter 26: Useful Circuits .869 26.1 Introduction. 869 26.2 Boundary Conditions . 873 26.3 Amplifiers . 873 26.4 Computing Circuits . 891 26.5 Oscillators . 902 26.6 Some Favorite Circuits . 910 References . 915

Chapter 27: Programmable Logic to ASICs.917 27.1 Programmable Read-Only Memory (PROM). 918 27.2 Programmable Logic Arrays (PLAs) . 922 27.3 Programmable Array Logic (PALs) . 923 27.4 The Masked Gate Array ASIC. 929 27.5 CPLDs and FPGAs. 931 27.6 Summary. 932 References . 932

Chapter 28: Complex Programmable Logic Devices (CPLDs) .933 28.1 CPLD Architectures . 933 28.2 Function Blocks . 934 28.3 I/O Blocks. 936 28.4 Clock Drivers . 937 28.5 Interconnect . 938 28.6 CPLD Technology and Programmable Elements . 940 28.7 Embedded Devices . 940 28.8 Summary: CPLD Selection Criteria . 944 References . 946

Chapter 29: Field Programmable Gate Arrays (FPGAs) .947 29.1 29.2 29.3 29.4 29.5 29.6 29.7 29.8

FPGA Architectures . 947 Configurable Logic Blocks . 948 Configurable I/O Blocks. 951 Embedded Devices . 954 Programmable Interconnect . 955 Clock Circuitry. 957 SRAM vs. Antifuse Programming. 957 Emulating and Prototyping ASICs . 961

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29.9 Summary. 964 References . 965

Chapter 30: Design Automation and Testing for FPGAs .967 30.1 Simulation . 967 30.2 Libraries. 971 30.3 Synthesis . 974 30.4 Physical Design Flow . 977 30.5 Place and Route . 977 30.6 Timing Analysis . 978 30.7 Design Pitfalls . 978 30.8 VHDL Issues for FPGA Design . 979 30.9 Summary. 979 References . 980

Chapter 31: Integrating Processors onto FPGAs .981 31.1 31.2 31.3 31.4

Introduction . 981 A Simple Embedded Processor . 982 Soft Core Processors on an FPGA . 1004 Summary. 1004

Chapter 32: Implementing Digital Filters in VHDL .1005 32.1 32.2 32.3 32.4 32.5 32.6 32.7

Introduction . 1005 Converting S-Domain to Z-Domain . 1006 Implementing Z-Domain Functions in VHDL . 1008 Basic Low-Pass Filter Model . 1013 FIR Filters. 1017 IIR Filters. 1018 Summary. 1018

Chapter 33: Microprocessor and Microcontroller Overview .1019 33.1 33.2 33.3 33.4 33.5 33.6 33.7 33.8 33.9

Microprocessor Systems . 1019 Single-Chip Microcomputers. 1020 Microcontrollers . 1020 Microprocessor Systems . 1020 Data Types . 1024 Data Storage. 1024 The Microprocessor . 1025 Microprocessor Operation . 1032 A Microcontroller System. 1038

Chapter 34: Microcontroller Toolbox .1043 34.1

Microcontroller Supply and Reference . 1043

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Contents 34.2 34.3 34.4 34.5 34.6 34.7 34.8 34.9

Resistor Networks . 1045 Multiple Input Control. 1046 AC Control. 1049 Voltage Monitors and Supervisory Circuits . 1050 Driving Bipolar Transistors. 1051 Driving MOSFETs . 1054 Reading Negative Voltages. 1057 Example Control System . 1059

Chapter 35: Power Supply Overview and Specifications .1071 35.1 35.2 35.3

Power Supplies. 1071 Specifications . 1078 Off-the-Shelf or Roll Your Own . 1078

Chapter 36: Input and Output Parameters .1081 36.1 36.2 36.3 36.4 36.5 36.6 36.7 36.8 36.9 36.10 36.11 36.12 36.13

Voltage . 1081 Current . 1082 Fuses. 1082 Switch-On Surge, or Inrush Current . 1084 Waveform Distortion and Interference . 1087 Frequency. 1090 Efficiency. 1090 Deriving the Input Voltage from the Output. 1092 Low-Load Condition. 1094 Rectifier and Capacitor Selection . 1095 Load and Line Regulation . 1097 Ripple and Noise . 1099 Transient Response. 1101

Chapter 37: Batteries.1103 37.1 37.2 37.3 37.4

Initial Considerations . 1103 Primary Cells . 1108 Secondary Cells. 1110 Charging . 1114

Chapter 38: Layout and Grounding for Analog and Digital Circuits.1117 38.1 38.2 38.3 38.4 38.5 38.6 38.7 38.8

The Similarities of Analog and Digital Layout Practices . 1117 Where the Domains Differ—Ground Planes Can Be a Problem. 1121 Where the Board and Component Parasitics Can Do the Most Damage. 1123 Layout Techniques that Improve ADC Accuracy and Resolution. 1131 The Art of Laying Out Two-Layer Boards . 1135 Current Return Paths With or Without a Ground Plane . 1140 Layout Tricks for a 12-Bit Sensing System . 1142 General Layout Guidelines—Device Placement. 1144

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38.9 General Layout Guidelines—Ground and Power Supply Strategy . 1144 38.10 Signal Traces. 1147 38.11 Did I Say Bypass and Use an Anti-Aliasing Filter?. 1148 38.12 Bypass Capacitors . 1148 38.13 Anti-Aliasing Filters . 1149 38.14 PCB Design Checklist . 1150 References . 1151

Chapter 39: Safety .1153 39.1 39.2 39.3 39.4 39.5

The Hazards of Electricity . 1154 Safety Classes . 1155 Insulation Types . 1156 Design Considerations for Safety Protection. 1156 Fire Hazard . 1158

Chapter 40: Design for Production.1161 40.1 40.2

Checklist . 1162 The Dangers of ESD . 1164

Chapter 41: Testability .1167 41.1 41.2 41.3 41.4

In-Circuit Testing . 1167 Functional Testing . 1168 Boundary Scan and JTAG . 1170 Design Techniques . 1174

Chapter 42: Reliability .1177 42.1 42.2 42.3 42.4 42.5

Definitions. 1177 The Cost of Reliability . 1179 Design for Reliability . 1180 The Value of MTBF Figures . 1184 Design Faults . 1186

Chapter 43: Thermal Management.1187 43.1 43.2 43.3 43.4

Using Thermal Resistance . 1187 Heatsinks. 1193 Power Semiconductor Mounting . 1197 Placement and Layout . 1201

Appendix A Standards.1203 A.1 A.2

British Standards . 1203 IEC Standards . 1206

Index.1207 www.newnespress.com

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About the Authors

Darren Ashby (Chapters 1, 19, 26, and 35) author of Electrical Engineering 101, is a self-described “techno geek with pointy hair.” He considers himself a Jack of all trades, master of none. He figures his common sense came from his dad and his book sense from his mother. Raised on a farm and graduating from Utah State University seemingly ages ago, he has nearly 20 years of experience in the real world as a technician, engineer and a manager. He has worked in diverse areas of compliance, production, testing and his personal favorite, R&D. He jumped at a chance some years back to teach a couple of semesters at his alma mater. For about two years, he wrote regularly for the online magazine “chipcenter. com.” He is currently the Director of electronics R&D at a billion dollar consumer product company. His passions are boats, snowmobiles, motorcycles and pretty much anything with a motor in it. When not at his day job, he spends most his time with his family and a promising R&D consulting/manufacturing firm he started a couple of years ago. He lives with his beautiful wife, four strapping boys and cute little daughter next to the mountains in Richmond, Utah. Bonnie Baker (Chapters 18, 19, 25 and 38) author of A Baker’s Dozen, also writes the monthly “Baker’s Best” for EDN magazine. She has been involved with analog and digital designs and systems for over 20 years. Bonnie started as a manufacturing product engineer supporting analog products at Burr-Brown. From there, Bonnie moved up to IC design, analog division strategic marketer, and then corporate applications engineering manager. In 1998, she joined Microchip Technology and served as their analog division analog/mixed-signal applications engineering manager and staff architect engineer for one of their PICmicro divisions. This expanded her background to

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About the Authors

not only include analog applications, but microcontroller solutions as well. At present, she has returned to the Precision Analog fold at Texas Instruments in Tucson, Arizona. Bonnie holds a Masters of Science in Electrical Engineering from the University of Arizona (Tucson, AZ) and a bachelor’s degree in music education from Northern Arizona University (Flagstaff, AZ). In addition to her fascination with analog design, Bonnie has a drive to share her knowledge and experience and has written almost 300 articles, design notes, and application notes and she is a frequent presenter at technical conferences and shows. Stuart Ball, P.E., (Chapters 20, 34) author of Analog Interfacing to Embedded Microprocessors, is an electrical engineer with over 20 years of experience in electronic and embedded systems. He is currently employed with Seagate Technologies, a manufacturer of computer hard disc drives. Bruce Carter (Chapter 19) a contributor to Electrical Engineering 101, is currently an Engineer for the Test and Measurement group of Texas Instruments. Carter earned a BS in Engineering Physics from Texas Tech University, and a BS in Electrical Engineering from the University of Texas. He authored several technical articles, including four chapters in Op-Amps for Everyone. New edition publishing soon. John Crowe (Chapter 13) co-author of Introduction to Digital Electronics, is Reader in Biomedical Informatics in the School of Electrical & Electronic Engineering, University of Nottingham, UK. His contribution to this book is based upon material used in a Digital Electronics module delivered to 1st and 2nd year undergraduate students. His research concerns the development of novel biomedical instrumentation such as fetal heart rate monitors and integrated optical and electronics ASICs for imaging skin blood flow. Ian Grout (Chapters 7, 8, 9, 10, 11, and 12) the author of Digital Systems Design received his B.Eng in Electronic Engineering (1991) and PhD (1994) from Lancaster University (UK). He has worked in both industry and the academic field in microelectronic circuit and electronics design and test. He currently works in the areas of mixed-signal integrated circuit (IC) design for testability (DfT) and digital electronic circuit design using programmable logic. The author is currently a lecturer within the Department of Electronic and Computer Engineering at the University of Limerick (Ireland). He currently teaches programmable logic and integrated circuit design and

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About the Authors

xvii

test principles within the university and has worked in Limerick since 1998. Prior to this he was a lecturer in the Engineering Department at Lancaster University (UK). Barrie Hayes-Gill (Chapter 13) co-author of Introduction to Digital Electronics, is Associate Professor in Integrated Circuit Design and Electronic Instrumentation in the School of Electrical & Electronic Engineering, University of Nottingham, UK. He has lectured inintegrated circuit design both within the University of Nottingham and at international locations around the World. His research and industrial work concerns the development of compact and low noise instrumentation for medical devices and instrumentation where he deploys off-the-shelf electronic components and semi-custom and full custom integrated circuits for integrated optical sensors. He has published widely with over 150 publications and 10 patents on medical devices and VLSI systems. In addition to his University post he is also an Executive Directorat Monica Healthcare Ltd. Ian Hickman, Eur. Ing. D. I. H. May B.Sc.Hons, C.Eng., MIEE, MIEEE (Chapters 2, 4, 5, 23, 24) is the author of Analog Electronics. He has been interested in electronics since the late 1940s, and professionally involved in it since 1954. Starting with a crystal set, his interests over the years have covered every aspect of electronics, though mainly concentrating on analog. Now retired, Ian was a consultant to Electronics World for many years. He internet explorer for windows 7 - Crack Key For U a Member of the Institution of Engineering and Technology: and a Life Member of the Institute of Electrical & Electronics Engineers. He has also written several books including Practical RF Handbook, Hickman’s Analog and RF Circuits, and Analog Circuits Cookbook, to name just a few. Walt Kester (Chapters 16, 17) is the author of Mixed Signal and DSP Design Techniques. He is a corporate staff applications engineer at Analog Devices. For over 35 years at Analog Devices, he has designed, developed, and given applications support for high-speed ADCs, DACs, SHAs, op-amps, and analog multiplexers. Besides writing many papers and articles, he prepared and edited eleven major applications books, which form the basis for the Analog Devices world-wide technical seminar series including the topics of op-amps, data conversion, power management, sensor signal conditioning, mixed-signal, and practical analog design techniques. He also is the editor of The Data Conversion Handbook, a 900þ page comprehensive book on data conversion published in 2005 by Elsevier. Walt has a BSEE from NC State University and MSEE from Duke University.

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About the Authors

Thomas Kugelstadt (Chapter 22) was a contributor to Op Amps for Everyone. He is a senior application engineer at Texas Instruments. He is writing many technical articles on various subjects, often system related. He also provides freelance writing services if your company were ever interested in a technical subject but experienced difficulties finding a writer. Ron Mancini (Chapter 26) the editor of Op Amps for Everyone has spent nearly fifty years in electronics. Recently retired, he was a Staff Scientist at Texas Instruments for many years. He was also a regular columnist for EDN. Richard Palmer (Chapter 26) was a contributor to Op Amps for Everyone. Robert A. Pease (Chapters 1, 3, 6) author of Troubleshooting Analog Circuits, attended Mt. Hermon School, and graduated from MIT in 1961 with a BSEE. He worked at Philbrick Researches up to 1975 and designed many Op-Amps and Analog Computing Modules. Pease joined National Semiconductor in 1976. He has designed about 24 analog ICs including power regulators, voltage references, and temp sensors. He has written 65þ magazine articles and holds about 21 US patents. Pease is the self-declared Czar of Bandgaps since 1986. He enjoys hiking and trekking in Nepal, and ferroequinology. His position at NSC is Staff Scientist. He is a Senior Member of the IEEE. Pease is a columnist in Electronic Design magazine, with over 240 columns published. The column, PEASE PORRIDGE, covers a wide range of technical topics. Pease also has posted many technical and semi-technical items on his main website: http://www.national.com/rap Many of Pease’s recent columns are accessible there. Pease was inducted into the E.E. Hall Of Fame in 2002. Refer to: http://www.elecdesign.com/Articles/Index.cfm?ArticleID=17269&Extension=pdf See Pease’s other web site at http://www.transtronix.com

Mike Tooley (Chapters 1, 21, and 33) author of Electronic Circuits, is a technical author and consultant. He was formerly Vice Principal at Brooklands College in Surrey, England, where he was responsible for the delivery of learning to over 10,000 Further and Higher Education students increasingly by flexible, open and online distance learning. Mike is the well-known author of several popular engineering and related text books, including widely adopted course texts for BTEC, GCE A-level and GCSE

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About the Authors

xix

qualifications in Engineering. Mike’s hobbies include astronomy, amateur radio, aviation, computing and electronic circuit design and construction. Tim Williams (Chapters 14, 15, 19, 35, 36, 37, 39, 40,41, 42, 43, and Appendix A) is the author of The Circuit Designer’s Companion, 2nd Edition. He works at Elmac Services, which provides consultancy and training on all aspects of EMC, including design, testing and the application of standards, to companies manufacturing electronic products and concerned about the implications of the EMC Directive. Tim Williams gained a BSc in Electronic Engineering from Southampton University in 1976. He has worked in electronic product design in various industry sectors including process instrumentation and audio visual control. He was design group leader at Rosemount Ltd before leaving in 1990 to start Elmac Services. He is also the author of “EMC for Product Designers” (now in its fourth edition, Elsevier 2006), and has presented numerous conference papers and seminars. He is also author of “EMC for Systems & Installations” with Keith Armstrong. He is an EMC technical assessor for UKAS and SWEDAC. Peter Wilson (Chapters 25, 30, 31, 32) author of Design Recipes for FPGAs, is Senior Lecturer in Electronics at the University of Southampton. He holds degrees from Heriot-Watt University, an MBA from Edinburgh Business School and a PhD from the University of Southampton. He worked in the Avionics and Electronics Design Automation Industries for many years at Ferranti, GEC-Marconi and Analogy prior to rejoining academia. He has published widely in the areas of FPGA design, modeling and simulation, VHDL, VHDL-AMS, magnetics and power electronics. He is a Senior Member of the IEEE, member of the IET, and a Chartered Engineer. Bob Zeidman (Chapters 27, 28, 29) author of Designing with FPGAs and CPLDs, is the president of Zeidman Consulting (www.ZeidmanConsulting.com), a premiere contract research and development firm in Silicon Valley. He is also the president of Zeidman Technologies (www.zeidman.biz), a developer of tools for embedded systems hardware and software development, and president of Software Analysis and Forensic Engineering Corporation (www.SAFE-corp.biz), the leading provider of software intellectual property analysis tools. Bob has designed ASICs, FPGAs, and PC boards for RISC-based parallel processor systems, laser printers, network switches and routers, and other systems for clients including Apple Computer, Cisco Systems, Mentor Graphics, and Ricoh. He is the inventor of SynthOSTM, a tool for synthesizing software

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xx

About the Authors

from a high-level description, and CodeSuiteW, a tool for measuring software source code correlation. His publications include papers on hardware and software design methods and three textbooks: Designing with FPGAs and CPLDs, Verilog Designer’s Library, and Introduction to Verilog. Bob has taught courses at conferences throughout the world. He holds several patents and earned bachelor’s degrees in physics and electrical engineering at Cornell University and a master’s degree in electrical engineering at Stanford University.

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CHAPTER 1

The Fundamentals Mike Tooley Darren Ashby Robert Pease

1.1 Electrical Fundamentals This chapter has been designed to provide you with the background knowledge required to help you understand the concepts introduced in the later chapters. If you have studied electrical science, electrical principles, or electronics then you will already be familiar with many of these concepts. If, on the other hand, you are returning to study or are a newcomer to electronics or electrical technology this chapter will help you get up to speed.

1.1.1

Fundamental Units

You will already know that the units that we now use to describe such things as length, mass and time are standardized within the International System of Units (SI). This SI system is based upon the seven fundamental units (see Table 1.1).

1.1.2

Derived Units

All other units are derived from these seven fundamental units. These derived units generally have their own names and those commonly encountered in electrical circuits are summarized in Table 1.2, together with the corresponding physical quantities. (Note that 0K is equal to 273 C and an interval of 1K is the same as an interval of 1 C.) If you find the exponent notation shown in Table 1.2 a little confusing, just remember that V1 is simply 1/V, s1 is 1/s, m2 is 1/m2, and so on.

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2

Chapter 1 Table 1.1: SI units Quantity

Unit

Abbreviation

Current

ampere

A

Length

meter

m

Luminous intensity

candela

cd

Mass

kilogram

kg

Temperature

Kelvin

K

Time

second

s

Matter

mol

mol

Table 1.2: Electrical quantities Quantity

Derived unit

Capacitance

farad

F

A s V1

Charge

coulomb

C

As

Energy

joule

J

Nm

Force

newton

N

kg m s1

Frequency

hertz

Hz

s1

Illuminance

lux

lx

lm m2

Inductance

henry

H

V s A1

Luminous flux

lumen

lm

cd sr

Magnetic flux

weber

Wb

Vs

Potential

volt

V

W A1

Power

watt

W

J s1

Resistance

ohm

O

V A1

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Abbreviation

Equivalent (in terms of fundamental units)

The Fundamentals

3

Example 1.1 The unit of flux density (the tesla) is defined as the magnetic flux per unit area. Express this in terms of the fundamental units. Solution The SI unit of flux is the weber (Wb). Area is directly proportional to length squared and, expressed in terms of the fundamental SI units, this is square meters (m2). Dividing the flux (Wb) by the area (m2) gives Wb/m2 or Wb m2. Hence, in terms of the fundamental SI units, the tesla is expressed in Wb m2. Example 1.2 The unit of electrical potential, the volt (V), is defined as the difference in potential between two points in a conductor, which when carrying a current of one amp (A), dissipates a power of one watt (W). Express the volt (V) in terms of joules (J) and coulombs (C). Solution In terms of the derived units: Volts ¼ ¼

Watts Joules=seconds ¼ Amperes Amperes Joules Joules ¼ Amperes  seconds Coulombs

Note that: Watts ¼ Joules/seconds and also that Amperes  seconds ¼ Coulombs. Alternatively, in terms of the symbols used to denote the units: V¼

W J=s J J ¼ ¼ ¼ ¼ JC1 A A As C

One volt is equivalent to one joule per coulomb.

1.1.3

Measuring Angles

You might think it strange to be concerned with angles in electrical circuits. The reason is simply that, in analog and AC circuits, signals are based on repetitive waves (often sinusoidal in shape). We can refer to a point on such a wave in one of two basic ways, either in terms of the time from the start of the cycle or in terms of the angle

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4

Chapter 1

FIGURE 1.1: One cycle of a sine wave voltage (a cycle starts at 0 and finishes as 360 —see Figure 1.1). In practice, it is often more convenient to use angles rather than time; however, the two methods of measurement are interchangeable and it’s important to be able to work in either of these units. In electrical circuits, angles are measured in either degrees or radians (both of which are strictly dimensionless units). You will doubtless already be familiar with angular measure in degrees where one complete circular revolution is equivalent to an angular change of 360. The alternative method of measuring angles, the radian, is defined somewhat differently. It is the angle subtended at the center of a circle by an arc having length that is equal to the radius of the circle (see Figure 1.2). You may sometimes find that you need to convert from radians to degrees, and vice versa. A complete circular revolution is equivalent to a rotation of 360 or

FIGURE 1.2: Definition of the radian

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The Fundamentals

5

2p radians (note that p is approximately equal to 3.142). Thus, one radian is equivalent to 360/2p degrees (or approximately 57.3 ). Try to remember the following rules that will help you to convert angles expressed in degrees to radians and vice versa:  From degrees to radians, divide by 57.3.  From radians to degrees, multiply by 57.3. Example 1.3 Express a quarter of a cycle revolution in terms of: (a)

degrees;

(b)

radians.

Solution (a)

There are 360 in one complete cycle (i.e., one full revolution. Hence, there are (360/4) or 90 in one quarter of a cycle).

(b)

There are 2p radians in one complete cycle. Thus, there are 2p/4 or p/2 radians in one quarter of a cycle.

Example 1.4 Express an angle of 215 in radians. Solution To convert from degrees to radians, divide by 57.3. So, 215 is equivalent to 215/57.3 ¼ 3.75 radians. Example 1.5 Express an angle of 2.5 radians in degrees. Solution To convert from radians to degrees, multiply by 57.3. Hence, 2.5 radians is equivalent to 2.5  57.3 ¼ 143.25 .

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6

Chapter 1

1.1.4

Electrical Units eset internet security 12.0.31.0 license key - Crack Key For U Symbols

Table 1.3 shows the units and symbols that are commonly encountered in electrical circuits. It is important to get to know these units and also be able to recognize their abbreviations and symbols. You will meet all of these units later in this chapter.

Table 1.3: Electrical units Unit

Abbrev.

Symbol

ampere

A

I

Unit of electric current (a current of 1A flows when a charge of 1C is transported in a time interval of 1s)

coulomb

C

Q

Unit of electric charge or quantity of electricity

farad

F

C

Unit of capacitance (a capacitor has a capacitance of 1F when a potential of 1V across its plates produced a charge of 1C)

henry

H

L

Unit of inductance (an inductor has an inductance of 1H when an applied current changing at 1 A/s produces a potential difference of 1V across its terminals)

hertz

Hz

f

Unit of frequency (a signal has a frequency of 1 Hz if one cycle occurs in an interval of 1s)

Joule

J

W

Unit of energy

Ohm

O

R

Unit of resistance

second

s

t

Unit of time

siemen

S

G

Unit of conductance (the reciprocal of resistance)

tesla

T

B

Unit of magnetic flux density (a flux density of 1T is produced when a flux of 1 Wb is present over an area of 1 square meter)

volt

V

V

Unit of electric potential (e.m.f. or p.d.)

watt

W

P

Unit of power (equivalent to 1J of energy consumed in 1s)

Weber

Wb

j

Unit of magnetic flux

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Notes

The Fundamentals

1.1.5

7

Multiples and Sub-Multiples

Unfortunately, many of the derived units are either too large or too small for convenient everyday use, but we can make life a little easier by using a standard range of multiples and sub-multiples (see Table 1.4). Table 1.4: Multiples and sub-multiples Prefix

Abbreviation

Multiplier

tera

T

1012 ( ¼ 1,000,000,000,000)

giga

G

109 ( ¼ 1,000,000,000)

mega

M

106 ( ¼ 1,000,000)

kilo

K

103 ( ¼ 1,000)

(none)

(none)

100 ( ¼ 1 )

centi

c

102 ( ¼ 0.01)

milli

m

103 ( ¼ 0.001)

micro

m

106 ( ¼ 0.000001)

nano

n

109 ( ¼ 0.000000001)

pico

p

1012 ( ¼ 0.000000000001)

Example 1.6 An indicator lamp requires a current of 0.075A. Express this in mA. Solution You can express the current in mA (rather than in A) by simply moving the decimal point three places to the right. Hence, 0.075A is the same as 75 mA. Example 1.7 A medium-wave radio transmitter operates on a frequency of 1,495 kHz. Express its frequency in MHz. Solution To express the frequency in MHz rather than kHz, we need to move the decimal point three places to the left. Hence, 1,495 kHz is equivalent to 1.495 MHz.

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8

Chapter 1

Example 1.8 Express the value of a 27,000 pF in mF. Solution To express the value in mF rather than pF we need to move the decimal point six places to the left. Hence, 27,000 pF is equivalent to 0.027 mF (note that we have had to introduce an extra zero before the 2 and after the decimal point).

1.1.6

Exponent Notation

Exponent notation (or scientific notation) is useful when dealing with either very small or very large quantities. It’s well worth getting to grips with this notation as it will allow you to simplify quantities before using them in formulae. Exponents are based on powers of ten. To express a number in exponent notation the number is split into two parts. The first part is usually a number in the range 0.1 to 100 while the second part is a multiplier expressed as a power of ten. For example, 251.7 can be expressed as 2.517  100, i.e., 2.517  102. It can also be expressed as 0.2517  1,000, i.e., 0.2517  103. In both cases the exponent is the same as the number of noughts in the multiplier (i.e., 2 in the first case and 3 in the second case). To summarize: 251:7 ¼ 2:517  102 ¼ 0:2517  103 As a further example, 0.01825 can be expressed as 1.825/100; that is, 1.825  102. It can also be expressed as 18.25/1,000, i.e., 18.25  103. Again, the exponent is the same as the number of zeros but the minus sign is used to denote a fractional multiplier. To summarize: 0:01825 ¼ 1:825  102 ¼ 18:25  103 Example 1.9 A current of 7.25 mA flows in a circuit. Express this current in amperes using exponent notation. Solution 1 mA ¼ 1  103 A;

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thus, 7.25 mA ¼ 7:25  103 A

The Fundamentals

9

Example 1.10 A voltage of 3.75  106V appears at the input of an amplifier. Express this voltage in (a) V, and (b) mV, using exponent notation. Solution (a)

1  106V ¼ 1 mV so 3.75  106V ¼ 3.75 mV

(b)

There are 1,000 mV in 1 mV so we must divide the previous result by 1,000 in order to express the voltage in mV. So 3.75 mV ¼ 0.00375 mV.

1.1.7

Multiplication and Division Using Exponents

Exponent notation really comes into its own when values have to be multiplied or divided. When multiplying two values expressed using exponents, you simply need to add the exponents. Here’s an example: ð2  102 Þ  ð3  106 Þ ¼ ð2  3Þ  10ð2 þ 6Þ ¼ 6  108 Similarly, when dividing two values which are expressed using exponents, you only need to subtract the exponents. As an example: ð4  106 Þ  ð2  104 Þ ¼ 4=2  10ð64Þ ¼ 2  102 In either case it’s important to remember to specify the units, multiples and sub-multiples in which you are working (e.g., A, kO, mV, mF, etc.). Example 1.11 A current of 3 mA flows in a resistance of 33 kO. Determine the voltage dropped across the resistor. Solution Voltage is equal to current multiplied by resistance. Thus: V ¼ I  R ¼ 3 mA  33 kO Expressing this using exponent notation gives: V ¼ ð3  103 Þ  ð33  103 ÞV

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10

Chapter 1

Separating the exponents gives: V ¼ 3  33  103  103 V Thus, V ¼ 99  10(3þ3) ¼ 99  100 ¼ 99  1 ¼ 99V Example 1.12 A current of 45 mA flows in a circuit. What charge is transferred in a time interval of 20 ms? Solution Charge is equal to current multiplied by time (see the definition of the ampere). Thus: Q ¼ It ¼ tally erp 9 release 6.4. Download - Crack Key For U mA  20 ms Expressing this in exponent notation gives: Q ¼ ð45  106 Þ  ð20  103 Þ coulomb Separating the exponents gives: Q ¼ 45  20  106  103 coulomb Thus, Q ¼ 900  10(63) ¼ 900  109 ¼ 900 nC Example 1.13 A power of 300 mW is dissipated in a circuit when a voltage of 1,500V is applied. Determine the current supplied to the circuit. Solution Current is equal to power divided by voltage. Thus: I ¼ P=V ¼ 300 mW=1; 500V amperes Expressing this in exponent notation gives: I ¼ ð300  103 Þ=ð1:5  103 ÞA

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The Fundamentals

11

Separating the exponents gives: I ¼ ð300=1:5Þ  ð103 =103 ÞA I ¼ 300=1:5  103  103 A Thus, I ¼ 200  10(33) ¼ 200  106 ¼ 200 mA

1.1.8

Conductors and Insulators

Electric current is the name given to the flow of electrons (or negative charge carriers). Electrons orbit around the nucleus of atoms just as the earth orbits around the sun (see Figure 1.3). Electrons are held in one or more shells, constrained to their orbital paths by virtue of a force of attraction toward the nucleus, which contains an equal number of protons (positive charge carriers). Since like charges repel and unlike charges attract, negatively charged electrons are attracted to the positively charged nucleus. A similar principle can be demonstrated by observing the attraction between two permanent magnets; the two North u.c. Poles of the magnets will repel each other, while a North and South u.c. Pole will attract. In the same way, the unlike charges of the negative electron and the positive proton experience a force of mutual attraction. The outer shell electrons of a conductor can be daum potplayer download - Crack Key For U easily interchanged between adjacent atoms within the lattice of atoms of which the substance is composed. This makes it possible for the material to conduct electricity. Typical examples of conductors are metals such as copper, silver, iron and aluminum. By contrast, the outer shell

FIGURE 1.3: A single atom of helium (He) showing its two electrons in orbit around its nucleus

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12

Chapter 1

electrons of an insulator are firmly bound to their parent atoms and virtually no interchange of electrons is possible. Typical examples of insulators are plastics, rubber, and ceramic materials.

1.1.9

Voltage and Resistance

The ability of an energy source (e.g., a battery) to produce a current within a conductor may be expressed in terms of electromotive force (e.m.f.). Whenever an e.m.f. is applied to a circuit a potential difference (p.d.), or voltage, exists. Both e.m.f. and p.d. are measured in volts (V). In many practical circuits there is only one e.m.f. present (the battery or supply), whereas a voltage will be developed across each component present in the circuit. The conventional flow of current in a circuit is from the point of more positive potential to the point of greatest negative potential (note that electrons move in the opposite direction!). Direct current results from the application of a direct e.m.f. (derived from batteries or a DC power supply). An essential characteristic of these supplies is that the applied e.m.f. does not change its polarity (even though its value might be subject to some fluctuation). For any conductor, the current flowing is directly proportional to the e.m.f. applied. The current flowing will also be dependent on the physical dimensions (length and cross-sectional area) and material of which the conductor is composed. The amount of current that will flow in a conductor when a given e.m.f. is applied is inversely proportional to its resistance. Therefore, resistance may be thought of as an opposition to current flow; the higher the resistance the lower the current that will flow (assuming that the applied e.m.f. remains constant).

1.1.10

Ohm’s Law

Provided that temperature does not vary, the ratio of p.d. across the ends of a conductor to the current flowing in the conductor is a constant. This relationship is known as Ohm’s Law and Windows 10 Activator 2020 Crack + Activation Code Free Download leads to the relationship: V=I ¼ a constant ¼ R

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The Fundamentals

13

where V is the potential difference (or voltage drop) in volts (V), I is the current in amperes (A), and R is the resistance in ohms (O) (see Figure 1.4).

FIGURE 1.4: Simple circuit to illustrate the relationship between voltage (V), current (I) and resistance (R). Note that the direction of conventional current flow is from positive to negative. The formula may be arranged to make V, I or R the subject, as follows: V ¼ I  R; I ¼ V=R

and R ¼ V=I

The triangle shown in Figure 1.5 should help you remember these three important relationships. However, it’s worth noting that, when performing calculations of currents, voltages and resistances in practical circuits it is seldom necessary to work with an accuracy of better than 1% simply because component tolerances are usually greater than this. Furthermore, in calculations involving Ohm’s Law, it can sometimes be convenient to work in units of kO and mA (or MO and mA) in which case potential differences will be expressed directly in V.

FIGURE 1.5: Triangle showing the relationship between V, I and R

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14

Chapter 1

Example 1.14 A 12O resistor is connected to a 6V battery. What current will flow in the resistor? Solution Here we must use I ¼ V/R PassFab iPhone Unlocker 2.2.1.1 Crack Keygen - Free Activators V ¼ 6V and R ¼ 12O): I ¼ V=R ¼ 6V=12O ¼ 0:5Aðor 500 mAÞ Hence a current of 500 mA will flow in the resistor. Example 1.15 A current of 100 mA flows in a 56O resistor. What voltage drop (potential difference) will be developed across the resistor? Solution Here we must use V ¼ I  R and ensure that we work in units of volts (V), amperes (A), and ohms (O). V ¼ I  R ¼ 0:1A  56O ¼ 5:6V (Note that 100 mA is the same as 0.1A.) This calculation shows that a p.d. of 5.6V will be developed across the resistor. Example 1.16 A voltage drop of 15V appears across a resistor in which a current of 1 mA flows. What is the value of the resistance? Solution R ¼ V=I ¼ 15V=0:001A ¼ 15; 000O ¼ 15 kO Note that it is often more convenient to work in units of mA and V, which will produce an answer directly in kO, that is: R ¼ V=I ¼ 15V=l mA ¼ 15 kO

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The Fundamentals

15

1.1.11 Resistance and Resistivity The resistance of a metallic conductor is directly proportional to its Password Recovery Bundle+Crack 5.2 With Serial Key [Latest]2021 and inversely proportional to its area. The resistance is also directly proportional to its resistivity (or specific resistance). Resistivity is defined as the resistance measured between the opposite faces of a cube having sides of 1 cm. The resistance, R, of a conductor is given by the formula: R ¼ r  l=A where R is the resistance (ft), r is the resistivity (Om), l is the length (m), and A is the area (m2). Table 1.5 shows the electrical properties of some common metals. Example 1.17 A coil consists of an 8m length of annealed copper wire having a cross-sectional area of 1 mm2. Determine the resistance of the coil. Solution We will use the formula, R ¼ r l/A. Table 1.5: Properties of some common metals Metal

Resistivity (at 20˚C) (Vm)

Silver

1.626  108

1.06

0.0041

Copper (annealed)

1.724  108

1.00

0.0039

Copper (hard drawn)

1.777  108

0.97

0.0039

Aluminum

2.803  108

0.61

0.0040

Mild steel

1.38  107

0.12

0.0045

0.08

0.0040

0.22

0.0062

7

Lead

adobe acrobat 9 pro crack download - Crack Key For U  10

Nickel

8.0  108

Relative conductivity (copper = 1)

Temperature coefficient of resistance (per ˚C)

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16

Chapter 1

The value of r for annealed copper given in Table 1.5 is 1.724  108 Om. The length of the wire is 4m, while the area is 1 mm2 or 1  106 m2 (note that it is important to be consistent in using units of meters for length and square meters for area). Hence, the resistance of the coil will be given by: R¼

1:724  108  8 ¼ 13:724  10ð8 þ 6Þ 1  106

Thus, R ¼ 13.792  102 or 0.13792O Example 1.18 A wire having a resistivity of 1.724  108 Om, length 20m and cross-sectional area 1 mm2 carries a current of 5A. Determine the voltage drop between the ends of the wire. Solution First, we must find the resistance of the wire (as in Example 1.17): R¼

rl 1:6  108  20 ¼ 32  102 ¼ 0:32O ¼ A 1  106

The voltage drop can now be calculated using Ohm’s Law: V ¼ I  R ¼ 5A  0:32O ¼ 1:6V This calculation shows that a potential of 1.6V will be dropped between the ends of the wire.

1.1.12

Energy and Power

At first you may be a little confused about the difference between energy and power. Simply put, energy is the ability to do work, while power is the rate at which work is done. In electrical circuits, energy is supplied by batteries or generators. It may also be stored in components such as capacitors and inductors. Electrical energy is converted into various other forms of energy by components such as resistors (producing heat), loudspeakers (producing sound energy), and light emitting diodes (producing light).

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The Fundamentals

17

The unit of energy is the joule (J). Power is the rate of use of energy and it is measured Internet Download Manager 6.32 Build 10 Serial Key - Crack Key For U watts (W). A power of 1W results from energy being used at the rate of 1J per second. Thus: P ¼ W=t where P is the power in watts (W), W is the energy in joules (J), and t is the time in seconds (s). The power in a circuit is equivalent to the product of voltage and current. Hence: P¼IV where P is the power in watts (W), I is the current in amperes (A), and V is the voltage in volts (V). The formula may be arranged to make P, I or V the subject, as follows: P ¼ I  P; I ¼ P=V and

V ¼ P=I

The triangle shown in Figure 1.6 should help you remember these relationships. The relationship, P ¼ I  V, may be combined with that which results from Ohm’s Law (V ¼ I  R) to produce two further relationships. First, substituting for V gives: P ¼ I  ðI  RÞ ¼ I2 R Secondly, substituting for I gives: P ¼ ðV=RÞ  V ¼ V 2 =R Example 1.19 A current of 1.5A is drawn from a 3V battery. What power is supplied? Solution Here we must use P ¼ I  V (where I ¼ 1.5A and V ¼ 3V). P ¼ I  V ¼ 1:5A  3V ¼ 4:5W Hence, a power of 4.5W is supplied.

