كتاب Theory and Design for Mechanical Measurements
منتدى هندسة الإنتاج والتصميم الميكانيكى
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منتدى هندسة الإنتاج والتصميم الميكانيكى
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 كتاب Theory and Design for Mechanical Measurements

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Theory and Design for Mechanical Measurements
Seventh Edition
Richard S. Figliola
Clemson University
Donald E. Beasley
Clemson University

كتاب Theory and Design for Mechanical Measurements  T_a_d_13
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Contents
Preface V
1 Basic Concepts of Measurement Methods 1
1.1 Introduction, 1
1.2 General Measurement System, 2
Sensor and Transducer, 2
Signal-Conditioning Stage, 3
Output Stage, 4
General Template for a Measurement System, 4
1.3 Experimental Test Plan, 5
Variables, 6
Noise and Interference, 8
Randomization, 9
Replication and Repetition, 13
Concomitant Methods, 14
1.4 Calibration, 14
Static Calibration, 14
Dynamic Calibration, 14
Static Sensitivity, 15
Range and Span, 15
Resolution, 16
Accuracy and Error, 16
Random and Systematic Errors and Uncertainty, 16
Sequential Test, 19
Hysteresis, 19
Random Test, 19
Linearity Error, 19
Sensitivity and Zero Errors, 21
Instrument Repeatability, 21
Reproducibility, 21
Instrument Precision, 21
Overall Instrument Error and Instrument Uncertainty, 22
Verification and Validation, 22
1.5 Standards, 22
Primary Unit Standards, 22
Base Dimensions and Their Units, 23
Derived Units, 25
Hierarchy of Standards, 28
Test Standards and Codes, 29
1.6 Presenting Data, 30
Rectangular Coordinate Format, 30
viiviii CONTENTS
Semilog Coordinate Format, 30
Full-Log Coordinate Format, 30
Significant Digits, 30
Summary, 33
Nomenclature, 34
References, 34
2 STATIC AND DYNAMIC CHARACTERISTICS OF SIGNALS 35
2.1 Introduction, 35
2.2 Input/Output Signal Concepts, 35
Generalized Behavior, 36
Classification of Waveforms, 36
Signal Waveforms, 38
2.3 Signal Analysis, 39
Signal Root-Mean-Square Value, 40
Discrete Time or Digital Signals, 40
Direct Current Offset, 41
2.4 Signal Amplitude and Frequency, 42
Periodic Signals, 43
Frequency Analysis, 45
Fourier Series and Coefficients, 48
Fourier Coefficients, 48
Special Case: Functions with T = 2π, 49
Even and Odd Functions, 49
2.5 Fourier Transform and the Frequency Spectrum, 55
Discrete Fourier Transform, 56
Analysis of Signals in Frequency Space, 60
Summary, 62
References, 63
Suggested Reading, 63
Nomenclature, 63
3 MEASUREMENT SYSTEM BEHAVIOR 64
3.1 Introduction, 64
3.2 General Model for a Measurement System, 64
Dynamic Measurements, 65
Measurement System Model, 66
3.3 Special Cases of the General System Model, 68
Zero-Order Systems, 68
First-Order Systems, 69
Second-Order Systems, 79
3.4 Transfer Functions, 88
3.5 Phase Linearity, 90
3.6 Multiple-Function Inputs, 91
3.7 Coupled Systems, 93
3.8 Summary, 95
References, 95
Nomenclature, 96
Subscripts, 96Contents ix
4 PROBABILITY AND STATISTICS 97
4.1 Introduction, 97
4.2 Statistical Measurement Theory, 98
Probability Density Functions, 98
4.3 Describing the Behavior of a Population, 103
4.4 Statistics of Finite-Sized Data Sets, 107
Standard Deviation of the Means, 110
Repeated Tests and Pooled Data, 113
4.5 Hypothesis Testing, 114
4.6 Chi-Squared Distribution, 117
Precision Interval in a Sample Variance, 118
Goodness-of-Fit Test, 119
4.7 Regression Analysis, 121
Least-Squares Regression Analysis, 121
