INSTRUMENTATION FOR ENGINEERING MEASUREMENTS

Second Edition

JAMES W. DALLY University of Maryland

WILLIAM F. RILEY KENNETH G. McCONNELL Iowa State University

JOHN WILEY & SONS, INC. New York Chichester Brisbane Toronto Singapore

CONTENTS

LIST OF SYMBOLS xv i i

CHAPTER 1 APPLICATIONS OF ELECTRONIC INSTRUMENT SYSTEMS 01

1.1 INTRODUCTION 01 1.2 THE ELECTRONIC INSTRUMENT SYSTEM 02 1.3 ENGINEERING ANALYSIS 03 1.4 PROCESS CONTROL 04

1.4.1 PROCESS CONTROL DEVICES 06 1.5 EXPERIMENTAL ERROR 12

1.5.1 ACCUMULATION OF ACCEPTED ERROR 13 1.5.2 IMPROPER FUNCTIONING OF

INSTRUMENTS 14 1.5.3 EFFECT OF THE TRANSDUCER ON THE

CHAPTER

1.6 1.7

R 2 2.1 2.2 2.3 2.4

2.5 2.6 2.7

2.8 2.9

PROCESS 1.5.4 DUAL SENSITIVITY ERRORS 1.5.5 OTHER SOURCES OF ERROR

MINIMIZING EXPERIMENTAL ERROR SUMMARY REFERENCES EXERCISES

ANALYSIS OF CIRCUITS INTRODUCTION AND DEFINITIONS BASIC ELECTRICAL COMPONENTS KIRCHHOFF'S CIRCUIT LAWS DIODES, TRANSISTORS, AND GATES

2.4.1 DIODES 2.4.2 TRANSISTORS 2.4.3 GATES

DC CIRCUITS PERIODIC FUNCTIONS AC CIRCUITS

2.7.1 IMPEDANCE FREQUENCY RESPONSE FUNCTION SUMMARY REFERENCES EXERCISES

15 17 18 19 20 20 21

24 24 26 28 29 29 29 31 33 34 38 40 42 44 45 45

vii

CONTENTS

CHAPTER 3 3.1 3.2

3.3

3.4

3.5

3.6

CHAPTER 4 4.1 4.2 4.3 4.4 4.5

4.6

4.7 4.8 4.9

4.10 4.11 4.12

ANALOG RECORDING INSTRUMENTS INTRODUCTION GENERAL CHARACTERISTICS OF RECORDING INSTRUMENTS VOLTMETERS FOR STEADY-STATE MEASUREMENTS

3.3.1 D'ARSONVAL GALVANOMETER 3.3.2 AMMETER 3.3.3 DC VOLTMETERS 3.3.4 VOLTMETER LOADING ERRORS 3.3.5 AMPLIFIED VOLTMETERS 3.3.6 POTENTIOMETRIC VOLTMETERS

VOLTMETERS FOR SLOWLY VARYING SIGNALS

3.4.1 STRIP-CHART RECORDERS 3.4.2 X-Y RECORDERS

VOLTMETERS FOR RAPIDLY VARYING SIGNALS

3.5.1 OSCILLOGRAPH RECORDERS 3.5.2 TRANSIENT RESPONSE

OF GALVANOMETERS 3.5.3 PERIODIC SIGNAL RESPONSE

OF GALVANOMETERS 3.5.4 OSCILLOSCOPES 3.5.5 MAGNETIC TAPE RECORDERS

SUMMARY REFERENCES EXERCISES

DIGITAL RECORDING SYSTEMS INTRODUCTION DIGITAL CODES CONVERSION PROCESSES DIGITAL-TO-ANALOG CONVERTERS ANALOG-TO-DIGITAL CONVERTERS

4.5.1 SUCCESSIVE-APPROXIMATION METHOD

4.5.2 INTERGRATION METHOD 4.5.3 PARALLEL OR FLASH METHOD

DATA DISTRIBUTION 4.6.1 BUS STRUCTURES

INTERFACES DIGITAL VOLTMETERS DATA-LOGGING SYSTEMS DATA-ACQUISITION SYSTEMS PC-BASED DATA-ACQUISITION SYSTEMS DIGITAL OSCILLOSCOPES