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18

Chapter 1

Example 1.20 A voltage drop of 4V appears across a resistor of 100O. What power is dissipated in the resistor? Solution Here we use P ¼ V2/R (where V ¼ 4V and R ¼ 100O). P ¼ V 2= R ¼ ð4V  4VÞ=100O ¼ 0:16W Hence, the resistor dissipates a power of 0.16W (or 160 mW). Example 1.21 A current of 20 mA flows in a 1 kO resistor. What power is dissipated in the resistor?

FIGURE 1.6: Triangle showing the relationship between P, I and V Solution Here we use P ¼ I2  R but, to make life a little easier, we will work in mA and kO (in which case the answer will be in mW). P ¼ I2  R ¼ ð20 mA  20 mAÞ  1 kO ¼ 400 mW Thus, a power of 400 mW is dissipated in the 1 kO resistor.

1.1.13

Electrostatics

If a conductor has a deficit of electrons, it will exhibit a net positive charge. If, on the other hand, it has a surplus of electrons, it will exhibit a net negative charge. An imbalance in charge can be produced by friction (removing or depositing electrons using materials such as silk and fur, respectively), or induction

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The Fundamentals

19

(by attracting or repelling electrons using a second body, which is, respectively, positively or negatively charged).

1.1.14 Force Between Charges Coulomb’s Law states that, if charged bodies exist at two points, the force of attraction (if the charges are of opposite polarity), or repulsion (if the charges have the same polarity), will be proportional to the product of the magnitude of the charges divided by the square of their distance apart. Thus: F¼

kQ1 Q2 r2

where Q1 and Q2 are the charges present at the two points (in coulombs), r the distance separating the two points (in meters), F is the force (in newtons), and k is a constant depending upon the medium in which the charges exist. In vacuum or “free space”: k¼

1 4pe0

where e0 is the permittivity of free space (8.854  1012 C/Nm2). Combining the two previous equations gives: F¼

kQ1 Q2 Newtons 4  8:854  1012 r2

1.1.15 Electric Fields The force exerted on a charged particle is a manifestation of the existence of an electric field. The electric field defines the direction and magnitude of a force on a charged object. The field itself is invisible to the human eye, but can be drawn by constructing lines, which indicate the motion of a free positive charge within the field; the number of field lines in a particular region being used to indicate the relative strength of the field at the point in question. Figures 1.7 and 1.8 show the electric fields between charges of the same and opposite polarity, while Figure 1.9 shows the field that exists between two charged parallel plates. You will see more of this particular arrangement when we introduce capacitors.

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FIGURE 1.7: Electric field between two unlike electric charges

FIGURE 1.8: Electric field between two like electric charges (in this case both positive)

FIGURE 1.9: Electric field between two parallel plates

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The Fundamentals

21

1.1.16 Electric Field Strength The strength of an electric field (E) is proportional to the applied potential difference and inversely proportional to the distance between the two conductors. The electric field strength is given by: E ¼ V=d where E is the electric field strength (V/m), V is the applied potential difference (V) and d is the distance (m). Example 1.22 Two parallel conductors are separated by a distance of 25 mm. Determine the electric field strength if they are fed from a 600V DC supply. Solution The electric field strength will be given by: E ¼ V=d ¼ ez cd audio converter 8.5 crack - Free Activators  103 ¼ 24 kV=m

1.1.17 Permittivity The amount of charge produced on the two plates shown in Figure 1.9 for a given applied voltage will depend not only on the physical dimensions, but also on the insulating dielectric material that appears between the plates. Such materials need to have a very high value of resistivity (they must not conduct charge) coupled with an ability to withstand high voltages without breaking down. A more practical arrangement is shown in Figure 1.10. In this arrangement the ratio of charge, Q, to potential difference, V, is given by the relationship: Q eA ¼ V d where A is the surface area of the plates (in m), d is the separation (in m), and e is a constant for the dielectric material known as the absolute permittivity of the material (sometimes also referred to as the dielectric constant). The absolute permittivity of a dielectric material is the product of the permittivity of free space (e0) and the relative permittivity (er) of the material. Thus:

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Chapter 1

FIGURE 1.10: Parallel plates with an insulating dielectric material e ¼ e0  e

and

Q e0 er A ¼ V d

The dielectric strength of an insulating dielectric is the maximum electric field strength that can safely be applied to it before breakdown (conduction) occurs. Table 1.6 shows values of relative permittivity and dielectric strength for some common dielectric materials. Table 1.6: Properties of some common insulating dielectric materials Dielectric material

Relative permittivity (free space = 1)

Dielectric strength (kV/mm)

Vacuum, or free space

1

1

Air

1

3

Polythene

2.3

50

Paper

2.5 to 3.5

14

Polystyrene

2.5

25

Mica

4 to 7

160

Pyrex glass

4.5

13

Glass ceramic

5.9

40

Polyester

3.0 to 3.4

18

Porcelain

6.5

4

Titanium dioxide

100

6

Ceramics

5 to 1,000

2 to 10

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The Fundamentals

23

1.1.18 Electromagnetism When a current flows through a conductor, a magnetic field is produced in the vicinity of the conductor. The magnetic field is invisible, but its presence can be detected using a compass needle (which will deflect from its normal North-South position). If two current-carrying conductors are placed in the vicinity of one another, the fields will interact with one another and the conductors will experience a force of attraction or repulsion (depending upon the relative direction of the two currents).

1.1.19 Force Between Two Current-Carrying Conductors The mutual force that exists between two parallel current-carrying conductors will be proportional to the product of the currents in the two conductors and the length of the conductors but inversely proportional to their separation. Thus: F¼

k I1 I2 l d

where I1 and I2 are the currents in the two conductors (in amps), l is the parallel length of the conductors (in meters), d is the distance separating the two conductors (in meters), F is the force (in newtons), and k is a constant depending upon the medium in which the charges exist. In vacuum or “free space”, k¼

m0 2p

where m0 is a constant known as the permeability of free space (4p  107 or 12.57  107H/m). Combining the two previous equations gives: F¼

m0 I1 I2 l 2pd

or, F¼

4p  107 I1 I2 l 2pd

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Chapter 1

or, F¼

1.1.20

2  107 I1 I2 l Newtons d

Magnetic Fields

The field surrounding a straight current-carrying conductor is shown in Figure 1.11. The magnetic field defines the direction of motion of a free North Pole within the field. In the case of Figure 1.11, the lines of flux are concentric and the direction of the field determined by the direction of current flow) is given by the right-hand rule.

1.1.21

Magnetic Field Strength

The strength of a magnetic field is a measure of the density of the flux at any particular point. In the case of Figure 1.11, the field strength will be proportional to the applied current and inversely proportional to the perpendicular distance from the conductor. Thus: B¼

kI d

where B is the magnetic flux density (in tesla), I is the current (in amperes), d is the distance from the conductor (in meters), and k is a constant. Assuming that the medium is vacuum or ”free space,” the density of the magnetic flux will be given by: B¼

m0 I 2p d

where B is the flux density (in tesla), m0 is the permeability of free space (4p  107 or 12.57  107), I is the current (in amperes), and d is the distance from the center of the conductor (in meters). The flux density is also equal to the total flux divided by the area of the field. Thus: B ¼ F=A where F is the flux (in webers) and A is the area of the field (in square meters).

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The Fundamentals

25

FIGURE 1.11: Magnetic field surrounding a straight conductor

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Chapter 1

FIGURE 1.12: Forming a conductor into a loop increases the strength of the magnetic field in the center of the loop

In order to increase the strength of the field, a conductor may be shaped into a loop (Figure 1.12) or coiled to form a solenoid (Figure 1.13). Note, in the latter case, how the field pattern is exactly the same as that which surrounds a bar magnet. Example 1.23 Determine the flux density produced at a distance of 50 mm from a straight wire carrying a current of 20A. Solution Applying the formula B ¼ m0I/2p d gives: B¼

12:57  107  20 251:4  107 ¼ 314:2  103 2  3:142  50  103

from which: B ¼ 0:8  104 tesla Thus, B ¼ 80  106 T or B ¼ 80 mT.

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The Fundamentals

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FIGURE 1.13: The magnetic field surrounding a solenoid coil resembles that of a permanent magnet

Example 1.24 A flux density of 2.5 mT is developed in free space over an area of 20 cm2. Determine the total flux. Solution Rearranging the formula B ¼ F/A to make F the subject gives F ¼ B  A thus: F ¼ ð2:5  103 Þ  ð20  104 Þ ¼ 50  107 webers from which B ¼ 5 mWb

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1.22

Chapter 1

Magnetic Circuits

Materials such as iron and steel possess considerably enhanced magnetic properties. They are employed in applications where it is necessary to increase the flux density produced by an electric current. In effect, magnetic materials allow us to channel the electric flux into a “magnetic circuit,” as shown in Figure 1.14. In the circuit of Figure 1.14(B), the reluctance of the magnetic core is analogous to the resistance present in the electric circuit shown in Figure 1.14(A). We can make the following comparisons between the two types of circuit (see Table 1.7).

FIGURE 1.14: Comparison of electric and magnetic circuits

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The Fundamentals

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Table 1.7: Comparison of electric and magnetic circuits Electric circuit Figure 1.14(A)

Magnetic circuit Figure 1.14(A)

Electromotive force, e.m.f. ¼ V

Magnetomotive force, m.m.f. ¼ N  I

Resistance ¼ R

Reluctance ¼ S

Current ¼ I

Flux ¼ F

e.m.f. ¼ current  resistance

m.m.f. ¼ flux  reluctance

V ¼ IR

NI¼SF

In practice, not all of the magnetic flux produced in a magnetic circuit will be concentrated within the core and some “leakage flux” will appear in the surrounding free space (as shown in Figure 1.15). Similarly, if a gap appears within the magnetic circuit, the flux will tend to spread out as shown in Figure 1.16. This effect is known as fringing.

FIGURE 1.15: Leakage flux in a magnetic circuit

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Chapter 1

FIGURE 1.16: Fringing of the magnetic flux at an air gap in a magnetic circuit

1.1.23

Reluctance and Permeability

The reluctance of a magnetic path is directly proportional to its length and inversely proportional to its area. The reluctance is also inversely proportional to the absolute permeability of the magnetic material. Thus: S¼

l mA

where S is the reluctance of the magnetic path, l is the length of the path (in meters), A is the cross-sectional area of the path (in square meters), and m is the absolute permeability of the magnetic material. The absolute permeability of a magnetic material is the product of Altium Designer 20.2.6 Build 244 Crack permeability of free space (m0) and the relative permeability of the magnetic medium (m0). Thus: m ¼ m0  m and S ¼

l m0 mr A

The permeability of a magnetic medium is a measure of its ability to support magnetic flux and it is equal to the ratio of flux density (B) to magnetizing force (H). Thus: m¼

B H

where B is the flux density (in tesla) and H is the magnetizing force (in ampere/meter). The magnetizing force (H) is proportional to the product of the number of turns and current but inversely proportional to the length of the magnetic path.

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The Fundamentals H¼

31

NI l

where H is the magnetizing force (in amperes/ meters), N is the number of turns, I is the current (in amperes), and l is the length of the magnetic path (in meters).

1.1.24 B-H Curves Figure 1.17 shows four typical B-H (flux density plotted against permeability) curves for some common magnetic materials. If you look carefully at these curves you will notice that they flatten off due to magnetic saturation and that the slope of the curve (indicating the value of m corresponding to a particular value of H) falls

FIGURE 1.17: B-H curves for three ferromagnetic materials

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Chapter 1

as the magnetizing force increases. This is important since it dictates the acceptable working range for a particular magnetic material when used in a magnetic circuit. Example 1.25 Estimate the relative permeability of cast steel (see Figure 1.18) at (a) a flux density of 0.6T, and (b) a flux density of 1.6T. Solution From Figure 1.18, the slope of the graph at any point gives the value of m at that point. We can easily find the slope by constructing a tangent at the point in question and then finding the ratio of vertical change to horizontal change.

FIGURE 1.18: B-H curve for a sample of cast steel

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The Fundamentals (a)

33

The slope of the graph at 0.6T is 0.6/800 ¼ 0.75  103

Since m ¼ m0  mr, mr ¼ m/m0 ¼ 0.75  103/12.57  107, thus mr ¼ 597 at 0.6T. (b)

The slope of the graph at 1.6T is 0.2/4,000 ¼ 0.05  103

Since m ¼ m0  mr, mr ¼ m/m0 ¼ 0.05  103 / 12.57  107, thus mr ¼ 39.8 at 1.6T. (This example clearly shows the effect of saturation on the permeability of a magnetic material!) Example 1.26 A coil of 800 turns is wound on a closed mild steel core having a length 600 mm and cross-sectional area 500 mm2. Determine the current required to establish a flux of 0.8 mWb in the core. Solution Now B ¼ F/A ¼ (0.8  103)/(500  106) ¼ 1.6T From Figure 1.17, a flux density of 1.6T will occur in mild steel when H ¼ 3,500 A/m. The current can now be determined by re-arranging H ¼ N I/l as follows: I¼

Hl 3; 500  0:6 ¼ ¼ 2:625A N 800

1.1.25 Circuit Diagrams Finally, and just in case you haven’t seen them before, we will end this section with a brief word about circuit diagrams. We are introducing the topic here because it’s quite important to be able to read and understand simple electronic circuit diagrams before you can make sense of some of the components and circuits that you will meet later on. Circuit diagrams use standard symbols and conventions to represent the components and wiring used in an electronic circuit. Visually, they bear very little relationship to the physical layout of a circuit but, instead, they provide us with a “theoretical” view of the circuit. In this section we show you how to find your way around simple circuit diagrams.

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Chapter 1

To be able to understand a circuit diagram you first need to be familiar with the symbols that are used to represent the components and devices. It’s important to be aware that there are a few (thankfully quite small) differences between the symbols used in circuit diagrams of American and European origin. As a general rule, the input to a circuit should be shown on the left of a circuit diagram and the output shown Activate Windows 8/8.1 Without Product key and Internet the right. The supply (usually the most positive voltage) is normally shown at the top of the diagram and the common, 0V, or ground connection is normally shown at the bottom. This rule is not always obeyed, particularly for complex diagrams where many signals and supply voltages may be present. Note also that, in order to simplify a circuit diagram (and avoid having too many lines connected to the same point) multiple connections to common, 0V, or ground may be shown using the appropriate symbol. The same applies to supply connections that may be repeated (appropriately labeled) at various points in the diagram. A very simple circuit diagram (a simple resistance tester) is shown in Figure 1.20. This circuit may be a little daunting if you haven’t met a circuit like it before but you can still glean a great deal of information from the diagram even if you don’t know what the individual components do.

FIGURE 1.19: Various types of switches. From left to right: a mains rocker switch, an SPDT miniature toggle (changeover) switch, a DPDT side switch, an SPDT push-button (wired for use as an SPST push-button), a miniature PCB mounting DPDT push-button (with a latching action).

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FIGURE 1.20: A simple circuit diagram

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Chapter 1

The circuit uses two batteries, B1 (a 9V multi-cell battery) and B2 (a 1.5V single-cell battery). The two batteries are selected by means of a double-pole, double-throw (DPDT) switch. This allows the circuit to operate from either the 9V battery (B1) as shown in Figure 1.20(A) or from the 1.5V battery (B2) as shown in Figure 1.20(B) depending on the setting of S1. A variable resistor, VR1, is used to adjust the current supplied by whichever of the two batteries is currently selected. This current flows first through VR1, then through the milliammeter, and finally through the unknown resistor, RX. Notice how the meter terminals are labeled showing their polarity (the current flows into the positive terminal and out of the negative terminal). The circuit shown in Figure 1.20(C) uses a different type of switch but provides exactly the same function. In this circuit a single-pole, double-throw (SPDT) switch is used and the negative connections to the two batteries are “commoned” (i.e., connected directly together). Finally, Figure 1.20(D) shows how the circuit can be redrawn using a common “chassis” connection to provide the negative connection between RX and the two batteries. Electrically this circuit is identical to the one shown in Figure 1.20(C).

1.2 Passive Components This section introduces several of the most common types of electronic component, including resistors, capacitors and inductors. These are often referred to as passive components as they cannot, by themselves, generate voltage or current. An understanding of the characteristics and application of passive components Altium Designer 20.2.6 Build 244 Crack an essential prerequisite to understanding the operation of the circuits used in amplifiers, oscillators, filters and power supplies.

1.2.1

Resistors

The notion of resistance as opposition to current was discussed in the previous section. Conventional forms of resistor obey a straight line law when voltage is plotted against current (see Figure 1.21) and this allows us to use resistors as a means of converting current into a corresponding voltage drop, and vice versa (note that doubling the applied current will produce double the voltage drop, and so on). Therefore, resistors provide us with a means of controlling the currents and voltages present in electronic

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The Fundamentals

37

FIGURE 1.21: Voltage plotted against current for three different values of resistor circuits. They can also act as loads to simulate the presence of a circuit during testing (e.g., a suitably rated resistor can be used to replace a loudspeaker when an audio amplifier is being tested). The specifications for a resistor usually include the value of resistance expressed in ohms (O), kilohms (kO) or megohms (MO), the accuracy or tolerance (quoted as the maximum permissible percentage deviation from the marked value), and the power rating (which must be equal to, or greater than, the maximum expected power dissipation). Other practical considerations when selecting resistors for use in a particular application include temperature coefficient, noise performance, stability and ambient temperature range. Table 1.8 summarizes the properties of five of the most common types of resistor. Figure 1.22 shows a typical selection of fixed resistors with values from 15O to 4.7 kO.

1.2.2

Preferred Values

The value marked on the body of a resistor is not its exact resistance. Some minor variation in resistance value is inevitable due to production tolerance. For example, a resistor marked 100O and produced within a tolerance of 10% will have a value which falls within the range 90O to 110O. A similar component with a tolerance of 1% would have a value that falls within the range 99O to 101O. Thus, where accuracy is important it is essential to use close tolerance components.

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Resistor type Carbon film

Metal film

Metal oxide

Ceramic wirewound

Vitreous wirewound

Metal clad

Resistance range (O)

10 to 10M

1 to 1M

10 to 10 M

0.47 to 22k

0.1 to 22k

0.05 to 10k

Typical tolerance (%)

5

1

2

5

5

5

Power rating (W)

0.25 to 2

0.125 to 0.5

0.25 to 0.5

4 to 17

2 to 4

10 to 300

Temperature coefficient (ppm/ C)

250

þ50 to þ100

þ250

þ250

þ75

þ50

Stability

Fair

Excellent

Excellent

Good

Good

Good

Noise performance

Fair

Excellent

Excellent

n.a.

n.a.

n.a.

Ambient temperature range ( C)

45 to þ125

45 to þ125

45 to þ125

45 to þ125

45 to þ125

55 to þ200

Typical applications

GeneralPurpose

Amplifiers, test equipment, etc., requiring low-noise hightolerance components

Property

Power supplies, loads, medium and high-power applications

Very high power applications

Chapter 1

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Table 1.8: Characteristics of common types of resistors

The Fundamentals

39

FIGURE 1.22: A selection of resistors including high-power metal clad, ceramic wirewound, carbon and metal film types with values ranging from 15V to 4.7 kV

Resistors are available in several series of fixed-decade values, the number of values provided with each series being governed by the tolerance involved. In order to cover the full range of resistance values using resistors having a 20% tolerance it will be necessary to provide six basic values (known as the E6 series). More values will be required in the series, which offers a tolerance of 10%, and consequently, the E12 series provides twelve basic values. The E24 series for resistors of 5% tolerance provides no fewer than 24 basic values and, as with the E6 and E12 series, decade multiples (i.e., 1, 10, 100, 1 k, 10 k, 100k and 1M) of the basic series. Figure 1.23 shows the relationship between the E6, E12 and E24 series.

1.2.3

Power Ratings

Resistor power ratings are related to operating temperatures and resistors should be derated at high temperatures. Where reliability is important resistors should be operated at well below their nominal maximum power dissipation. Example 1.27 A resistor has a marked value of 220O. Determine the tolerance of the resistor if it has a measured value of 207O.

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Chapter 1

FIGURE 1.23: The E6, E12, and E24 series Solution The difference between the marked and measured values of resistance (the error) is (220O  207O) ¼ 13O. The MailWasher Pro 7.12.68 Crack + Keygen [Latest Version] is given by: Tolerance ¼

error  100% marked value

The tolerance is thus, (13/220)  100 ¼ 5.9%.

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The Fundamentals

41

Example 1.28 A 9V power supply is to be tested with a 39O load resistor. If the resistor has a tolerance of 10% find: (a)

the nominal current taken from the supply;

(b)

the maximum and minimum values of supply current at either end of the tolerance range for the resistor.

Solution (a)

If a resistor of exactly 39O is used the current will be: I ¼ V=R ¼ 9V=39O ¼ 231 mA

(b)

The lowest value of resistance would be (39O  3.9O) ¼ 35.1O. In which case the current would be: I ¼ V=R ¼ 9V=35:1O ¼ 256:4 mA

At the other extreme, the highest value would be (39O þ 3.9 O) ¼ 42.9O. In this case, the current would be: I ¼ V=R ¼ 9V=42:9O ¼ 209:8 mA The maximum and minimum values of supply current will thus be 256.4 mA and 209.8 mA, respectively. Example 1.29 A current of 100 mA (20%) is to be drawn from a 28V DC supply. What value and type of resistor should be used in this application? Solution The value of resistance required must first be calculated using Ohm’s Law: R ¼ V=I ¼ 28V=100 mA ¼ 280O The nearest preferred value from the E12 series is 270O (which will actually produce a current of 103.7 mA (i.e., within 4% > of the desired value). If a resistor

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Chapter 1

of 10% tolerance is used, current will be within the range 94 mA to 115 mA (well within the 20% accuracy specified). The power dissipated in the resistor (calculated using P ¼ IV) will be 2.9W and thus a component rated at 3W (or more) will be required. This would normally be a vitreous enamel coated wirewound resistor (see Table 1.8).

1.2.4

Resistor Markings

Carbon and metal oxide resistors are normally marked with color codes which indicate their value and tolerance. Two methods of color-coding are in common use; one involves four colored bands (see Figure 1.24), while the other uses five color bands (see Figure 1.25).

FIGURE 1.24: Four-band resistor color code

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The Fundamentals

43

FIGURE 1.25: Five band resistor color code

Example 1.30 A resistor is marked with the following colored stripes: brown, black, red, silver. What is its value and tolerance? Solution See Figure 1.26. Example 1.31 A resistor is marked with the following colored stripes: red, violet, orange, gold. What is its value and tolerance? Solution See Figure 1.27.

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Chapter 1

FIGURE 1.26: See Example 1.30

FIGURE 1.27: See Example 1.31

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The Fundamentals

45

Example 1.32 A resistor is marked with the following colored stripes: green, blue, black, gold. What is its value and tolerance? Solution See Figure 1.28. Example 1.33 A resistor is marked with the following colored stripes: red, green, black, black, brown. What is its value and tolerance? Solution See Figure 1.29.

FIGURE 1.28: See Example 1.32

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Chapter 1

FIGURE 1.29: See Example 1.33

Example 1.34 A 2.2 kO of 2% tolerance is required. What four-band color code does this correspond to? Solution Red (2), red (2), red (2 zeros), red (2% tolerance). Thus, all four bands should be red.

1.2.5

BS 1852 Coding

Some types of resistor have markings based on a system of coding defined in BS 1852. This system involves marking the position of the decimal point with a letter to indicate the multiplier concerned as shown in Table 1.9. A further letter is then appended to indicate the tolerance as shown in Table 1.10.

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The Fundamentals

47

Table 1.9: BS 1852 resistor multiplier markings Letter

Multiplier

R

1

K

1,000

M

1,000,000

Table 1.10: BS 1852 resistor tolerance markings Letter

Multiplier

F

1%

G

2%

J

5%

K

10%

M

20%

Example 1.35 A resistor is marked coded with the legend 4R7K. What is its value and tolerance? Solution 4.7O  10% Example 1.36 A resistor is marked coded with the legend 330RG. What is its value and tolerance? Solution 330O  2% Example 1.37 A resistor is marked coded with the legend R22M. What is its value and tolerance? Solution 0.22O  20%

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1.2.6

Chapter 1

Series and Parallel Combinations of Resistors

In order to obtain a particular value of resistance, fixed resistors may be arranged in either series or parallel as shown in Figures 1.30 and 1.31. The effective resistance of each of the series circuits shown in Figure 1.30 is simply equal to the sum of the individual resistances. So, for the circuit shown in Figure 1.30(A): R ¼ R1 þ R2 while for Figure 1.30(B): R ¼ R1 þ R2 þ R3 Turning to the parallel resistors shown in Figure 1.31, the reciprocal of the effective resistance of each circuit is equal to the sum of the reciprocals of the individual resistances. Hence, for Figure 1.31(A): 1 1 1 ¼ þ R R1 R2 while for Figure 1.32(B): 1 1 1 1 þ þ ¼ R R1 R2 R3 In the former case, the formula can be more conveniently rearranged as follows: R¼

R1  R2 R1 þ R2

You can remember this as the product of the two resistance values divided by the sum of the two resistance values.

Example 1.38 Resistors of 22O, 47O, and 33O are connected (a) in series and (b) in parallel. Determine the effective resistance in each case.

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FIGURE 1.30: Resistors in series

FIGURE 1.31: Resistors in parallel Solution (a)

In the series circuit R ¼ R1 þ R2 þ R3, thus R ¼ 22O þ 47O þ 33O ¼ 102O

(b)

In the parallel circuit: 1 1 1 1 þ þ ¼ R R1 R2 R3

Thus, 1 1 1 1 ¼ þ þ R 22O 47O 33O Or, 1 ¼ 0:045 þ 0:021 þ 0:03 R

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Chapter 1

from which, 1 ¼ 0:096 ¼ 10:42O R Example 1.39 Determine the effective resistance of the circuit shown in Figure 1.32. Solution The circuit can be progressively simplified as shown in Figure 1.33. The stages in this simplification are: (a) R3 and R4 are in series and they can replaced by a single resistance (RA) of (12O þ 27O) ¼ 39O. (b)

RA appears in parallel with R2. These two resistors can be replaced by a single resistance (RB) of (39O þ 47O)/(39O þ 47O) ¼ 21.3O.

(c) RB appears in series with R1. These two resistors can be replaced by a single resistance (R) of (21.3O þ 4.7O) ¼ 26O.

FIGURE 1.32: See Example 1.39

FIGURE 1.33: See Example 1.39

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Example 1.40 A resistance of 50O rated at 2W is required. What parallel combination of preferred value resistors will satisfy this requirement? What power rating should each resistor have? Solution Two 100O resistors may be wired in parallel to provide a resistance of 50O as shown below: R¼

R1  R2 100  100 10; 000 ¼ ¼ 50O ¼ 100 þ 100 200 R1 þ R2

Note, from this, that when two resistors of the same value are connected in parallel the resulting resistance will be half that of a single resistor. Having shown that two 100O resistors connected in parallel will provide us with a resistance of 50O we now need to consider the power rating. Since the resistors are identical, the applied power will be shared equally between them. Hence, each resistor should have a power rating of 1W.

1.2.7

Resistance and Temperature

Figure 1.34 shows how the resistance of a metal conductor (e.g., copper) varies with temperature. Since the resistance of the material increases with temperature, this characteristic is said to exhibit a positive temperature coefficient (PTC). Not all materials have a PTC characteristic. The resistance of a carbon conductor falls with temperature and it is therefore said to exhibit a negative temperature coefficient (NTC). The resistance of a conductor at a temperature, t, is given by the equation: Rt ¼ R0 ð1 þ a t þ b t2 þ g t3. . Þ where a, b, g, etc. are constants and R0 is the resistance at 0 C. The coefficients, b, g, etc. are quite small and since we are normally only dealing with a relatively restricted temperature range (e.g., 0  C to 100  C), we can usually

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Chapter 1

approximate the characteristic shown in Figure 1.34 to the straight line law shown in Figure 1.35. In this case, the equation simplifies to: Rt ¼ R0 ð1 þ a tÞ where a is known as the temperature coefficient of resistance. Table 1.11 shows some typical values for a (note that a is expressed in O/O/ C or just / C). Example 1.41 A resistor has a temperature coefficient of 0.001/ C. If the resistor has a resistance of 1.5 kO at 0  C, determine its resistance at 80  C.

FIGURE 1.34: Variation of resistance with temperature for a metal conductor

FIGURE 1.35: Straight line approximation of Figure 1.34

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53

Solution Now: Rt ¼ R0 ð1 þ a tÞ thus, Rt ¼ 1:5 kO  ð1 þ ð0:001  80ÞÞ Hence, Rt ¼ 1:5  1:08 ¼ 1:62 kO Example 1.42 A resistor has a temperature coefficient of 0.0005/ C. If the resistor has a resistance of 680O at 20  C, what will its resistance be at 80  C? Solution First we must find the resistance at 0 C. Rearranging the formula for Rt gives: R0 ¼

Rt 680 680 ¼ ¼ 1 þ ð0:0005  20Þ 1 þ 0:01 1 þ at

Hence, R0 ¼

680 ¼ 673:3O 1 þ 0:01

Now, Rt ¼ R0 ð1 þ a tÞ thus, R90 ¼ 673:3  ð1 þ ð0:0005  90ÞÞ Hence, R90 ¼ 673:3  1:045 ¼ 704O

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Example 1.43 A resistor has a resistance of 40O at 0 C and 44O at 100 C. Determine the resistor’s temperature coefficient. Solution First we need to make a the subject of the formula: Rt ¼ R0 ð1 þ a tÞ Now,     1 Rt 1 44 a¼ 1 ¼ 1 t Ro 100 40 from which, a¼

1 1 ð1:1  1Þ ¼  0:1 ¼ 0:001= C 100 100

Filmora x crack free download - Free Activators 1.11: Temperature coefficient of resistance

1.2.8

Material

Temperature coefficient of resistance, a (/˚C)

Platinum

þ0.0034

Silver

þ0.0038

Copper

þ0.0043

Iron

þ0.0065

Carbon

0.0005

Thermistors

With conventional resistors we would normally require resistance to remain the same over a wide range of temperatures (i.e., a should be zero). On the other hand, there are applications in which we could use the effect of varying resistance to detect a temperature change. Components that allow us to do this are known as thermistors.

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The resistance of a thermistor changes markedly with temperature and these components are widely used in temperature sensing and temperature compensating applications. Two basic types of thermistor are available, NTC and PTC (see Figure 1.36).

FIGURE 1.36: Characteristics of (A) NTC and (B) PTC thermistors

Typical NTC thermistors have resistances that vary from a few hundred (or thousand) ohms at 25  C to a few tens (or hundreds) of ohms at 100  C. PTC thermistors, on the other hand, usually have a resistance-temperature characteristic that remains substantially flat (typically at around 100O) over the range 0  C to around 75  C.

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Above this, and at a critical temperature (usually in the range 80  C to 120  C) their resistance rises very rapidly to values of up to, and beyond, 10 kO (see Figure 1.36). A typical application of PTC thermistors is over-current protection. Provided the current passing through the thermistor remains below the threshold current, the effects of self-heating will remain negligible and the resistance of the thermistor will remain low (i.e., approximately the same as the resistance quoted at 25  GoodSync 10.9.10.5 Full Download - Free Activators. Under fault conditions, the current exceeds the threshold value by a considerable margin and the thermistor starts to self-heat. The resistance then increases rapidly and, as a consequence, the current falls to the rest value. Typical values of threshold and rest currents are 200 mA and 8 mA, respectively, for a device which exhibits a nominal resistance of 25O at 25  C.

1.2.9

Light-Dependent Resistors

Light-dependent resistors (LDR) use a semiconductor material (i.e., a material that is neither a conductor nor an insulator) whose electrical characteristics vary according to the amount of incident light. The two semiconductor materials used for the manufacture of LDRs are cadmium sulphide (CdS) and cadmium selenide (CdSe). These materials are most sensitive to light in the visible spectrum, peaking at about 0.6 mm for CdS and 0.75 mm for CdSe. A typical CdS LDR exhibits a resistance of around 1 MO in complete darkness and less than 1 kO when placed under a bright light source (see Figure 1.37).

FIGURE 1.37: Characteristic of a light-dependent resistor (LDR)

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1.2.10 Voltage Dependent Resistors The resistance of a voltage dependent resistor (VDR) falls very rapidly when the voltage across it exceeds a nominal value in either direction (see Figure 1.38). In normal operation, the current flowing in a VDR is negligible; however, when the resistance falls, the current will become appreciable and a significant amount of energy will be absorbed. VDRs are used as a means of “clamping” the voltage in a circuit to a predetermined level. When connected across the supply rails to a circuit (either AC or DC) they are able to offer a measure of protection against voltage surges.

FIGURE 1.38: Characteristic of a voltage dependent resistor (VDR)

1.2.11 Variable Resistors Variable resistors are available in several forms including those which use carbon tracks and those which use a wirewound resistance element. In either case, a moving slider makes contact with the resistance element. Most variable resistors have three (rather than two) terminals and as such are more correctly known as potentiometers. Carbon potentiometers are available with linear or semi-logarithmic law tracks (see Figure 1.39) and in rotary or slider formats. Ganged controls, in which several potentiometers are linked together by a common control shaft, are also available. Figure 1.40 shows a selection of variable resistors. You will also encounter various forms of preset resistors that are used to make occasional adjustments (e.g., for calibration). Various forms of preset resistor are commonly used including open carbon track skeleton presets and fully encapsulated carbon and multiturn cermet types, as shown in Figure 1.41.

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FIGURE 1.39: Characteristics for linear and semi-logarithmic law variable resistors

FIGURE 1.40: A selection of common types eset internet security 12.0.31.0 license key - Crack Key For U carbon and wirewound variable resistors/potentiometers

FIGURE 1.41: A selection of common types of standard and miniature preset resistors/potentiometers

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59

1.2.12 Capacitors A capacitor is a device for storing electric charge. In effect, it is a reservoir into which charge can be deposited and then later extracted. Typical applications include reservoir and smoothing capacitors for use in power supplies, coupling AC signals between the stages of amplifiers, and decoupling supply rails (i.e., effectively grounding the supply rails as far as AC signals are concerned). A capacitor can consist of nothing more than two parallel metal plates as shown in Figure 1.10. To understand what happens when a capacitor is being charged and discharged take a look at Figure 1.42. If the switch is left open (position A), no charge will appear on the plates and in this condition there will be no electric field in the space between the plates nor will there be any charge stored in the capacitor. When the switch is moved to position B, electrons will be attracted from the positive plate to the positive terminal of the battery. At the same time, a similar number of electrons will move from the negative terminal of the battery to the negative plate. This sudden movement of electrons will manifest itself in a momentary surge of current (conventional current will flow from the positive terminal of the battery toward the positive terminal of the capacitor). Eventually, enough electrons will have moved to make the e.m.f. between the plates the same as that of the battery. In this state, the capacitor is said to be fully charged and an electric field will be present in the space between the two plates. If at some later time the switch is moved back to position A, the positive plate will be left with a deficiency of electrons while the negative plate will be left with a surplus of electrons. Furthermore, since there is no path for current to flow between the two plates the capacitor will remain charged and a potential difference will be maintained between the plates. Now assume that the switch is moved to position C. The excess electrons on the negative plate will flow through the resistor to the positive plate until a neutral state once again exists (i.e., until there is no excess charge on either plate). In this state the capacitor is said to be fully discharged and the electric field between the plates will rapidly collapse. The movement of electrons during the discharging of the capacitor will again result in a momentary surge of current (current will flow from the positive terminal of the capacitor and into the resistor). Figure 1.43 shows the direction of current flow in the circuit of Figure 1.42 during charging (switch in position B) and discharging (switch in position C). It should be

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FIGURE 1.42: Capacitor charging and discharging

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61

FIGURE 1.43: Current flow during charging and discharging

noted that current flows momentarily in both fonelab 9.1.82 registration code - Free Activators even though you may think that the circuit is broken by the gap between the capacitor plates!

1.2.13 Capacitance The unit of capacitance is the farad (F). A capacitor is said to have a capacitance of 1F if a current of 1A flows in it when a voltage changing at the rate of 1 V/s is applied to it. The current flowing in a capacitor will thus be proportional to the product of the capacitance, C, and the rate of change of applied voltage. Hence: i ¼ C  ðrate of change of voltageÞ Note that we’ve used a small i to represent the current flowing in the capacitor. We’ve done this because the current is changing and doesn’t remain constant.

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The rate of change of voltage is often represented by the expression dv/dt where dv represents a very small change in voltage and dt represents the corresponding small change in time. Expressing this mathematically gives: i¼C

dV dt

Example 1.44 A voltage is changing at a uniform rate from 10V to 50V in a period of 0.1s. If this voltage is applied to a capacitor of 22 mF, determine the current that will flow. Solution Now the current flowing will be given by: i ¼ C  ðrate of change of voltageÞ Thus,

    change in voltage 50  10 6 i¼C ¼ 22  10  change in time 0:1

From which, i ¼ 22  106 



40 0:1



¼ 22  106  400

so, i ¼ 8:8  103 ¼ 8:8 mA

1.2.14

Charge, Capacitance and Voltage

The charge or quantity of electricity that can be stored in the electric field between the capacitor plates is proportional to the applied voltage and the capacitance of the capacitor. Thus: Q ¼ CV where Q is the charge (in coulombs), C is the capacitance (in farads), and V is the potential difference (in volts).