Linear Polynomials, 124
4.8 Data Outlier Detection, 126
4.9 Number of Measurements Required, 127
4.10 Monte Carlo Simulations, 129
Summary, 131
References, 132
Nomenclature, 132
5 UNCERTAINTY ANALYSIS 133
5.1 Introduction, 133
5.2 Measurement Errors, 134
5.3 Design-Stage Uncertainty Analysis, 136
Combining Elemental Errors: RSS Method, 137
Design-Stage Uncertainty, 137
5.4 Identifying Error Sources, 140
Calibration Errors, 141
Data-Acquisition Errors, 141
Data-Reduction Errors, 142
5.5 Systematic and Random Errors and Standard Uncertainties, 142
Systematic Error, 142
Random Error, 143
Other Ways Used to Classify Error and Uncertainty, 144
5.6 Uncertainty Analysis: Multi-Variable Error Propagation, 144
Propagation of Error, 145
Approximating a Sensitivity Index, 146
Sequential Perturbation, 149
Monte Carlo Method, 151
5.7 Advanced-Stage Uncertainty Analysis, 151
Zero-Order Uncertainty, 152
Higher-Order Uncertainty, 152
Nth-Order Uncertainty, 152
5.8 Multiple-Measurement Uncertainty Analysis, 157
Propagation of Elemental Errors, 157
Propagation of Uncertainty to a Result, 163
5.9 Correction for Correlated Errors, 168
5.10 Nonsymmetrical Systematic Uncertainty Interval, 170x CONTENTS
Summary, 172
References, 172
Nomenclature, 172
6 ANALOG ELECTRICAL DEVICES AND MEASUREMENTS 174
6.1 Introduction, 174
6.2 Analog Devices: Current Measurements, 174
Direct Current, 174
Alternating Current, 178
6.3 Analog Devices: Voltage Measurements, 179
Analog Voltage Meters, 179
Oscilloscope, 179
Potentiometer, 181
6.4 Analog Devices: Resistance Measurements, 182
Ohmmeter Circuits, 182
Bridge Circuits, 182
Null Method, 184
Deflection Method, 185
6.5 Loading Errors and Impedance Matching, 188
Loading Errors for Voltage-Dividing Circuit, 189
Interstage Loading Errors, 190
6.6 Analog Signal Conditioning: Amplifiers, 193
6.7 Analog Signal Conditioning: Special-Purpose Circuits, 196
Analog Voltage Comparator, 196
Sample-and-Hold Circuit, 197
Charge Amplifier, 197
4–20 mA Current Loop, 199
Multivibrator and Flip-Flop Circuits, 199
6.8 Analog Signal Conditioning: Filters, 201
Butterworth Filter Design, 202
Improved Butterworth Filter Designs, 203
Bessel Filter Design, 208
Active Filters, 209
6.9 Grounds, Shielding, and Connecting Wires, 211
Ground and Ground Loops, 211
Shields, 212
Connecting Wires, 213
Summary, 213
References, 214
Nomenclature, 214
7 SAMPLING, DIGITAL DEVICES, AND DATA ACQUISITION 215
7.1 Introduction, 215
7.2 Sampling Concepts, 216
Sample Rate, 216
Alias Frequencies, 218
Amplitude Ambiguity, 221
Leakage, 221
Waveform Fidelity, 223
7.3 Digital Devices: Bits and Words, 223Contents xi
7.4 Transmitting Digital Numbers: High and Low Signals, 226
7.5 Voltage Measurements, 227
Digital-to-Analog Converter, 227
Analog-to-Digital Converter, 228
Successive Approximation Converters, 232
7.6 Data Acquisition Systems, 237
7.7 Data Acquisition System Components, 238
Analog Signal Conditioning: Filters and Amplification, 238
Components for Acquiring Data, 241
7.8 Analog Input–Output Communication, 242
Data Acquisition Modules, 242
7.9 Digital Input–Output Communication, 246
Data Transmission, 247
Universal Serial Bus, 248
Bluetooth Communications, 248
Other Serial Communications: RS-232C, 249
Parallel Communications, 249
7.10 Digital Image Acquisition and Processing, 252
Image Acquisition, 252
Image Processing, 253
Summary, 256
References, 256
Nomenclature, 256
8 TEMPERATURE MEASUREMENTS 258