49 49

49

54 54 55 56 57 57 58

59 59 60

61 61

62

68 73 77 81 82 82

86 86 86 88 89 92

92 94 97 98 99 101 102 108 109 112 112

CONTENTS ix

4.13 WAVEFORM RECORDERS 4.14 ALIASING

4.14.1 ANTIALIASING FILTERS 4.15 SUMMARY

REFERENCES EXERCISES

CHAPTER 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9

10 11 12 13 14

CHAPTER 6 6.1 6.2

6.3

6.4

6.5 6.6

6.7 6.8

SENSORS FOR TRANSDUCERS INTRODUCTION POTENTIOMETERS DIFFERENTIAL TRANSFORMERS RESISTANCE STRAIN GAGES CAPACITANCE SENSORS EDDY-CURRENT SENSORS PIEZOELECTRIC SENSORS PIEZORESISTIVE SENSORS PHOTOELECTRIC SENSORS

5.9.1 VACUUM-TUBE DETECTORS 5.9.2 PHOTOCONDUCTIVE CELLS 5.9.3 SEMICONDUCTOR PHOTODIODES

RESISTANCE TEMPERATURE DETECTORS THERMISTORS THERMOCOUPLES CRYSTAL OSCILLATORS SUMMARY REFERENCES EXERCISES

SIGNAL CONDITIONING CIRCUITS INTRODUCTION POWER SUPPLIES

6.2.1 BATTERY SUPPLIES 6.2.2 LINE VOLTAGE SUPPLIES

POTENTIOMETER CIRCUIT (CONSTANT VOLTAGE) POTENTIOMETER CIRCUIT (CONSTANT CURRENT) WHEATSTONE BRIDGE (CONSTANT VOLTAGE) WHEATSTONE BRIDGE (CONSTANT CURRENT) AMPLIFIERS OPERATIONAL AMPLIFIERS

6.8.1 INVERTING AMPLIFIER 6.8.2 DIFFERENTIAL AMPLIFIER 6.8.3 VOLTAGE FOLLOWER 6.8.4 SUMMING AMPLIFIER

116 117 119 119 120 120

124 124 124 126 129 135 137 139 142 144 146 149 149 151 152 153 155 157 157 158

162 162 162 162 165

166

169 170

173 176 181 181 184 186 187

x CONTENTS

6.8.5 INTEGRATING AMPLIFIER 188 6.8.6 DIFFERENTIATING AMPLIFIER 189

6.9 FILTERS 189 6.9.1 HIGH-PASS RC FILTER 190 6.9.2 LOW-PASS RC FILTER 191 6.9.3 ACTIVE FILTER 193

6.10 AMPLITUDE MODULATION AND DEMODULATION 194

6.11 TIME-MEASURING CIRCUITS 197 6.11.1 BINARY COUNTING UNIT 197 6.11.2 GATES IN COUNTER APPLICATIONS 198 6.11.3 TRIGGERS 198 6.11.4 COUNTING INSTRUMENTS 199

6.12 SUMMARY 202 REFERENCES 205 EXERCISES 206

CHAPTER 7 RESISTANCE-TYPE STRAIN GAGES 211 7.1 INTRODUCTION 211 7.2 ETCHED-FOIL STRAIN GAGES 212 7.3 STRAIN-GAGE INSTALLATION 212 7.4 WHEATSTONE BRIDGE SIGNAL CONDITIONING 214 7.5 RECORDING INSTRUMENTS FOR STRAIN

GAGES 219 7.5.1 DIRECT-READING STRAIN INDICATOR 220 7.5.2 NULL-BALANCE BRIDGES 220 7.5.3 STRAIN-GAGE SIGNAL CONDITIONERS 222 7.5.4 WHEATSTONE BRIDGE AND

OSCILLOSCOPE 222 7.5.5 WHEATSTONE BRIDGE AND

OSCILLOGRAPH 224 7.6 CALIBRATION METHODS 227 7.7 EFFECTS OF LEAD WIRES, SWITCHES, AND

SLIP RINGS 229 7.7.1 LEAD WIRES 229 7.7.2 SWITCHES 232 7.7.3 SLIP RINGS 234

7.8 ELECTRICAL NOISE 234 7.9 TEMPERATURE-COMPENSATED GAGES 236

7.10 ALLOY SENSITIVITY, GAGE FACTOR, AND CROSS-SENSITIVITY FACTORS 238

7.11 DATA-REDUCTION METHODS 241 7.11.1 THE UNIAXIAL STATE OF STRESS 241 7.11.2 THE BIAXIAL STATE OF STRESS 242 7.11.3 THE GENERAL STATE OF STRESS 242