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Example 1.45 A 10 mF capacitor is charged to a potential of 250V. Determine the charge stored. Solution The charge stored will be given by: Q ¼ CV ¼ 10  106  250 ¼ 2:5 mC

1.2.15 Energy storage The energy stored in a capacitor is proportional to the product of the capacitance and the square of the potential difference. Thus: W ¼ ½C V 2 where W is the energy (in joules), C is the capacitance (in farads), and V is the potential difference (in volts). Example 1.46 A capacitor of 47 mF is required to store 4J of energy. Determine the potential difference that must be applied to the capacitor. Solution The Bandicam Full Awesome 5.2.1.1860 Crack With Keygen Latest Free Download [2021] formula can be rearranged to make V the subject as follows: rffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E 2E 24 V¼ ¼ ¼ 0:5C C 47  106 from which, rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8 ¼ 0:170  106 ¼ 0:412  103 ¼ 412V V¼ 47  106

1.2.16 Capacitance and Physical Dimensions The capacitance of a capacitor depends upon the physical dimensions of the capacitor (i.e., the size of the plates and the separation between them) and the

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Chapter 1

dielectric material between the plates. The capacitance of a conventional parallel plate capacitor is given by: e0 er A C¼ d where C is the capacitance (in farads), e0 is the permittivity of free space, er is the relative permittivity of the dielectric medium between the plates), and d is the separation between the plates (in meters).

Example 1.47 A capacitor of 1 nF is required. If a dielectric material of thickness 0.1 mm and relative permittivity 5.4 is available, determine the required plate area.

Solution Rearranging the formula: C¼

e0 er A d

to make A the subject gives: A¼

Cd 1  109  0:1 VSDC Video Editor 6.8.2.341 Crack With Product Key Free Download 103 ¼ e0 er 8:854  1012  5:4

from which: A¼

0:1  1012 47:8116  1012

thus, A ¼ 0:00209 m2

or 20:9 cm2

In order to increase the capacitance of a capacitor, many practical components employ multiple plates (see Figure 1.44). The capacitance is then given by:

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FIGURE 1.44: A multi-plate capacitor



e0 er ðn  1Þ A d

where C is the capacitance (in farads), e0 is the permittivity of free space, er is the relative permittivity of the dielectric medium between the plates), and d is the separation between the plates (in meters) and n is the total number of plates. Example 1.48 A capacitor consists of six plates each of area 20 cm2 separated by a dielectric of relative permittivity 4.5 and thickness 0.2 mm. Determine the value of capacitance. Solution Using: C¼

e0 er ðn  1Þ A d

gives: C¼

8:854  1012  4:5  ð6  1Þ  20  104 0:2  103

from which, C¼

3; 984:3  1016 ¼ 19:921  1013 ¼ 190  1012 0:2  103

Thus, C ¼ 190  1012 F

or 1:992 nF

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1.2.17

Chapter 1

Capacitor Specifications

The specifications for a capacitor usually include the value of capacitance (expressed in microfarads, nanofarads or picofarads), the voltage rating (i.e., the maximum voltage which can be continuously applied to the capacitor under a given set of conditions), and the accuracy or tolerance (quoted as the maximum permissible percentage deviation from the marked value). Other practical considerations when selecting capacitors for use in a particular application include temperature coefficient, leakage current, stability and ambient temperature range. Table 1.12 summarizes the properties of five of the most common types of capacitor. Note that electrolytic capacitors require the application of a polarizing voltage in order to the chemical action on which they depend for their operation.

Table 1.12: Characteristics of common types of capacitor Capacitor type Property

Ceramic

Electrolytic

Polyester

Mica

Polystyrene

Capacitance range (F)

2.2p to 100n

100n to 10m

10n to 2.2m

0.47 to 22k

10p to 22n

Typical tolerance (%)

10 and 20

10 to þ50

10

1

5

Typical voltage rating (W)

50V to 200V

6.3V to 400V

100V to 400V

350V

100V

Temperature coefficient (ppm/ C)

þ100 to 4700

þ1000 typical

þ100 to þ200

þ50

þ250

Stability

Fair

Poor

Good

Excellent

Good

Ambient temperature range ( C)

85 to þ85

40 to þ80

40 to þ100

40 to þ125

40 to þ100

Typical applications

High-frequency and low-cost

Smoothing and decoupling

GeneralPurpose

Tuned circuits and oscillators

GeneralPurpose

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The polarizing voltages used for electrolytic capacitors can range from as little as 1V to several hundred volts depending upon the working voltage rating for the component in question. Figure 1.45 shows some typical nonelectrolytic capacitors (including polyester, polystyrene, ceramic and mica types), while Figure 1.46 shows a selection of electrolytic (polarized) capacitors. An air-spaced variable capacitor is shown later in Figure 1.54.

FIGURE 1.45: A typical selection of nonelectrolytic capacitors (including polyester, polystyrene, ceramic and mica types) with values ranging from 10 pF to 470 nF and working voltages from 50V to 250V

FIGURE 1.46: A typical selection of electrolytic (polarized) capacitors with values ranging from 1 mF to 470 mF and working voltages from 10V to 63V

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1.2.18

Capacitor Markings

The vast majority of capacitors employ written markings which indicate their values, working voltages, and tolerance. The most usual method of marking resin dipped polyester (and other) types of capacitor involves quoting the value (mF, nF or pF), the tolerance (often either 10% or 20%), and the working voltage (often using _ and  to indicate DC and AC, respectively). Several manufacturers use two separate lines for their capacitor markings and these have the following meanings: First line:

capacitance (pF or mF) and tolerance (K ¼ 10%, M ¼ 20%)

Second line:

rated DC voltage and code for the dielectric material

A three-digit code is commonly used to mark monolithic ceramic capacitors. The first two digits of this code correspond to the first two digits of the value, while the third digit is a multiplier which gives the number of zeros to be added to give the value in picofarads. Other capacitors may use a color code similar to that used for marking resistor values (see Figure 1.48).

FIGURE 1.47: Examples of capacitor markings

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FIGURE 1.48: Capacitor color code

Example 1.49 A monolithic ceramic capacitor is marked with the legend “103K”. What is its value? Solution The value (pF) will be given by the first two digits (10) followed by the number of zeros indicated by the third digit (3). The value of the capacitor is thus 10,000 pF or 10 nF. The final letter (K) indicates that the capacitor has a tolerance of 10%.

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FIGURE 1.49: See Example 1.50 Example 1.50 Activate Windows 8/8.1 Without Product key and Internet tubular capacitor is marked with the following colored stripes: brown, green, brown, red, brown. What is its value, tolerance, and working voltage? Solution See Figure 1.49.

1.2.19

Series and Parallel Combination of Capacitors

In order to obtain a particular value of capacitance, fixed capacitors may be arranged in either series or parallel (Figures 1.50 and 1.51). The reciprocal of the effective capacitance of each of the series circuits Macrium Reflect 8.0.6036 Crack + License Keygen Full Free {2021} in Figure 1.50 is equal to the sum of the reciprocals of the individual capacitances. Hence, for Figure 1.50(A): 1 1 1 þ ¼ C C1 C2 while for Figure 1.50(B): 1 1 1 1 þ þ ¼ C C1 C2 C3

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FIGURE 1.50: Capacitors in series

FIGURE 1.51: Capacitors in parallel

In the former case, the formula can be more conveniently rearranged as follows: C¼

C1  C2 C1 þ C2

You can remember this as the product of the two capacitor values divided by the sum of the two values—just as you did for two resistors in parallel. For a parallel arrangement of capacitors, the effective capacitance of the circuit is simply equal to the sum of the individual capacitances. Hence, for Figure 1.51(A): C ¼ C1 þ C2

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while for Figure 1.51(B): C ¼ C1 þ C2 þ C3 Example 1.51 Determine the effective capacitance of the circuit shown in Figure 1.52. Solution The circuit of Figure 1.52 can be progressively simplified as shown in Figure 1.53. The stages in this simplification are: (a) C1 and C2 are in parallel and they can be replaced by a single capacitor (CA) of (2 nF þ 4 nF) ¼ 6 nF. (b)

CA appears in series with C3. These two resistors can be replaced by a single capacitor (CB) of (6 nF  2 nF)/(6 nF þ 2 nF) ¼ 1.5 nF.

(c) CB appears in parallel with C4. These two capacitors can be replaced by a single capacitance (C) of (1.5 nF þ 4 nF) ¼ 5.5 nF.

FIGURE 1.52: See Example 1.51

Example 1.52 A capacitance of 50 mF (rated at 100V) is required. What series combination of preferred value capacitors will satisfy this requirement? What voltage rating should each capacitor have?

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Solution Two 100 mF capacitors wired in series will provide a capacitance of 50 mF, as follows: C¼

C1  C2 100  100 10; 000 ¼ ¼ ¼ 50 mF 100 þ 100 200 C1 þ C2

FIGURE 1.53: See Example 1.51 Since the capacitors are of equal value, the applied DC potential will be shared equally between them. Thus each capacitor should be rated at 50V. Note that, in a practical circuit, we could take steps to ensure that the DC voltage was shared equally between the two capacitors by wiring equal, high-value (e.g., 100 kO) resistors across each capacitor.

1.2.20 Variable Capacitors By moving one set of plates relative to the other, a capacitor can be made variable. The dielectric material used in a variable capacitor can be either air (see Figure 1.54) or plastic (the latter tend to be more compact). Typical values for variable capacitors tend to range from about 25 pF to 500 pF. These components are commonly used for tuning radio receivers.

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FIGURE 1.54: An air-spaced variable capacitor. This component (used for tuning an AM radio) has two separate variable capacitors (each of 500 pF maximum) operated from a common control shaft.

1.2.21

Inductors

Inductors provide us with a means of storing electrical energy in the form of a magnetic field. Typical applications include chokes, filters and (in conjunction with one or more capacitors) frequency selective circuits. The electrical characteristics of an inductor are determined by a number of factors including the material of the core (if any), the number of turns, and the physical dimensions of the coil. Figure 1.55 shows the construction of a typical toroidal inductor wound on a ferrite (high permeability) core. In practice every coil comprises both inductance (L) and a small resistance (R). The circuit of Figure 1.56 shows these as two discrete components. In reality the inductance and the resistance (we often refer to this as a loss resistance because it’s something that

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we don’t actually want) are both distributed throughout the component but it is convenient to treat the inductance and resistance as separate components in the analysis of the circuit.

FIGURE 1.55: A practical coil contains inductance and resistance

FIGURE 1.56: A practical coil contains inductance and a small amount of series loss resistance To understand what happens when a changing current flows through an inductor, take a look at the circuit shown in Figure 1.57(A). If the switch is left open, no current will flow and no magnetic flux will be produced by the inductor. If the switch is closed, as shown in Figure 1.57(B), current will begin to flow as energy is taken from the supply in order to establish the magnetic field. However, the change in magnetic flux resulting from the appearance of current creates a voltage (an induced e.m.f.) across the coil which opposes the applied e.m.f. from the battery.

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FIGURE 1.57: Flux and e.m.f. generated when a changing current is applied to an inductor

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The induced e.m.f. results from the changing flux and it effectively prevents an instantaneous rise in current in the circuit. Instead, the current increases slowly to a maximum at a rate which depends upon the ratio of inductance (L) to resistance (R) present in the circuit. After a while, a steady-state condition will be reached in which the voltage across the inductor will have decayed to zero and the current will have reached a maximum value determined by the ratio of V to R (i.e., Ohm’s Law). This is shown in Figure 1.57(C). If, after this steady-state condition has been achieved, the switch is opened, as shown in Figure 1.57(D), the magnetic field will suddenly collapse and the energy will be returned to the circuit in the form of an induced back e.m.f., which will appear across the coil as the field collapses. For large values of magnetic flux and inductance this back e.m.f. can be extremely large!

1.2.22 Inductance Inductance is the property of a coil which gives rise to the opposition to a change in the value of current flowing in it. Any change in the current applied to a coil/inductor will result in an induced voltage appearing across it. The unit of inductance is the henry (H) and a coil is said to have an inductance of 1H if a voltage of 1V is induced across it when a current changing at the rate of 1 A/s is flowing in it. The voltage induced across the terminals of an inductor will thus be proportional to the product of the inductance (L) and the rate of change of applied current. Hence: e ¼  L  ðrate of change of currentÞ Note that the minus sign indicates the polarity of the voltage, i.e., opposition to the change. The rate of change of current is often represented by the expression di/dt where di represents a very small change in current and dt represents the corresponding small change in time. Using mathematical notation to write this we arrive at: e ¼ L

di dt

You might like to compare this with the similar relationship that we obtained for the current flowing in a capacitor shown in Section 1.2.13.

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Example 1.53 A current increases at a uniform rate from 2A to 6A in a period of 250 ms. If this current is applied to an inductor of 600 mH, determine the voltage induced. Solution Now the induced voltage will be given by: e ¼  L  ðrate of change of currentÞ Thus,

    change in current 62 3 e ¼ L ¼  60  10  change in time 250  103

From which, 3

e ¼  600  10



 4  ¼  0:6  103  16 0:25

so, e ¼ 9:6V

1.2.23 Energy Storage The energy stored in an inductor is proportional to the product of the inductance and the square of the current flowing in it. Thus: W ¼ ½ L I2 where W is the energy (in joules), L is the capacitance (in henries), and I is the current flowing in the inductor (in amps). Example 1.54 An inductor of 20 mH is required to store 2.5J of energy. Determine the current that must be applied.

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Solution The foregoing formula can be rearranged to make I the subject as follows: rffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E 2E 2  2:5 ¼ ¼ I¼ 0:5L L 20  103 From which

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi 5 3 ¼ 250 ¼ 15:81A I¼ ¼ 0:25  10 20  103

1.2.24 Inductance and Physical Dimensions The inductance of an inductor depends upon the physical dimensions of the inductor (e.g., the length and diameter of the winding), the number of turns, and the permeability of the material of the core. The inductance of an inductor is given by: L¼

m0 mr n2 A l

where L is the inductance (in henries), m0 is the permeability of free space, mr is the relative permeability of the magnetic core, l is the mean length of the core (in meters), and A is the cross-sectional area of the core (in square meters). Example 1.55 An inductor of 100 mH is required. If a closed magnetic core of length 20 cm, cross-sectional area 15 cm2 and relative permeability 500 is available, determine the number of turns required. Solution First we must rearrange the formula: L¼

m0 mr n2 A l

in order to make n the subject: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ll 100  103  20  102 ¼ n¼ m0 mr n2 A 12:57  107  500  15  104

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From which: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2  102 n¼ ¼ 21; 215 ¼ 146 11 94; 275  10 Hence, the inductor requires 146 turns of wire.

1.2.25

Inductor Specifications

Inductor specifications normally include the value of inductance (expressed in henries, millihenries or microhenries), the current rating (i.e., the maximum current which can be continuously applied to the inductor under a given set of conditions), and the accuracy or tolerance (quoted as the maximum permissible percentage deviation from the marked value). Other considerations may include the temperature coefficient of the inductance (usually expressed in parts per million, p.p.m., per unit temperature change), the stability of the inductor, the DC resistance of the coil windings (ideally zero), the Q-factor (quality factor) of the coil, and the recommended working frequency range. Table 1.13 Table 1.13: Characteristics of common types of inductor Inductor type Property

Air cored

Ferrite cored

Ferrite pot cored

Iron cored

Core material

Air

Ferrite rod

Ferrite pot

Laminated steel

Inductance range (H)

50n to 100m

10m to 1m

1m to 100m

20m to 20

Typical DC resistance (O)

0.05 to 5

0.1 to 10

5 to 100

10 to 200

Typical tolerance (%)

5

10

10

20

Typical Q-factor

60

80

40

20

Typical frequency range (Hz)

1M to 500M

100k to 100M

1k to 10M

50 to 10k

Typical applications

Tuned circuits and filters

Filters and HF transformers

LF and MF filters and transformers

Smoothing chokes and filters

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summarizes the properties of four common types of inductor. Some typical small inductors are shown in Figure 1.58. These have values of inductance ranging from 15 mH to 1 mH.

FIGURE 1.58: A selection of small inductors with values ranging from 15 mH to 1 mH

1.2.26 Inductor Markings As with capacitors, the vast majority of inductors use written markings to indicate values, working current, and tolerance. Some small inductors are marked with colored stripes to indicate their value and tolerance (in which case the standard color values are used and inductance is normally expressed in microhenries).

1.2.27 Series and Parallel Combinations of Inductors In order to obtain a particular value of inductance, fixed inductors may be arranged in either series or parallel as shown in Figs 1.59 and 1.60. The effective inductance of each of the series circuits shown in Figure 1.59 is simply equal to the sum of the individual inductances. So, for the circuit shown in Figure 1.59(A): L ¼ L1 þ L2 while for Figure 1.59(B): L ¼ L1 þ L2 þ L3

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FIGURE 1.59: Inductors in series Turning to the parallel inductors shown in Figure 1.60, the reciprocal of the effective inductance of each circuit is equal to the sum of the reciprocals of the individual inductances. Hence, for Figure 1.60(A): 1 1 1 þ ¼ L L1 L2 while for Figure 1.60(B): 1 1 1 1 þ þ ¼ L L1 L2 L3 In the former case, the formula can be more conveniently re-arranged as follows: L¼

L1  L2 L1 þ L2

You can remember this as the product of the two inductance values divided by the sum of the two inductance values.

FIGURE 1.60: Inductors in parallel

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Example 1.56 An inductance of 5 mH (rated at 2A) is required. What parallel combination of preferred value inductors will satisfy this requirement? Solution Two 10 mH inductors may be wired in parallel to provide an inductance of 5 mH as shown below: L¼

L1  L2 10  10 100 ¼ ¼ ¼ 5 mH 10 þ 10 20 L1 þ L2

Since the inductors are identical, the applied current will be shared equally between them. Hence, each inductor should have a current rating of 1A. Example 1.57 Determine the effective inductance of the circuit shown in Figure 1.61. Solution The circuit can be progressively simplified as shown in Figure 1.62. The stages in this simplification are as follows: (a)

L1 and L2 are in series and they can be replaced by a single inductance (LA) of (60 þ 60) ¼ 120 mH.

(b)

LA appears in parallel with L2. These two inductors can be replaced by a single inductor (LB) of (120  120)/(120 þ 120) ¼ 60 mH.

(c)

LB appears in series with L4. These two inductors can be replaced by a single inductance (L) of (60 þ 50) ¼ 110 mH.

FIGURE 1.61: See Example 1.57

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FIGURE 1.62: See Example 1.57

1.2.28

Variable Inductors

A ferrite cored inductor can be made variable by moving its core in or out of the former onto which the coil is wound. Many small inductors have threaded ferrite cores to make this possible (see Figure 1.63). Such inductors are often used in radio and highfrequency applications where precise tuning is required.

FIGURE 1.63: An adjustable ferrite cored inductor

1.2.29

Surface Mounted Components (SMC)

Surface-mount technology (SMT) is now widely used in the manufacture of printed circuit boards for electronic equipment. SMT allows circuits to be assembled in a much smaller space than would be possible using components with conventional wire leads and pins that are mounted using through-hole techniques. It is also possible to mix the

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two technologies, i.e., some through-hole mounting of components and some surface mounted components present on the same circuit board. The following combinations are possible:  Surface mounted components (SMC) on both sides of a printed circuit board.  SMC on one side of the board and conventional through-hole components (THC) on the other.  A mixture of SMC and THC on both sides of the printed circuit board. Surface mounted components are supplied in packages that are designed for mounting directly on the surface of a PCB. To provide electrical contact with the PCB, some SMC have contact pads on their surface. Other devices have contacts which extend beyond the outline of the package itself but which terminate on the surface of the PCB rather than making contact through a hole (as is the case with a conventional THC). In general, passive components (such as resistors, capacitors and inductors) are configured leadless for surface mounting, while active devices (such as transistors and integrated circuits) are available in both surface mountable types as well as lead as well as in leadless terminations suitable for making direct contact to the pads on the surface of a PCB. Most surface mounted components have a flat rectangular shape rather than the cylindrical shape that we associate with conventional wire leaded components. During manufacture of a PCB, the various SMC are attached using re-flow soldering paste (and in some cases adhesives) which consists of particles of solder and flux together with binder, solvents and additives. They need to have good “tack” in order to hold the components in place and remove oxides without leaving obstinate residues. The component attachment (i.e., soldering!) process is completed using one of several techniques including convection ovens in which the PCB is passed, using a conveyor belt, through a convection oven which has separate zones for preheating, flowing and cooling, and infra-red reflow in which infrared lamps norton antivirus full cracked download - Free Activators used to provide the source of heat. Surface mounted components are generally too small to be marked with color codes. Instead, values may be marked using three digits. For example, the first two digits marked on a resistor normally specify the first two digits of the value while the third digit gives the number of zeros that should be added.

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Example 1.58 In Figure 1.65, R88 is marked “102”. What is its value? Solution R88 will have a value of 1,000O (i.e., 10 followed by two zeros).

FIGURE 1.64: Conventional components mounted on a printed circuit board. Note that components such as C38, R46, etc. have leads that pass through holes in the printed circuit boards

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FIGURE 1.65: Surface mounted components (note the appearance of capacitors C35, C52, and C53, and resistors, R87, R88, R91, etc.)

1.3 DC Circuits In many cases, Ohm’s Law alone is insufficient to determine the magnitude of the voltages and currents present in a circuit. This section introduces several techniques that simplify the task of solving complex circuits. It also introduces the concept of exponential growth and decay of voltage and current in circuits containing capacitance and resistance and inductance and resistance. It concludes by showing how humble C-R

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circuits can be used for shaping the waveforms found in electronic circuits. We start by introducing two of the most useful laws of electronics.

1.3.1

Kirchhoff’s Laws

Kirchhoff’s Laws relate to the algebraic sum of currents at a junction (or node) or voltages in a network (or mesh). The term “algebraic” simply indicates that the polarity of each current or voltage drop must be taken into account by giving it an appropriate sign, either positive (þ) or negative (). Kirchhoff’s Current Law states that the algebraic sum of the currents present at a junction (node) in a circuit is zero (see Figure 1.66).

FIGURE 1.66: Kirchhoff’s Current Law Example 1.59 In Figure 1.67, use Kirchhoff’s Current Law to determine: (a) the value of current flowing between A and B, and (b)

the value of I3.

Solution (a) I1 and I2 both flow toward Node A so, applying our polarity convention, they must both be positive. Now, assuming that a current I5 flows between A and B and that this

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FIGURE 1.67: See Example 1.59 current flows away from the junction (obvious because I1 and I2 both flow toward the junction), we arrive at the following Kirchhoff’s Current Law equation: þI1 þ I2  I5 ¼ 0 From which: I5 ¼ I1 þ I2 ¼ 1:5 þ 2:7 ¼ 4:2A (b) Moving to Node B, let’s assume that I3 flows outward, so we can say that: þI4 þ I5  I3 ¼ 0 From which: OutByte Antivirus 4.0.7.59141 Crack With License Key Free Download ¼ I4 þ I5 ¼ 3:3 þ 4:2 ¼ 7:5A Kirchhoff’s Voltage Law states that the algebraic sum of the potential drops in a closed network (or “mesh”) is zero (see Figure 1.68). Example 1.60 In Figure 1.69, use Kirchhoff’s Voltage Law to determine: (a)

the value of V2, and

(b)

the value of E3.

Solution (a)

In Loop A, and using the conventions shown in Figure 1.68, we can write down the Kirchhoff’s Voltage Law equations: E1  V2  E2 ¼ 0

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FIGURE 1.68: Kirchhoff’s Voltage Law

FIGURE 1.69: See Example 1.60 From which: V2 ¼ E1  E2 ¼ 6  3 ¼ 3V (b)

Similarly, in Loop B, we can say that: E2  V2 þ E3 ¼ 0

From which: E3 ¼ V2  E2 ¼ 4:5  3 ¼ 1:5V

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Example 1.61 Determine the currents and voltages in the circuit of Figure 1.70.

FIGURE 1.70: See Example 1.61 Solution In order to solve the circuit shown in Figure 1.70, it is first necessary to mark the currents and voltages on the circuit, as shown in Figures 1.71 and 1.72. By applying Kirchhoff’s Current Law at Node A that we’ve identified in Figure 1.70: þI1 þ I2  I3 ¼ 0 Therefore: I1 ¼ I3  I2

ðiÞ

By applying Kirchhoff’s Voltage Law in Loop A we obtain: 12  V1  V3 ¼ 0 From which: V1 ¼ 12  V3

ðiiÞ

By applying Kirchhoff’s Voltage Law in Loop B we obtain: 9  V2  V3 ¼ 0 From which: V2 ¼ 9  V3

ðiiiÞ

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FIGURE 1.71: See Example 1.61

FIGURE 1.72: See Example 1.61 Next we can generate three further relationships by applying Ohm’s Law: V1 ¼ I1 R1 V2 ¼ I2 R2

V1 R1 V2 from which I2 ¼ R2 from which I1 ¼

and, V3 ¼ I3 R3

from which I3 ¼

V3 R3

Combining these three relationships with the Current Law equation (i) gives: V1 V3 V2 ¼  R1 R3 R2

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from which: V1 V3 V2 ¼  110 22 33 Combining (ii) and (iii) with (iv) gives: ð12  V3 Þ V3 ð9  V3 Þ ¼  110 33 22 Multiplying both sides of the expression by 330 gives: 330ð12  V3 Þ 330V3 330ð9  V3 Þ ¼  110 33 22 3ð12  V3 Þ ¼ 15 V3  10ð9  V3 Þ From which: 36  3 V3 ¼ 15 V3  90 þ V3 36 þ 90 ¼ 15 V3 þ 10 V3 þ 3 V3 and: 126 ¼ 28V3

so V3 ¼ 126=28 ¼ 4:5V

From (ii): V1 ¼ 12  V3

so

V1 ¼ 12  4:5 ¼ 7:5V

V2 ¼ 9  V3

so

V2 ¼ 9  4:5 ¼ 4:5V

From (iii):

Using the Ohm’s Law equations that we met earlier gives: V1 7:5 ¼ ¼ 0:068A ¼ 68 mA 110 R1 V2 4:5 I2 ¼ ¼ ¼ 0:136A ¼ 136 mA 33 R2 V3 4:5 I3 ¼ ¼ ¼ 0:204A ¼ 204 mA 22 R3 I1 ¼

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Finally, it’s worth checking these results with the Current Law equation (i): þI1 þ I2  I3 ¼ 0 Inserting our values for I1, I2 and I3 gives: þ0:068 þ 0:136  204 ¼ 0 Since the left and right hand sides of the equation are equal we can be reasonably confident that our results are correct.

1.3.2

The Potential Divider

The potential divider circuit (see Figure 1.73) is commonly used to reduce voltages in a circuit. The output voltage produced by the circuit is given by: Vout ¼ Vin

R2 R1 þ R2

FIGURE 1.73: Potential divider circuit It is, however, important to note that the output voltage (Vout) will fall when current is drawn from the arrangement. Figure 1.74 shows the effect of loading the potential divider circuit. In the loaded potential divider (Figure 1.74) the output voltage is given by: Vout ¼ Vin

Rp R1 þ Rp

where: Rp ¼

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R2  RL R2 þ RL

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FIGURE 1.74: Loaded potential divider circuit

Example 1.62 The potential divider shown in Figure 1.75 is used as a simple voltage calibrator. Determine the output voltage produced by the circuit: (a)

when the output terminals are left open-circuit (i.e., when no load is connected); and

(b)

when the output is loaded by a resistance of 10 kO.

FIGURE 1.75: See Example 1.62

Solution (a)

In the first case we can simply apply the formula: Vout ¼ Vin

R2 R1 þ R2

where Vin ¼ 5V, R1 ¼ 4 kO and R2 ¼ 1 kO.

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Hence: Vout ¼ 5  (b)

1 ¼ 1V 4þ1

In the second case we need to take into account the effect of the 10 kO resistor connected to the output terminals of the potential divider.

First we need to find the equivalent resistance of the parallel combination of R2 and RL: Rp ¼

R2  RL 1  10 10 ¼ ¼ 0:909 kO ¼ 1 þ 10 11 R2 þ RL

Then we can determine the output voltage from: Vout ¼ Vin

1.3.3

Rp 0:909 ¼5 ¼ 0:925V 4 þ 0:909 R1 þ Rp

The Current Divider

The current divider circuit (see Figure 1.76) is used to divert a known proportion of the current flowing in a circuit. The output current produced by the circuit is given by: Iout ¼ Iin

R1 R1 þ R2

It is, however, important to note that the output current (Iout) will fall when the load connected to the output terminals has any appreciable resistance.

FIGURE 1.76: Current divider circuit

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Example 1.63 A moving coil meter requires a current of 1 mA to provide full-scale deflection. If the meter coil has a resistance of 100O and is to be used as a milliammeter reading 5 mA full-scale, determine the value of parallel shunt resistor required. Solution This problem may sound a little complicated so it is worth taking a look at the equivalent circuit of the meter (Figure 1.77) and comparing it with the current divider shown in Figure 1.76. We can apply the current divider formula, replacing Iout with Im (the meter full-scale deflection current) and R2 with Rm (the meter resistance). R1 is the required value of shunt resistor, Rs, Hence: Iout ¼ Iin

Rs Rs þ Rm

FIGURE 1.77: See Example 1.63

Rearranging the formula gives: Im  ðRs þ Rm Þ ¼ Iin  Rs thus, Im Rs þ Im Rm ¼ Iin Rs

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or, Iin Rs  Im Rs ¼ Im Rm from which, Rs ðIin  Im Þ ¼ Im Rm So, Rs ¼

Im Rm Iin  Im

Now Iin ¼ 1 mA, Rm ¼ 100O and Iin ¼ 5 mA, thus: Rs ¼

1.3.4

1  100 100 ¼ ¼ 25O 51 4

The Wheatstone Bridge

The Wheatstone bridge forms the basis of a number of useful electronic circuits including several that are used in instrumentation and measurement. The basic form of Wheatstone bridge is shown in Figure 1.78. The voltage developed between A and B will be zero when the voltage between A and Y is the same as that between B and Y. In effect, R1 and R2 constitute a potential divider as do R3 and R4.

FIGURE 1.78: Basic Wheatstone bridge circuit

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The bridge will be balanced (and VAB ¼ 0) when the ratio of R1:R2 is the same as the ratio R3:R4. Hence, at balance: R1 R3 ¼ R2 R4 A practical form of Wheatstone bridge that can be used for measuring unknown resistances is shown in Figure 1.79.

FIGURE 1.79: See Example 1.64 In this practical form of Wheatstone bridge, R1 and R2 are called the ratio arms while one arm (that occupied by R3 in Figure 1.78) is replaced by a calibrated variable resistor. The unknown resistor, Rx, is connected in the fourth arm. At balance: R1 Rv ¼ R2 Rx

thus Rx ¼

R2  Rv R1

Example 1.64 A Wheatstone bridge is based on the circuit shown in Figure 1.79. If R1 and R2 can each be switched so that they have values of either 100O or 1 kO and RV is variable between 10O and 10 kO, determine the range of resistance values that can be measured.

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Solution The maximum value of resistance that can be measured will correspond to the largest ratio of R2:R1 (i.e., when R2 is 1 kO and R1 is 100O) and the highest value of RV (i.e., 10 kO). In this case: Rx ¼

1; 000  10; 000 ¼ 100; 000 ¼ 100 kO 100

The minimum value of resistance that can be measured will correspond to the smallest ratio of R2:R1 (i.e., when R1 is 100O and R1 is 1 kO) and the smallest value of RV (i.e., 10O). In this case: Rx ¼

100  10 ¼ 0:1  10 ¼ 1O 1; 000

Hence the range of values that can be measured extends from 1O to 100 kO.

1.3.5

The´venin’s Theorem

The´venin’s Theorem allows us to replace a complicated network of resistances and voltage sources with a simple equivalent circuit comprising a single voltage source connected in series with a single resistance (see Figure 1.70). The single voltage source in the The´venin equivalent circuit, Voc, is simply the voltage that appears between the terminals when nothing is connected to it. In other words, it is the open-circuit voltage that would appear between A and B. The single resistance that appears in the The´venin equivalent circuit, R, is the resistance that would be seen looking into the network between A and B when all of the voltage sources (assumed perfect) are replaced by short-circuit connections. Note that if the voltage sources are not perfect (i.e., if they have some internal resistance) the equivalent circuit must be constructed on the basis that each voltage source is replaced by its own internal resistance. Once we have values for Voc and R, we can determine how the network will behave when it is connected to a load (i.e., when a resistor is connected across the terminals A and B).

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Example 1.65 Figure 1.81 shows a Wheatstone bridge. Determine the current that will flow in a 100O load connected between terminals A and B. Solution First we need to find the The´venin equivalent of the circuit. To find Voc we can treat the bridge arrangement as two potential dividers. The voltage across R2 will be given by: V ¼ 10 

R2 600 ¼ 10  ¼ 5:454V 500 þ 600 R1 þ R2

Hence, the voltage at A relative to Y, VAY, will be 5.454V. The voltage across R4 will be given by: V ¼ 10 

R4 400 ¼ 10  ¼ 4:444V 500 þ 400 R3 þ R4

Hence, the voltage at B relative to Y, VBY, will be 4.444V. The voltage VAB will be the difference between VAY and VBY. This, the open-circuit output voltage, VAB, will be given by: VAB ¼ VAY  VBY ¼ 5:454  4:444 ¼ 1:01V Next we need to find the The´venin equivalent resistance looking in at A and B. To do this, we can redraw the circuit, replacing the battery (connected between X and Y) with a short circuit, as shown in Figure 1.82. The The´venin equivalent resistance is given by the relationship: R¼

R1  R2 R3  R4 500  600 500  400 þ þ ¼ 500 þ 600 500 þ 400 R1 þ R2 R3 þ R4

From which: R¼

300; 000 200; 000 þ ¼ 272:7 þ 222:2 ¼ 494:9O 1; 100 900

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FIGURE 1.80: The´venin equivalent circuit

FIGURE 1.81: See Example 1.65

FIGURE 1.82: See Example 1.65 The The´venin equivalent circuit is shown in Figure 1.83. To determine the current in a 100O load connected between A and B, we can simply add a 100O load to the The´venin equivalent circuit, as shown in Figure 1.84. By applying Ohm’s Law in Figure 1.84 we get: I¼

Voc 1:01 1:01 ¼ ¼ 1:698 mA ¼ 494:9 þ 100 594:9 R þ 100

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FIGURE 1.83: The´venin equivalent of Figure 1.81

FIGURE 1.84: Determining the current when the The´venin equivalent circuit is loaded

1.3.6

Norton’s Theorem

Norton’s Theorem provides an alternative method of reducing a complex network to a simple equivalent circuit. Unlike The´venin’s Theorem, Norton’s Theorem makes use of a current source rather than a voltage source. The Norton equivalent circuit allows us to replace a complicated network of resistances and voltage sources with a simple equivalent circuit comprising a single constant current source connected in parallel with a single resistance (see Figure 1.85). The constant current source in the Norton equivalent circuit, Isc, is simply the shortcircuit current that would flow if A and B were to be linked directly together. The resistance that appears in the Norton equivalent circuit, R, is the resistance that would be seen looking into the network between A and B when all of the voltage sources are replaced by short-circuit connections. Once again, it is worth noting that, if the voltage sources have any appreciable internal resistance, the equivalent circuit must be constructed on the basis that each voltage source is replaced by its own internal resistance.

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FIGURE 1.85: Norton equivalent circuit As with the The´venin equivalent, we can determine how a network will behave by obtaining values for Isc and Amazing slow downer for mac free. Example 1.66 Three temperature sensors having the following characteristics shown in Table 1.14 are connected in parallel as shown in Figure 1.86: Determine the voltage produced when the arrangement is connected to a moving-coil meter having a resistance of 1 kO. Table 1.14: Temperature sensor characteristics Sensor

A

B

C

Output voltage (open circuit)

20 mV

30 mV

10 mV

Internal resistance

5 kO

3 kO

2 kO

FIGURE 1.86: See Example 1.66 Solution First we need to find the Norton equivalent of the circuit. To find Isc we can determine the short-circuit current from each sensor and add them together.

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For sensor A: I¼

V 20 mV ¼ ¼ 4 mA R 5 kO



V 30 mV ¼ ¼ 10 mA R 3 kO



V 10 mV ¼ ¼ 5 mA R 2 kO

For sensor B:

For sensor C:

The total current, Isc, will be given by: Isc ¼ 4 mA þ 10 mA þ 5 mA ¼ 19 mA Next we need to find the Norton equivalent resistance. To do this, we can redraw the circuit showing each sensor replaced by its internal resistance, as shown in Figure 1.87.

FIGURE 1.87: Determining the equivalent resistance in Figure 1.86 The equivalent resistance of this arrangement (think of this as the resistance seen looking into the circuit in the direction of the arrow shown in Figure 1.87) is given by: 1 1 1 1 1 1 1 þ þ ¼ ¼ þ þ R R1 R2 R3 5; 000 3; 000 2; 000 where R1 ¼ 5kO, R2 ¼ 3kO, R3 ¼ 2kO, hence: 1 1 Altium Designer 20.2.6 Build 244 Crack 1 1 1 1 ¼ þ þ þ þ ¼ R R1 R2 R3 5; 000 3; 000 2; 000

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or, 1 ¼ 0:0002 þ 0:00033 þ 0:0005 ¼ 0:00103 R from which: R ¼ 968O The Norton equivalent circuit is shown in Figure 1.88. To determine the voltage in a 1 kO moving coil meter connected between A and B, we can make use of the Norton equivalent circuit by simply adding a 1 kO resistor to the circuit and applying Ohm’s Law, as shown in Figure 1.89. The voltage appearing across the moving coil meter in Figure 1.90 will be given by: V ¼ Isc 

R  Rm 1; 000  968 ¼ 19 mA  1; 000 þ 968 R þ Rm

hence: V ¼ 19 mA  492O ¼ 9:35 mV

FIGURE 1.88: Norton equivalent of the circuit in Figure 1.86

FIGURE 1.89: Determining the output voltage when the Norton equivalent circuit is loaded with 1 kV

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FIGURE 1.90: The voltage drop across the meter is found to be 9.35 mV

1.3.7

C-R Circuits

Networks of capacitors and resistors (known as C-R circuits) form the basis of many timing and pulse shaping circuits and are thus often found in practical electronic circuits.