8.1 Introduction, 258
Historical Background, 258
8.2 Temperature Standards and Definition, 259
Fixed Point Temperatures and Interpolation, 259
Temperature Scales and Standards, 260
8.3 Thermometry Based on Thermal Expansion, 261
Liquid-in-Glass Thermometers, 262
Bimetallic Thermometers, 262
8.4 Electrical Resistance Thermometry, 263
Resistance Temperature Detectors, 264
Thermistors, 271
8.5 Thermoelectric Temperature Measurement, 276
Seebeck Effect, 276
Peltier Effect, 277
Thomson Effect, 277
Fundamental Thermocouple Laws, 278
Basic Temperature Measurement with Thermocouples, 279
Thermocouple Standards, 280
Thermocouple Voltage Measurement, 287
Multiple-Junction Thermocouple Circuits, 289
Applications for Thermoelectric Temperature Measurement: Heat
Flux, 291
Data Acquisition Considerations, 294
8.6 Radiative Temperature Measurements, 297
Radiation Fundamentals, 297
Radiation Detectors, 299xii CONTENTS
Radiometer, 299
Pyrometry, 300
Optical Fiber Thermometers, 301
Narrow-Band Infrared Temperature Measurement, 302
Fundamental Principles, 302
Two-Color Thermometry, 303
Full-Field IR Imaging, 303
8.7 Physical Errors in Temperature Measurement, 304
Insertion Errors, 305
Conduction Errors, 306
Radiation Errors, 308
Radiation Shielding, 310
Recovery Errors in Temperature Measurement, 311
Summary, 313
References, 313
Suggested Reading, 313
Nomenclature, 314
9 PRESSURE AND VELOCITY MEASUREMENTS 315
9.1 Introduction, 315
9.2 Pressure Concepts, 315
9.3 Pressure Reference Instruments, 318
McLeod Gauge, 318
Barometer, 319
Manometer, 320
Deadweight Testers, 324
9.4 Pressure Transducers, 325
Bourdon Tube, 326
Bellows and Capsule Elements, 326
Diaphragms, 327
Piezoelectric Crystal Elements, 330
9.5 Pressure Transducer Calibration, 331
Static Calibration, 331
Dynamic Calibration, 331
9.6 Pressure Measurements in Moving Fluids, 333
Total Pressure Measurement, 334
Static Pressure Measurement, 335
9.7 Modeling Pressure–Fluid Systems, 336
9.8 Design and Installation: Transmission Effects, 337
Liquids, 338
Gases, 339
Heavily Damped Systems, 340
9.9 Acoustical Measurements, 341
Signal Weighting, 341
Microphones, 342
9.10 Fluid Velocity Measuring Systems, 345
Pitot–Static Pressure Probe, 346
Thermal Anemometry, 348
Doppler Anemometry, 350
Particle Image Velocimetry, 352
Selection of Velocity Measuring Methods, 353Contents xiii
Summary, 354
References, 354
Nomenclature, 355
10 FLOW MEASUREMENTS 357
10.1 Introduction, 357
10.2 Historical Background, 357
10.3 Flow Rate Concepts, 358
10.4 Volume Flow Rate through Velocity Determination, 359
10.5 Pressure Differential Meters, 361
Obstruction Meters, 361
Orifice Meter, 364
Venturi Meter, 366
Flow Nozzles, 368
Sonic Nozzles, 373
Obstruction Meter Selection, 374
Laminar Flow Elements, 376
10.6 Insertion Volume Flow Meters, 377
Electromagnetic Flow Meters, 377
Vortex Shedding Meters, 379
Rotameters, 381
Turbine Meters, 382
Transit Time and Doppler (Ultrasonic) Flow Meters, 383
Positive Displacement Meters, 384
10.7 Mass Flow Meters, 386
Thermal Flow Meter, 386
Coriolis Flow Meter, 387
10.8 Flow Meter Calibration and Standards, 391
10.9 Estimating Standard Flow Rate, 392
Summary, 393
References, 393
Nomenclature, 393
11 STRAIN MEASUREMENT 395
11.1 Introduction, 395
11.2 Stress and Strain, 395
Lateral Strains, 397
11.3 Resistance Strain Gauges, 398
Metallic Gauges, 398
Strain Gauge Construction and Bonding, 400
Semiconductor Strain Gauges, 403
11.4 Strain Gauge Electrical Circuits, 404