7.12 HIGH-TEMPERATURE STRAIN MEASUREMENTS 244

CONTENTS xi

7.13 SUMMARY REFERENCES EXERCISES

245 248 249

CHAPTER 8 FORCE, TORQUE, AND PRESSURE MEASUREMENTS

8.1 INTRODUCTION 8.2 FORCE MEASUREMENTS (LOAD CELLS)

8.2.1 LINK-TYPE LOAD CELL 8.2.2 BEAM-TYPE LOAD CELL 8.2.3 RING-TYPE LOAD CELL 8.2.4 SHEAR-WEB-TYPE LOAD CELL

8.3 TORQUE MEASUREMENT (TORQUE CELLS) 8.3.1 TORQUE CELLS - DESIGN CONCEPTS 8.3.2 TORQUE CELLS-DATA TRANSMISSION

8.4 COMBINED MEASUREMENTS OF FORCE AND MOMENTS OR TORQUES

8.4.1 FORCE-MOMENT MEASUREMENTS 8.4.2 FORCE-TORQUE MEASUREMENTS

8.5 PRESSURE MEASUREMENTS (PRESSURE TRANSDUCERS)

8.5.1

8.6

8.7

8.9

DISPLACEMENT-TYPE PRESSURE TRANSDUCER DIAPHRAGM-TYPE PRESSURE TRANSDUCER PIEZOELECTRIC-TYPE PRESSURE TRANSDUCER

MINIMIZING ERRORS IN TRANSDUCERS 8.6.1 DUAL SENSITIVITY

ZERO SHIFT WITH TEMPERATURE CHANGE BRIDGE BALANCE SPAN ADJUST SPAN CHANGE WITH TEMPERATURE

FREQUENCY RESPONSE OF TRANSDUCERS 8.7.1 RESPONSE OF A FORCE TRANSDUCER TO

A TERMINATED RAMP FUNCTION 8.7.2 RESPONSE OF A FORCE TRANSDUCER TO

A SINUSOIDAL FORCING FUNCTION CALIBRATION OF TRANSDUCERS SUMMARY REFERENCES EXERCISES

8.5.2

8.5.3

8.6.2

8.6.3 8.6.4 8.6.5

253 253 253 254 256 258 260 262 262 264

268 268 271

271

272

272

275 276 277

279 280 280 280 280

282

285 286 288 289 290

CHAPTER 9 DISPLACEMENT, VELOCITY, AND ACCELERATION MEASUREMENTS

9.1 INTRODUCTION 9.2 THE SEISMIC TRANSDUCER MODEL

293 293 294

xii CONTENTS

9.3 DYNAMIC RESPONSE OF THE SEISMIC MODEL 295

9.3.1 SINUSOIDAL EXCITATION 295 9.3.2 TRANSIENT EXCITATIONS 298

9.4 SEISMIC MOTION TRANSDUCERS 299 9.4.1 SEISMIC DISPLACEMENT

TRANSDUCERS 300 9.4.2 SEISMIC VELOCITY TRANSDUCERS 301 9.4.3 SEISMIC ACCELERATION

TRANSDUCERS 301 9.5 PIEZOELECTRIC FORCE TRANSDUCERS 305 9.6 PIEZOELECTRIC SENSOR CIRCUITS 306

9.6.1 CHARGE SENSITIVITY MODEL 306 9.6.2 VOLTAGE-FOLLOWER CIRCUIT 308 9.6.3 CHARGE-AMPLIFIER CIRCUIT 311 9.6.4 BUILT-IN VOLTAGE FOLLOWERS 313