1.3.8

Charging

A simple C-R circuit is shown in Figure 1.91. In this circuit C is charged through R from the constant voltage source, Vs. The voltage, nc, across the (initially uncharged) capacitor voltage will rise exponentially as shown in Figure 1.92. At the same time, the current in the circuit, i, will fall, as shown in Figure 1.93. The rate of growth of voltage with time (and decay of current with time) will be dependent upon the product of capacitance and resistance. This value is known as the time constant of the circuit. Hence: Time constant, t ¼ C  R where C is the value of capacitance (F), R is the resistance (F), and t is the time constant (s).

FIGURE 1.91: A C-R circuit in which C is charged through R

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FIGURE 1.92: Exponential growth of capacitor voltage, nc, in Figure 1.92

FIGURE 1.93: Exponential decay of current, i, in Figure 1.91

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The voltage developed across the charging capacitor, nc, varies with time, t, according to the relationship:   t nc ¼ Vs 1  eCR where nc is the capacitor voltage, Vs is the DC supply voltage, t is the time, and CR is the time constant of the circuit (equal to the product of capacitance, C, and resistance, R). The capacitor voltage will rise to approximately 63% of the supply voltage, Vs, in a time interval equal to the time constant. At the end of the next interval of time equal to the time constant (i.e., after an elapsed time equal to 2CR) the voltage will have risen by 63% of the remainder, and so on. In theory, the capacitor will never become fully charged. However, after a period of time equal to 5CR, the capacitor voltage will to all intents and purposes be equal to the supply voltage. At this point, the capacitor voltage will have risen to 99.3% of its final value and we can consider it to be fully charged. During charging, the current in the capacitor, i, varies with time, t, according to the relationship: i¼

Vs  t e CR R

where Vs is the DC supply voltage, t is the time, R is the series resistance and C is the value of capacitance. The current will fall to approximately 37% of the initial current in a time equal to the time constant. At the end of the next interval of time equal to the time constant (i.e., after a total time of 2CR has elapsed) the current will have fallen by a further 37% of the remainder, and so on. Example 1.67 An initially uncharged 1 mF capacitor is charged from a 9V DC supply via a 3.3 MO resistor. Determine the capacitor voltage 1s after connecting the supply.

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Solution The formula for exponential growth of voltage in the capacitor is:   t nc ¼ Vs 1  eCR Here we need to find the capacitor voltage, nc, when Vs ¼ 9V, t ¼ 1s, C ¼ 1 mF and R ¼ 3.3 MO. The time constant, CR, will be given by: CR ¼ 1  106  3:3  106 ¼ 3:3s Thus:   t nc ¼ 9 1  e3:3 and, nc 9ð1  0:738Þ ¼ 9  0:262 ¼ 2:358V Example 1.68 A 100 mF capacitor is charged from a 350V DC supply through a series resistance of 1 kO. Determine the initial charging current and the current that will flow 50 ms and 100 ms after connecting the supply. After what time is the capacitor considered to be fully charged? Solution At t ¼ 0 the capacitor will be uncharged (nc ¼ 0) and all of the supply voltage will appear across the series resistance. Thus, at t ¼ 0: i¼

Vs 350 ¼ 0:35A ¼ 1; 000 R

When t ¼ 50 ms, the current will be given by: i¼

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Vs  t e CR R

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Where Vs ¼ 350V, t ¼ 50 ms, C ¼ 100 mF, R ¼ 1 kO. Hence: i¼

350 0:05 e 0:1 ¼ 0:35 e0:5 ¼ 0:35  0:607 ¼ 0:21A 1; 000

When t ¼ 100 ms (using the same equation but with t ¼ 0.1s) the current is given by: i¼

350 0:1 e0:1 ¼ 0:35 e1 ¼ 0:35  0:368 ¼ 0:129A 1; 000

The capacitor can be considered to be fully charged when t ¼ 5CR ¼ 5  100  106  1  103 ¼ 0.5s. Note that, at this point the capacitor voltage will have reached 99% of its final value. Discharge Having considered the situation when a capacitor is being charged, let’s consider what happens when an already charged capacitor is discharged.

FIGURE 1.94: C-R circuits are widely used in electronics. In this oscilloscope, for example, a rotary switch is used to select different C-R combinations in order to provide the various timebase ranges (adjustable from 500 ms/cm to 1 ms/cm). Each C-R time constant corresponds to a different timebase range.

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When the fully charged capacitor from Figure 1.89 is connected as shown in Figure 1.95, the capacitor will discharge through the resistor, and the capacitor voltage, nC, will fall exponentially with time, as shown in Figure 1.96. The current in the circuit, i, will also fall, as shown in Figure 1.97. The rate of discharge (i.e., the rate of decay of voltage with time) will once again be governed by the time constant of the circuit, C  R.

FIGURE 1.95: A C-R circuit in which C is initially charged and then discharges through R

FIGURE 1.96: Exponential decay of capacitor voltage, nc, in Figure 1.95

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FIGURE 1.97: Exponential decay of current, i, in Figure 1.95

The voltage developed across the discharging capacitor, nC, varies with time, t, according to the relationship: nc ¼ Vs eCR t

where Vs, is the supply voltage, t is the time, C is the capacitance, and R is the resistance. The capacitor voltage will fall to approximately 37% of the initial voltage in a time equal to the time constant. At the end of the next interval of time equal to the time constant (i.e., after an elapsed time equal to 2CR) the voltage will have fallen by 37% of the remainder, and so on. In theory, the capacitor will never become fully discharged. However, after a period of time equal to 5CR, the capacitor voltage will to all intents and purposes be zero. At this point the capacitor voltage will have fallen below 1% of its initial value. At this point we can consider it to be fully discharged.

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As with charging, the current in the capacitor, i, varies with time, t, according to the relationship: i¼

Vs  t e CR R

where Vs, is the supply voltage, t is the time, C is the capacitance, and R is the resistance.The current will fall to approximately 37% of the initial value of current, Vs/R, in a time equal to the time constant. At the end of the next interval of time equal to the time constant (i.e., after a total time of 2CR has elapsed) the voltage will have fallen by a further 37% of the remainder, and so on. Example 1.69 A 10 mF capacitor is charged to a potential of 20V and then discharged through a 47 kO resistor. Determine the time taken for the capacitor voltage to fall below 10V. Solution The formula for exponential decay of voltage in the capacitor is: nc ¼ Vs eCR t

where Vs ¼ 20V and CR ¼ 10 mF  47 kO ¼ 0.47s. We need to find t when nC ¼ 10V. Rearranging the formula to make t the subject gives:   nC t ¼ CR  ln Vs thus,

  10 t ¼ 0:47  ln ¼ 0:47  lnð0:5Þ 20

or, t ¼  0:47 693 ¼ 0:325s In order to simplify the mathematics of exponential growth and decay, Table 1.15 provides an alternative tabular method that may be used to determine the voltage and current in a C-R circuit.

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115

Table 1.15: Exponential growth and decay t/CR or t /(L/R)

k (growth)

k (decay)

0.0

0.0000

1.0000

0.1

0.0951

0.9048

0.2

0.1812

0.8187 (1)

0.3

0.2591

0.7408

0.4

0.3296

0.6703

0.5

0.3935

0.6065

0.6

0.4511

0.5488

0.7

0.5034

0.4965

0.8

0.5506

0.4493

0.9

0.5934

0.4065

1.0

0.6321

0.3679

1.5

0.7769

0.2231

2.0

0.8647 (2)

0.1353

2.5

0.9179

0.0821

3.0

0.9502

0.0498

3.5

0.9698

0.0302

4.0

0.9817

0.0183

4.5

0.9889

0.0111

5.0

0.9933

0.0067

Notes: (1) See Example 1.70 (2) See Example 1.74 k is the ratio of the value at time, t, to the final value (e.g., nc/Vs)

Example 1.70 A 150 mF capacitor is charged to a potential of 150V. The capacitor is then removed from the charging source and connected to a 2 MO resistor. Determine the capacitor voltage 1 minute later.

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116

Chapter 1

Solution We will solve this problem using Table 1.15 rather than the exponential formula. First we need to find the time constant: C  R ¼ 150 mF  2 MO ¼ 300s Next we find the ratio of t to CR: After 1 minute, t ¼ 60s therefore the ratio of t to CR is 60/300 or 0.2. Table 1.15 shows that when t/CR ¼ 0.2, the ratio of instantaneous value to final value (k in Table 1.15) is 0.8187. Thus, nc =Vs ¼ 0:8187 or, nc ¼ 0:8187  Vs ¼ 0:8187  150V ¼ 122:8V

1.3.9

Waveshaping with C-R Networks

One of the most common applications of C-R networks is in waveshaping circuits. The circuits shown in Figures 1.98 and 1.100 function as simple square-to-triangle and square-to-pulse converters by, respectively, integrating and differentiating their inputs. The effectiveness of the simple integrator circuit shown in Figure 1.98 depends on the ratio of time constant, C  R, to periodic time, t. The larger this ratio is, the more effective the circuit will be as an integrator. The effectiveness of the

FIGURE 1.98: A C-R integrating circuit

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The Fundamentals

117

circuit of Figure 1.98 is illustrated by the input and output waveforms shown in Figure 1.99. Similarly, the effectiveness of the simple differentiator circuit shown in Figure 1.100 also depends on the ratio of time constant C  R, to periodic time, t. The smaller this ratio is, the more effective the circuit will be as a differentiator. The effectiveness of the circuit of Figure 1.100 is illustrated by the input and output waveforms shown in Figure 1.101.

FIGURE 1.99: Typical input and output waveforms for the integrating circuit shown in Figure 1.98

FIGURE 1.100: A C-R differentiating circuit

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118

Chapter 1

FIGURE 1.101: Typical input and output waveforms for the integrating circuit shown in Figure 1.98

Example 1.71 A circuit is required to produce a train of alternating positive and negative pulses of short duration from a square wave of frequency 1 kHz. Devise a suitable C-R circuit and specify suitable values. Solution Here we require the CCleaner Pro 5.81.8895 Crack + Keygen For [Win/Mac] Free Download of a differentiating circuit along the lines of that shown in Figure 1.100. In order that the circuit operates effectively as a differentiator, we need to make the time constant, C  R, very much less than the periodic time of the input waveform (1 ms). Assuming that we choose a medium value for R of, say, 10 kO, audacity full version crack download - Crack Key For U maximum value which we could allow C to have would be that which satisfies the equation:

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The Fundamentals

119

C  R ¼ 0:1t where R ¼ 10 kO and t ¼ 1 ms. Thus: C¼

0:1t 0:1  1 ms ¼ ¼ 0:1  103  104 ¼ 1  108 F R 10 kO

or, C ¼ 10  109 F ¼ 10 nF In practice, any value equal or less than 10 nF would be adequate. A very small value (say less than 1 nF) will, however, generate pulses of a very narrow width. Example 1.72 A circuit is required to produce a triangular waveform from a square wave of frequency 1 kHz. Devise a suitable C-R arrangement and specify suitable values. Solution This time we require an integrating circuit like that shown in Figure 1.98. In order that the circuit operates effectively as an integrator, we need to make the time constant, C  R, very much less than the periodic time of the input waveform (1 ms). Assuming that we choose a medium value for R of, say, 10 kO, the minimum value which we could allow C to have would be that which satisfies the equation: C  R ¼ 10t where R ¼ 10 kO and t ¼ 1 ms. Thus: C¼

10t 10  1 ms ¼ ¼ 10  103  104 ¼ 1  106 F R 10 kO

or, C ¼ 1  106 F ¼ 1 mF

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120

Chapter 1

In practice, any value equal or greater than 1 mF would be adequate. A very large value (say more than 10 mF) will, however, generate a triangular wave which has a very small amplitude. To put this in simple terms, although the waveform might be what you want there’s not a lot of it!

1.3.10

L-R Circuits

Networks of inductors and resistors (known as L-R circuits) can also be used for timing and pulse shaping. In comparison with capacitors, however, inductors are somewhat more difficult to manufacture and are consequently more expensive. Inductors are also prone to losses and may also require screening to minimize the effects of stray magnetic coupling. Inductors are, therefore, generally unsuited to simple timing and waveshaping applications. Figure 1.102 shows a simple L-R network in which an inductor is connected to a constant voltage supply. When the supply is first connected, the current, i, will rise exponentially with time, as shown in Figure 1.103. At the same time, the inductor voltage VL, will fall, as shown in Figure 1.104). The rate of change of current with time will depend upon the ratio of inductance to resistance and is known as the time constant. Hence: Time constant, t ¼ L/R where L is the value of inductance (H), R is the resistance (O), and t is the time constant (s).

FIGURE 1.102: A C-R circuit in which C is initially charged and then discharges through R

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121

FIGURE 1.103: Exponential growth of current, i, in Figure 1.102

FIGURE 1.104: Exponential decay of voltage, nL, in Figure 1.102

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Chapter 1

The current flowing in the inductor, i, varies with time, t, according to the relationship: i¼

 Vs  tR 1  e L R

where Vs is the DC supply voltage, R is the resistance of the inductor, and L is the inductance. The current, i, will initially be zero and will rise to approximately 63% of its maximum value (i.e., Vs/R) in a time interval equal to the time constant. At the end of the next interval of time equal to the time constant (i.e., after a total time of 2L/R has elapsed) the current will AdGuard Premium Free Download risen by a further 63% of the remainder, and so on. In theory, the current in the inductor will never become equal to Vs/R. However, after a period of time equal to 5L/R, audacity full version crack download - Crack Key For U current will to all intents and purposes be equal to Vs/R. At this point, the current in the inductor will have risen to 99.3% of its final value. The voltage developed across the inductor, nL, varies with time, t, according to the relationship: nL ¼ Vs e L

tR

where Vs is the DC supply voltage, R is the resistance of the inductor, and L is the inductance. The inductor voltage will fall to approximately 37% of the initial voltage in a time equal to the time constant. At the end of the next interval of time equal to the time constant (i.e., after a total time of 2L/R has elapsed) the voltage will have fallen by a further 37% of the remainder, and so on. Example 1.73 A coil having inductance 6H and resistance 24O is connected to a 12V DC supply. Determine the current in the inductor 0.1s after the supply is first connected.

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123

Solution The formula for exponential growth of current in the coil is: i¼

 Vs  tR 1  e L R

where Vs ¼ 12V, L ¼ 6H and R ¼ 24O. We need to find i when t ¼ 0.1s i¼

   12  0:124 1  e 6 ¼ 0:5 1  e0:4 ¼ 0:5ð1  0:67Þ 24

thus, i ¼ 0:5  0:33 ¼ 0:165A In order to simplify the mathematics of exponential growth and decay, Table 1.15 provides an alternative tabular method that may be used to determine the voltage and current in an L-R circuit. Example 1.74 A coil has an inductance of l00 mH and a resistance of 10O. If the inductor is connected to a 5V DC supply, determine the inductor voltage 20 ms after the supply is first connected. Solution We will solve this problem using Table 1.15 rather than the exponential formula. First we need to find the time constant: L=R ¼ 0:1H=10O ¼ 0:01s Next we find the ratio of t to L/R. When t ¼ 20 ms the ratio of t to L/R is 0.02/0.01 or 2. Table 1.15 shows that when t/(L/R) ¼ 2, the ratio of instantaneous value to final value (k) is 0.8647. Thus:

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124

Chapter 1 nL =Vs ¼ 0:8647

or, nL ¼ 0:8647  Vs ¼ 0:8647  5V ¼ 4:32V

1.4 Alternating Voltage and Current This section introduces basic alternating current theory. We discuss the terminology used to describe alternating waveforms and the behavior of resistors, capacitors, and inductors when an alternating current is applied to them. The chapter concludes by introducing another useful component, the transformer.

1.4.1

Alternating Versus Direct Current

Direct currents are currents which, even though their magnitude may vary, essentially flow only in one direction. In other words, direct currents are unidirectional. Alternating currents, on the other hand, are bidirectional and continuously reverse their direction of flow. The polarity of the e.m.f. which produces an alternating current must consequently also be changing from positive to negative, and vice versa. Alternating currents produce alternating potential differences (voltages) in the circuits in which they flow. Furthermore, in some circuits, alternating voltages may be superimposed on direct voltage levels (see Figure 1.105). The resulting voltage may be unipolar (i.e., always positive or always negative) or bipolar (i.e., partly positive and partly negative).

1.4.2

Waveforms and Signals

A graph showing the variation of voltage or current present in a circuit is known as a waveform. There are many common types of waveform encountered in electrical circuits including sine (or sinusoidal), square, triangle, ramp or sawtooth (which may be either positive or negative going), and pulse. Complex waveforms, like speech and music, usually comprise many components at different frequencies. Pulse waveforms are often categorized as either repetitive

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The Fundamentals

125

FIGURE 1.105: (A) Bipolar sine wave; (B) unipolar sine wave (superimposed on a DC level)

or nonrepetitive (the former comprises a pattern of pulses that repeats regularly while the latter comprises pulses which constitute a unique event). Some common waveforms are shown in Figure 1.106. Signals can be conveyed using one or more of the properties of a waveform and sent using wires, cables, optical and radio links. Signals can also be processed in various ways using amplifiers, modulators, filters, etc. Signals are also classified as either analog (continuously variable) or digital (based on discrete states).

1.4.3

Frequency

The frequency of a repetitive waveform is the number of cycles of the waveform which occur in unit time. Frequency is expressed in hertz (Hz) and a frequency of 1 Hz is equivalent to one cycle per second. Hence, if a voltage has a frequency of 400 Hz, 400 cycles of it will occur in every second. The equation for the voltage shown in Figure 1.105(A) at a time, t, is: n ¼ Vmax sinð2pf tÞ

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126

Chapter 1

FIGURE 1.106: Common waveforms

FIGURE 1.107: One cycle of a sine wave voltage showing its periodic time

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The Fundamentals

127

while that in Figure 1.105(B) is: n ¼ VDC þ Vmax sinð20pftÞ where n is the instantaneous voltage, Vmax is the maximum (or peak) voltage of the sine wave, VDC, is the DC offset (where present), and f is the frequency of the sine wave. Example 1.75 A sine wave voltage has a maximum value of 20V and a frequency of 50 Hz. Determine the instantaneous voltage present (a) 2.5 ms and (b) 15 ms from the start of the cycle. Solution We can find the voltage at any instant of time using: n ¼ Vmax sinð20pftÞ where Vmax ¼ 20V and f ¼ 50 Hz. In (a), t ¼ 2.5 ms, hence: n ¼ 20 sinð20p  50  0:0025Þ ¼ 20 sinð0:785Þ ¼ 20  0:707 ¼ 14:14V In (b), t ¼ 15 ms, hence: n ¼ 20 sinð20p  50  0:0015Þ ¼ 20 sinð4:71Þ ¼ 20  1 ¼ 20V

1.4.4

Periodic Time

The periodic time (or period) of a waveform is the time taken for one complete cycle of the wave (see Figure 1.107). The relationship between periodic time and frequency is thus: t ¼ 1=f

or f ¼ 1=t

where t is the periodic time (in s) and f is the frequency (in Hz). Example 1.76 A waveform has a frequency of 400 Hz. What is the periodic time of the waveform?

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128

Chapter 1

Solution t ¼ 1=f ¼ 1=400 ¼ 0:0025s ðor 2:5 msÞ Example 1.77 A waveform has a periodic time of 40 ms. What is its frequency? Solution f ¼

1.4.5

1 1 1 ¼ ¼ Adobe Photoshop CC 2021 v22.3.1.122 Free Download with Crack 25Hz 3 t 0:04 40  10

Average, Extreme Picture Finder 3.51.4 Crack - Activators Patch, Peak-Peak, and r.m.s. Values

The average value of an alternating current which swings symmetrically above and below zero will be zero when measured over a long period of time. Hence, average values of currents and voltages are invariably taken over one complete half-cycle (either positive or negative) rather than over one complete full-cycle (which would result in an average value of zero). The amplitude (or peak value) of a waveform is a measure of the extent of its voltage or current excursion from the resting value (usually zero). The peak-to-peak value for a wave which is symmetrical about its resting value is twice its peak value (see Figure 1.108). The r.m.s. (or effective) value of an alternating voltage or current is the value which would produce the same heat energy in a resistor as a direct voltage or current of the same magnitude. Since the r.m.s. value of a waveform is very much dependent upon its shape, values are only meaningful when dealing with a waveform of known shape. Where the shape of a waveform is not specified, r.m.s. values are normally assumed to refer to sinusoidal conditions. For a given waveform, a set of fixed relationships exist between average, peak, peakpeak, and r.m.s. values. The required multiplying factors are summarized for sinusoidal voltages and currents in Table 1.16.

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The Fundamentals

129

FIGURE 1.108: One cycle of a sine wave voltage showing its peak and peak-peak values Table 1.16: Multiplying factors for average, peak, peak-peak and r.m.s. values Given Quantity

Wanted quantity Average

Peak

Peak–peak

r.m.s.

Average

1

1.57

3.14

1.11

Peak

0.636

1

2

0.707

Peak-peak

0.318

0.5

1

0.353

r.m.s.

0.9

1.414

2.828

1

Example 1.78 A sinusoidal voltage has an r.m.s. value of 240V. What is the peak value of the voltage? Solution The corresponding multiplying factor (found from Table 1.16) is 1.414. Hence: Vpk ¼ 1:414  Vr:m:s: ¼ 1:414  240 ¼ 339:4V Example 1.79 An alternating current has a peak-peak value of 50 mA. What is its r.m.s. value?

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130

Chapter 1

Источник: https://epdf.pub/circuit-design-know-it-all.html

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English

Drilling And Blasting Of Rocks Lengkap.pdf

DRILLING ÄND BLASTING OF ROCKS CARLOS LOPEZ JIMENO Project Director for EPM, SA

EMLIO LOPEZ JIMENO FRANCISCO JAVIER AYALA CARCEDO Proshow producer 9.0.3797 crack with keygen free download - Crack Key For U Director for ITGE Translated by

YVONNE VISSER DE RAMIRO

A.A. BALKEMA / ROTTERDAM / BROOKFIELD / 1995

This work has been totally financed by the Geornining Technological Institute of Spain under contract with the E.F?M.,S.A. Cornpany (Estudios y Proyectos Mineros, S.A.).

Authorization to photocopy iterns for internal or personal use, or the internal or personal use of specific clients, is granted by A.A.Balkerna, Rotterdarn, provided that the base fee of US$1.50 per copy, plus US$O.lO per Page is paid directly to Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, USA. For those organizations that have been granted a photocopy license by CCC, a separate systern of payrnent has been arranged. The fee code for users of the Transactional Reporting Service is: 90 5410 199 7/95 US$1.50 + US$O. 10. Original text: Manual de perforacion y voladura de rocas O 1987 Instituto Geologico y Minero de Espaila Revised and updated edition in English: O 1995 A.A. Balkerna, PO. Box 1675,3000 BR Rotterdarn, Netherlands (Fax: +3 1.10.4135947)

Distributed in USA & Canada by: A.A. Balkema Publishers, Old Post Activate Windows 8/8.1 Without Product key and Internet, Brookfield, VT 05036, USA (Fax: 802.276.3837) Printed in the Netherlands

Contents

FOREWORD PREFACE ACKNOWLEDGEMENTS 1 ROCK DRILLING METHODS 1.1 Introduction 1.2 Types of drilling operations used in rock breakage 1.3 Fields of application for the different drilling methods 1.4 Classification of the rocks and their principal physical properties References 2 ROTARY PERCUSSIVE DRILLING 2.1 Introduction 2.2 Fundamentals of rotary percussive drilling 2.3 Top hammer drilling 2.4 Drilling with down the Express VPN 2018 Crack + Serial Key Free Full Download harnmer 2.5 Advance systems 2.6 Mounting systems 2.7 Dust collectors 2.8 Inclination instruments 2.9 Penetration rate 2.10 Average penetration rate 2.1 1 Calculation of drilling 'costs References 3 ROTARY PERCUSSIVE DRILLING ACCESSORIES 3.1 Introduction 3.2 Types of threads 3.3 Shank adaptors 3.4 Dnll steel 3.5 Couplings 3.6 Dnll bits 3.7 Calculation of the necessary drilling accessories 3.8 Care and maintenance of the bits 3.9 Care and maintenance of drill steel 3.10 Guide for identifying accessory failure and its causes References

4 ROTARY DRILLING WITH ROLLING TRICONE BITS 4.1 Introduction 4.2 Mounting and propulsion systems 4.3 Power sources 4.4 Rotation systems 4.5 Pulldown/hoisting systems 4.6 Mast and pipe changer 4.7 Control cabin 4.8 System for flushing drill cuttings 4.9 Dnll string 4.10 Auxiliary elements 4.1 1 Operative practice. Drilling parameters 4.12 Penetration rate 4.13 Calculation of drilling costs References 5 ROLLING CONE ROCK BITS 5.1 Rolling cone rock bits 5.2 Major components and design features 5.3 The metallurgy of rolling cone rock bits 5.4 Types of rolling cone bits 5.5 Bit type selection 5.6 Effects of the operating parameters on the rolling cone bits 5.7 Nozzle selection 5.8 Evaluation of du11 rolling cones 5.9 Example of roller iricone bit selection 5.10 IDAC Codes References

6 ROTARY DRILLING WITH CUTTING ACTION 6.1 Introduction 6.2 Fundamentals of drilling with cutting action 6.3 Flushing of drill cuttings 6.4 Cutting tools References 7 SPECIAL DRILLING METHODS AND MOLINTING SYSTEMS 7.1 Introduction 7.2 Drilling through overburden 7.3 Shaft sinking 7.4 Raise driving

Contents

7.5 Jet piercing 7.6 Water-jet drilling 7.7 Drilling ornamental rock References

12.2 Explosive cost 12.3 Charge diameter 12.4 Rock characteristics 12.5 Volume of rock to be blasted 12.6 Atmospheric conditions 12.7 Presence of water 12.8 Environmental problems 12.9 Fumes 12.10 Safety conditions 12.11 Explosive atmospheres 12.12 Supply problems References

8 COMPRESSORS 8.1 Introduction 8.2 Types of compressors 8.3 Drive 8.4 Auxiliary elements 8.5 Calculating pressure drops References 9 THERMOCHEMISTRY OF EXPLOSIVES AND THE DETONATION PROCESS 9.1 Introduction 9.2 Deflagration and detonation 9.3 Detonation process of an explosive 9.4 Thermochemistry of the explosives 9.5 Heat of explosion 9.6 Oxygen balance 9.7 Volume of explosion 9.8 Minimum energy available 9.9 Temperature of the explosion 9.10 Pressure of the explosion References

92 92 92 93 94 94 95 95 96 96 96 97

10 PROPERTIES OF EXPLOSIVES 10.1 Introduction 10.2 Strength and energy 10.3 Detonation velocity 10.4 Density 10.5 Detonation pressure 10.6 Stability 10.7 Water resistance 10.8 Sensitivity 10.9 Detonation transmission 10.10 Desensitization 10.11 Resistance to low temperatures 10.12 Fumes References

98 98 98 101 102 102 102 102 102 103 104 104 104 105

11 INDUSTRIAL EXPLOSIVES 11.1 Introduction 11.2 Dry blasting agents 11.3 Slurries 11.4 Emulsions 11.5 Heavy ANFO 11.6 Gelatin dynamites 11.7 Granular dynamite 11.8 Permissible explosives ultraedit gratuit crack - Crack Key For U Blackpowders 11.10 Two-component explosives 11.11 Explosives cornmercialized in Spain References

106 106 106 110 111 113 115 115 116 116 117 117 117

12 EXPLOSIVE SELECTION CRITERIA 12.1 Introduction

119 119

13 BLASTING ACCESSORIES 13.1 Introduction 13.2 Nonelectric initiation systems 13.3 Electric initiation systems 13.4 Sources of energy 13.5 Other accessories References

123 123 123 127 130 132 135

14 INITIATION AND PRIMING SYSTEMS 14.1 Introduction 14.2 Priming and boostering bulk ANFO-type blasting agents 14.3 Priming cartridge ANFO type blasting agents 14.4 Priming pumped or poured slurry and emulsion blasting agents 14.5 Priming cartridged watergel and emulsion blasting agents 14.6 Location of primers 14.7 Priming Folder Guard 21.4.0 Crack With License Key Free Download cartridged explosives References

136 136

15 MECHANIZED SYSTEMS FOR CHARGING AND DEWATERING BLASTHOLES 15.1 Introduction 15.2 Mechanized blasthole charging Systems 15.3 Blasthole dewatenng Systems References 16 MECHANISMS OF ROCK BREAKAGE 16.1 Introduction 16.2 Rock breakage mechanisms 16.3 Transmission of the strain wave through the rock mass 16.4 Energetic yield of the blastings References 17 ROCK AND ROCK MASS PROPERTIES AND THEIR INFLLTENCE ON THE RESULTS OF BLASTING 17.1 Introduction 17.2 Rock properties 17.3 Properties of the rock mass References

136 138 139 140 140 143 143 144 144 144 152 153 154 154 154 156 157 159

V11

Contents

18 CHARACTERIZATION OF THE ROCK MASSES FOR BLAST DESIGNING 18.1 Introduction 18.2 Diamond drilling with core recovery and geomechanic testing 18.3. Characteristics of the joint systems 18.4 Seismic survey 18.5 Geophysical techniques to obtain rock mass data 18.6 Logging of production blastholes 18.7 Characterization of the rock mass during blasthole drilling 18.8 The attempt to correlate drilling indexes with the blasting design parameters 18.9 System of drilling data management in actual time References 19 CONTROLLABLE PARAMETERS OF BLASTING 19.1 Introduction 19.2 Blasthole diameter 19.3 Height of bench 19.4 Blasthole inclination 19.5 Sternrning length 19.6 Subdrilling 19.7 Burden and spacing 19.8 Blasthole patterns 19.9 Geometry of the free face 19.10 Sizeandshapeof the blast 19.11 Available expansion volume 19.12 Charge configuration 19.13 Decoupling of the charges 19.14 Explosives 19.15 Distribution of explosives in the blastholes 19.16 Powder factor 19.17 Initiation and priming 19.18 Delay timing and initiation sequences 19.19 Influence of loadiniequipment on the design of the blasts 19.20 Specific dtilling 19.21 Blasthole deviation References

167 167 167 167 170 170 170 171 174 177 178 179 179 179 181 181 182 182 183 183 184 185 186 186 186 187 187 188 188 188 189 189 190 190

20 BENCH BLASTING 20.1 Introduction 20.2 Small diameter bench blasting 20.3 Large diameter blasting 20.4 Bench blasting with horizontal blastholes 20.5 Rip-rap production blasting 20.6 Cast blasting Appendix 1: Formulas to calculate bench blasting patterns References

199 203

21 BLASTING IN OTHER SURFACE OPERATIONS 2 1.1 Introduction 2 1.2 Excavations for highways and railways

205 205 205

191 191 191 193 195 195 196

21.3 Trench blasting 2 1.4 Ramp blasting (sinking cut) 2 1.5 Blasting for ground leveling 21.6 Blastings for foundations 21.7 Mini-hole blasting 2 1.8 Preblastings References

208 210 212 213 2 14 215 216

22 BLASTING FOR TUNNELS AND DRIFTS 22.1 Introduction 22.2 Advance systems 22.3 Blasting Patterns for tunnels 22.4 Types of cuts and calculation of the blasts 22.5 Equipment for marking out dtilling patterns References

217 217 217 218 219

23 SHAFT SINKING AND RAISE DRIVING 23.1 Introduction 23.2 Shaft sinking 23.3 Raise driving References

23 1 23 1 23 1 232 237

230 230

24 UNDERGROUND PRODUCTION BLASTiNG IN MINING AND CIVIL ENGINEERING 239 24.1 Introduction 239 24.2 Crater retreat method 239 24.3 Longhole method 243 24.4 Sublevel stoping with blastholes in fan pattern 245 24.5 Room and pillar mining 248 24.6 Cut and fill mining 248 24.7 Underground chambers in civil engineering projects 249 References 25 1 25 CONTOUR BLASTiNG 25.1 Introduction 25.2 Mechanisms responsable for overbreak 25.3 The theory of contour blasting 25.4 Types of contour blasts 25.5 The parameters that intervene in a contour blasting 25.6 Tendencies in the field of contour blasting 25.7 Evaluation of the results 25.8 Exarnple 25.9 Extraction of ornamental rock with contour blasting References 26 UNDERWATER BLASTiNG 26.1 Introduction 26.2 Methods of execution 26.3 Calculations for charges and drilling patterns 26.4 Charging the blastholes and priming systems 26.5 Types of explosives 26.6 Environmental effects associated with underwater blastings

252 252 252 253 254 256 264 267 268 268 270 272 272 272 247 275 276 276

V11

Contents

18 CHARACTERIZATIONOF THE ROCK MASSES FOR BLAST DESIGNING 18.1 Introduction 18.2 Diamond drilling with core recovery and geomechanic testing 18.3- Characteristics of the joint systems 18.4 Seismic survey 18.5 Geophysical techniques to obtain rock mass data 18.6 Logging of production blastholes 18.7 Characterization of the rock mass during blasthole drilling 18.8 The attempt to correlate drilling indexes with the blasting design parameters 18.9 System of drilling data management in actual time References 19 CONTROLLABLE PARAMETERS OF BLASTING 19.1 Introduction 19.2 Blasthole diameter 19.3 Height of bench 19.4 Blasthole inclination 19.5 Sternming length 19.6 Subdrilling 19.7 Burden and spacing 19.8 Blasthole patterns 19.9 Geometry of the free face 19.10 Size and shape of the blast 19.11 Available expansion volume 19.12 Charge configuration 19.13 Decoupling of the charges 19.14 Explosives 19.15 Distribution of explosives in the blastholes 19.16 Powder factor 19.17 Initiation and prirning 19.18 Delay timing and initiation sequences 19.19 Influence of loadingequipment on the design of the blasts 19.20 Specific drilling 19.21 Blasthole deviation References

167 167 167 167 170 170 170 171 174 177 178 179 179 179 181 181 182 182 183 183 184 185 186 186 186 187 187 188 188 188 189 189 190 190

20 BENCH BLASTING 20.1 Introduction 20.2 Small diameter bench blasting 20.3 Large diameter blasting 20.4 Bench blasting with horizontal blastholes 20.5 Rip-rap production blasting 20.6 Cast blasting Appendix 1: Formulas to calculate bench blasting patterns References

199 203

21 BLASTING IN OTHER SURFACE OPERATIONS 21.1 Introduction 21.2 Excavations for highways and railways

205 205 205

191 191 191 193 195 195 196

21.3 Trench blasting 21.4 Ramp blasting (sinking cut) 21.5 Blasting for ground leveling 21.6 Blastings for foundations 21.7 Mini-hole blasting 2 1.8 Preblastings References

208 210 212 213 214 215 216

22 BLASTING FOR TUNNELS AND DRIFTS 22.1 Introduction 22.2 Advance systems 22.3 Blasting Patterns for tunnels 22.4 Types of cuts and calculation of the blasts 22.5 Equipment for marking out drilling patterns References

217 217 217 218 219 230 230

23 SHAFT SINKING AND M I S E DRIVING 23.1 Introduction 23.2 Shaft sinking 23.3 Raise driving References

23 1 23 1 23 1 232 237

24 UNDERGROUND PRODUCTION BLASTING 239 IN MINING AND CIVIL ENGINEERING 24.1 Introduction 239 24.2 Crater retreat method 239 24.3 Longhole method 243 24.4 Sublevel stoping with blastholes in fan pattern 245 24.5 Room and pillar mining 248 24.6 Cut and fill mining 248 24.7 Underground chambers in civil engineering projects 249 References 25 1 25 CONTOUR BLASTING 25.1 Introduction 25.2 Mechanisms responsable for overbreak 25.3 The theory of contour blasting 25.4 Types of contour blasts 25.5 The parameters that intervene in a contour blasting 25.6 Tendencies in the field of contour blasting 25.7 Evaluation of the results 25.8 Example 25.9 Extraction of ornamental rock with contour blasting References 26 UNDERWATER BLASTING 26.1 Introduction 26.2 Methods of execution 26.3 Calculations for charges and drilling patterns 26.4 Charging the blastholes and priming systems 26.5 Types of explosives 26.6 Environmental effects associated with underwater blastings

252 252 252 253 254 256 264 267 268 268 270 272 272 272 247 275 276 276

V111 26.7 Shaped or concussion charges References 27 INITIATION SEQUENCE AND DELAY TIMING 27.1 Introduction 27.2 Single-row delayed blast 27.3 Multi-row sequenced bench blastings 27.4 Bench blasting sequences for underground stopes 27.5 Delay timings 27.6 Underground blasts in tunnels and drifts References 28 EVALUATION OF BLAST RESULTS 28.1 Introduction 28.2 Fragmentation and swelling of the muckpile 28.3 Geometry of the muckpile, its height and displacement 28.4 Condition of the remaining mass 28.5 Analysis of the bench floor 28.6 Boulders in the muckpile 28.7 Vibrations and airblast 28.8 Profiles of underground excavations 28.9 Conclusions References 29 SECONDARY FRAGMENTATION AND SPECIAL BLASTINGS 29.1 Introduction 29.2 Pop shooting 29.3 Secondary breakage by mechanical means and special methods 29.4 Special blastings References 30 PLANNING THE WORK OF DRILLING \ AND BLASTING 30.1 Introduction 30.2 Factors that have influence on the planning of drillling and blasting 30.3 Planning the Stages of excavation References 31 STRUCTURE AND BUILDING DEMOLITION 3 1.1 Introduction 3 1.2 Drilling diameters and types of explosive 3 1.3 Demolition of structural elements 3 1.4 Demolition of structures 31.5 Demolition of buildings 3 1.6 Demolition of steel structures References

Contents 32 OPTIMIZING COSTS OF FRAGMENTATION WITH DRILLING AND BLASTING 323 32.1 Introduction 323 32.2 Econornical aspects of drilling and blasting 323 32.3 Model for determining cost optimization 325 32.4 Predicting the fragmentation 326 32.5 Probabilistic analysis optimization model 331 References 33 1 33 LAND VIBRATIONS, AIR BLAST AND THEIR CONTROL 33.1 Introduction 33.2 Parameters which affect vibration characteristics 33.3 Characteristics of ground vibrations 33.4 Air blast charactenstics 33.5 Instrumentation for recording and analyzing vibrations and air blast 33.6 Calculators of propogation laws for land and air vibrations 33.7 Studies of vibration and air blast 33.8 Damage prevention critena for buildings 33.9 Effects of vibrations and air blast on people 33.10 Effects of vibrations on rock masses 33.11 Effect of vibrations on freshly poured concrete 33.12 Recommendations for reducing ground vibration and air blast levels References 34 FLYROCKS AND THEIR CONTROL 34.1 Introduction 34.2 Models to calculate the throw of flyrock 34.3 Coverings 34.4 Recommendations for carrying out bench blastings References

333 333 333 337 339 340 342 346 350 357 358 360 36 1 364 366 366 366 368 370 370

35 SAFETY MEASURES FOR DRILLING AND BLASTING OPERATIONS 35.1 Introduction 35.2 Blasthole drilling 35.3 Blastings References

37 1 37 1 37 1 375 38 1

CONVERSION FACTORS

382

GENERAL INFORMATION, WEIGHT OF MATERIALS

383

GLOSSARY

385

SUBJECT INDEX

389

Foreword

During the past two decades, there have been numerous technical contributions which have brought a better understanding of rock fragmentation with explosives, an improvement in drilling equipment and a noticeable evolution in the development of new explosives and blasting accessones. The Geomining Technological Institute of Spain (ITGE), aware of this Progress and of the importance which the breakage process has acquired in mining and civil engineering projects, has considered the publication of a 'Rock Drilling and Blasting Handbook' of great interest. This handbook was conceived with integration in mind, as the Systems and machines of drilling, the types and characteristics of explosives and the methods for calculating the blasts are treated together, without ever forgetting that these breakage operations form part of a

macrosystem and that the results obtained by them influence the production and economy of the whole exploitationor construction process. At the Same time, the objectives and contents of this handbook contribute to improved safety in mining. There are very few similar works in other languages, and certainly none other in Spanish. We sincerely hope that this handbook, which brings together practical and theoretical aspects, will be of use to all engineers who work with drilling and blasting as a rock breakage method. Camilo Caride de Liiian Director of the Geomining Technological Institute of Spain

Preface

'\

Rock breakage with explosives has existed since the XVII century when black powder came into use in mining, rapidly becoming one of the most popular methods. The important historical events which have marked an era were the invention of dynamite by Alfred Nobel in 1867, the use of ANFO starting in 1955, the development of slumes from the late fifties on and, lastly, the preparation of blasting agents such as emulsions, heavy ANFO, etc., which are still in evolution. At the Same time, blasthole drilling progressed with such decisive events as the the use of compressed air as the source of energy in rotary percussive rigs in 1861, the use of large rotary drills and of down-the-hole hammers in the fifties and the development of hydraulic hammers in the late seventies. However, rock blasting was always considered, until recently, as an art bom from the skill and experience of the blasters. Now it has become a technique based on scientific principles derived from knowledge of the action of explosives, the mechanisms of breakage and the geomechanic properties of the rock masses. The purpose of this handbook is to give basic knowledge of the drilling Systems, the types of available explosives and accessaries and the Parameters that intervene in blast designing, whether controllable or not. The handbook is primarily meant for students of the Technical Schools, to be useq as a textbook, and for all professionals who are involved with explosives in mining operations and civil engineenng projects. Carlos and Emilio Lopez Jimeno

This handbook was written by the following engineers: Carlos Lopez Jimeno, Doctor of Mining Engineering, Project Director for EPM., S.A. Emilio Lopez Jimeno, Doctor of Mining Engineering. Francisco Javier Ayala Carcedo, Doctor of Mining Engineering, Project Director for ITGE. Translated by: Yvonne Visser de Ramiro This work has been totally financed by the N track studio 9 pro apk unlocked - Activators Patch Technological Institute of Spain under contract with the EPM, S.A. Company (Estudios y Proyectos Mineros, S.A.).