11.5 Practical Considerations for Strain Measurement, 407
The Multiple Gauge Bridge, 407
Bridge Constant, 408
11.6 Apparent Strain and Temperature Compensation, 409
Temperature Compensation, 410
Bridge Static Sensitivity, 412
Practical Considerations, 413
Analysis of Strain Gauge Data, 413xiv CONTENTS
Signal Conditioning, 416
11.7 Optical Strain Measuring Techniques, 418
Basic Characteristics of Light, 418
Photoelastic Measurement, 419
Moiré Methods, 421
Fiber Bragg Strain Measurement, 422
Summary, 424
References, 424
Nomenclature, 424
12 MECHATRONICS: SENSORS, ACTUATORS, AND CONTROLS 426
12.1 Introduction, 426
12.2 Sensors, 426
Displacement Sensors, 426
Measurement of Acceleration and Vibration, 430
Velocity Measurements, 437
Angular Velocity Measurements, 441
Force Measurement, 444
Torque Measurements, 447
Mechanical Power Measurements, 448
12.3 Actuators, 450
Linear Actuators, 450
Pneumatic and Hydraulic Actuators, 452
Rotary Actuators, 455
Flow-Control Valves, 455
12.4 Controls, 457
Dynamic Response, 460
Laplace Transforms, 460
Block Diagrams, 463
Model for Oven Control, 464
Proportional–Integral (PI) Control, 468
Proportional–Integral–Derivative Control of a Second-Order
System, 469
Summary, 474
References, 474
Nomenclature, 474
PROBLEMS (AVAILABLE IN E-TEXT FOR STUDENTS) P-1
A PROPERTY DATA AND CONVERSION FACTORS A-1
B LAPLACE TRANSFORM BASICS A-8
B.1 Final Value Theorem, A-9
B.2 Laplace Transform Pairs, A-9
Reference, A-9
GLOSSARY G-1
INDEX
X
Note: Page numbers in italics refer to illustrations
A
Absolute viscosities, 480
Acceleration measurement, 430–435
piezoelectric accelerometer, 436, 436
with a seismic instrument, 435–437
Acceleration, velocity measurement from, 437–441
Accelerometer, 67, 79, 243, 436–437
piezoelectric, 436, 436–437
vibrometer, 433
AC component, 40
AC coupling, 240
Accuracy, 16
AC generators, 450
Acoustical measurements, 341–345
A-weighting scale, 342, 342
condenser microphone, 343, 343
C-weighting scale, 342, 342
microphones, 342–345
signal weighting, 341–342
sound level meter (SLM), 344, 344
Acoustic wave speed, 347
Active filters, 201, 209–211
inverting bandpass, 209, 210
inverting high-pass, 209, 210
inverting low-pass, 209, 209
Lowpass Butterworth Active Filter program, 210
Sallen–Key unit-gain filter, 210
Actuators, 450, 452. See also Hydraulic actuators; Linear
actuators; Pneumatic actuators; Rotary actuators;
Solenoids
flow-control valves, 455–457
A/D converters, 241
Address, 224
Advanced-stage uncertainty analysis, 151–157, 153
higher-order uncertainty, 152
Nth-order uncertainty, 152–157
single-measurement uncertainty analysis, 151
zero-order uncertainty, 152
Aleatory uncertainty, 144
Alias frequencies, 218–221
folding diagram for, 219
Alloys, properties of, 475
Alternating current measurement, using analog devices, 178–179
American National Standards Institute (ANSI), 29, 134
American Society of Mechanical Engineers (ASME), 29, 134,
362, 368, 368–369, 449
American Society of Mechanical Engineers’ Performance Test
Code (ASME PTC), 315, 449
American Society of Testing and Materials (ASTM), 29
ASTM E29—Standard Practice for Using Significant Digits, 31
Ammeter, 176, 183
Amontons, Guillaume, 258
Ampere (A), 25
Amplification, 238–240
Amplifiers, 193–196, 239–240
closed loop gain, 193
operational amplifier, 193, 194–195
Amplitude, 38
ambiguity, 221
of signal, 42–54
Analog devices, 174–213
analog signal conditioning, 193–196
