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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