Acknowledgements

The authors wish to express their most sincere gratitude to the following experts, companies and official organisms for their collaboration and release of technical material rhino 6 license key crack - Activators Patch well as permission to reproduce certain data and figures. Amerind-Mackissic,Inc.: G. J. Knotts Amos L. Dolby Co.: J. Petrunyak App1ex:S.O. Olofsson Atlas Copco S.A.E.: E Menendez Atlas Powder Company: VA. Sterner, L. Osen & PM. Miller Atlas Powder International: J. Garcia Milla Bauer, Calder & Workman, Inc.: J.L. Workman & A. Bauer (T) Bill Lane Inc.: W.C. Lane Blasting & Mining Consultants, Inc.: J. Ludwiczak Bucyrys Erie Co.: J.D. Nelmark & G. Rekoske Bendesanstalt für Geowissenschaften und Rohstdffe: R. Lüdeling Canmet: G. Larocque Ci1 Inc.: S. Chung, B. Mohanty, K.C. Joyce, PR. Day, W.K. Webster, D. Dayphinais, I. Huss & K.R. Sharpe Cominco Ltd.: W Russe11 Crowsnest Resources Ltd.: R.A. Reipas David, S. Robertson & Associates Inc.: C. Davenport Dupont Canada: D. Tansey E. I. Du Pont De Nemours & Co.: P D. Porter, B. L. Glenn, J. R. Knudson & A. B. Andrews Entrecanales y Tavora, S.A.: J. Aznar Gardner Denver Mining and konstruction Group Geovanca: R. Ucar Golder Associates: T. N. Hagan, E. Hoek & Guy Le Bell Hullera Vasco Leonesa: E. Castells Hydro-Quebec: F! Lacomte Iberduero, S.A.: J. Fora ICI Australia Operations Pty Ltd.: G. Harries, J. K. Mercer & G.G. Paine Ilmeg: S. Johansson Ingersoll Rand Instituto Tecnologico Geominero de Espaiia: EJ. Ayala & M. Abad Instituto Superior Tecnico de Lisboa: C. Dinis Da Gama Ireco Canada Inc.: L. de Couteur Irish Industrial Explosives, Ltd.: J. P Higgins Julius Kruttschnitt Mineral Research Centre, University of Queensland: C. K. Mckenzie & K. E. Mathews Kaiser Engineers, Inc.: G.V. Borquez

Kemira Oy Kenneth Medearis Associates: K. Medearis Kometa Oy: R. Ikola Kontinitro A.G. L.C. Lang & Associates, Inc.: L.C.Lang Lewis L. Oriard, Inc.: L.L.Oriard LKAB: L. Hermansson Martin Marietta Laboratories: D.A. Anderson & S. R. Winzer McGill University: R.E Favreau, R.R. MacLachlan, W. Comeau & J.C. Leighton Michigan Technological University: F.O. Otuonye New Jersey Institute of Technology: W. Konon Nitro Consult, A.B.: I. Hansson Nitro Nobel AB: B. Larsson, PA. Persson, M. Landberg & G. Lande Nobel's Explosives Company Limited: M. J. Ball The Norwegian Institute of Technology: K. Nielsen The Ohio State University: R.G. Lundquist Oy Forcit Palabora Mining Co.: G. P Fauquier Petromin: \! Cobeiia Precision Blasting Services: C.J. Konya Queen's University: P N. Calder Reed Mining Tools, Inc.: M. Suiirez Richard L. Ash & Associates: R. L. Ash Rietspruit Mining Co.: K. I. Macdonald Societa Esplosivi Industriali S.PA.: G. Calarco & G. Berta Strornrne: A. M. Heltzen Thermex Energy Corporation: R.C. Paddock T Peal, S.A.: J. Alonso & R.Arnaiz Union Espaiiola de Explosivos: R. Blanco University of Missouri Rolla: P N. Worsey, R. R. Rollins & N.S. Smith U.S. Bureau of Mines Twin Cities. Research Center: L. R. Fletcher At the Same time we would also like to acknowledge the drawings and photography done by Jose Maria de Salas and the corrections made by Carlos Ramiro Visser.

CHAPTER 1

Rock drilling methods

1.1 INTRODUCTION Rock drilling, in the field of blasting, is the first operation carried out and its purpose is to Open holes, with the adequate geometry and distribution within the rock masses, where the explosive charges will be placed along with their initiating devices. The systems of rock drilling that have been developed and classified according to their order of present day applicability are: - Mechanical: Percussion, rotary, rotary-percussion. - Themzal: Flame, plasma, hot fluid, Freezing. - Hydraulic: Jet, erosion, cavitation. - Sonic: High frequency vibration. - Chemical: microblast, dissolution. - Electrical: Electric arc, magnetic induction. - Seismic: Laser ray. - Nuclear: Fusion, fission. Even though there is an enormous variety of possible rock drilling systems, in mining and civil engineering drilling is presently canied out, almost exclusively, by mechanical energy. Therefore, in this handbook only the mechanical means will be discussed, reviewing the fundalmentals, tools and equipment for each of them. The main components of a drilling system of this type are: the drilling rig which is the source of mechanical energy, the drill steel which is,the means of transmitting that energy, the bit which is the tool that exercises that energy upon the rock, and the flushing air that cleans out and evacuates the drilling cuttings and waste produced. 1.2 TYPES OF DRILLING OPERATIONS USED IN ROCK BREAKAGE Within the large variety of excavations using explosives, numerous machines have been developed which can be classified in two types of drilling procedures: - Manual drilling. This is canied out with light equipment that is hand held by the drillers. It is used in small operations where, due to the size, other machinery cannot be used or its cost is not justified. - Mechanized drilling. The drilling equipment is mounted upon rigs with which the Operator can control all drilling Parameters from a comfortable position. Brave Browser Free Download structures or chasis can themselves be mounted on wheels or tracks and either be self-propelled or towable. On the other hand, the types of work, in surface as well

as in underground operations, can be classified in the following groups: - Bench drilling. This is the best method for rock blasting as a free face is available for the projection of material and it allows work tobe systemized. It is used in surface projects as well as in underground operations, usually with vertical blastholes, although horizontal holes can be drilled on occasion. - Drilling fordrifting and tunnelling. An initial cavity or cut must be opened towards which the rest of the fragmented rock from the other charges is directed. Blasthole drilling can be carried out with hand held drills, but the trend is towards total mechanization, using jumbos with one or various booms. - Production drilling. This term is used in rnining operations, fundamentally underground, to describe the labors of ore extraction. The equipment and methods used v a q with the exploitation systems, having the common factor of little available space in the drifts for blasthole drilling. - Drilling for raises. In many underground and civil engineering projects it is necessary to Open raises. Although there is a tendency to apply the Raise Bonng method, still today the long blasthole method AOMEI OneKey Recovery Pro For Windows used as well as other special drilling systems combined with blasting. - Drilling rocks with overburden. The drilling of rock masses which are covered with beds of unconsolidated materials calls for special drilling methods with casing. This method csv editor mac - Crack Key For U also used in underwater operations. - Rock supports. In many underground operations and sometimes in surface ones it is necessary to support the rocks by means of bolting or cementing cables, in which drilling is the first phase. 1.3 FiELDS OF APPLICATION FOR THE DIFFERENT DRILLING METHODS The two most used mechanical drilling methods are rotary-percussion and rotary. - Rotary-percussive methods. These are the most frequently used in all types of rocks, the top harnrner as well as the down-the-hole hammer. - Rotary methods. These are subdivided into two groups, depending upon if the penetration is canied out by crushing, with tricones or by cut with drag bits. The first system is used in medium to hard rocks, and the second in soft rocks.

2

Drilling and blasfing of rocks

By taking into account the compressive strength of the rocks and the drilling diameter, the fields of application of the different methods can be defined as refiected in Fig. 1.1. On the other hand, depending upon the type of mining or civil engineenng surface project, the most comrnon equipment and diameters for bench blastings are indicated in Fig. 1.2.

In the Same manner, the most frequently used equipment for the different underground mining methods and the charactenstic drilling data are indicated in Fig. 1.3. Other criteria to be accounted for in the selection of drilling equipment are: cost, mechanical design, maintenance and semice, operative capacity, adaptability to equipment of the exploitation, and the work area conditions (accessability, type of rock, sources of energy, etc.).

DOWN TUE HOLE

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Drilling and blasting of rocks

the same sense that igneous rocks are poorer in silica, they are richer in ferromagnesian silicates. The acids are more abrasive and harder than the basic ones, but they are also more dense and resistant to impact.

1.4.1.2 Metamorphic rocks Metamorphic rocks are derived from other pre-existing endogenic or exogenic rocks through important transformations of their mineral components. These marked changes are produced by the necessity of stabilizing their minerals under the new conditions of temperature, pressure and chemism. These rocks are intermediate in physicai and chemical characteristics, between the igneous and the sedimentary, because they have associations of minerais that pertain to the two types. Thus, minerals such as quartz, feldspars, rnicas, amphiboles, and olivines, essential in igneous rocks, are also found in metamorphic rocks; however they do not contain aikali feldspars. As in sedimentary rocks, they can have calcite, dolomite, silica and hematites; but they do not contain evaporites. Minerals comrnon to the two other types also appear such as tourmaline, zircon, magnetite, topaz and corundum; all of which are very stable in any exogenous or endogenous medium. There is a series of minerals that are very specific to metamorphic rocks, which can form part of the grains of detrital rocks, owing to their stability in exogenous medium~,and others are at the same time products of meteoric alteration of the minerals in endogenic rocks. Actually, meteorization is a mineralogical transformation that is both a physical and chemical process, but at low temperature and pressure. 1.4.1.3 Sedimentary rocks Sedimentary rocks are formed by accumulation of broken and decomposed rock material, by chemical precipitation of solubilized minerals or by accumulation of shells or other organic material: animal or vegetable. In the first case, detritic sediments are produced such as gravels, conglomerates or sands in which gravity has played a role in their precipitation. In the second case one

Fig. 1.4. Geological cycle of rocks.

Table 1.1 Classification Very hard Hard Medium hard Medium soft Soft Very soft

Mohs' scale of hardness +7 6-7 4.5-6 3-4.5 2-3 1-2

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can find, as an example, the evaporites or saline rocks precipitated by over-saturationof a brine that is subjected to intense evaporation. The third type are accumulations of shells, skeletons of animals or remains of plants, such as the conchiferous limestones. This last group is subdivided into organogenous biochemistry and mineral biochemistry depending upon whether their components are of organic or inorganic nature. For the first we have coal and petroleum, and for the second the limestones, dolornites and phosphatic rocks. For an initial classification of sedimentary rocks, their formation process is taken into account, later the grain size, the characteristics of their bonding, apart from the types and quantities of their rninerai components. 1.4.2 Rock properties that affect drilling The principal physical rock properties that have influence upon penetration mechanisms and, as a consequence, on choice of the drilling method are: hardness, strength, elasticity, plasticity, abrasiveness, texture, structure, characteristics of breakage. 1.4.2.1 Hardness Hardness is considered to be the resistance of a surface layer to be penetrated by another body of harder consistency. In rock, it is a function of the hardness and composition of its mineral grains, the porosity, degree of humidity, E etc. The hardness of rocks is the principal type of resistance that must be overcome during drilling, because once the bit has penetrated, the rest of the operation is easier. Rocks are classified as to their hardness by using Friedrich von Mohs' Scale of Hardness (1882), in which the concept is that any mineral can scratch anything that has a lower or equai number to it, numbering from 1 to 10. As can be seen from Table 1.1, there is a certain correlation between hardness and compressive strength of the rocks. 1.4.2.2 Strength Mechanical strength of a rock is the property of opposing destruction by an extemal force, either static or dynarnic. The rocks give maximum resistance to compression, normally, as the tensile strength is not more than 10 or 15% of the compressive strength. This is due to the fragility of rocks, to the large quantity of local defects and irregularities that exist and to the small cohesion between the particles of which they are constituted.

Rock drilling rnethods

5

stratification sense or schistosity is larger than in a parallel sense. The quotient that is usually obtained between both strength values varies between 0.3 and 0.8, and it is equal to 1 only for isotropic rocks. In Fig. 1.5, the most frequent compressive strengths for different types of rock are indicated.

The rock strength fundamentally depends on its mineralogical composition. Among the integrating minerals, quartz is the most solid with a strength that goes over 500 MPa, while that of the ferromagnesian silicates and the aluminosilicates vary between 200 and 500 MPa, and that of calcite from 10 to 20 MPa. Therefore, the higher the quartz content, the more the strength increases. The mineral strength depends upon the size of the crystals and diminishes with their increase. This influence is significative when the crystal size is under 0.5 mm. In rocks, the size factor has less influence on strength as the intercrystallinecohesion force also intervenes. For example, the compressive strength of a fine grained arkose sandstone is almost double that of a coarse grained; that of marble composed of 1 rnrn graines is equal to 100 MPa, whereas a fine grained limestone - 3 to 4 mm - has a strength of 200 to 250 MPa. Amongst the sedimentary rocks the ones with highest strength are those that contain silica cement. With the presence of clay cement, the strength is drastically reduced. Porosity in rocks with the Same lithology also reduces strength proportionately, more porosity - less strength; as it simultaneously reduces the number of contacts of the mineral particles and the force of reciprocal action between them. The depth at which rocks were formed arid the degree of metamorphism also have influence upon their strength. Therefore, the strength of clay beddings near the ground surface can be of 2 to 10 MPa, whereas in clay rocks that went through a certain metamorphism the strengths can reach 50 to 100 MPa. On the other hand, the strength of ansiotropic rocks depends upon the sense of action of the force. The compressive strength of rocks in the perpendicular to

1.4.2.3 Elasticity The majonty of rock minerals have an elastic-fragile behavior, which obeys the Law of Hooke, and are destroyed when the strains exceed the limit of elasticity. Depending upon the nature of deformation,as function of the Stresses produced by static charges, three groups of rocks are taken into consideration: 1) The elastic-fragile or those which obey the Law of Hooke, 2) The plasticfragile, that have plastic deformation before destruction, 3) The highly plastic or very porous, in which the elastic deformation is insignificant. The elastic properties of rocks are charactenzed by the elasticity module 'E' and the Poisson coefficient ' V '. The elasticity module is Video Editor - Crack All Windows/Mac OS Software Full Version proportionality factor between the normal Stress in the rock and the relative correspondant deformation, its value in most rocks varies between 0.03 X 104and 1.7 X 1o5 MPa, basically depending upon the mineralogical composition,porosity, type of deformation and magnitud of the applied force. The values of the elasticity modules in the majority of sedimentary rocks are lower than those corresponding to the minerals in their composition.The texture of the rock also has influence on this Parameter, as the elasticity module in the direction of the bedding or schistosity is usually larger than when perpendicular. Poisson's coefficient is the factor of proportionality between the relative longitudinal deformations and the transversal deformations. For most rocks and minerals it is between 0.2 and 0.4, and only in quartz is it abnonnally low, around 0.07.

0

I0

20

30

40

60

SO

DEFORMATION (mm x 108) Fig. 1.6. Curves of stress-deformationfor different types of rocks.

6

Drilling und blasting of rocks

1.4.2.4 Plasticity As indicated before, in some rocks the plastic deformation preceeds destruction. This begins when the Stresses exceed the limit of elasticity. In the case of an ideally plastic body, that deformation is developed with an invariable stress. Real rocks are deformed and consolidated at the Same time: in order to increase the plastic deformation it is necessary to increase the effort. The plasticity depends upon the mineral composition of the rocks and diminishes with an increase in quartz content, feldspar and other hard minerals. The humid clays and some homogeneous rocks have plastic properties. The plasticity of the stony rocks (granites, schistoses, crystallines and sandstones) becomes noticeable especially at high temperatures. 1.4.2.5 Abrasiveness Abrasiveness is the capacity of the rocks to wear away the contact surface of another body that is harder, in the rubbing or abrasive process during movement. The factors that enhance abrasive capacities of rocks are the following: - The hardness of the grains of the rock. The rocks that contain quartz grains are highly abrasive. - The shape of the grains. Those that are angular are more abrasive than the round ones. - The size of the grains. - The porosity of the rock. It gives rough contact surfaces with local stress concentrations. - The heterogeneity. Polymineral rocks, although these are equally hard, are more abrasive because they leave rough Altium Designer 20.2.6 Build 244 Crack with hard grains as, for exarnple, quartz grains in a granite. This property has great influence upon the life of drill steel and bits. In Table 1.2, the mean arnounts of quartz for different types of rock are indicated.

Table 1.2 Rock type Amphibolite Anorthosite Diabase Diorite Gabbro Gneiss Granite Greywacke Limestone Marble Mica gneiss Mica schist Nori te Pegmatite Phyllite Quartzite Sandstone Shale Slate Taconite

Quartz content %

1.4.2.6 Texture The texture of a rock refers to the structure of the grains of minerals that constitute it. The size of the grains are an indication, as well as their shape, porosity etc. All these aspects have significative influence on drilling performance. When the grains have a lenticular shape, as in a schist, drilling is more difficult than when they are round, as in a sandstone. The type of material that makes up the rock matrix and unites the mineral grains also has an important influence. As to porosity, those rocks that have low density and, consequently, are more porous, have low crushing eset internet security 12.0.31.0 license key - Crack Key For U and are easier to drill. In Table 1.3 the classification of some types of rocks is shown, with their silica content and grain size.

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Rock drilling methods

7

Table 1.4. Properties of rock types according to origin-based classification. Rock type

Specific gravity (m3)

Grain Swell Compressive size factor strength (mm) (MPa*)

TntruDiorite sive Gabbro INGENOUS Granite Andesite Extrusive Basalt Rhyolite Trachyte

2.65-2.85 2.85-3.2 2.7 2.7 2.8 2.7 2.7

1.5-3 2 0.1-2 0.1 0.1 0.1 0.1

.-

Congomerate 2.6 Sandstone 2.5 SEDIMEN- Shale 2.7 TARY 2.7 Dolomite Limestone 2.6 Limerock 1.5-2.6

1.5

170-300

2 0.1-1 1 1-2 1-2 1-2

Gneiss 2.7 2 Marble 2.7 0.1-2 METAMOR- Quartzite 2.7 0.1-1 PHIC Schist 2.7 0.1-L Serpentine 2.6 Slate 2.7 0. L * 1 MPa = 1 MN/^^ = 10 kg/cm2 = 142.2 psi

In Table 1.4, the characteristic properties of different types of rocks are indicated, according to their origin. 1.4.2.7 Structure The stmctural properties of the rock masses, such as schistosity, bedding planes, joints, diabases and faults, as well as their dip and strike affect the allignment of the blastholes, the drilling performance and the stability of the blasthole walls.

SPACING OF JOINTS A) B) C) D)

lOOOcm

105

10

1

0.1

STRONG ROCK MEDIUM ROCK WEAK ROCK VERY WEAK ROCK

Fig. 1.7. Classification of the rock masses.

In Fig. 1.7, the rock masses are classified from the spacing between joints and the strength of the r o c h material. REFERENCES Atlas Copco: Manual atlas copco, 4th edition. 1984. Heinz, W. F.: Diamond drilling handbook. 1989. Hunt, R.E.: Geotechnical engineeßng techniques und pracdces. McGraw Hill. 1986. Sandvik-Coromant: Manual de perforacibn de rocas. Teoria y tkcnica. 1983.

Tamrock: Handbook of surface drilling. 1989.

CHAPTER 2

Rotary percussive diilling

2.1 INTRODUCTION Drilling by rotary percussion is the most classic system for drilling blastholes, and its chronological appearance coincides with the industrial development of the ninteenth century. The first Prototype machines made by Singer (1838) and Couch (1848) were run by steam, but it was when compressed air was used as the source of energy, in the execution of the tunnel of Mont Cenis in 1861, that this system evolved and was put into extensive use. This event, along with the arrival of dynamite, was decisive in the rapid development of rock breakage in mining and civil engineering at the end of the last century. The drilling pnnciple of these rigs is based upon the impact of a steel piece (piston) that hits a utensil which transrnits at the Same time that energy to the bottom of the blasthole by means of the final element called the bit. The rotary percussive rigs are classified in two large groups, depending upon where the hammer is located: - Top hammer. In these drills, two of the basic actions, rotation and percussion, are produced outside the blasthole, and are transmitted by the shank adaptor and the dnll steel to the dnll bit. The hamrners can be driven hydraulically or pneumatically. - Down the hole hammer. The percussion is delivered directly to the drill bit, whereas the rotation is performed outside the hole. The piston is driven pneumatically, while the rotation can be hydraulic or pneumatic. Depending upon the fields of application of these drilling ngs, surface or underground, the most comrnon range of diameters are shown in Table 2.1. The main advantages of rotary percussive dnlling are: - It can be applied to any type of rock, from soft to hard. - Wide range of diameters; - Versatile equipment, it adapts well to different operations and is very Mobile; - Only requires one Operator; - Easy, quick maintenance, and - The capital cost is not high. In view of these advantages and characteristics, the type of operations where it is used are: - Underground civil engineering; tunnels, underground hydraulic plants, residual deposits, etc., and in surface operations; roads, highways, indusirial excavations, etc.

- In underground mines and in small to medium sized surface operations.

2.2 FUNDAMENTALS OF ROTARY PERCUSSIVE DRILLING Rotary percussion drilling is based upon the combination of the following: - Percussion. The impacts produced by repeated blows of the piston generate shock waves that are transmitted to the bit through the drill steel (in top harnmer) or directly upon it (down the hole). - Rotation. With this movement, the bit is turned so that the impacts are produced on the rock in Privacy Drive Free Activate positions. - Feed, or thrust load. In order to maintain the contact of the dnll bit with the rock, a thrust load or feed force is applied to the drill siring. - Flushing. aushing removes the drill cuttings from the blasthole. The indentation forming process with which penetration is achieved in this drilling system is divided into five times, as indicated in Fig. 2.2. a) Crushing of the rough edges of the rock upon bit contact. b) Radial cracks appear from the points of Stress concentration and a V shaped wedge is formed. C) The rock of the wedge is pulverized. d) The larger fragments are chipped in the zones next to the wedge. e) The drill cuttings are flushed away. This sequence repeats itself with the Same impact rhythrn of the piston upon the system of energy transmission to the bit. The yield of this process increases proportionally with the size of the rock chippings. 2.2.1 Percussion The kinetic energy E, of the piston is transmitted from the hammer to the drill bit, through the dnll steel, in the form of a shock wave. The wave travels at high speed and its shape depends basically on the design of the piston. When the shock wave reaches the drill bit, part of the energy is transformed into work, causing the bit to penetrate, and the rest is reflected and returns through the drill steel. The efficiency of this transmission is difficult to

Rotary percussive drilling Tahle 2.1. Drilling method Top hammer Down the hole

Drilling diameter (mm) Surface Underground 38- 65 50- 127 75-200 100- 165

The percussion mechanism consumes from 80 to 85%of the total power of the equipment.

ROTATION

2.2.2 Rotation

FEED FORCE

Fig. 2.1. Basic actions in rotary percussive drilling.

Fig. 2.2. Sequence of rock failure during Center formation (Hartman, 1959).

evaluate as it depends upon many factors such as: type of rock, shape and size of piston, drill steel characteristics, bit design, etc. Another thing to take into account is that energy is lost through the sleeves of the rod couplings, due to reflection and fricton which is converted into heat and wear on the drill steel threads. In the first coupling the losses oscillate between 8 and 10%of the shock wave energy. In down the hole drilling the piston energy is transrnitted directly to the bit, giving greater performance. In these drilling Systems, percussion force is the parameter that most influences the penetration rate. The energy freed per hammer stroke can be estimated from the following equations:

where: m, = Mass of the piston, V = Maximum piston speed, p, = Pressure of the work ffuid (oil or air) inside the cylinder, A, = Surface area of the piston face, I, = Stroke of the piston. In the majority of hydraulic hammers, the manufacturers indicate the impact energy value, but this is not the case with the pneumatic hammers. Special care should be taken in estimating the p, for these, as it is 30 to 40% lower in the cylinder than in the compressor, owing to charging and expansion losses of air with each stroke of the piston. Thus, the hamrner power is the energy per stroke multiplied by the frequency of strokes n,:

.

.

and taking into account the previous equations, the following can be stated:

Rotation, which tums the dnll bit between consecutive blows, has the function of making the bit stnke upon different points of the rock in the bottom of the blasthole. In each type of rock there is an optimum rotation speed which produces larger sized cuttings taking advantage of the free area of the hole created with each impact. When drilling with insert bits, the most common rotation speeds oscillate between 80 and 150 r.p.m. with angles between indentations of 10 to 20°, Fig. 2.3. For button bits from 51 to 89 mm, the speeds should be lower, between 40 and 60 r.p.m., that bring turning angles between 5 and 7". Bits of larger diameters require even lower speeds.

2.2.3 Thrust load The energy generated by the mechanism of hammer blows should be transfered to the rock, for which it is n e c e s s q to have the dnll bit in permanent contact with the bottom of the hole. This is achieved with the thrust load or pull down, supplied by a pull down motor, which should be adapted to rock type and drill bit. Insufficient thrust load has the following negative effects: lower penetration rates, greater wear of rods and sleeves, loosening of drill steel threads and heating of the Same. On the contrary, if the pull down is excessive the penetration rate is also diminished, there is increased

INSERT BIT

BUTTON BIT

Fig. 2.3. Rotation speed between consecutive blows as a function of penetration rate and bit diameter.

10

Drilling und blasting of rocks FLUSHING FLUID

FEE0

Fig. 2.4. The effect of thmst load upon penetration rate in top hammer dnlling.

rotation resistance, drill steel can become jammed, the wear on the bits increases as well as the rotation rate and equipment vibrations, and the blastholes can be deviated. As occurs with rotation, this Parameter does not have decisive influence on the penetration rates, Fig. 2.4. Pnnciple of fiushing.

2.2.4 Flushing In order to have efficient drilling, the bottoms of the blastholes must be maintained clean by evacuating drill cuttings as soon as they appear. If this is not done, a large quantity of energy will be consumed in regrinding with the consequent wear on drill bits and decrease in penetration, apart from the risk of jamming. Blasthole flushing is carried out with a flow of air, water or foam that is injected by pressure to the bottom through an opening in the Center of the drill steel and flushing holes in the dnll bits. The cuttings are removed up through the space between the rod and the blasthole walls, Fig. 2.5. Fiushing with air is used in surface operations, where the dust produced can be eliminated by means of dust collectors. Water flushing is mostly used in underground drilling, which also keeps dust down, although it reduces performance by about 10 to 20%.Foam is used as a complement to air as it helps bring large particles up to the surface and also acts as a seaier for blasthole walls when drilling through loose material. The velocity of air flow for efficient cleaning with air goes from 15 to 30 mls. The minimum velocities for each case can be calculated from the following equation:

where: V= Velocity of air flow (mls), pr = Rock density (g/cm3),d, = Diameter of the particles (mm). Therefore, the flow that should be supplied by the compressor is:

where: Qa = Fiow (m3/min), D = Blasthole diameter, d = Diameter of the rods (m). When water is used for flushing, the velocity of air

flow should be between 0.4 and 1 m/s. In these cases the pressures are maintained between 0.7 and 1 MPa, to keep the flow from entering into the hammer. When using air with top hammers, it is not common to have a high pressure compressor for flushing alone. Only in down the hole hammer drilling is a high pressure compressor used (1 - 7 MPa) because the percussion power is increased along with the flushing of cuttings. An important factor to remember when estimating the flushing flow is that of charging losses produced due to the narrow conducts through which the fluid must pass (flushing needle, drill steel holes) as well as along the dnll stnng. In Table 2.2, the flushing velocities for top hammer drilling are indicated as function of air compressor flow and drill steel diameter. 2.3 TOP HAMMER DRILLING This drilling System can be qualified as the most conventional or classic, and although its use by pneumatic drive was limited by the down the hole and rotary equipment, the appearance of the hydraulic hammers in the sixties has given a new boost to this method, complementingand widening its field of application. 2.3.1 Pneumatic drilling rigs Hammers driven by compressed air basicaily consist in: - A cylinder with a front Cover that has an axial opening where the rotation chuck goes, as well as a retaining device for the drill rods. - The piston that altemately strikes the dnll steel shank through which the shock wave is transmitted to the rod.

Rotarypercussive drilling - The valve that regulates the passage of compressed air in a pre-set volume and in alternating form to the front and back of the piston. NCH PhotoPad Image Editor Pro 7.56 Crack A rotation mechanism, that can be a spirally fluted nfle bar or of independent rotation. - A flushing System that consists in a tube that allows the passage of air to the inside of the drill steel. These elements are cornrnon to all the types of hammers on the market, with only a few design charactenstics that differ: diameter of the cylinder, length of the piston stroke, distribution valves, etc. The following describes the working pnnciple of a pneumatic harnrner, Figs. 2.6 to 2.12. 1. The piston is at the end of its return stroke and is ready to Start its working stroke. The air, at line pressure, fills the backhead (1) and passes through the back supply port (2) into the cylinder (3). The air pushes the piston fonvard, beginning the working stroke. Meanwhile, the cylinder front end (5) is at atmospheric pressure since the exhaust port (6) is Open. 2. The piston (4) continues to accelerate forward, driven by the line pressure, until the leading edge (7) of the pistons control head shuts off the entrance of compressed air. The air confined in the back end of the cylinder (3) starts to expand and contiunes to drive the piston forward. Note that the piston flange (4) closes the exhaust port (6) and that the front end is still at atmospheric pressure. 3. The air confined at the back of the piston (3) continues to expand until the back edge of the piston flange starts to uncover the exhaust port (6). Remember that the piston control head (7) has already shut off the compressed air entrance, so that no compressed air will be wasted when the exhaust port is opened. Up front, the piston has trapped air that was a atmopheric pressure (5), and has now compressed it to slightly above atmospheric pressure. 4. The piston continues to move forward because of its momentum until it strikes the drill shank steel. Now, the back edge of the piston flange (8) has uncovered the exhaust port (6) and the air in the back end is exhausted into the atmosphere. While this was going On, the back edge (10) of the control head opened the front supply port adrnitting compressed air to the front end (5) driving the piston back on the return stroke. During this Stage there is compressed air pushing against the piston from the front end (5) and also pushing against the back end (10). The front surface area is much larger than the back (10) so the piston moves towards the rear. 5. The piston is accelerated back on the return stroke, until the back edge of the control head (10) Covers up the front air supply port. The air up front then continues to push the piston back. 6. The piston continues to accelerate backwards while the air in the front end (5) expands until the front end of the piston flange (11) uncovers the exhaust port, trapping the air in the back end of the cylinder and compressing it to a pressure slightly more than atmospheric. Note than the front edge of the control head (7) is just about to Open the back supply port.

11

W

Fig. 2.6. Piston at the end of its return stroke.

I Fig. 2.7. The piston accelerates forward.2.

W-

Fig. 2.8. The backedge of the piston flange uncovers the exhaust port.

w-

Fig. 2.9. The piston compresses the air in front of it.

I Fig. 2.10. The piston is accelerated back.

7

Fig. 2.1 1. The front edge of the piston flange uncovers the exhaust port.

Fig. 2.12. Return stroke of the piston finishes.

CHAPTER 6

Rotary drillling with cutting action

6.1 INTRODUCTION Rotary drilling by cutting action was at its peak in the forties, in American coal mines, for blastholes in overburden and in the ore itself. With growing use in surface operations using rotary rigs with rolling tricone rock bits, this method has been limited to soft rocks, usually with small to medium diameters, clearly competing with direct breakage Systems. In underground jobs, rotary percussive drilling has taken over most of the work, leaving only low to medium strength rocks that are non-abrasive (potash, coal, etc.) to the rotary rigs. Drilling by cutting action in production blastholes is carried out with bits whose stnictures have elements of tungsten carbide or other materials such as synthetic diamonds or polycrystalines, which vary in shape and angle and can be classified in the following types: a) Two-wing drag bits, with diameters from 36 to 50

mm. b) Three and four-wing drag bits with diameters from 50 to 115 mm. C) Three replaceable blade bit with fluted reamers in diameters that go from 160 to 400 mm.

of cut. This force is divided into two, one tangential N, and another vertical E, Fig. 6.4. The tangential force Altium Designer 20.2.6 Build 244 Crack the one that overcomes the compressive rock strength when confronted with the bit. The resisting torque T., measured in the axis of the drilling element, is the product of the tangential force multiplied by the radius of the bit. The resisting torque on the total cutting area, supposing that it is a circularcrown, is given by:

where: T, = Resisting torque, p = Coefficient of friction, E = Thrust on the bit, r, = Outside radius of the bit, r, = Inner radius of the bit. This resisting torque is determined by the rninimum torque of the rock drill that allows the rock to be penetrated. Calling r, the effective radius of the bit, which is equal to

6.2 FUNDAMENTALS OF DRILLING W H CUTTING ACTION

the previous equation is transformed into

The cutting actions of a' rotary drag-bit on rock are, according to Fish, the following: 1. Beginning the cycle immediately after the formation of a large fragment, elastic deformations by stresses owing to the angular deflexion of the bit and to torsional strain in the drill rod. 2. Strain energy is released, with consequent impact of the cutting edge against the rock surface, and comrninution of rock fragments. 3. Build up of stresses at the bit-rock contact area, with further crushing and displacement of rock debris, until the cutting edge is effectively bearing on a step of unbroken rock which subsequently microsoft office 365 - Activators Patch to create a large fragment or chip which, once bailed out, allow a new cycle to start, Fig. 6.2. The field tests carried out by Fairhurst (1964) show that the pulldown load and the rotary torque upon the bit undergo great variations owing to the discontinuous nature in chip formation, Fig. 6.3. The cutting force is in function with the geometry of the bit, the compressive strength of the bit and the depth

It is deduced that if p is constant, the torque is proportional to the thrust load on the cutting tool. In reality, the coefficient p is not constant, as it oscillates with the thickness of the cut and with the feed force itself. The index that determines the penetration in the rock is obtained by the relationship between the energy consumed by the drill and the specific rock energy. The total energy consumed by the equipment is 2xNrTr?where Nr is the rotary speed, which gives the following:

where: E, = Specific rock energy, Ar = Area of the blasthole Cross section. From this relationship it can be deduced that the penetration rate for a given rock and for a determined drilling diameter is linearly proportional to the thrust and rotary speed, although this is not completely true in practice, as it has been indicated that the friction coefficient of the rock varies with the Uinist. In Fig. 6.5, it can be obsemed

Rotary drilling with cutting action

73

-THRUST N W 667 -

DARLEY DALE SANDSTONE 229mm/min CUTTING SPEED

---TORQUE

1 150

0 III

2 445-

100

222-

50

a) TWO WlNG DRAG BIT

oL

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CUTTING EDGE CHIP

I

b) THREE AND FOUR WlNG DRAG BIT

CRACKS

v / / t ; 3

NEW SURFACE

Fig. 6.4. Forces that act upon the cutting tool.