special-purpose circuits, 196–201
connecting wires, 211, 213
current measurements using, 174–179
alternating current, 178–179
D’Arsonval meter movement, 175, 175
direct current, 174–178
simple multirange ammeter, 176
ground and ground loops, 211–212
impedance matching, 188–192
loading errors, 188–192
measurements using, 174–213
potentiometer, 181–182
resistance measurements, 182–188
shields, 212–213
voltage measurements using, 179–182
analog voltage meters, 179
oscilloscope, 179–181
Analog filters, 238
Analog input-output communication, 242–246
data acquisition modules, 242–246
Analog signal, 36, 36
conditioning, 201–211, 238–240. See also Filters
amplification, 238–240
Analog-to-digital converter, 228–232
conversion error, 230–232
quantization error, 228–229
I-1I-2 INDEX
Analog-to-digital converter (contd.)
resolution, 228
saturation error, 229–230
Analog voltage comparator, 196–197, 197
Analog voltage meters, 179
Anemometry, 350–352. See also Doppler anemometry; Thermal
anemometry
Angular velocity measurements, 441–444, 443
electromagnetic techniques, 443–444
mechanical measurement techniques, 441
stroboscopic, 442, 442–443
ANSI. See American National Standards Institute (ANSI)
Anti-aliasing filter, 219
Aperiodic signal, 38
Apparent strain, 409–418, 410
bridge static sensitivity, 412–413
practical considerations, 413
ASME. See American Society of Mechanical Engineers
(ASME)
Astable multivibrator, 199
ASTM. See American Society of Testing and Materials (ASTM)
Asynchronous transmission, 247
Average value, 14, 17, 39n2, 41, 97, 276
analog signal, 39
moving, 239
A-weighting scale, 342, 342
Axial strain, 395
B
Balance, null, 181, 236, 279n3
Bandpass filter, 201
Barometer, 319–320
Fortin barometer, 319, 319
Base dimensions and units, 23–25
current, 25
frequency, 24
length, 24
luminous intensity, 25
mass, 23–24
measure of substance, 25
temperature, 24–25
time, 24
Bellows, 326–327
Bending beam load cell, 444, 445
Bernoulli, Daniel, 358, 368
Bernoulli effect, 361
Bessel filters, 202
design, 208–209
Best estimate, 101, 146, 163
Beta ratio, 363
Biaxial strain gauge rosettes, 414, 415
rectangular strain gauge rosettes, 414, 415
single plane type, 415
stacked type, 415
BIH. See Bureau International de l’ Heure (BIH)
Bimetallic thermometers, 262–263, 263
Binary codes, 224–225
Binary numbers, 37, 224, 227–228
Binomial distribution, 102
Bistable multivibrator, 200
Bits, 223–225
Block diagrams, 463–464
Bluetooth communications, 248–249
Boltzmann’s constant, 298
Borda, Jean, 363
Bourdon tube, 326
Bourdon tube pressure gauge, 326, 327
Bragg grating, 422, 422–423
Bridge circuits, 182–184, 266, 267
Callender-Griffiths 3-wire bridge, 267, 267
Mueller 4-wire bridge, 267
Wheatstone bridge, 182–183, 184
Bridge constant, 408–409
Bridge static sensitivity, 412–413
Buffer, 248
Bulb thermometer, 2, 3
Bureau International de l’Heure (BIH), 24
Butterworth filters, 202, 202
design, 202–203
first-order low-pass resistor-and-capacitor (RC) Butterworth
filter circuit, 202, 202
improved designs, 203–208
ladder circuit for multistage high-pass LC filter, 205, 205
magnitude characteristics, 203, 204
Byte, 224
C
Calibration, 14
accuracy, 16
dynamic, 14–15
errors, 16, 141, 141
hysteresis, 19
instrument precision, 21
instrument repeatability, 21
instrument uncertainty, 22
linearity error, 19–20, 20
measured value, 16
overall instrument error, 22
random errors, 16–17
random test, 19
range, 15
reproducibility, 21
resolution, 16