9.7 RESPONSE OF PIEZOELECTRIC CIRCUITS TO TRANSIENT SIGNALS 317

9.8 ACCELEROMETER CALIBRATION 320 9.9 DYNAMIC CALIBRATION OF FORCE

TRANSDUCERS 323 9.9.1 FORCE TRANSDUCER CALIBRATION

BY IMPACT 325 9.10 OVERALL SYSTEM CALIBRATION 327 9.11 SOURCES OF ERROR WITH PIEZOELECTRIC

TRANSDUCERS 328 9.12 DISPLACEMENT MEASUREMENTS IN A

FIXED REFERENCE FRAME 331 9.12.1 DISPLACEMENT MEASUREMENTS WITH

RESISTANCE POTENTIOMETERS 331 9.12.2 DISPLACEMENT MEASUREMENTS WITH

MULTIPLE-RESISTOR DEVICES 335 9.12.3 PHOTOELECTRIC DISPLACEMENT

TRANSDUCERS 336 9.13 OPTICAL DISPLACEMENT MEASUREMENTS 337

9.13.1 OPTICAL TRACKER SYSTEM 337 9.13.2 VIDEO CAMERA MOTION

ANALYSIS 338 9.14 VELOCITY MEASUREMENTS 339

9.14.1 LINEAR-VELOCITY MEASUREMENTS 340

9.14.2 ANGULAR-VELOCITY MEASUREMENTS 342

9.14.3 LASER-DOPPLER SYSTEM 343 9.15 SUMMARY 344

REFERENCES 345 EXERCISES 347

CONTENTS xiii

CHAPTER 10 ANALYSIS OF VIBRATING SYSTEMS 356 10.1 INTRODUCTION 356

10.1.1 TEMPORAL MEAN 358 10.1.2 TEMPORAL MEAN SQUARE

AND ROOT MEAN SQUARE 358 10.2 SINUSOIDAL SIGNAL ANALYSIS 358 10.3 CHARACTERISTICS OF SIGNALS 3 61

10.3.1 PERIODIC SIGNALS 362 10.3.2 TRANSIENT SIGNALS 363 10.3.3 RANDOM SIGNALS 366

10.4 LUMPED MASS-SPRING VIBRATION MODELS 368

10.4.1 UNDAMPED NATURAL FREQUENCY AND MODE SHAPE 369

10.4.2 FORCED VIBRATION RESPONSE (DIRECT SOLUTION) 370

10.4.3 FORCED VIBRATION RESPONSE (MODAL SOLUTION) 370

10.5 CONTINUOUS VIBRATION MODELS 373 10.5.1 FUNDAMENTAL EQUATION

OF MOTION 373 10.5.2 STEADY-STATE MODAL SOLUTION 374

10.6 THE LINEAR INPUT-OUTPUT MODEL 376 10.6.1 IMPULSE RESPONSE 377 10.6.2 RANDOM INPUT-OUTPUT

RELATIONSHIPS 379 10.7 BASICS OF A DIGITAL FREQUENCY

ANALYZER 380 10.7.1 TIME SAMPLING PROCESS 380 10.7.2 CONVOLUTION 381 10.7.3 FILTER LEAKAGE 385 10.7.4 BLOCK DIAGRAM 387

10.8 USING A DIGITAL FREQUENCY ANALYZER 387 10.8.1 RELATIONSHIPS FOR FREQUENCY

ANALYZERS 388 10.8.2 FILTER CHARACTERISTICS 390 10.8.3 FOUR COMMON WINDOW

FUNCTIONS 392 10.8.4 UNCERTAINTY IN THE MAGNITUDE

OF SPECTRAL LINES 394 10.8.5 SUMMARY OF WINDOW USE 395

10.9 ACCELEROMETER CROSS-AXIS SENSITIVITY 396 10.9.1 SINGLE ACCELEROMETER CROSS-AXIS

COUPLING MODEL 396 10.9.2 TRIAXIAL ACCELEROMETER

MODEL 397 10.9.3 CORRECTING ACCELERATION VOLTAGE

READINGS 397

xiv CONTENTS

10.9.4 APPLICATION TO MODAL ANALYSIS SIGNALS 399

10.9.5 CROSS-AXIS RESONANCE 399 10.10 FORCE TRANSDUCER-STRUCTURE

INTERACTION 400 10.10.1 GENERAL TWO-DEGREE-OF-FREEDOM

FORCE TRANSDUCER MODEL 401 10.11 SUMMARY 406

REFERENCES 408 EXERCISES 409

CHAPTER 11 TEMPERATURE MEASUREMENTS 412 11.1 INTRODUCTION 412 11.2 EXPANSION METHODS FOR MEASURING

TEMPERATURE 415 11.3 RESISTANCE THERMOMETERS 416

11.3.1 RESISTANCE TEMPERATURE DETECTORS (RTDS) 417

11.3.2 RTDS AND THE WHEATSTONE BRIDGE 420 11.3.3 THERMISTORS 424

11.4 THERMOCOUPLES 428 11.4.1 PRINCIPLES OF THERMOCOUPLE

BEHAVIOR 430 11.4.2 THERMOELECTRIC MATERIALS 434 11.4.3 REFERENCE IUNCTION TEMPERATURE 437 11.4.4 FABRICATION AND INSTALLATION