Q

LT

LINEAR PORTION BY CLOGGING AT THE BITS C)

THREE REPLACEABLE BLADE BIT

W

Z

Fig. 6.1. Rotary drag bits.

W

a

DEPARTURE FROM LlNEARlTY DUE T 0 EXCESSlVE WEAR ON BIT

APPLIED THRUST

Fig. 6.5. Basic th~st-penetrationrate curve for rotary drag-bit drilling (Fish and Barker, 1956).

ACCUMULATION TNEw: OF ; R*FINE .!::;CuTTINGs ::::. ?. .:.::.:: :,

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that there is a thrust value under which a theoreticai penetration rate is not achieved, only excessive wear, and a limit vaiue which, if surpassed, will produce clogging of the bit. The rotary speed is limited by the growing frictional wear on the bits as the number of revolutions increases. Apart from the abrasiveness of the rocks, it must be taken into consideration that the wear increases with higher feed loads and the frictional forces between the rock and bit become higher. In Table 6.1, the recornrnended thrusts and rotary speeds are given in function with blasthole diarneter and compressive rock strength.

74

Drilling und blasting of rocks

Table 6.1. Cornpressive rock strenth IMPa)

Unitary thmst (Nimm)

Blasthole diameter (mm)

Rotary speed (rlrnin)

Two practical limits of rotary drilling can be given: compressive rock strength, which should be under 80 MPa, and the siliceous content, which should be less than 8% because, if not, the wear could be uneconomicai. Eimco-Secoma has developed a test for measuring the drillability and abrasiveness of the rocks. It consists of drilling a hole in a rock sample with constant thrust and rotary speed. The bit is of tungsten carbide and the flushing is carried out with water. A penetration-time curve is obtained and, from this, the drillability index or hardness expressed in 1110 mm of advance and, by measuring the wear undergone by the calibrated tool during 30 seconds, the abrasiveness is determined in tenths of mm of bit edge wear. The rocks are clasified in four groups or zones, in ccleaner professional plus crack 2019 - Free Activators with the two parameters, which define the most adequate drilling methods.

Zone I Zone with soft formation and low abrasiveness. Dry, low-thrust rotary drilling is suggested with low air presSure. Zone II Medium hard formation and low abrasivity. Dry mediumthrust rotary drilling with medium pressure air injection. Zone III Fairly hard rock, low abrasiveness. High-thmst rotary drilling and high pressure water flushing. The thrust can reach 20 kN.

O V)

0.9

Zone IV Very hard formation and high abrasiveness. Use rotary percussive dnlling with air or water flushing. The dnlling parameters for each Zone, for drilling diameters between 30 and 51 rnm are, according to Secoma, the following: Zone I Rotary dnlling with little thrust. - Thrust: From 1 to 8 kN. - Rotary speed: 800 to 1.100 rlmin. - Dry drilling - Types of rock: coai, potash, salt, gypsum and soft phosphate. - Tools: Spiral rods; Two wing drag-bits, 6 = 110125", ß = 75", y = 0-14". - Drilling rates = 3.5 to 5 mlmin. - With humid air the penetration rates are multiplied by 1.5 and 2.

Zone I1 Thrust: 8 to 12 kN. - Rotary speed: 550 to 800 rlrnin. - Drilling with humid air injection. - Types of rock: Limestone and soft bauxites, soft iron ores. - Cutting bits: 6 = 125", ß = 75-80", y = 0-2". - Penetration rate: 2 to 3.5 mlrnin. Zone III Thrust: 12 to 18 kN. - Rotary speed: 300 to 550 rlmin. - Drilling with water injection. - Types of rock: Bauxites and medium limestones, schists without quartzites, hard gypsums and hard phosphates. - Cutting bits: 6 = 125-140°, ß = 80°, y = -2-6" - Penetration rate: 1 to 1.8 mlmin. The rotary power, in HP, necessary to make a drag-bit rotate, is calculated with the following equation:

ROTARY PERCUSSIVE-DRILLING

ROTARY DRILLING

75

Rotary drilling with cutting action

where: D = Diameter (mm), N, = Rotary speed (rlmin), E = Thrust load (W). The necessary rotary torque is deterrnined from the equation:

T, =

HP,

X

7.14

Y

Table 6.2. Type of rock Hard gypsum Limestone, bauxite Soft iron ore Soft gypsum Phosphate, coal, salt, potash

Penetration rate (m/min) 1.5-2 1.5-2.5 1.5-3 3.8-6 3.5-10

Flushing System Water Water Water or dry Humid air or dry Humid air or dry

where: T, = Rotary Torque (kN.m). 6.3 FLUSHING OF DRLLL CUTTINGS Drill cuttings are eliminated with a flushing fluid that can be air, in surface operations, or water or humid air in underground jobs. The advantages that the use of air with water injection brings are the following: - It facilitates upward bailing, thus increasing the advance rate. - It cools the dnll bit, reducing wear. - It avoids blasthole filling. - It eliminates dust which is very important in abrasive formations. According to Eimco-Secoma, in order to inject humid air around 1.000 to 1.500 llmin of air are necessary and, for each rock drill, about 250 cm3/minof water. In very soft rocks, from 30 to 40 MPa, helicoidal dnll steel can be used, with larger pitch as the penetration rate increases for efficient removal of the drill cuttings, Fig. 6.7. In Table 6.2, apart from the typical penetration rates in different types of rocks, the most commonly used flushing systems are indicated. 6.4 CUTTING TOOLS The cutting efficiency of a to?l depends largely upon its

design, according to the type of rock that is to be drilled. Fig. 6.8. The attack angle 6 usually varies between 110" and 140°, becoming increasingly obtuse in harder rock: if not, the hard meta1 would splinter. On occasions bits have been designed with rounded contours. The angle of the cutting wing ß varies between 75 and 80" and that of the cut y between -6 and 14", being positive in soft rocks and negative in hard rocks. Lastly, the backing-off angle or clearance angle is 6 = 90' - ß = Y. During drilling, a point on the cutting bit located at a distance r advances along a helical path. The angle of inclination of this helix is: 0.l

= arc tan

(&)

wherep is the advance of the bit per revolution. Owing to the movement of the bit along the helix, the effective clearance angle is reduced: For points near the center of the bit the effective clearance angle is Zero, as in these zones the tool compresses the rock. For this reason, drag-bits designed with a central gap usually reach higher drilling speeds. At the end of the seventies, General Electric manufactured the first Compact Diamond Polycrystalline-PDC,

CUTTER HEAD ASSEMBLY LEAD ASSEMBLY

-

.

REVERSIBLE LOCKING TYPE

I) HOLLOW STEM AUGER. 1.6m LENGTH 2) HEX DRIVE CAP 3) ROD T 0 DRIVE CAP ADAPTOR 4) LOCKING PIN 6) LOCKING PIN BOLT 6, CENTRE DRILL ROD7) PLUG 8) PLUG BOLT

9) 10) 11) 12) 13) 14) 16)

BIT TYPE CUTTER HEAD BODY CARBIDE INSERT BIT BIT LOCK RING BLADE TYPE CUTTER HEAD CARBIDE INSERT BLADE BLADE BOLT TUNGSTEN CARBIDE PILOT BIT

Fig. 6.7. Helicoidal drill rod and bits with differentconfigurations.

16) PlLOT BIT SHANK

17) 18) 19) 20) 21) 22)

BOLT. PILOT BIT SHANK TUNGSTEN CARBIDE PILOT BIT. LARGE SlZE PILOT BIT, SOFT FORMATION HEX QUICK BREAKOUT ADAPTOR LOCKlNG WEDGE WEDGE PUNCH

Drilling and blasting of rocks

7r

NEGATIVE SIDE RAKE ALL CUTTERS '6

,TER FLUSH HOLES

3- DIAMETER

-E F O R AIR W A T E R FLUSt 7-C2542 STRATAPAX BLANKS

(0)

BIT ROTATION

CORE CRUSHER (TUNGSTEN CARBIDE) SECTION X-X

Fig. 6.10. Drill bit with diarnond cutting elernents. Fig. 6.8. Sorne characteristics of a cutting tool (Fish and Barker, 1956).

RAKE ANGLE ECTIVE DEARANCE W -HELIX ANGLE

"-z

MOVEMENT

BIT AXlS

Fig. 6.9. Direction of a point on the the bit (Fairhurst, 1964).

obtained from a mass of very fine diamond particles that are sinterized under extreme pressure and embedded in tungsten carbide bases that are shaped at high pressures and temperatures. The resulting alloy has exceptional abrasion resistance along with the high resistance of tungsten carbide to impacts. The present day diamonds are thermically stable up to 1200°C in non oxidizing atmospheres and are available in sizes that range from 0.005 to 0.1 8 g (0.025 to 0.9 carats) in triangular prism, parallepiped or cylinder shape. Apart from their use in exploration drilling, diamond bits are used in underground mining for coal, potash, salts and gypsums to drill small diameter blastholes, from 35 to 110 mrn. In many instances, the penetration rates obtained and the Service lives of these bits are quite Superior to their conventional Counterparts.

Atkins, B.C.: Drilling Application Successes Using Stratapax Blank Bits in Mining und Construction. Australian Drilling Association Symposium, 1982. Bemaola, J.: Petforacibn Rotativa. 11 Serninario de Ingeniena de Arranque de Rocas con Explosivos en Proyectos Subterrineos. Fundacibn Gbrnez-Pardo. 1987. Morales, V.: La Seleccibn y el Funcionamiento de los Triconos. Canteras y Explotaciones. Septiembre, 1984. Roberts, A.: Applied Geotechnology. Pergamon Press, 1981. Rodriguez, L.: Petforacibn Hidrbuiica Rotativa en Proyectos Subterrbneos. I Seminario de Ingenieria de Arranque de Rocas con Explosivos imyfone tunesmate crack - Free Activators Proyectos Subterrineos. Fundacibn Gornez-Pardo, 1986. Tandanand, S.: Principles of Drilling. Mining Engineering Handbook. SME. 1973.

Photo 6.1. Rotaiy drilling equiprnent with heicoidal drill steel in a potash mine.

CHAPTER 7

Special drilling methods and mounting systems

7.1 INTRODUCTION Apart from the standard drilling equipment, there are units and mounting systems on the market for special or very specific applications. Among these jobs, a few can be mentioned such file magic 2019 license key - Activators Patch drilling rock masses with overburden of a nonconsolidated material andlor sheets of water, drilling rigs for shafts and raises, thermal and water jet drilling, etc. 7.2 DRILLING THROUGH OVERBURDEN These drilling methods were developed to solve problems that appeared when drilling in rocky ground, unconsolidated or alterated masses, overburdens, etc., that require continuous casing tubes to maintain blasthole stability. Some of Video Editor - Crack All Windows/Mac OS Software Full Version applications for these systems that are in use at present are: - Drilling for underwater blasting - Drilling for rock rnass blasting with overburden that has not been removed previously. - Anchonng - Foundations - Water wells - Soil and core sampling, etc. The overburdens can be b ~ d sof natural clay, sand, gravel, etc., as well as of fill with compact or noncompact materials, rock fill, etc. Drilling can be canied out, as will be noted later on, with top hammer or down-the-hole hammer, and consists of drilling through the overburden at the Same time that the casing tube is passed down into the hole, to keep loose material from caving in and blocking the hole, so that drilling can proceed into solid rock. One important feature of these techniques is that adobe acrobat standard dc vs pro dc - Crack Key For U flushing, or bailing out, of the debris be very effective. It can be canied out centrally through the shank adaptor or through a separate flushing head, in which case the fluid pressure should be higher. The two methods that have been developed are known as OD and ODEX. 7.2.1 OD (Overburden Drilling) Method In this method, the descent of the casing tube is canied out by percussion and rotation. The equipment consists of an outer casing tube with a tungsten carbide ring bit

mounted on the lower end. The casing tube encloses an inner drill stnng of standard drill steel which is extended by use of coupling sleeves that are independent from those of the casing tube. The casing tubes as well as the drill steel is connected to the hammer by a special shank adaptor, which transmits impact force and rotary force to both, Fig. 7.1. The basic operations for application of the System are: - The casing tubes, with or without the inner drill steel, proceed simultaneously through the overbur-den. - The outer ring bit advances a few centimeters when it reaches the bedrock. - Drilling is carried out with the inner drill steel unless decomposed or sand beds are encountered, in which case the casing tube would descend at the Same time. - The extension rods are drawn up. - The plastic casing tubes are allowed to remain in the hole to serve as channels for charging the explosive, or plastic tubes are inserted for this purpose, and - The casing tubes can be removed. As between the casing tube and the blasthole walls there is friction which increases with depth, the rock drills should be used with high rotary torque. Water is usually the flushing fluid in these cases, or compressed air with or without foam. If the upward bailing of the cuttings is insufficient with central flushing, then lateral flushing can be added. 7.2.2 ODEX Method (Overburden Drilling with Eccentric) In this method, based on the principle of underreaming, the casing tube is driven into place by vibrations from the drill and its own weight. Very little rotation is necessary. The equipment consists of an eccentric reamer bit that drills a hole with a larger diameter than the casing tube which descends as drilling advances. Once the required depth has been reached, the drill string reverses and the reamer bit becomes concentric, loosing diameter, and can then be drawn up through the casing tube. The standard drill steel is then introduced and drilling continues, Fig. 7.3. The rotary percussive rigs can be top or down-the-hole hammers. If top hammers are used, the percussion impacts are transmitted to the casing tube by means of a driving cap and shank adaptor which make the tube rotate slightly and vibrate. The flushingcan be central or lateral, Fig. 7.4.

78

Drilling und blasting of rocks

1 ii L

CHANK ADAPTER

CASING TUBE

Fig. 7.3. The ODEX method (Atlas Copco).

CASlNG TUBE

7.1. The OD Equipment (Atlas Cop-

4

5

6

Fig. 7.2. Operations in the OD System.

Table 7.1. Data

For-down-the-hole-drilis XD X 90 115 Min. inside diameter (mm) 115 90 123 152 Diameter of reamed hole (mm) Normal max hole depth in overburden (m)* 60 100 3"DTH 4"DTH Inner equipment Weld thread Weld thread Casina tube *ODEX 90 at 1.2 MPa, ODEX 115-215 at 1.8 MPa. Source: Atlas Copco.

i5' Fig. 7.4. ODEX top hammer equipment (Atlas Copco).

For top hamrners ODEX OD 140 165 215 127 72 127 72 140 165 215 76 187 212 162 108 278 96 100 40 40 40 100 100 5"DTH 6"DTH 7-8"DTH R38 R38 R38 Weld Weld thread Weld thread Thread Weld Weld X

ODEX 76

Special drilling methods and mounting Systems

Photo 7.1. ODEX drill bit. DTH

Table 7.2.

BIT TUBE

ODEX 90 115 0 X 0 0

GUlDE REAMER

Fig. 7.5. ODEX down-the-hole drilling equiprnent (Atlas Copco).

When down-the-hole hammer is used, the unit has only one wing coupling, as drill tubes are used instead of extension rods. The string of casing tubes is pulled down by means of a specially designed bit tube, and the flushing is carried out through the rotary head, Fig. 7.5. In both methods the cuttings are swept upwards through the annulus that remains between the casing and the drill steel, going out through the headstocks. The flushing fluid can be air up to a depth of 20 m, below which the addition of a foam is recommended to increase the bailing efficiency, wall stability, lower wear and increase penetration rate. This method has numerous advantages, although some important aspects that should be studied are: the sizes of the casing tubes, the flushing and the drilling System. The depth of the blastholes must be taken into account when choosing the equipment. In Table 7.1, a selection guide for both drilling methods is given. On the other hand, as to the applications for these drilling methods, aside from the one described for rock fragmentation blastholes, Table 7.2 indicates other possibilities.

140 165 X X 0 0

76

OD 127 72

Water well drilling Roadembankrnent 0 0 Underwatter drilling O O Blasthole drilling 0 0 X Anchoring X X X Injection X X X O Pros~ectine X X X O X = Suitable, 0 = Cm be used. Source: Atlas Copco.

X X X X X X

7.3 SHAFT SINKING When excavating long, large section shafts or metal structures pneumatic or hydraulic jumbos are used with three or four booms with the Same number of feeds and rock drills. When working, these rigs rest on the bottom of the shaft and are anchored to the walls with horizontal hydraulic cylinders. The central supporting column can turn 360°, and the booms, which are similar to the jumbos used for tunnelling, can vary their inclination withrespect to the vertical and lengthen themselves if they are telescopic. Once each round is drilled and charged, the rig is folded and moved to a safe position, later carrying out the mucking operation with twin valve ladles or hydraulic clam shells, as shown in Fig. 7.6. There are also platforms that have been designed to widen shafts.

80

Drilling und blasting of rocks

1. DRILLING

3. VENTILATION

2. BLASTING

4. SCALING

Fig. 7.7. Work cycle with an Alimak platform.

7.4 RAISE DRIVING 7.4.1 Alimak raise climber This excavation method for raise driving was introduced in 1957 and since then, due to its flexibility, economy and Speed, it is one of the most widely used in the world, especially in cases when there is no other access to the upper Password Recovery Bundle+Crack 5.2 With Serial Key [Latest]2021. This equipment consists of a cage, the work platform, the driving motors, the guide rail and auxiliary elements. In Fig. 7.7, a complete work cycle is shown. The platform climbs along a pin rack welded to a guide rail and driven by either compressed air, electric or dieselhydraulic motors. The guide rail is bolted to the wall with Special Alimak design expansion bolts. The air and water pipes, which supply the necessary ventilation and water Spray, are placed on the inside of the guide rail for their protection. During work, the drillers are on a Safe platform, as it is covered and has a protective railing. Men ride up to the face safely in the cage, which is under the platform. In each work shift two drillers can advance from 2.2 to 3 m. Air engines are adequate for lengths under 200 m, the electric for up to 800 rn, and from these distances On, diesel-hydraulicengines are recornrnended. The main benefits of these rigs are: - They can be used for raises of any length and inclination. - Different lengths and geometries of the raises can be achieved by changing the platforms. It is possible to drive cross sections from 3 to 30 m2, Fig. 7.8.

- In the Same operation it is possible to change the direction and inclination of raises by using side-bent (curved) guide rails. - The length or height of the raises is practically unlirnited. Up to the moment, the longest raise driven is 1.040 m long with a 45O inclination. - It can be used as production equipment Altium Designer 20.2.6 Build 244 Crack some ore beds by applying the Alimak Raise Mining method, Fig. 7.9. - The enlarging of pilot raises for excavation of large cross section shafts can be aided by using horizontal drilling units. - The basic equipment can be used to Open various raises simultaneously. - In poor ground the platforms can be used as supports with bolting, injection, etc. - The investment is lower than with the Raise Borer System. - The labor does not have to be highly specialized. - The initial preparation of the work area is minimum. On the other hand, there are a few disadvantages: - Poor quality work environment. - 'The walls are very rough which is a problem for ventilation raises and an advantage in ore Passage outlets. - The remaining rock mass is left in poorer condition than with the Raise Boring method.

7.4.2 The Jora method This rnachine is manufactured by Atlas Copco and can

Special drilling methods und mounting Systems

Fig. 7.8. Different platforrn configurations.

PILOT HOLE

HORIZONTAL BLAST AND LOADNQ DRILLING

Fig. 7.9. Altium Designer 20.2.6 Build 244 Crack method in narrow and inclined beds.

Fig. 7.10. Jora method for vertical and inclined raises (Atlas Copco).

Photo 7.2. Work on Alimak platform.

81

82

Drilling and blasting of rocks

also be used in raising and ore outlets, whether vertical or inclined. The principal difference when compared to the previous equipment is the drilling of a pilot hole with a diameter between 75 and 100 mm through which the cable which holds the lifts is lowered. The main components are the work platform, the lift basket, the hoisting mechanism and, in inclined raises, the guide rail, Fig. 7.10. During drilling, the platform is anchored to the raise walls by a system of telescopic booms. The main inconvenience of this method, against the former, is the pilot hole drilling, as the maximum raise height will depend upon the accuracy of its alignment. Its practical and economical field of application is between 30 and 100 m. For each round it is necessary to remove the cage from the hoisting cable, because, if not, the cable would be damaged during blasting. The central blasthole serves as expansion space for parallel cuts, obtaining advances per round of 3 to 4 m, and also as an entrance for fresh air. 7.4.3 Raise Boring (Full-face)method This method, which has become increasingly popular over the past 20 years, consists of the cutting or reaming of the rock with mechanical equipment. Its main advantages are: - Excellent personnel safety and good work conditions. - Higher productivity than in conventional methods of rock breakage with explosives. - Smooth walls, with minimum losses due to air friction in the ventilation circuits. - Overbreak does not exist. - High advance output. - Possibility of drilling inclined raises although it is better adapted to vertical ones. The most important disadvantages are: - Very high investment. - High excavation costper lineal meter. - Lack of flexibility, as the sizes and shapes of the raises cannot be varied nor the direction changed. - Gives problems in rocks that are in poor condition. - Requires highly specialized personnel and previous preparations of the work area. At the moment there are over 300 rigs in operaton around the world, with the following subsystems of Raise Boring: standard, reversible and blind hole raising. a) Standard raise boring This is the most widely used system and consists of setting up the equipment on the upper of the two levels to be intercomected, or even outside the mine, so that a pilot hole can be drilled down to a previously opened level. Aftenvards, the reamer head is attached to the drill string and the raise is drilled upwards to the rig. b) Reversible raise boring The Same operations are carried out as before, with the difference of placing the equipment on the lower level and inverting the pilot hole and raising execution, which

are ascending and descending, respectively. C) Blind hole raise boring Once the rig has been erected on the lower level, the drilling is done upwards in full section, without the pilot hole, as there is no access to a second level. The basic elements to cany out the work, apart from the rig itself which exerts the rotation and feed force from its point of installation are, for the blasthole, the tricone bit, the roller stabilizers and the drill rods; and for the reaming, the axis, base, Cutters and their sockets, Fig. 7.12. The heads can be integral, segmented or extensible. The first are used for diameters from 1 to 3 m with pilot holes of 200 to 250 mm, the segmented for raise diameters that are between 1.5 and 3 m, and AMT Emulator 0.9.2 Download Same pilot holes as before, and, lastly, the extensible heads are for sections that range from 2 to 6.3 m with pilot holes up to 350 m. The power for the equipment is usually over 600 kW with rotary speed, rotary torque and thrust loads on the rock having values that oscillate between: 15 and 30 r.p.m., 150 and 820 kNm and 4 and 12.5 MN, respectively.

CHAPTER 14

Initiation and priming systems

14.1 INTRODUCTION ries and emulsions in rock breakage has brought about an important development of initiation and priming techniques. This is due to, on one hand, the relative insensitivity of these compounds and, on the other hand, a desire to obtain maximum performance from the energy released by the explosives. The detonation process requires initiation energy so that it can develop and majntain stable conditions. The most frequent tenninology used in initiation is: Primer: High strength, sensitive explosive used to initiate the main column in the blasthole. They are cap and detonating cord sensitive, including ones of low core load. Booster. Powerful explosive charge with no initiation accessory that has two functions: I. Complete the initiation work of the pnmer in the explosive column, and 2. Create zones of high energy release along the length of the column. Since the seventies, various theories have been devel.oped on initiaTion, ~~~~~~~~~~~i~creätIng-sömc confusion amongst operetors. In the following paragraphs present day knowledge is discussed and a series of practical recommendations are given in order to obtain maximum yield from the explosives.

14.2 PRIMING AND BOOSTERING BULK ANFO-TYPE BLASTING AGENTS When blastholes have a length of under 10 in and are kept dry, initiation of ANFO can be carried out safely with only one bottom dimension models. However, if the bench is very high and the holes pass through zones of different lithological charactenstics and fracture frequency, water can appear and there is the possibility of separation of the explosive column during charging, due to dnll cuttings and loose rock that can fall into the blasthole. In these cases, multiple priming is recommended with an initiator every 4 or 5 m, which, although slightly more costly, would eliminate the risk of incomplete detonation in any of the holes.

14.2.1 Initiation by aprimer In the priming of ANFO, the efficiency of a primer is detined by its detonation pressure, dimensions and -shape. The higher the detonation pressure PD, the greater its initiating ability. The effect of the 'PD' on the detonation velocity VD of ANFO is shown in Fig. 14.1. As can be observed, with detonation pressure that is less than a certain value, a partial reduction in VD is produced, and the contrary is true when PD is above the mentioned value. Following the Same procedure, the effect of the diarneter of the pnmer has alio been studied, Fig. 14.2. Therefore, the conditions that a primer should comply with in order to eliminate low VD zones in the ANFO are: the highest possible detonation pressure and a diameter above 213 that of the charge, - approximately. -The length of the primer is also imkrtant, as the primer itself is initiated by a blasting cap or detonating cord and they have a run-up distance in the VD. For exarnple, for a slurry to reach the detonation velocity regime it usually has a characteristic run-up distance of 3 to 6 times that of the charge. In Table 14.1, the minimum dimensions of pentolite boosters for different blasthole diameters are shown. As to the shape of the primers, the latest investigations have demonstrated that it has a significative effect upon performance, which means that it is a field Open to study. Although it is generally believed that the energy produced by ANFO increases with the transient velocity of the charge, this concept is false because the total energy releasedby an explosive is constant and independent of that velocity. An increase in VD brings about an increase in Strain Energy ET, thus lowering that of the gases EB -butthesum of-both remains constant. The relationship ETIEB is lower in zones of VD reduction and higher when the primer produces a raise in VD. The increase in Strain Energy is only beneficial for fragmentation when hard, fragile and massive rocks are being blasted. In sedimentary bedding planes or highly fissured rocks, the bubble energy should be increased in order to take advantage of the fractures and planes of weakness and obtain adequate rock displacement. Finally, it has been found that the VD steady-state in ANFO is independent of type, weight and shape of the primers (Junk, 1972).

Initiation und priming systems

137

DETONATMG CORD

-

Y

C ~ V E

f

DETONATION PPESSURE OF PRIMER !MP!l

24.000

b 0

$! 7W 4.000-

Fig. 14.3. Conventional primers. STEADY-STATE VOD

3CGU-

P M E R MAMETER- W O MAMETER- 7Omi

2000ASBESTOS TVBE C W N E K N T

K M

200

3m

I

500

400

Fig. 14.4. Primer cartridges with Detaprime primer (Du Pont)

MSTANCE FROM WTlATlON P W T (mm)

Fig. 14.1. Effect of primer's detonation pressure on initial VD of ANFO (Junk, 1972)

14.2.2 Types of primers und boosters

At present time, the most used primers are those made of pentolite as they have numerous advantages, such as: - Insensitivity to impacts and frictions. - High physical strength, therefore dimensionally stable. - They have one or two longitudinal tunnels through which the detonating cord can be threaded and re-ained, or into which a detonator can be inserted, Fig. 14.3. - They are small, compact and easy to handle, and they do not have adverse physiological effects. - They are not alterated by age. ~ e s l u r r i e s a n d e m d s ~ h a ~ e e a ~ ive can be used as primers or primer cartridges, with the advantage that they occupy the entire cross-section of the blasthole and are very efficient. When these explosives require a primer for initiation, they can only be used as boosters (secondary primers) unless special accessories are used such as Detaprime by Du Pont, Fig. 14.4.

STEADY-STATE VOO

M

O

DULIETER- 7

h

ASBESTOS TVBE C O H - N K N T

14.2.3 Initiation by downline P -

iia

k 3 .

350

Sb0

Sb0

MSTANCE FROM MTIATIOW PONT (mnl

Fig. 14.2. Effect of primer's diameter on initial VD of ANFO (Junk, 1972).

Table 14.1 Titanium backup pro key 1.3.2 apk - Free Activators diameter (mm) -50 50-1 15 115-160 160-320

Size of pentolite booster (Mass X diameter X length) 3 0 g x 2 3 m m x 52mm 60gx28mmx70mm 150g X 40mm X 79mm 400 e X 80 mm X 59 mm

W e n a d e t o n a t i i ~ i i n s u f f i c i e n core t loadto initiate a charge of ANFO, the detonation of said cord creates a pressure front that expands in cylindrical shape and a chimney of gas inside the ANFO. If the crosssection of the blasthole is small then the lateral pressure can compress and desensitize the explosive. According to Hagan, in blastholes of 75 to 125 mm, a downline with core loads of 10 glm that lies along or near the axes densifies and desensitizes at least some of the ANFO. If the downline is along the blasthole wall, there is very little risk of desensitization with a properly rnixed ANFO, but it is possible in blastholes with water where the explosive is alterated.

138

Drilling und blasting of rocks

1 ANFO DETONATION VELOCITY(VERY LOW)

combustion or deflagration of part of the explosive charge.

3/8 RADNS OF TUE CHARGE

\

14.2.4 Initiation by primer and detonating Cord REACTION FRONT. C

o

+ Z

BLASTHOLE WALL

W

o

-

1B

I

G -

U

DETONATION V E L ~ ~ lrnlsl l ~ y

I

W t- -

4000

DETONATING CORD

4200

DETONATION PRESSURE (MP4

When the detonating cord does not completely initiate ANFO charges, the following Situations may appear: - In blastholes with diameters larger than 200 rnrn and cords with core loads under 10 g/m, the detonation of the cord has an insignificant effect and the ANFO is only affected by the primer. - When a cord of 10 g/m lies along or near the axis of a 75 to 125 mm blasthole, the detonation of the downline, as indicated before, compresses and desesitized the ANFQ 0. . are not dose to the primer. When this occurs, the fraction of ANFO that detonates decreases as the detonation wave propagates into the ANFO. In practice, above all in angled blastholes, as the downline lies along the blasthole wall and not the charge axis, this situation is not produced. If the downline side-initiates the charges, the primers have little influence on the effect of the ANFO detonation, unless they are very close together.

'"Mo 1300 500

1000

RACMAL DISTANCE (-1

Fig. 14.5. Detonation effect of a downline lying along the axis of a blasthole upon the VD of ANFO.

14.3 PRIMING CARTRIDGE ANFO TYPE BLASTING AGENTS If the covering of an ANFO charge has been damaged, permitting its contents to be alterated by water, the propagation of the detonation can be interrupted unless several primers are placed along the colurnn of cartriged explos-

DOWNLME

0

2

4

6

8

-

X)

gIrn

ALL CARTROGES EXCEPT TWS ONE OETONATE

Fig. 14.6. Energy losses provoked by the downline in ANFO columns (K0nya-&Walter,-1-9-~0>.-

If the downline side-initiates the ANFO, the initial VD is slower and incieases gradually while the detonation wave front passes through the section of the explosive colurnn. With axial initiation an increase in Bubble Energy is produced at expense of the Strain Energy, which can be quite advantageous in soft and highly fissured rocks, and when a controlled trajectory blast is desired with maximum displacement. On the other hand, in Fig. 14.6, the energy losses are shown for ANFO when it suffers damagefrom the downline, owing to the pre~0mpreSSi0nbrought On by the

al I N A o E o U A T E

b) S A T I S F A C T o R Y

Fig. 14.7. Inadequate and satisfactory pnming for cartridged loosepoured ANFO in wet Blastholes (Hagan, 1985).

Initiation und priming Systems ives, Fig. 14.7, and there is certainty that they are in contact. In blastholes with 150 m diameters, pnmers of 125 g weight are recommended, and in larger holes of 500 g. When ANFO has been pressure-packed in cartndges at the factory, the densities reached (1.1 g/cm3) are higher than when the explosive is loose-poured (0.8 g/cm3). Thus, although water is present in the blastholes, it is more probable that the cartridges will come into contact with the pnmers and, apart from this, the wrappings are usually more water and abrasion resistant, requiring less number of primers than in the previous cases. 144 P R T 4 ? Y AND EMULSION BLASTING AGENTS Generally speaking, slumes and emulsions are less sensitive to initiation than ANFO. These blasting agents tend to be more easily compressed and can be desensitized by cord detonation inside the explosive column. Less porosity and the presence of a liquid phase reduce the atenuation of the shock wave produced by the detonating cord and prolong the action of the high pressured gases after the shock wave passes. In order to minimize the risk of cut-offs originated by the detonating cord, in large diarneter blastholes (150 to 381 mm) a multiple pnming system is used. The number of equidistant boosters n, inside a blasthole of D diameter with a column length L is deterrnined, according to Hagan, with the following equation:

Photo 14.1.Placing a booster to initiate a column of poured slurry.

In a 20 m high bench with a diameter of 229 mm, a stemming of 5.70 m and a subdcilling of 1.80 m, the number of cast pnmers required will be:

In order to be certain that the boosters are correctly placed, a weight or heavy rock should be put on the end of the detonating cord to tense the line, and the first boosters should be placed at the calculated depth. When the density of the multiple pnmers is not more -thrthat-of-t~ti~igagentsused-0-that-f-tk mud itself that can exist in the hole, there could be a nsk of inadequate positioning of adobe cc all apps download - Crack Key For U pnmers as a consequence of their flotation or being pushed upwards. In these cases it is recomrnended that the downline be prepared for multiple prirning outside the hole, threading twice SecuritySpy 5.3.2 Crack+ License Key 2021 - Free Activators of the pnmers, Fig. 14.8.

Fig. 14.8. Recommended priming system for pumped watergel and emulsion changes (Hagan, 1985).

140

Drilling und blasting of rocks

In some place the accessories are lowered with clips in the shape of tweezers that avoid their rising towards the surface. 14.5 PRIMING CARTRIDGED WATERGEL AND EMULSION BLASTING AGENTS Watergels and emulsions have high water resistance, which allows primers to be widely spaced within charges if it were not for the potential problem of desensitization by the downline. The multiple initiation system is recommended, as shown in Fig. 14.9. In blastholes with diameters under 150 mm, the recommended weights of the 13< n

should be increased to 500. As with pourable slurries and emulsions, if two lines of detonating cord are used in the blasthole, only one of these should reach the top of the column to avoid nsk of desensitization.

PACKAGED WATE OR EMULSION

14.6 LOCATION OF PRIMERS 14.6.1 Bottom priming Bottom priming gives maximum use of explosive energy, increasing fragmentation and displacement of the rock with a minimum of flyrock. This is due to the fact that the detonation Progress towards the stemming while the gases of the explosion are entirely confined within the rock mass, until the stemrning material is ejected and allows their escape. This time of confinement is usually around 3 to 4 ms, according to detonation velocity and length of column. The subsequent fall of pressure through escape on bench toe level takes place much later, Fig. 4 4 e ~ a ~as well. e as~a lower vibration level due to shock wave propagation towards the top part of the bench. In bench blasts, as the breakage at floor level is extremely important, the priming should be such as to produce maximum strain at that point. If the priming takes place at floor level and not at the bottom of the blasthole, an increase in peak strain of 37% is obtained (Staxiield, 1966) due to simultaneous detonation of the two parts of the charge that are equidistant from that point, Fig. 14.11. In the Same manner, a 37%greater peak strain can be generated in any strong bed if the primer is placed centrally within the bed. In blastholes without subdrilling, the bottom primer should be located as low as possible but never upon the drill cuttings or in mud, recommending that there be a distance of approximately 4D above the effective base. Apart from the cited advantages, bottom priming has much less chance of cut-offs than top or multiple priming. In Fig. 14.12, two 270 mrn diameter and 20 m long blastholes are shown as an example, where the spacing between explosive columns and sternming height is 7 m. The detonation velocities are 70OCCiKäKand mis in the cord and in the ANFO, respectively, and between ytd video downloader not working - Crack Key For U blastholes there is a milisecond delay interval of 25 ms. As blasting failures are produced by cut-off of the cord through ground movement, the larger the difference in

B

W

0

O

T INITIATION

I-

Q W

a

3

V) V)

t'

W

CAST PRIMER

h

(VENTING BEGINS AT COLLAR)

Y1

nN I

I I

VENTlNG REACHES TOE

(RAPID DROP DUE T 0 VENTlNG BEHIND DETONATION WAVE)

\ r

TIME

Fig. 14.9. Priming system for packaged watergel or emulsion blasting agents (Hagan, 1985).