sequential test, 19
span, 15–16
standard, 14
static calibration, 14
static calibration curve, 14, 15
static sensitivity (K), 15
systematic errors, 16–17
true value, 16
uncertainty, 17–18Index I-3
validation, 22
verification, 22
Callender-Griffiths 3-wire bridge, 267, 267
Candela (cd), 25
Canny method, 253, 254, 255
Capacitance, 26, 27
farad, 26
Capacitance elements, 328–330, 329
Capillary tube viscometer, 376n2
Capsule elements, 326–327
Cascading filters, 203
Catch-and-weigh technique, 391
Celsius (∘C) scale, 25, 260
Central tendency, 99
Charge
coulomb (C), 26, 27
Charge amplifier, 197, 198, 199
Chauvenet’s criterion, 126
Chi-squared (χ2) distribution, 117–121
goodness-of-fit test, 119–121
precision interval in a sample variance, 118–119
Circular frequency, 44
Closed-loop control, 458
Closed-loop controller, 241–242, 242
Closed loop gain, 193
Coaxial cable, 213
Combined standard uncertainty, 159, 164
Common-mode voltage (cmv), 212, 245–246
Comparator, 463
Complete immersion thermometer, 262
Complex periodic waveform, 38
Complex waveforms, 45
Compliance, 336
Compressibility effects, 363
Concomitant methods, 14
Condenser microphone, 343, 343
Conduction errors, 305–308
Conductive plastic potentiometer, 427, 427
Confidence interval, 97, 112, 123, 126–129, 131, 159, 171
Connecting wires, 211, 213
coaxial cable, 213
optical cable, 213
single cable, 213
triaxial cable, 213
twisted pairs, 213
Continuous variable, 6
Controlled variable, 6
Controller model, 465
Controls, 457–473
block diagrams, 463–464
closed-loop control, 458
dynamic response, 460
feedback control, 458
Laplace transforms, 460–462
on–off control, 458, 459–460
open-loop control, 458, 458
operational blocks, 463
oven control model, 464–467
proportional-integral (PI) Control, 468–469
Conversion error, 230–232
Conversion factors, 475–481
Conversion resolution, 229, 230
Coriolis, Gaspard de, 387
Coriolis, 387–391
flow meter, 387–391, 388–389
turndown, 375–377, 382–383, 387, 390
Correction for correlated errors, 168–170
Correlation, 14
coefficient, 124–125
photon, for LDA, 351
Coulomb (C), 26, 27
Coupled systems, 93–95, 94
Cradled dynamometers, 449–450
AC generators, 450
DC generators, 450
eddy current dynamometers, 450
waterbrake dynamometers, 450, 451–452
Critically damped system, 80
Critical pressure ratio, 373
Current, 25
ampere (A), 25
measurement, using analog devices, 174–179
4–20mA current loop, 199
C-weighting scale, 342, 342
D
D/A converters, 241
Damping ratio, 82
D’Arsonval meter movement, 175, 175
Data-acquisition errors, 141, 141
Data acquisition modules, 242–246
differential-ended connection, 245, 245–246
self-contained, portable multipurpose, 244
single-ended connection, 245, 245–246
special signal conditioning modules, 246
USB-based, 244
Data acquisition systems (DAS), 215–256
analog signal flow scheme using, 237, 238
components, 238–242
A/D converters, 241
amplifiers, 239–240
analog filters, 238
closed-loop controller, 241–242, 242
D/A converters, 241
digital filters, 238–239
digital input/output, 241
filters, 238–240
multiplexer, 241, 241
offset nulling circuit, 240
shunt resistor circuits, 240, 240
Data acquisition triggering, 246
Data outlier detection, 126–127I-4 INDEX
Data presentation, 30–33
full-log, 30, 31
numerical operations, 32
plotting, 30, 31
rectangular, 31
rounding, 32
semilog, 30, 31
significant digits, 30–33
Data-reduction errors, 142, 142
Data transmission, 247–248
DC component, 40