PROCEDURES 439 11.4.5 RECORDING INSTRUMENTS FOR

THERMOCOUPLES 442 11.4.6 NOISE SUPPRESSION IN THERMOCOUPLE

CIRCUITS 444 11.5 INTEGRATED-CIRCUIT TEMPERATURE

SENSORS 444 11.6 DYNAMIC RESPONSE OF TEMPERATURE

SENSORS 446 11.7 SOURCES OF ERROR IN TEMPERATURE

MEASUREMENTS 449 11.8 CALIBRATION METHODS 453 11.9 RADIATION METHODS (PYROMETRY) 454

11.9.1 PRINCIPLES OF RADIATION 454 11.9.2 THE OPTICAL PYROMETER 456 11.9.3 INFRARED PYROMETERS 458 11.9.4 PHOTON DETECTOR TEMPERATURE

INSTRUMENTS 460 11.10 SUMMARY 463

REFERENCES 465 EXERCISES 466

CONTENTS xv

CHAPTER 12 12.1 12.2

12.3

12.4 12.5

12.6

12.7

12.8

FLUID FLOW MEASUREMENTS INTRODUCTION FLOW VELOCITY (INSERTION-TYPE TRANSDUCERS)

12.2.1 PITOT TUBE (INCOMPRESSIBLE FLOW) 12.2.2 PITOT TUBE (COMPRESSIBLE FLOW) 12.2.3 HOT-WIRE AND HOT-FILM

ANEMOMETERS 12.2.4 DRAG-FORCE VELOCITY TRANSDUCERS 12.2.5 CURRENT METERS 12.2.6 TURBINE FLOW METERS 12.2.7 VORTEX-SHEDDING TRANSDUCERS

FLOW RATES IN CLOSED SYSTEMS BY PRESSURE-VARIATION MEASUREMENTS

12.3.1 VENTURI METER 12.3.2 FLOW NOZZLE 12.3.3 ORIFICE METER 12.3.4 ELBOW METER

FLOW RATES IN PARTIALLY CLOSED SYSTEMS FLOW RATES IN OPEN CHANNELS FROM PRESSURE MEASUREMENTS

12.5.1 SLUICEGATE 12.5.2 WEIRS

COMPRESSIBLE FLOW EFFECTS IN CLOSED SYSTEMS OTHER FLOW-MEASUREMENT METHODS FOR CLOSED SYSTEMS

12.7.1 CAPILLARY FLOW METER 12.7.2 POSITIVE-DISPLACEMENT FLOW

METERS 12.7.3 HOT-FILM MASS FLOW TRANSDUCERS 12.7.4 LASER VELOCIMETRY SYSTEMS

SUMMARY REFERENCES EXERCISES

473 473

476 476 479

481 486 489 491 492

493 494 495 496 498 499

500 500 501

503

504 504

505 506 507 512 512 514

CHAPTER 13 STATISTICAL METHODS 521 13.1 INTRODUCTION 521 13.2 CHARACTERIZING STATISTICAL

DISTRIBUTIONS 522 13.2.1 GRAPHIC REPRESENTATIONS OF THE

DISTRIBUTION 522 13.2.2 MEASURES OF CENTRAL TENDENCY 524 13.2.3 MEASURES OF DISPERSION 524

13.3 STATISTICAL DISTRIBUTION FUNCTIONS 526 13.3.1 GAUSSIAN DISTRIBUTION 526 13.3.2 WEIBULL DISTRIBUTION 529

CONTENTS

13.4 13.5 13.6 13.7

13.8 13.9

13.10

CONFIDENCE INTERVALS FOR PREDICTIONS 532 COMPARISION OF MEANS 537 STATISTICAL CONDITIONING OF DATA 537 REGRESSION ANALYSIS 538

13.7.1 LINEAR REGRESSION ANALYSIS 539 13.7.2 MULTIVARIATE REGRESSION 541

CHI-SQUARE TESTING 544 ERROR ACCUMULATION AND PROPAGATION 545 SUMMARY 548 REFERENCES 549 EXERCISES 550

APPENDIX A

APPENDIX

558

572

AUTHOR INDEX 577

SUBJECT INDEX 579