Fig. 14.10. Effect of the position of the pnmer upon the pressure-time profile in the blasthole.

Initiation und priming Systems /: RESULTANT STRAIN r

\PULSE AT POHT P

I

I I

:

RESULTANT STRAIN PULSE AT POINT P

,i

I I

--

TIME

TIME

Fig. 14.11. Strain pulses at point P for charges pnmed (a) at their bases and (b) at bench floor level (Hagan, 1974).

A bottom priming pattern called safety is the one indicated in Fig. 14.13. In this case, if the low core load cord of the detonator N failedfor some reason, at the end of a time equal to the nominal intewal of the series of milisecond delay the top primer would initiate, producing the detonation of the

iai

(b)

Fig. 14.12. The reduced probability of cut-offs where charges arebottom pnmed.

Up until a short time ago, Operators were not interested in bottom priming because the use of detonators inside the blastholes had certain risks, but nowadays nonelectric accessories are available such as low core load downlines and those of very low energy that offer a wide field of possibilities for this initiation System.

14.6.2 Toppriming

Fig. 14.13. Safety Pattern with bottom pnming.

In bench blasts where top priming is used, a high strain wave is propagated towards the subdrilling Zone where, of course, its energy is dissipated and therefore wasted. In blasting overburden for a dragline, this strain energy can be more usefully employed in fragmenting the rock between the bottom of the blasthole and the top of the coal, but not the coal itself, especially if there is a strong bed irnrnediately above the coal andlor a well defined Zone between the waste and the ore. If peak strain is to be maximized along the rock that surrounds the stemming column, the top primer should be atleastl~M-af-the-hurden-be1~~_thetop-af-the~ (Starlield, 1966). If the explosive is initiated with a primer at the highest point, the superposition of the strains generated by adjacent charge elements gives a lower result in any point of the stemming, Fig. 14.14. The elimination of premature escape of the gases into the atmosphere, with adequate stemming height, improves fragmentation and rock displacement by Bubble Energy. For elongated charges, the efficiency of the stemming with top priming is less because the inerte stemming material, as well as the rock itself at the top, start moving some miliseconds before detonation of the lower part of the explosive. The fall of the presure of the gases is greater in long explosive columns with low

142

Drilling and blasting of rocks

RESULTANT STRAIN PULSE AT POINT P

STRAIN PULSES

's.

-

0 INITIATION POINT

detonation velocity and insufficient sternming, or small burden size. When the detonation reaches bench floor level, the pressure of the gases falls rapidly from its highest value, due to their escape towards lower pressure zones. This phenomenon gives poor fragmentation in the bottom of the blasthole and especially a reduced displacement of the lower rock.

TIME

/\

RES~LTANT

14.6.3 Multi-pointpriming If various primers are used, they should be located in positions such as to produce collision of the detonation

OIN(TIATIMI PciNT

TIME

Fig. 14.14. Strain pulses on burden alongside stemming column for charges primed at and somewhat below their uppermost point.

(Starfield, 1966). When the charges do not offer loss of velocity, fragmentation is improved in multi-point prirning through strain energy reinforcement. 14.6.4 Continuous side iniriation When the explosive columns are continuously side initiated by a detonating cord (downline), the detonation velocities are relatively lower than the regime. Thus, side initiation is more effective in highly fissurized soft rock

il

a) ELECTRIC

. .

+ig~l4-l-5;Applieationssoffmu1

p-it-

b) ELECTRIC

. I. L-,

. . .

.

.

C) WlTH DETONATING CORD

CORRECT

INCORRECT

Fig. 14.16. Cartridge priming with an electnc detonator.

Fig. 14.17. Priming cartridges and blastholes.

P P

Initiation andpriming Systems

143

formations where more bubble energy is preferible. The theory that continuous side initiation significantly increases the VOD of ANFO cannot be maintained, as has been demonstrated in practice.

C) Detonating cord. Contour blasthole or in soft rock, with decking to lower the total charge along the length of the column.

14.7 PRIMING CONVENTIONAL CARTRIDGED EXPLOSIVES

REFERENCES

The priming of cartridges consists of inserting a detonator or the end of a detonating cord in the cartridge to activate or initiate the detonation of the main charge in the blasthole. To maximize the use of the shock effect produced by

Anonymous: Puuled about primers for large-diameter ANFO charges? Here's some help to end the mystery. Coal Age. August, 1976. Anonymous:Safe und eficient initiation of explosives. Downline, ICI, NO.7, 10, 1988- 1990. Condon, J. L. & J. J. Snodgmss: Effects of primer type und borehole diamerer on ANFO deronation velociries. Min. Cong. J. June,

t h ~

r

cartridge and to the axis of the explosive column, Fig. 14.16. Any primer is an activated explosive ready to detonate under different stimulations, fire, strikes, etc., which means that they Secret Disk Pro Crack be handled with extreme care, in transportation as well as when being placed in the blastholes. They should never be directly tamped. For priming cartridges and blastholes with electric detonators and detonating cords, the Patterns given in Fig. 14.17 should be followed. The procedures for priming blastholes are as follows: a) With instantaneous electric detonators. For isolated or simultaneous blastholes in rock of low to medium strength. Wet blastholes. b) With electric delay detonator. Bottom priming for simultaneous blastholes or without a face, without water and in medium to hard type rock. With this System fragmentation is improved.

1 Y14.

_

G ~. ~ r n o ~ ~ ~ l ~ n sifenvrac. Annales des Mines de Belgique, September, 1977. Hagan, T. N. & C. Rashleigh: Initiating systems for underground mass Jiring using large diameter blastholes. The Aus. IMM. 1978. Hagan, T.N.: Optimum priming systems for ammonium nitrate fuel-oil type explosives. The Aus. IMM.July, 1974. Hagan, T.N.: Optimum initiating, priming und boostering IBM SPSS Statistics 27.0.1 Crack+ Keygen Code Free Download 2021 - Free Activators. AME 1985. Junk, N.M.: Overburden blasting takes on new dimensions. Coal Age, January, 1972. Konya, C.J.: Initiierungstechnick für Lange Bohrlochladungen. 1974. Konya, C.J. & E.J. Walter: Surface Blast Design. Prentice Hall, 1990. Neil, I.A. & A.C. Torrance: The injuence of primer size on explosive perfonnance. Explosives in Mining Workshop. The Australasian Institute of Mining and Metallurgy. 1988. Smith, N.S.: An investigation of the effects of explosive primer location on rock fragmentation und ground vibration. University of Missoun-Rolla. 1980. Thiard, R. & A. Blanchier: Evolution des systemes d'Amorcage. Industrie Minerale Les Techniques. Fevner, 1984

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CHAPTER 15

Mechanized systems for charging and dewatering blastholes

15.1 INTRODUCTION

man team, oscillates between 500 and 1.000 kilos per shift, depending upon the cartridge sizes. ' AlOng witn tne aeveiopment of 11 Tat>te 15.1, Par~ e w a t e - ~ ~ W h 0 ~ ~ ~ ~ ~ ~ j e c t e d - t 0~ rim d gee c d ahs eaf na rid izf f~e r e n t blasthole diameters are tion, driven by the numerous advantagesthat this offers to indicated. blasting as described below: The chargers, Fig. 15.1, consist of a tubular chamber - Better use of the volume drilled in rock by being with a flip valve at each end, a charging funnel through able to fill the entire blasthole with the explosive and put which the cartrigdes are introduced, a plastic loading it into contact with the blasthole walls. hose and an ensemble of pressure-release pneumatic - Increase in charge density inside the blastholes. valves. - The possibility of forming selective charges by The pressurized air reaches the charger at a maximum varying densities and specific energies along the column pressure of around 1 MPa and with a senes of regulators, length. it is reduced to 0.3 MPa. There is also a safety valve. - The use of bulk or loose-poured explosives which The loading hoses are made of black anti-static plastic, are less costly than cartridged. although in certain special operations metal tubes can be - Less charging time. used. The diameters of these hoses is in function with the - Less personnel required for the chargng operation. cartridge sizes, and its length should not exceed 50 m. At - The possibility of using ANFO, of lower cost than the end of the hose where the explosive emerges there are watergels and emulsions, after dewatering the blast-oles. Cutter blades which slit the cartridges Open, and the force - Better control over explosives and their supply. of ejection drives them to the bottom of the blasthole, All these advantages lower drilling and blasting costs compacting and completely filling it. as the dnlling Patterns can be more Open and the charging The tamping of these units is done manually, unless a tirnes reduced. Robot, which can be attached to the charger, is used, Photo 15.1, which substitutes the Operator in this tedious and tiring work, especially in long blastholes, and allows 15.2 MECHANIZED BLASTHOLE CHARGING a more regular and unitorm charging. SYSTEMS This complement consists of a double-action pneumatic cylinder with a piston that is joined to a pneumatic The mechanized charging systems are classified in two pusher, a front spacer tube and a support that holds the large groups, depending upon whether they are merely aparatus in place against the blasthole. The cylinder has charging instruments or integral systems of manufacture an oscillating movement hat is transmitted by the pusher and charge. to the loading hose which, upon return, allows another In the following, the present day methods for the most cartridge to emerge. The degrees of stemming achieved important types of explosives are described: with the forward movements of the hoses vary between Gartridged slurriesandgelatindynamites--1.4aCcl16. - ANFO and its derivatives (ALANFO and Heavy The use of these chargers is especially interesting ANFO). when the rounds are made up of horizontal blastholes or - Bulk slurries and emulsions. long, inclined upholes. The only limitations are based upon the sensitivity to impact or friction of the cartridges, thus in some instances the velocity has windows repair toolbox crack - Crack Key For U be drastically 15.2.1 Cartridged explosives reduced. Owing to the recent tendency towards using large Pneumatic cartridge charging equipment was developed diameter blastholes. above 100 mm in underground rnin-in Sweden during the decade of the fifties. These units ing the conventional chargers have become useless. allow the charging of blastholes with diameters between However, the largest chargers on the market with hose 35 and 100 mm, obtaining a 15 to 20% increase in centralizers have been used. This way, the cartridges of packing densities when compared to manual tamping, or emulsion or slurry make impact in the center of the even up to 30% if a robot is used. column, reducing the risk of dislodging or falling back of The charging capacities for these Systems, with a twoT

-

\

P -

Mechanized systemsfor churging und dewatering blastholes

k WHEEL

SWITCHER VALVE

TRIP00 MOUNT

FLAP VALVE

Fig. 15.1. Pneumatic charger.

Photo 15.1. Robot charger.

Fig. 15.2. The Half-Pusher technique (Nitro-Nobel).

Table 15.1. Drill bit diameter minlmax (mm) 38-45 40-5 1 [email protected]=

5 1 -76 64- 102

Cartridge diameter (mm)

Hose dimensions (mm) Inside diam. Outside diam.

22 25 29 32 38-40

23.2 27 30 33.5 41

30 34 38 41.5 51

the explosive in upholes. It has also been demonstrated, in experimental tests, that a standoff distance must be maintained between the end of the loading hose and the explosive column. The optimum is 45 cm for 165 mm blastholes, and 60 cm for those of 100 mrn diameter. In order to reduce friction of the cartridges against the inside walls of the hose, reaching high impact energy, water lubrication is recommended.

At present, Nitro-Nobel A. B is developing new equipment for charging upholes with diameters of up to 165 mrn. Of the two systems that are in experimental phase, Charge-Pusher and Half-Pusher, Fig. 15.2 shows the working principle of the latter. W i t h o u t going into detail, this device has a cfimbing mechanism with which, by upward movements, it pushes the charge ahead to the desired position. In each pushing movement an expansion element presses against the walls of the blasthole, retaining the climber in place while the piston rod forces the cartridge upwards which is held in place by a spider-like piece. 15.2.2 ANFO type explosives Charging systems Depending upon the capacities of the containers, the charging systems are classified as follows: - Pneumatic chargers - Charging trucks (Mix-Load and Mix-Pump) The first System is mainly used in underground operations and small surface mines, whereas the second is exclusively for large mines and surface operations. Pneumatic churgers. In these chargers, Fig. 15.3, the explosive is propelled through an antistatic, semiconductive hose by air pressure contained in a metal vessel or pot that is hermetically closed. The design

146

Drilling and blasting of rocks

Fig. 15.3. Pneumatic charger.

SEMl'33tJWIiVC ANFO PRESSVRE VESSEL

AIR HOSE

SEMlCONDUCTlVE PATH T 0 GROVHD

Fig. 15.4. Control of static energy in pneumatic loading.

consists in a funnel-shaped bottom, a cylinder-shaped body and another cone-like shaped of stainless steel that is corrosion resistant. The capacity of these chargers varies from 100 to 750 liters, and when transported they are mounted individually on wheels or upon a vehicle, Photo 15.2. For the latter, the air is pressurized by compressor activated by the motor of the vehicle, which also has recipients of the explosive for the automatic recharging of the vessels, or a prepared space for ANFO sack Storage when the refilling is done by hand. When upholes are loaded in underground operations, the pressure of the vessel must be combined with the Venturi effect created by blowing pressurized air through i I L t h e 4. ~ ü o ~ n o f t hblasthole e MATLAB R2021a Crack + Activation Key Free Download that they will stick and not fall out. The working pressures go from 0.15 to 0.3 MPa in the vessels, and from 0.2 to 0.35 MPa in the injectors. This type of charging equipment is recommended for blastholes with diameters between 26 and 150 mm, unless they are upholes, where the diameters are limited to 100 mm. The yield of the chargers depends upon the interior diameters of the hoses and their length, which should never be over 50 m, and the inclination of the boreholes. The maximum charging capacity oscillates between 2 and 4 tons. Apart from the equipment already described, there are lighter models on the market which can be transported by the Operator himself, with a capacity of from 25 to 40 kg of ANFO. These are used in underground operations to charge blastholes of 28 to 65 mm in diameter and basically consist of small vessels of polyethylene plastic with Straps for their transport. They work with air pressures that go from 0.4 to 0.8 MPa and the charging capacity reaches 7 kglmin. A very importantaSpect,from a the elimination of the large amount of static electricity that is produced. In order to do this, it is necessary to properly connect the loading hose, made of semiconductive material, and properly textaloud free download with crack - Crack Key For U the whole equipment, Fig. 15.4. In the particular case of large diameter upholes, the traditional method of pneumatic loading, consisting of a lower closing plug and a charging tube has been progressi v e l y s y b s t i h t e d by the direct method repre=ed in Fig. 15.5, where the pressure given to the A G ~whichvaries between 0.14 and 0.2 MPa, is sufficient to make the ANFO prills stick to the bottom of the holes giving charge densities of 0.95 to 1 g/cm3. It is of vital importance in this System to have a correct design of the centralizer in the charging tube. If there is water present in the blastholes, the loading can be done after placing a plastic liner. The primers that are connected to downlines or to the detonator are usually placed in the bottom of the blastholes by means of a retainer with help of the loading hose itself. P

Fig. 15.5.Pneumatic loading of ANFO in upholes. P

Photo 15.2.ANFO loader on vehicle.

~~~~~~~~~~~~--

Mechanized systemsfor charging und dewatering blastholes

147

STER/DETONATOR

CENTRALIZER

CONWCTIVE HOSE

"270-340

Fig. 15.7. Types of bulk loading tmcks, (a) pneumatic delivery, (b, C, and d) auger delivery.

KPa AR

Fig. 15.6. Placing the primer in the bottom o f a large diameter uphole -hreI-m&mg.

Photo 15.3. Bulk loading truck with helicodial auger (Courtesy of Amennd-MacKissic, Inc). -

-

Bulk loading trucks. The types of tank irucks used for charging granular ANFO-type explosives are: - Pneumatic delivery System - Auger delivery, Fig. 15.7. The first type of iruck is the most used in Spain at the moment, and it consists of a closed aluminum deposit (AN hopper) with top and bottom V-shaped charge openings to aid in the descent of the explosive towards the conveyer or feed auger which conveys the ANFO for mixing and should be protected by an inverted V-trough which keeps the conveyer from holding the whole weight of the charge.

On the outside part of the deposit is a mechanism which regulates the height of the explosive on the feed auger, as well as a tachometer for the roller motor permittimg variations in the speed, dosifying the supply of the rotary air-lock feeder which discharges the explosive by air pressure through an antistatic hose to the inside of the blasthole. The rotary air-lock feeder is composed of a drum wheel with plastic blades which also keeps the pressured air out of the ANFO bin. The engine of the vehicle is connected to the hydraulic pumps that activate the feed auger and the rotary air-lock

148

Drilling and blasting of rocks

feeder, as well as the air compressor. The loading hose is located in the back of the truck and is about 10 m in length which permits the charging of 3 or 4 blastholes from the Same position when the truck is driven between two rows. The problems with this System are the segregation of the aluminum when ALANFO is used, and the impossibility of loading Heavy ANFO. The second model of truck has, at the bottom of the deposit and lengthwise, a helicoid auger that is also protected by deflecting plates. This auger feeds another vertical one which then delivers the product to a third subhorizontal, pivoting boom auger. This last auger has a length of between 5 and 6 b l a s t h o l e s g h a flexible hose that are 6 or 7 m from the back part of the truck, Photo 15.3. When the truck is between two rows of large-diarneter blastholes, the number of these that can be loaded from one position is limited to one or two. The loading flow of these tmcks varies between 150 and 750 kglmin. A more simple version of this truck is one called Side Auger Discharge System. In the back of the vehicle there is an inclined discharge auger that delivers the explosive to another swiveling boom auger of approximately 3 m in

FUEL OIL TANK

ALUMINUM TANK

AN HOPPER

Fig. 15.8. Deposits on a rnix-load tmck.

- r o t a t i o n ~ w e l l M e Y a t i o nnr Inwenng.gkpxu2meansoL small hand winch. During transit the auger rests in a cradle along the lower left side of the body. During the last few years, there has been a progressive tendency towards trucks having an auger delivery system, owing to the following advantages: - The possibility of charging Heavy ANFO as well as ANFO and ALANFO. - Greater discharge rates, and - Lower loss of ammonium nitrate and distillate vapor around the collars of blastholes.

Photo 15.4. Bowl-type rnix-load tmck.

Mix and load systems Conventional Mix-Load truck. These have a hopper of ammonium nitrate and a tank of fuel oil. If ALANFO or Heavy ANFO is required, there is also a third tank with the emulsion blasting agent or aluminum powder, Fig. 15.8. Moments before loading the blastholes, the two or three components are mixed in the truck, in the desired proportions, and the resulting explosive is then delivered by either of the two systems described previously. The hopper of ammonium-s simi-i already mentioned. In the pneumatic discharge units the fuel is added with the air whereas in those of auger delivery, the fuel oil and other additives are delivered through the vertical auger.

Photo 15.5. ANFO cartridges (Arnerind Mackissic, Inc.).

Bowl-Qpe Mix-Load truck. These trucks are similar to concrete trucks with slight modifications to make them safe for mixing and charging bulk blasting agents. The ~=ompomenLs~ae~p~kced~in_the bowl in adequate provortions and are Gxed accordingly before being discharged. The explosive obtained with these units is characterized by: - Smaller errors in the overall chemical composition - More uniform blending and, therefore, - The energy outputs closely resembles those achieved in laboratories. When compared with conventional mix-load trucks, bowl-type trucks offer the following advantages: - Lower capital cost (about 30%). - Hinher discharge rates, close to 2.000 kglmin. (this is 2.5 to-4 times those obtained by conventionil trucks).

Mechanized systems for charging and dewatering blastholes

-

149

On the other hand, bowl-type tmcks have the following disadvantages: - The truck must be positioned very close to the blasthole for loading, losing time in changing posi-ions. - Only one type of explosive can be charged each time, eliminating the possibility of selective charg-ng. - The quantity of explosive mixed must be exactly the arnount required in order to avoid excess, which must be removed. - The capacity of these tmcks (approxirnately 1 1.5 t) is 25% less than conventional trucks.

which the products are continuously rnixed and are pumped directly into the blastholes through a Aexible hose. This system is quite versatil, as it allows variation in the cornpositions before charging begins. The vehicles have a capacity of between 5 and 15 t and are designed to produce at least two types of explosives, one for bottom charging and one for the column charge. These mobile plants are very safe as the ingredients they carry are not explosive alone and they are mixed only instants before charging. On the other hand, quality control is more difficult than with pump trucks.

Cartridged ANFO When drilling 76 to 190 mm diarneter blastholes and

a) Slurry mix-pump truck These trucks transport the following ingredients: A A oxidizers such as sodiurn nitrate. calciurn nitrate. etc., thickened by gurns. This solution is prepared at a static plant near the minesite. - Ammonium nitrate in pourous prill form (optional). - Liquid fuel-oil or a mixture of solid fuels that are called pre-mixes, with a percentage of aluminum as high as the required weight strength of the watergel. - A cross-linking solution and a gassing agent. The ingredients are put into the tmck's mixing funnel from which they pumped into the blasthole through a flexible hose. The charging rates vary between 80 and 350 kglmin. Thickening and cross-linking starts as soon as the products are mixed so that the watergel is highly viscous by the time it enters the blasthole. The gelling can be controlled by adjusting the crosslinking solution. When the gelling ocurrs too rapidly, purnping difficulties appear, whereas if the gelling time is too long the s1un-y can become diluted or even dissolved before its viscosity permits it to resist the effect of the water present in the blastholes. The loading hose Operator should be certain that there 1s a mnimum agitation oI the explosive

-edr.t-t The packaging of ANFO is done with simple equiprnent consisting in a hopper, a one meter long tube, a feed auger and a piston system that works with pressurized air to achieve the required charge density that can reach 1.1 g/cm3. The yield is around 3 cartridges per minute. 15.2.3 Slurry and emulsion-type explosives Pump trucksfor slurries and emulsions. These tmcks are used for pumping explosives such as slumes and emulsions, and mixtures Password Recovery Bundle+Crack 5.2 With Serial Key [Latest]2021 emulsions with ANFO, whenever the solid phase of these mixtures is not rnore than 35%, because then the product would no longer be purnpable. The physical consistency of these blasting agents is so high that for their pumping the injection of a liquid lubricant along the inside wall of the loading hose is usually necessary to reduce friction and facilitate easy, rapid purnping. It is important to use the lowest feasible arnount of lubricant, and that it contribute to enhancing the effective explosion energy whenever possible.

M i x - p u m p t r u c E A mix-pump truck is a mobilF$plantin

Photo 15.6. Static plant and pump tmck (Nitro Nobel).

Drilling und blasting of rocks HOPPER THERMIC

DELIVERY AUGER THAT CAN BE REGVLATED

CONTROL PANNEL

ALWINUM FEEDER MlXlNG HOPPER

Fig. 15.9.Mix-pump tmck (Ireco Inc.).

when it enters into contact with the water. The proportion of gassing agent should be adjusted to give the sluny the required sensitivity and bulk strength. If the gassing is insufficient, a density in the botton of the column will be produced, reducing the optimum yield of the explosive. On the other hand, excessive gassing can reduce the density of the explosive making it float in the water. The flow of gassing solution can be controlled and can give slumes with a wide range of densities. This possibility is the basis of the technique called Powerdecking. b) MLx-pump trucksfor charging emulsions und mixtures of emulsion/dty phase Inlhis type of trucks, a continuous mixture of a saturated solution of oxidizers is proquced, with an oil phase and some other ingredients in smail amounts. The resulting product is pumped into the blasthole. If a dry phase such as ANFO or ammonium nitrate prills are added to the mixture, it is important to ensure that the emulsion produced does not lose its pumpable qualities.

Drift driving. The motor-pump system used is customarily mounted on a small size vehicle that sometimes has a hydraulically powered man basket enabling the blaster to have access to the back holes, operating the pump with remote control. The most popular types of pumps are those of diaphragm and those with auger which aspirates the explosive from the tanks which have a capacity of up to 500 kg and load it with a pressure of about 0.5 MPa, Photo 15.7. The loading hoses Ge semi-conductive to eliminate static electricity and are introduced into the blastholes up to about 20 cm from the bottom, then pumping the explosive which gradually pushes the hose QuarkCopyDesk Free Download of the hole until the desired charge height is reached. Initiation is usuaily achieved with a primer cartridge and an electric blasting cap, previously placed in the bottom of the hole. The flow rates are comparable to those obtained with' ANFO pneumatic chargers. Depending upon the pump speed, a 3 meter long blasthole with 41 rnm in diameter can be charged in 6 to 10 seconds.

Pump trucks. When pump trucks are~sed~tbe41asring agent is previously manufactured in a static plant near or on the minesite. The advantages of this system are: - The static plant can be located in the Center of the various points of consumption,supplying the sluny or the emulsion in severai trucks, and - The product is of higher quaiity than that produced in the rnix truck. Underground charging of slurried und emulsions Loading blastholes in underground operations has different methods, depending upon the type of work at hand: Photo 15.7. Charging equipment for development headings.

Mechanized systemsfor charging and dewatering blastholes

151

Shaft sinking. Pressurized vessels are used, similar to those used with buk ANFO. The discharge of the explosive through a main hose of 45 mm,reaches a flow rate of 77 kglmin, that is at the Same time divided into 5 flexible hoses of 17 rnm diameter which permits the loading of blastholes in a very short time, Fig. 15.10. Production blasts. In production blasts with large diameter blastholes, more than 125 mrn, there are two different charging situations: upholes and downholes. a) Downholes. They are used in the operational methods of inverted craters and in levelling with long blastholes. Charging is camied out very easily because the explosive is pumped and descends by gravity to the

- & ~ s i ~ - l ~ ) x p r ~ i l i t ~ h e i r a r n p f explosive from the surface as well as in the mines. The exchangeable tanks of explosive are made of stainless steel with capacities of close to 2.000 kg. The pump, hose and the inclination hinge of the tank are hydraulically powered. b) Upholes. The charging of upholes with blasting agents such a slumes and emulsions is even more difficult than with ANFO, as it is first necessary to apply a borehole plug to keep the explosive from falling out and, secondly, the product must have an adequate consistency for pumping. The latter seems to have been solved for emulsions by cooling. As to plugs, there are various systems used. The first ones used a wooden plug with an interior tube that had a check valve with a brass anti-retum ball, Fig. 15.11. Plastic tubes have also been used to make up the explosive columns, and wooden plugs with holes that

photo 15.8. Pneumatic pump (Bill Lane Inc.):

V ALVES

017rrm HOSE

BROKEN MUCKPILE

ing.

DETONATHG CORD

L O A W G PiPE

DELAY LEADS CHECK VALVE

Fig. 15.11. Wooden plug with anti-return check valve.

Fig. 15.12. Tubed charging with wooden plug.

Drilling and blasting of rocks

152

inflatable lances have been tned with success. These devices have two inches of flexible hose with a rigid tube on one end, upon which an inflatable rubber bladder is mounted and inflated by pressurized air, Fig. 15.14. The advantages of this System are its simplicity and low cost. It is quick and efficient, having been successfully tned in blastholes of up to 115 mm in diameter.

LIOMD FOAM CONTAHER

15.3 BLASTHOLE DEWATERING SYSTEMS stholes widens th

- Air operated pumps and, - Submergible impellent pumps. The first are applied to small and medium diameter (63 to 172 rnm) blastholes with a maximum bench height of about 15 meters. Pressunzed air supplied by compressors of the dnlling rigs is used, which is introduced into the blastholes through a flexible plastic hose. In some equipment, Fig. 15.15, the pushing effect is achieved when the obturator'or plastic closing sleeve expands when the air pass through. The pumping rates are approximately 50 to 80llmin. The second dewatenng System has a submergible impellent pump and a reel for the hose. The unit can be installed on a jeep-type vehicle or on the back of an ANFO charge truck. The reel and pump are hydraulically driven and the hydraulic fluid tubes of the latter arejoined inside the water hose, enabling the whole ensemble to be lowered into the blasthole at of approximately m/s. To avoid stoppageproduced by coarse waste material, the pump should by placed at a few centimeters from the bottom. - Once the dewatenng of the blastholes is finished, the mechanism of the drum wheel reverses to clean it of sand and waste that might have entered. These units can dewater blastholes in a few seconds,

Fig. 15.13. Polyurethane foam uphole plug.

-R,MT

N F L A T A B ~ ~B L A D ~ P

EUULS~~~ HOPPER

Fig. 15.14. Charging of a rcpumpablc emulrion in an uphole with an inflatable lance. WATER DISCHARGES FROM HOSE

AIR SUPPLY

SLEEVE

Photo. 15.9. Hydraulic dewatenng pump (Swanson Eng. Inc.)

W

Fig. 15.15. Pneumatic pump.

SLEEVE W L A l

Mechanized systernsfor charging and dewatering blastholes

153

Table 15.2. Flow (Ilmin)

Total elevation height (m)

a Ipm, I I MPa

Table 15.3. Blasthole diameters Imm)

Ipm, 13 MPa

Ipm, 13 MPa

Nominal diameter of plastic liner Imm)

owing to the strong pumping rates, Table 15.2, permitting use of the plastic sieeves and charging before the Water enters again. The type of plastic used should be flexible and resistant so that it will not tear when in contact with the rock, recommending h a t it be of 600 to 1.000 gage, depending upon each case. The liners Or plastic sleeves, which the bulk explosive, should have a diameter that is slightly more than that of the holes, Table 15.3, so that the volume of rock drilled can be used to maximum advantage and achieve a good adaptation of the charge.

Amerind-Mackissic, Inc.: Technical fnformation 1986 Bauer, A.: Trends in Explosives, Drilling und Blasting. CIM Bulletin, February, 1974. Bauer, A. et al.: Drilling und Blasting in Open Pits und Quarries. 1980. Bill Lane, INC.: Lane Pump. 1986. Champion, M.M.: Explosives Loading Equipment. Underground Mining Methods Handbook. AIME, 1982. Dannenberg, J.: Contemporary history of industrial explosives in America. Day, F!R. & D. K. Joyce: Lwding explosives in large diameter upholes. SEE. 1988. Giorgio, C.: Evolucibn de los Explosivos en los Treinta UltimosAEos. Rocas y Minerales.

Photo 15.10. Preparation of the primer charge in a plastic sleeve.

Gustafsson, R.:Swedish Blasting Technique. SPI, 1973. Hagan, T.N.: Charging and Dewatering Equipment. AMF. 1985. Irvine, J.C.: Pillar recovery at the Pea Ridge Mine. Mining Engineering. September, 1976. Jerberyd, L.: Half-pusher - A method to charge large diameter upholes. Swedish Mining Research Foundation, 1985. Legorburu, V.: Sistemas Mecanizadas de Carga de Explosives en Proyectos Subterrhneos. I Seminario de Ingenieria de Arranque de Rocas con Explosivos en Proyectos Subterrineos. Fundaci6n G6mez-Pardo, 1986. Lopez Jimeno, C.: Desagüe y Drenaje de Explotaciones a Cielo Abierto. IV Curso sobre Mantenimiento y Servicios en Mineria a Cielo Abierto. Fundaci6n G6mez-Pardo. 1984. _ M a i r s~ B B T ~ + ~ u & i ~ ~ - e x p W n underground. CIM Meeting, 1985. Michaud, F! & A. Laveault: Essai d'un Systeme de chargement en vrac pouremulsions aux Mines d'Amiente Video Editor - Crack All Windows/Mac OS Software Full Version. SEEQ, 1984. Nitro-Nobel: ANFO Mixing and Charging Equipment. 1986. Swedish Methodsfor Mechanized Blasthole Charging. Puntous, R.: Mkthodes Modernes de Chargementdes Explosifs. Industrie Minerale - Les Techniques. Fevrier, 1984. Sharpe, K. R.: Plugging and loading upholes at La Mine Bosquet. CIL Inc. 1986. Swanson Engineering Inc.: Blasthole dewatering - Cuts costs. Union Espaiiola De Explosivos: Tendencias Actuales en el Almacenamiento.Traßspo~e~arga-Meeaninida-deExptmivos-en~aMineria a Cielo Abierto. Jornadas Tecnicas, UEE. VME-Nitro Consult, Inc.: Pneumatic Cartridge Charging. Yetter, A. & R. Malo: The evolution of loading 4.5 inch diameter upholes at Kidd Creek No. 1 Mine. SEE. 1984.

CHAPTER 16

Mechanisms of rock breakage

16.1 INTRODUCTION

increase the surface area by crushing, it has a slower rate of stress decay than (A).

theconditionspresencharactenzedbytm-phaes2onsumes of action: Ist. phase. A strong impact is produced by the shock wave linked to the Strain Energy, during a short period of time. 2nd. phase. The gases produced behind the detonation front come into action, at high temperature and pressure, carrying the Thermodynamicor Bubble Energy. Since the decade of the fifties, many theories have been developed to explain the behavior of rocks under the effect of an explosion; even nowadays it still remains a problem to be solved and defined in the technology of application of free download avg antivirus full version with crack - Crack Key For U to breakage. Without entering into detail, the different mechanisms of rock breakage that have been identified in blasting up to now are exposed in the following paragraphs. 16.2 ROCK BREAKAGE MECHANISMS In the fragmentation of rocks with explosives at least eight breakage mechanisms are involved, with more or less responsabiXty, but they an exert influence upon the - results of the blastings. 16.2.1 Crushing of rock In the first instants of detonation, the pressure in front of the strain wave, which expands in cylindrical form, reaches values that well exceed the dynamic compressive strength of the rock, provoking the destruction of its intercrystalline and internranular structure. The thickness of the so cailed crushed zone increases with detonation pressure of the explosive and with the coupling between the charge and the blasthole wall. According to Duvall and Atchison (1957), with high strength explosives in porous rocks it might reach a radius of up to 8 D, but it is normally between 2 and 4 D. In Fig. 16.1. the variations in compressive stresses generated by two fully-coupled charges are shown. The crushing of the rock is produced at a pressure of 4 GPa, so the curve of the explosive (A) which produces a tension of 7 GPa on the blasthole wall has a very sharp decrease in peak stress due to the large increase in surface area during the pulverization of the rock. As explosive (B) does not

almost 30% of the energy transported by the strain wave, only contributing a very small volume to the actual rock fragmentation, around 0.1% of the total volume corresponding to the normal breakage per blasthole. Therefore, there is no incentive to use high explosives that Driver Booster 7.4.0.742 Pro License key + Crack Free high stresses on the blasthole walls: which would even make it advisable to decouple the charges and increase EB in detriment of ET. 16.2.2 Radial fracturing

During propagation of the strain wave, the rock surrounding the blasthole is subjected to an intense radial compression which induces tensile components in the tangential planes of the wave front. When the tangential strains exceed the dynamic tensile strength of the rock, the formation of a dense area of radial cracks around the crushed Zone that surrounds the blasthole is initiated, Fig. 16.2. The number and length of these radial cracks increase with: 1. The intensity of the strain wave on the blasthole wall or on the extenor Iimit ot the crushed z m d 2. The decrease in dynamic tensile strength of the rock and the attenuation of the Strain Energy. Beyond this inner Zone of intense fractunng, some of the cracks extend noticeably and are symmetrically distributed around the blasthole. The propagation velocity of the cracks is from 0.15 to 0.40 times that of the strain wave, although the first microcracks are developed in a very short time, around 2 ms. When the rock has natural fractures, the extension of the cracks is closely related to these. If the explosive columns are intersected lengthwise by a pre-existing crack, these will Open with the effect of the strain wave and the development of radial cracks in other directions will be limited. The natural fractures that are parallel to the blastholes, but at some distance from them, will interrupt the propagation of the radial cracks, Fig. 16.3. 16.2.3 Rejlection breakage or spalling When the strain wave reaches a free surface two waves are generated, a tensile wave and a shear wave. This occurs when the radial cracks have not propagated farther

Mechanisms of rock breakage

Fig. 16.4. Reflection of a wave upon a cylindncal cavity.

Fig. 16.1. Variation of peak compressive stress with distance from OmsihotewatUHaga~~).

UD COMPRESSION TENSION

Fig. 16.2. Radial fracturing.

FRACTURES CAUSED B Y INTERNAL SPALLIN

X)(NT PLANE

ZONE OF- DENSE RADIAL CRACKlNG

-

-

WATER FILLED JOINT PLANE

/ RADIAL CRACKS A R R E S T E D ~ PREMATURELY AT JOlNT

Fig. 16.3. Radial fracturing and breakage through reflection of the strain wave.

than one third the distance between the charge and the free face. Although the relative magnitud of the energies associated with the two waves depends upon the incident angle of the compressive strain wave, the fracturing is usually caused by the reflected tensile wave. If the tensile wave is strong enough to exceed the dynamic strength of the rock, the phenomenon known as spalling will corne about, back towards the interior of the rock. The tensile

strengths of the rock reach values that are between 5 and 15% of the compressive strengths. The front of the reflected Altium Designer 20.2.6 Build 244 Crack is more convex than that of the incident wave, which means that the dispersion index of the tensile wave energy is much larger when the surface is cylindncal, such as that of the central blasthole of a cut instead of when there is a plane as Altium Designer 20.2.6 Build 244 Crack bench blasting, Fig. 16.4. This mechanism does not contribute much to the global fragmentation process, estimating that eight times more explosive charge would be necessary if rock were to be fragmented solely by reflected waves. However, in the inner discontinuities of the rock mass which are close to the charge, less than 15 D, and are not infilled with rneteorized material, the effect of the reflected waves is more important due to the difference in impedances. When excavating inclined ramps or shafts by blasting, it must be checked that the empty blastholes are not be filled with water in order to achieve the benefits of this mechanism of breakage.

After the strain wave passes, the pressure of the gases cause a quasi-static stress field around the blasthole. During or after the formation of radial cracks by the tangential tensile component of the wave, the gases start to expand and penetrate into the fractures. The radial cracks are prolonged under the influence of the stress concentrations at their tips. The number and length of the opened and developed cracks strongly depend upon the pressure of the gases, and a premature escape of these due to insufficient stemming or by the presence of a plane of weakness in the free face could lead to a lower performance of the explosive energy. 16.2.5 Fracturing by release-of-load Before the strain wave reaches the free face, the total energy transferred to the rock by initial cornpression varies between 60 and 70% of the blast energy (Cook et al. 1966). After the compressive wave has passed, a state of quasi-static equilibrium is produced, followed by a subsequent fall of pressure in the blasthole as the gases escape through the stemming, through the radial cracks

Drilling und blasting of rocks

156

t:Xmr

I=O

and with rock displacement. The stored Stress Energy is rapidly released, generating an initiation of tensile and shear fractures in the rock mass. This affects a large volume of rock, not only in front of the blastholes but behind the line of the blast cut as well, having registered damages in up to dozens of meters away, Fig. 16.5. 16.2.6 Fracturing along boundaries ojmodülus contrast of shearfracturing In sedimentary rock formations when the bedding planes, joints etc., have different elasticity modulus or geomechanic Parameters, breakage is produced in the separation planes when the strain wave passes through because of the strain differential in these points, Fig. 16.6.

Fig. 16.5. Separation of layers of compressible medium by release-of-load.

t=~xrnr

where n, is the relationship between the impedance of the explosive and that of the rock:

t h r o u L rock mass (m/s), D. = Rock density (g/cm3). This means that the explosive wave is better transmitted to the rock when the impedance of the explosive is close to that of the rock, given that n, will tend towards 1, while PT will simultaneously tend towards PD. The pressure of the wave inside the rock decreases with the law of exponentials, so the radial stress generated at a determined distance will be:

16.2.7 Breakage byflexion During and after the mechanisms of radial fracturing and lightweight csv editor - Crack Key For U, the pressure applied by the explosion gases upon the material in front of the explosive column makes the rock act like a k a m embedded in the bottom of the blasthole G d in the stemming area, producing the deformation and fracturing of the Same buy the phenomena of flexion, Fig. 16.7. 16.2.8 Fracture by in-flight collisions The rock fragments created by the previous mechanisms and acceleratedby the gases are projected towards the free face, colliding with eachother and thereby producing additional fragmentation which has been demonstrated by ultra-speed photographs (Hino, 1959;Petkof, 1969). 16.3 TRANSMISSION OF THE STRAIN WAVE THROUGH THE ROCK MASS

-Asshown-befo~ehand&theDetonationessure can be expressed by the following simplified equation:

where: o = Radial compressive stress, PB = Pressure on the blasthole wall, r, = Radius of the blasthole, DS = Distance from the Center of the blasthole to the point in study, X = Exponent of the law of absorption which, for cylindrical charges is near 2. If the wave encounters diverse material in its path, with different impedances and in correspondance with separating surfaces that can be in contact or separated by air or water, the transmission of the strain wave will be govemed by the ratios of the acoustic impedances of the -dlPf=es-of rmercparmf-transferred in the material and at the Same time some is reflected back, as a function of the ratio. When the impedances of the mediums are equal (pr2 X VC2 = pri X VC,), a large part of the energy will be transmitted and the rest will be reflected, arriving at the lirnit when (pr2 X VC2
.--_

P -

#

where: PD = Detonation pressure (kPa), p, = Explosive density (g/cm3),VD SparkoCam Crack 2.7.3 With Full Serial Number [2021] Detonation velocity (mls). The maximum Pressure Transmitted to the rock is the equivalent of: PT,, =

L

-PD 1 + n,

n, =

Pri

X

'CI

Pr2 X 2" the following will be obtained:

Mechanisms of rock breakage I BED X

EXPLOSIVE CHARGE

I

Fig. 16.6.Shear Fracturing (Hagan).

MSCONTINUITY

where: PI = Pressure of the incident wave, PT= Pressure of the transmitted wave, PR = Pressure of the reflected wave.

16.4 ENERGETIC YIELD OF THE BLASTINGS Itaneously in a few miliseconds, associated with the effects of the strain wave which transports the Stress Energy, and with the effects of the explosion gases or Bubble Energy, Fig. 16.8. The total energy developed by the explosive and measured by the method proposed by Cole can thus be expressed as the sum of these two components.

fare.ag.roupofelementalmmwh&pe

ETD = ET Fig. 16.7.Mechanism of breakage by flexion.

+ EB

where:

The estimates canied out by Hagan (1977) have demonstrated that only a 15%of the total energy generated in the blasting is used as a working tool in the mechanisms of rock fragmentation and displacement. R a s c h e f f a n d G v 7 7 F h a v e esta6IiSEd a model that theoretically distributes the energy, as represented in Fig. 16.9, from tests made upon cubic blocks of rock placed underwater in swimrning pools. These investigators assure that approximately 53%of the explosive energy is associated with the strain wave. This value depends upon the conditions of the experiment and very different results can be found that go from 5 to 50%of the total energy, depending upon the various types of rock that are to be fra~mentedand the explosives used. Therefore, in hard rock the Strain Energy of a breaking explosive is more important in fragmentation than the Bubble Energy, and the contrary is true for soft, porous or fissured rocks and in low density explosives. From the tests canied out by Rascheff and Geomans, Table 16.1 s u k a r i z e s the energy distribution of the strain wave. It can be observed that in conventional bench blastings a large part of the strain wave energy is transformed into seismic energy which causes ground vibrations to which some of the gas energy must be added. The data exposed are quite in accordance with that Photo 16.1. Rock breakage by flexion.

Drilling und blasting of rocks PHASE

I

FREE FACE ORIGiNAL

Fig. 16.8. Summary of the breakage mechanisms.

PO R

-

U. -

- ~slll

nm

p i e p e s l v. m bhmlho* w i l

p e s ~ of a expindhp p i s s i rpon hipmonled r a *

-snmgm

01

aiifui w a t w wu

Fig. 16.9. Distribution model of the explosive energy in ablast.

W '

a

3

V)

VOLUME

Fig. 16.10. Pressurelvolumediagram of explosion product gases showing partition of energy in blasting.

1

I

Mechanisms of rock breakage Table 16.1. Distribution of shock wave energy. Granite block Conventional with infinite bench blastconfinernent ing of granite Pulverization 15% 15% Primary radial cracking 3% 3% 0% 16% Crack extension Energy transrnitted 82% 34%

Granite block submerged in water 15% 2% 39% 22%

Useful energy

56%

18%

34%

Table 16.2 Zone

1 + 2 + 3 +4 + 5

159 Energv Kinetic component of shock energy Strain component of shock energy Brissance energy Energy released during crack propagation Fragmentationenergy Strain energy in burden at time gases escape Blast energy Heave energy Total available energy or absolute strength value

pressed by the gas in ihe cracks with a strain energy obtained by other investigators such as Mancini and stored in ihe rock (Zone 4). This energy has little Occella. Ic snouia no-~gorrerrnizittcter co o m n from Zones 2 and 3 is the most useful in - c ~ r i r ~ ~ e b ~ ~ t - i s R o ~ ~ n e c eThes energy s n ~ rock blasting and is called Fragmentation Energy. to fragment the rock but also to cause swelling and At ihe time of escape, some of the energy in the gases displace it a dete&ned distance. For ihis reason, in ihe (Zone 5) moves ihe burden and represents fonelab 9.1.82 registration code - Free Activators energy. latter stages the gases also play a Garden Planner 3.7.93 Crack + License Key Free Latest role. The rest of this energy is lost as heat and noise in the Lowends' used a simplified model of explosivelrock escaping gases. interaction to describe the partition of explosive energy in Alihough this model of energy partition overthe process of rock blasting. The energy is partitioned simplifies the blasting process, it gives valuable insight into different zones h a t are related to the pressurel into where ihe energy goes during the various phases of volume expansion of ihe gases during ihe different the process. It also provides approximate comparisons of phases of blasting. An illustration of ihis partition of ihe magnitude of ihe energy fractions used in the various energy is given in Fig. 16.10. phases of the blasting process as the explosive gases The energies associated wiih the different zones given expand from the initial pressure in the blasthole to atrnosin the figure are, as follows: pheric pressure. Not all of ihe availableenergy is useful in When ihe explosive detonates in the blasthole, the high fragmentation and heave. It may be possible to improve pressure gases at the initial or explosion state P3 send a the efficiency of the blasting process by using explosives, shock wave into the rock. The strains from this shock wheiher ideal or not, ihat are designed to keep energy near the blasthole are greater than the dynamic compresslosses at a minimum. ive and shear strength of the rock. They cause v q i n g amounts of rock compression and crushing in ihe sur: rounding area of the blasthole depending upon ihe REFERENCES strength and stiffness of the rock. With rock compression and crushing ihe volume of the blasihole increases and Ash. R.L.: The Mechanics qf-e. Pit and Q u a q no. 56. ihe pressure decreases until ihe strain in ihe rock balances 1963. Duvall, W. I. & T.C. Atchison: Rock Breakage by Explosives. U.S. B.M. the pressure. This is shown as74 on ihe pressurelvolume RI 5356,1957. curve of Figure 16.10, and is called blasihole equilibrium Hagan, T.N.: Rock Breakage by Explosives. Proc. National Syrnpostate. During the expansion, the work being done by ihe sium on Rock Fragrnentation. Australian Geornechanics Society. explosive is called bnssance energy and consists of the. Adelaide, Feb. 1973. Hagan, T.N. & G.D. Just: Rock Breakage by Explosives. T h e o q strain energy stored in the rock (Zone 2) and ihe kinetic Practice und Optimization. Proc. Congress International Society of energy of the shock wave (Zone 1). The kinetic shock Rock Mechanics. Vol. 11, 1974 energy is essentially lost as useful work during ihe blastHagan, T.N.: Rock Breakage by Explosives. 6th Symposium on Gas ing process and appears as crushed rock surrounding ihe Dynarnics of Explosives and Reactive Systems. Stockhlom, 1977, b l a s t h n l e a n d aq s e i s m i c p a p a g a i e d h LL ~a n d J A L L R & E w r e a & a d e m a p p r a a I n p e a p i h l n ~ r design und anulysis. CIM Bulletin. June, 1972. ground. Lopez Jirneno, C.: Los Mecanismos de Fragmentacibn con Explosivos The strains in the rock coming from ihe residual blasty la Injluencia de las Propiedades de las Rocns en los Resultados hole pressure P4 cause fracture. The explosion product de las Voladuras. I Serninario de Ingenieria de Arranque de Rocas gases enter at least the cracks existing between the hole con Explosivos en Proyectos Subterriineos. Fundation GornezPardo, 1986. and the free face, resulting in fragmentation and possibly Rascheef, N. & I? Goernans: Contribution 6 l'etude quantitative de contributing to the heave. When ihe gases reach the free l'energie consommie dans la fragmentation pur explosif. 0ct.face through the burden, the process ends more or less Dec., 1977. abruptly. The pressure of the gases at escape is shown at Thurn, W.: Quantite d'energie requisepour L'extraction et lafragmentation des roches au moyen d'explosives. Explosifs, 1972. P5 in Figure 16.10. During escape, the burden is comP

CHAPTER 17

Rock and rock mass properties and their influence on the results of blasting

17.1 INTRODUCTION ,

-

The matenals of which rock masses are maae possess ~ ~ ~ ~ ~ ~ h a t origin and of the posterior geological processes which have affected them. The whole of these phenomena make up a certain environment, a particular lithology with heterogeneities caused by the added polycrystalline minerals and by the discontinuities of the rock matrix (pores and fissures): and by a geological structure in a characteristic state of Stress, with a large number of structural discontinuities such as bedding planes, fractures, diabases, joints, etc. 17.2 ROCK PROPERTIES

Persson et al., 1970) arriving at values that are between 5 and 13 times more than the static. . W nen me ~ y ~ t w mn m &n r ip 9 ec i ~v p 't r r ~ n g t ~ 4 surrounding the blasthole wall is produced by collapse of the intercrystalline structure. However, this excessive crushing does little to aid in fragmentation and gravely reduces the strain wave energy. Therefore the following is recommended: - Explosives that develop blasthole wall strain energy that is lower than or equal to RC must be chosen. - Provoke a variation in the Pressure-Time curve (P t) by decoupling the charge in the blasthole. These points are of maximum importance in perimeter or contour blastings. The powder factors required in bench blastings can be correlated with the compressive strength, as indicated in Table 17.1 (Kutuzov, 1979). m

m -

The densities and strengths of rocks are normally quite well correlated. In general, low density rocks are deThere are two types of porosity: intergranular or formaformed and broken quite easily, requiring relatively low energy factors, whereas dense rocks need a higher quanttional, and that of disolution or post-formation. ity of energy to achieve a satisfactory fragmentation, as The first, which has a uniform distribution in the rock mass, provokes two effects: d and swelling. well as a ~ o o disdacement In high density rocks, the following measures should - Attenuation of the strain wave energy. be taken to ensure adequate hegvy energy: - Reduction of the dynarnic compressive strength and, - Increase the drilling diameter in order to elevate the consequently, an increase in crushing and percentage of where VD is the detoblasthole pressure, PB = k X VD2, fines. nating velocity of the explosive. The fragmentation of very porous rocks is carried out, - Reduce the Pattern and modifj the initiation sealmost exclusively, by bubble energy, so the following quence. recommendations should be observed: - Improve the effectivity of the stemming to increase - Use explosives with a high EBIET ratio, such as the time of gas performance and make certain that they ANFO. eseapeheugkchefr e e f a ~ ~ ~ s t e a B O ~ u g U -~ I kn cmr e~a s e _ E B a t t h e o o f E T y decoupling the charges and the initiation Systems. ming. - Use explosives with high bubble energy EB. - Maintain the explosion gases at high pressure with an adequate stemming height and type. - Maintain the burden equal for each hole by using 17.2.2 The dynarnic strengths of the rocks various free faces. The static compressive RC and tensile RT strengths are The post-fomation porosity is caused by spaces and initially used as indicative parameters of the suitability of cavities that result from the disolving of the rock material the rock for blasting. The Index of Blastability was by underground water (karstification).The empty spaces defined (Hino, 1959) as the relationship 'RC/RT1, the are much larger and their distribution is much less unilarger the value, the easier the fragmentation. form than in the intergranular porosity. The rational treatment of the existing problems require In rock of volcanic origin it is also frequent to find a taking into consideration the dynamic strengths, as these large number of cavities formed during its consolidation. increase with the index of the charge (Rinehart, 1958: The cavities that are intersected by blastholes not only

161

Rock and rock muss properties Table 17.1. Rock classificationaccording to their facility of fragmentatiin by explosives in Open pit mines. Powder factor Mean distance between natural Uniaxial compressive rock strength (MPa) Class limit (kglm') Average value (kglm') fractures in rock mass (m)

r

aI .-encqnnfiheblasr,eqecid&if

loosepacked or pumpable explosives are used, Fig. 17.1. If the boreholes do not intersect the cavities, the yield of the blast also descends because: - The propagation of radial cracks is intermpted by the cavities. - The rapid fall in pressure of the gases as the blastholes intercommunicate with the cavities, halting the opening of the radial cracks, while the gases escape towards the empty spaces.

As the rocks do not form an elastic media, part of the strain wave energy that propagates through them is converted to heat by diverse mechanisms. These mechanisms are known as intemal friction or specijic darnping c a p a c i ~SDC, which measure the ability of the rock to attenuate sirain waves generated by the detonation of the explosive. SDC varies considerably with the type of rock from values of 0.02-0.06 for granites (Windes, 1950; Blair, 1956) up to 0.07-0.33 for sandstones. SDC increases with porosity, permeabillity, joints and water content of the rock. It also increqses considerably with the meteorized levels in function with their thickness and weathering. The intensity of the fracturation by the strain wave increases as the SDC decreases. Therefore, watergel type explosives are more effective in hard and crystalline formations than in soft and decomposed materials (Cook, 1961;Lang, 1966). On the other hand, in the latter, ANFO

Rock density (tlm3)

.

iated ana protectea. l t 1s recommende -~e&o~~beuse& The failure of one of the detonators could considerably affect the results of the blast. 17.2.6 The cornposition of the rock and the secondary dust explosions The secondary dust explosions usually occur in coal mines and in highly pyritic areas such as underground meta1 mines, and are more frequent each day due to the use of large diameter blastholes. The first charges'fired create, on one hand, a high quantity of fines which are thrown into the atmosphere and, on the other, agitate the dust deposited on the sidewalls and roof of the excavation with the airblast and vibrations. If the energy of the gases from the last charges is sufficiently high, it could ignite the concenirated dust causing secondary explosions with devastating effects upon the ventilation installations, doors, mobile equipment, etc. The probability of secondary explosions can be reduced by taking some of the following steps: - Eliminate the use of aluminized explosives since the particles of A1203at high temperatures in the detonation products are potential ignition centers. - Select an explosive and blasthole gqmetry for bum cuts which produce coarse material. - Stem all blastholes with sand, clay plugs or water. - Create a cloud of limestone or another inhibitor in front of the face by exploding a bag of said material with a detonator fired some miliseconds before the blast.

isb~sade~eventhoughitsstrainenergyis-

-

Waskth~~md-Boo~eex~a~tior

lower.

quently to remove the deposited dust. - Fire the blasts after evacuating all personnel from the mine.

The leakageor shunting of electrical current can occur when the detonators are placed in blastholes that are in rock of certain conductivity, such as complex sulfides, magnetites, etc., especially when the rocks are abrasive and water is present near the round. The measures that should be taken to avoid these problems are: - Check that the cables of the detonators are well enclosed in plastic and, - That all the connections of the circuit are well insu-

17.3 PROPERTIES OF THE ROCK MASS 17.3.1 Lithology The blasts in zones where an abrupt lithological change is produced, for example in waste and ore and, in consequence, a variation in the strength of the rocks, the design must be reconsidered. One of the two following methods could be used:

Drilling and blasting of rocks

162

Fig. 17.1. Correct use of a bulk explosive charge in ground with large cavities.

RELAY

SOFT ROCK

DETONATING CORD

---+-

-

Fig. 17.2. Recommended change in blasthole pattem of V type blast at contact between waste and ore. Photo 17.1. Blocks with columnar geometry in basaltic formations. STRONG UNFISSURED BOULDERS O F LIMESTONE

SOFT. PLASTIC ACTING MATERIAL (SOIL. GRAVEL. CLAY)

Photo 17.2. Intenselyjointed limestone rock mass.

-a+Eq&a1~m**fOfre-~

Fig. 17.3. Typical cases of lithological changes with contact between competent rocks and plastic matenals (Hagan).

. .

in the unitary charges. b) Different Patterns with equal charges per hole. This placement is usually adopted maintaining equal burden, Fig. 17.2, as the introduction of a different S X B pattern for each Zone would entail a more complex dnlling and the newly created face may be stepped. The serni-horizontal stratiform Altium Designer 20.2.6 Build 244 Crack presented by some very resistant layers may lead to a peculiar type of blastings in which the charges are placed in the blastholes and completely confined at these levels. It is also recommended that the pnmers of the explosive columns coincide with the strongest levels in order to obtain maximum effect from the strain energy.

Rock and rock muss properties Table 17.2. Absorption of strain wave energy by joints 1. Small(< 20%) 2. Slight (20-40%) 3. Medium (40-80%) 4. Large (> 80%)

163

Joint width (mm)

Natureof joints

('4) 0 (B) 0-4.0 (A) Up to 0.5 (B) Up to 4.0 0.5-1 .O (A)O.l-1.0 (B) 1.0

(A) Tightly stacked (B) Cemented with material of acoustic impedance close to that of the main rock (A) Open joints filled with air or water (B) Cemented with material of acoustic impedance 1.5-2 times less than that of main rock Open joints filled with air or water (A) Joints filled with loose and porous material (B) Open joints filled with loose, porous material, air and water

When two matenals of very different strengths come Table 17.3. Possible combinations of spacing between blastholes (S), joints (J), and maximum adrnissable block size (M). into contact as, for example, a competent limestone with Case Js:S Js:M S:M Fragmentation % of very plastic clays and, if the blastholes pass through these sensitive to Iormations, a great 105s of energy associated with a drop aomei backupper keygen - Crack Key For U charge ~ p r e ~ s e ; t p e o f g m w i t t a ap ~ ~ g Yes Medium S>M Js>M I J,>S rapid deformation of soft material and, as a consequence, Yes Low S<M Js>M Js>S 2 poor fragmentation, Fig. 17.3. Yes Low S<M Js<M 3 J,>S In order to increase the yield of the blasts in these No High S>M Js>M 4 J,<S No Low S<M Js<M J,<S 5 cases, the following is recomrnended: No Low S > M J < M 6 J< S - Stem with adequate material the zones of the blastholes that are in contact with or near plastic material. - Use explosive charges that are totally coupled to the competent rock with a high detonation velocity and ET/ OVERBREAK ZONE b BACK-ROW BLASTHOLE EB relationship. JOINT OF PREVIOUS BLAST PLANES NEXT FACE - Place the primers in the rniddle of the hard rock to \ increase the resulting strain wave that acts upon both sides. - Avoid premature escape of gases to the atrnosphere insuring that both the sternming height (at least 20 D) and the size of the burden are correct at the top of the blastholes. 17.3.2 Pre-existingfractures

~

Fig. 17.4. Excessive toe burden caused bv stmcturally. - controlled backbreak Zone and face angle. All rocks in nature have some type of discontinuity, microfissusandmacrofissiares, which deckkelyY influence the physical and mechanical properties of the that might arise are indicated, taking into account the rocks and, consequently, the bbting results, Photos 17.1 inclination of the discontinuititesand the relative angle of and 17.2. the strike and dip. The areas of discontinuity can be varied: bedding Special precautions should be taken when the discontiplanes, planes of lamination and primary foliation, planes nuities are subvertical and the direction of the shot is of schistose and slate, fractures and joints. normal (parallel) to theirs, because overbreak is frequent The discontinuities can be tight, Open or filled and, for behind the last row of blastholes and inclined dnlling this reason, can exhibit different degrees of explosive becomes necessary to maintain the burden dimension in energy transmission. Table 17.2. The walls of these disthe first row of the round. Fig. 17.4 and Photo 17.3. ~ ~ i e ~ - ~ v e f t ~ w f a e s +entkie&&ni-m7he t t p e ~ t h ~ jöinrsystem~a-an-xnsie n waves may be reflected, suffering attenuation and dispersmaller than 30°, it is recommended that the blastholes be sion. normal to said planes in order to increase the yield of the The fragmentation is influenced by the spacing beblasts. tween blastholes S, the separation between joints J and In tunnel excavations, the structural characteristics the maximum admissible block size M. In Table 17.3, largely condition the geometry of their profile, almost various possible combinations are indicated, as well as rectangular if the rocks are massive and with a curved their repercussion upon the percentage of forseen arch if the rock is more unstable. When the discontinuiboulders. ties are normal to the tumel's axis, the blasts usually have Another aspect of the design of the blastings is referred good results. Fig. 17.5a. If the bedding or the discontinuito as geostructural control of the rock mass, which refers ties are parallel to the axes of the tunnels, Fig. 17.5b, to the relative orientation of the face and break direction frequently the advances are not satisfactory and the faces of the round with respect to the strike and dip of the Strata. are uneven. When the bedding has an oblique direction In Table 17.4, the forseen results for the different cases with respect to the axis of the tunnel, there will be one "

164

Drilling and blasting oj'rocks

Photo 17.3. Face of a blast that coincides with a bedding plane.

side on which it is easier to blast, such as in the case of Fig. 17.5c, the left side. On the other hand, very laminated rocks with high schistosity and fissurization rese-a-4 deep pulls of up to 6 m are possible with this type of cut. When V cuts are used in sinki~grectangular shafts, the best results are obtained when the discontinuities are parallel to the line joining the bottom of the V cut, Fig. 17.6.

When the stress fields, either tectonic andlor gravita~nnai-(non-hydrostatic)-ac~e-fracture-pattem-gen~ rated around the blastholes can be influenced by the non-uniform stress concentrationsaround the same. In hornogeneous massive rock, the cracks which Start to propagate radially frorn the blastholes tend to follow the direction of the principai stresses. Therefore, when driving shafts in rock masses with a high concentration of residual stresses, as in the case of Fig. 17.7, the firing sequence in the blastholes of the cut should be adapted to this situation. If in the presplitting planes of the planned excavation the influencing stresses are normal to the same, the obtained results will not be satisfactory unless the spacing is considerably reduced or a pilot excavation is carried out

Fig. 17.5. Relative directions of the beds with regard to the axes of the tunnels.

to relax the mass and free the stresses, and presplitting is substituted for smooth blasting. 17.3.4 Water content Porous and intensely fissured rock, when saturated with water, usually Pose certain problems:

Rock und rock muss properties Table 17.4. Design of the blasts with attention to geostmctural control.

Inclination of the strata a =0°

Angle between the direction of the Strata and the blast break Indifferentbreak direction

3 = 45" = 135" = 225' = 315" ß = 90" = 270"

face Variable fngmentation. sawtooth face Most favorable direction

Good Unfavorable Not very favorable Acceptable Very favorable

(Sirnilar to the previous case hardness is determining factor)

45" < a < 90"

MAJOR. PHYSICAL DlSCONTlNUlTlES

SHAFT PERIMETER

ß =22S0 =31S0 = 2700

Good Unfavorable Not very favorable Acceptable Very favorable

ß = 90"

Not very favorable ß = 270" Favorable (Depending upon the value of a and upon the rock competence, the results will be closer a a = 45" 6 a = 90")

3 --

-/ L

.

NITIATION SEOUENCE

\

3

BLASTHOLE 4 DlRECTlON OF MAL~MuM PRINCIPAL STRESS

-

-7/

Fig. 17.7. Initiation sequence for burn cut in high horizontal Stress field: (a) tobe avoided, (b) satisfactory.(Hagan, 1983).

Fig. 17.6. Rectangular sinking shaft with V cut. (Hagan, 1983)

166

Drilling und blasting of roch

- Only explosives that are unaltered by water can be used. - Blastholes are lost due to caving, and - Inclined drilling is difficult. On the other hand, water affects the rock and the rock masses by the following: - Increase in propagation velocity of the elastic waves in porous and fissured ground. - Reduction of the compressive and tensile strength of the rocks (Obert and Duvall, 1967) as the friction between particles is lower. - Reduction of the Stress wave attenuation and, because of this, the breakage effects are intensified by ET (Ash, 1968).

which it is in contact and, because of this, great attention must be paid to this phenomenon. A general recommendation when these problems are present is to limit the number of blastholes per blast, in order to lower the time that passes between the charging and the firing.

REFERENCES Ash, R.I.: The design of blasting roundi. Ch. 7.3. Surface Mining, Ed. E. F? Pfleider, AIME, 1968. Atchison, TC.: Fragmentation principles. Ch. 7.2. Surface Mining, Ed. E.F?Pfleider, AIME, 1968. Belland, J.M.: Structure as a control in rock fragmentation. Carol - i%b. LaKe rron ore deposrts. L ~ u i i e r i nMarchBhandari, S.: Blastinn in non-homogeneous rocks. Australian Mining, i e r ~ i ~ May, 1974. Blair, B.E.: Physical properties of mine rock. Part 111. USBM RI No. 5 130, 1955: Part IV USBM-RI, No. 5244,1956. Grant, C. H.: How to muke explosives domore work. Mining- Magazine, August, 1970. Hagan, T.N.: The effects of some structural properties of rock on the design und fonelab 9.1.82 registration code - Free Activators of blasting. ICI Australia Operations PTY.Ltd. Melboume, 1979. Hagan, T. N.: 'The influence of rock properties of blasts in underground construction. Proc. Int. Symp. on Engineering Geology and Underground Construction. Lisboa, Portugal, 1983. Hanies, G.: Breakage of rock by explosives. Aus. I.M.M., London, 1978. Kutuzov, B.N. et al.: Classification des roches d'apres leur explosibi1it.i pour les decouvertes. Gomyl, Zumal, Moscow, 1979. Lopez Jimeno, E.: Inpuencia de Iaspropiedades de las rocas y Macizos Rocosos en el diseiio y resultado de las voladuras. Tecniterrae, 1982. Memt, A. H.: Geological predictions for underground excavations. North American RETC Conference. Polak, E.J.: Seismic attenuation in engineering site investigations. Proc. Ist. Aust. N.Z. Conf. Geomechanics, Melboume, 1971. Rinehart, J.S.: Fractures und strain generated in joints and layered rock masses by explosions. Proc. Symp. Mechanism of Rock Failure by Explosions. Fontainebleau, October. 1970. Sassa, K. & I. Ito: On the relation berween the strength of a rock und the panern of breakage by blasting. Proc. 3rd. Congress Intemational Society of Rock Mechanics. Denver, 1974. Sjogren, B. et al.: Seismic classification of anvi folder locker - Activators Patch muss qualities. Geophysical Prospecting, No, 27,1979. Wild, H.W.: Geology und blasting in openpits. Erzmetall, 1976. U

w i t h n i i t i n t P. m ~ i n ~ R i i t e ~ e m a s s _ e n tension, the water is mobilized, forming a wedge which could provoke a great overbreak.

17.3.5 Temperature of the rock muss The orebeds that contain pyrites usually have high rock temperature problems because of the effect of slow oxidation of this mineral, causing the explosive agents such as ANFO to react exothermically with the pyrite, with stimulation from 120°C f 10°C. The latest investigations point to a first reaction between ANFO and hydrated ferrous sulphate, and even more so between the latter and amrnonic nitrate, initiating an exothermic reaction that is self-maintaining from 80°C On. This ferrous sulphate is one of the products of decomposition of the pyrites, apart from the femc sulphate and the sulfuric acid. To avoid this problem, which has caused severe accidents on several occasions, diverse substances which inhibit ANFO have been added, such as urea, potassic oxalate, etc., arriving at the conclusion that by adding to ANFO a 5% in weight of urea, the exothermic reaction of the ternary mixture is avoided up to a temperature of 180°C (Miron et al., 1979). The sensitivity of the water gel type explosives also depends highly upon the temperature of the rock with

.

%

*

CHAFIER 18

Characterization of the rock masses for blast designing

18.1 INTRODUCTION The properties ot rock masses that most infiuence blast

- Dynamic strengths of the rocks. - Spacing and orientation of the planes of weakness. - Lithology and thickness of the sedimentary bedding planes. - Velocity of wave propagation. - Elastic properties of the rocks. - Types of infilling material and tightness of the joints. - Indexes of anisotropy and heterogeneity of the rock masses, etc. The determination of these parameters by direct or laboratory methods is very costly and difficult, as the samples tested do not usually include discontinuities and the lithologicalchanges of the rock mass from where they were taken. In order to obtain a representative sample, it would be necessary for it to have a size ten times larger than the mean spacing between joints. However, these methods sandboxie 5.30 license key - Activators Patch complement the characterization of the rock masses to be blasted. At the moment, the most common geomechanic techniques for monitoring are: - Diamond drilling with core recovery and geomechanic testing. - - Structural studies of the joint System. - Seismic survey profiles. - Geophysical logs of investigation drill holes. - Geophysical logs of production blastholes. - Logging and individual treatment during drilling of production blastholes.

RC (MPa) = 24. 1, (50) (MPa) the Pierce equation, for the calculation of the Burdm from the RQD index, corrected by a Coefficient of Alteration which takes into account the Joint Strength as a function of their tightness and the type of infilling, Fig. 18.1 and Table 18.2. The company Steffen, Robertson and Kirsten, Ltd. (1985), used various geomechanic Parameters to calculate the powder factors in bench blasting, among which RQD, the Uniaxial Compressive Strength (MPa), the Interna1 Friction Angles and Abrasiveness of the joints and the Density are found (t/m3),Fig, 18.2. This procedure is one of the few that take into account the effect of blasthole diameter (mm) or spacial distribution of the explosives upon the powder factor of the blast. 18.3 CHARACTERISTICS OF THE JOINT SYSTEMS There are various properties of the joints that can be measured in a characterization study, but the most important from a breakage point of view are spacing and onentation. An index obtained frequently is that known as the Volumetric Joint Count, J, which is defined by the total number of joints per cubic meter, obtained from the summing of the joints present per meter for each one of the existing families. The relationship between the index J, and the RQD is, according to Pallsmtrom (1974), the following: RQD = 115 - 3.3 J,For J, < 4.5, RQD = audacity full version crack download - Crack Key For U 18.2 DIAMOND DRILLING WITH CORE RECOVERY AND GEOMECHANIC TESTING With core recovery by diamond drilling, one of the most extensive rock mass clasifications known can be applied, called RQD (Rock Quality Designation, Deere 1968) which is defined as the percentage of the core length recovered in pieces larger than 10 cm with respect to the length of the core run, Table 18.1. Apart from this, the geomechanic testing of Point Load Strength I, can be canied out either in the diametral or axial position, to be able to estimate the Uniaxial Compressive Strength RC.

According to the orientation of the joints, the in-situ blocks will show different geometries that doubly affect the fragmentation of the blast and the most useful break direction of the round. In Fig. 18.3, the approximate volume of the blocks taken from J, and the relationship of the three characteristic intersections of the Same can be estimated. An attempt to take into consideration the structural discontinuities when designing the rounds is owed to Ashby (1977), which relates the fracture frequency and their shear strength to the powder factors of the explosive, Fig. 18.4. Lilly (1986) defined a Blastability Index BI that is

168

Drilling und blasting of rocks

Table 18.1. RQD 0-25 25-50 50-75 75-90 90-100

Rock quality Very poor Poor Fair GOO~ Excellent

Table 18.2. Joint strength Strong Medium weak Very weak

Y = a + b l n X

m

Correction factor 1O. 0.9 0.8 0.7

0.9

-

0.8

-

0.7

-

3.6

Table 18.3. J

>I 1-3 3-10 10-30 > 30

Characteristicsof the mass Massive blocks Large blocks Medium size blocks Small blocks Very small%locks

0.3

1

"'1

0.1

0.0

DESCRlPTlON OF ROCK OUALITY

1

VERY POOR

POOR

I

I

0

10

20

I

FAIR

GO09

I

I

:

I

I

i

I

30

I

I

I

I

I

40

50

60

70

I

1

80

p-~ I 90

100

EOUIVALENT ROCK QUALITY DESIGNATION (%) €ROD = ROD X ALTERATION FACTOR

Table 18.4. Geomechanic ~arameters 1. Rock mass description (RMD) I. I Powderylfriable 1.2 Blocky 1.3 Totally massive

Ratine

Fig. 18.1. Blastability factor k vs equivalent rock quality designation, RQDE.

10 20 50

2. Joint Plane Spacing (JPS) 2.1 Close (< 0.1 m) 2.2 Intermediate (0. I to 1 m) 2.3 Wide (> 1 m)

10 20 50

-

3. Joint Plane Onentation (JPO) 3.1 Horizontal 3.2 Dip out of face 3.3 Strike normal to face 3.4 Dip into face

10 20 30

4. Specific Gravity Influence (SGI) SGI = 25 SG - 50 (where SG is In Tonslcu metre) 5. Hardness (H)

1-10

obtained by summing the representative values of five geomechanics parameters. Rl= Q 5 ( R M 1 3 t l m - u D L

In Table 18.4, the ratings for Blastability Index parameters are described. The Powder Factors CE or the Energy Factors FE are : or the equations calculated with ~ i g18.5, CE (Kg ANFO/t) = 0.004

X

BI, or

FE (MJ/t) = 0.015 X BI

From the numerous experiences canied out in Australia, it has been concluded that the Rock Factor of the Model Kuz-Ram of Cunningham (1983) can be obtained by multiplying BI by 0.12.

Fig. 18.2. Calculation of the Powder Factor as a function of the different geomechanicparameters of the rock mass.

Example: Consider a highly laminated, soft ferruginous shale which has horizontal to sub-horizontal bedding to which the-fofIowing~due~me~ri.

RMD = 15 P S = 10 JPO = 10 SGI = 10 H=l The total sum is 46 and the Blastability Index is BI = 23. From Fig. 18.4, a powder factor of 0.1 kg/t is obtained. Ghose (1988) also proposes a geomechanic classification System of the rock masses in coal mines for predicting powder factors in surface blastings. The four parametersmeasured are indicated in Table 18.5.

Characterization of the rock masses for blast designing

Fig. 18.3. Estimation of the volume of the in-situ blocks.

Parameters 1. Density Ratio 2. Spacing of discontinuities (m) Ratio 3. Point load strength Index (MPa) Ratio 4. Joint plane onentation Ratio

Range of values 1.3-1.6 20 < 0.2 35
1.6-2.0 15 0.2-0.4 25 1-2 20 Strike at an acute angle to face 15

20

Table 18.6. Adjustment factors I. Degree of confinement Highly confined Reasonably free

-5 0

2. Bench stiffness Hole depthlburden > 2 Hole depthlburden C 1.5 Hole depthlburden 1.5-2

0 -5 -2

Values

2.0-2.3 12 0.4-0.6 20 2-4 15 Strike normal to face

2.3-2.5 6 0.6-2.0 12 46 8 Dip out of face

> 2.5

12

10

6

Table 18.7. Blastability index 80-85 60-70 5MO 40-50 30-40

4

> 2.0 8 >6 5 Horizontal

Powder factor (kg/m3) 0.2-0.3 0.3-0.5 0.5-0.6 O.M.7 0.7-0.8

170

Drilling and bhsting of rocks

POWDEA FACTOR

'

BLASTING

-

POWDEA FACTOR ,KO A N F O ~ ~ J

'

lag

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4 Replies to “Altium Designer 20.2.6 Build 244 Crack”

  1. Great tips and thanks for letting us know this exists! I was wondering how to do a screen recording to demo something at work. I do not use Powerpoint at all, great to know this feature is in there.

  2. Yes it would, I'd drill a hole in each end of the crack beforehand tho, so it doesn't continue cracking after the repair

  3. Hermano! Dios te bendiga mucho. Acabo de recuperar diez aГ±os de fotos familiares que casi daba por perdidos. Un abrazo!!!

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