DC generators, 450
Dead volume, 329, 337
Deadweight Testers, 324, 324–325
Deflection method, 185–188
Degrees of freedom, 108
Dependent variable, 6
Derived dimensions and units, 25–28
electrical dimensions, 26–28
energy, 26
force, 25–26
power, 26
pressure, 26
stress, 26
Design of experiments, 135–136
Design-stage uncertainty analysis, 136–140
in combining uncertainties, 137, 138
elemental errors, combining, RSS method, 137
Detailed uncertainty analysis, 136
general versus, 136
Deterministic signal, 38
Deviation, 108
plot, 117
DFT. See Discrete Fourier transform (DFT)
Diaphragms, 327–330
capacitance elements, 328–330, 329
diaphragm meters, 385
piezoelectric crystal elements, 330–331
pressure transducer using four active resistance strain gauges,
329, 329
strain gauge elements, 328
Differential-ended connection, 245, 245–246
Digit, 30
least significant digit, 31
most significant digit, 30
significant digit, 30
Digital devices, 223–225
address, 224
bits, 223–225
offset binary, 224
ones-complement binary code, 224
twos-complement binary code, 224
words, 223–225
Digital filters, 238–239
Digital image acquisition and processing, 252–256
Canny method, 253, 254, 255
edge detection methods, 253, 254, 254
image acquisition, 252, 252–253, 253
image processing, 253–256
Sobel method, 253, 254, 255
Digital input/output, 241
Digital input–output communication, 246–252
asynchronous transmission, 247
bluetooth communications, 248–249
data transmission, 247–248
parity, 247
RS-232C protocol, 249
synchronous transmission, 247
Universal Serial Bus (USB), 248
Digital numbers, transmitting, 226–227
high and low signals, 226–227
methods for, 226, 226
Digital signals, 37, 37, 40–41
Digital-to-analog converter, 227, 227–228
Digital voltmeters, 235–237
Dimension, 22
base, 23–25
derived, 25–28
electrical, 26–28
length, 24
mass, 23–24
temperature, 24–25
time, 24
Direct current measurement, using analog devices, 174–178
Direct current offset, 41–42
Discharge coefficient, 363
Discrete Fourier transform (DFT), 56–60, 216
fast Fourier transform (FFT), 57
one-sided or half-transform, 57
Discrete time signals, 36, 37, 40–41
Discrete variable, 6
Displacement sensors, 426–430
conductive plastic potentiometer, 427, 427
dynamic response, 429–430
linear variable differential transformer (LVDT), 428,
428–429
rotary variable differential transformer (RVDT), 430
Displacement, velocity measurement from, 437–441
Distortion, 90
Doppler, Johann, 350
Doppler anemometry, 350–352, 354
laser Doppler anemometer (LDA), 350, 351
phase Doppler anemometry, 351
Doppler (ultrasonic) flow meters, 383–384
Dynamic calibration, 14–15
Dynamic error, 78
Dynamic measurements, 65–66
Dynamic pressure, 346
in moving fluids, 334
transducer calibration, 331–333
shock tube facility, 331, 332
Dynamic response, 460Index I-5
Dynamic signal, 38, 39
analog representation of, 39
discrete representation of, 39
Dynamometer, 447, 449
absorbing, 449
ac and dc generators, 450
cradled, 449–450
eddy current, 450
engine, 447
waterbrake, 450
E
Earth ground, 211
Eddy current dynamometers, 450
Edge detection methods, 253, 254, 254
Elastic behavior of materials, 396
Elastic load cell designs, 444, 445
Electrical dimensions, 26–28
capacitance, 26
charge, 26
electrical potential, 26
resistance, 26
Electrical potential, 26
volt (V), 26, 27
Electrical resistance thermometry, 263–276
practical considerations, 270–271
resistance temperature device resistance measurement,
266–270
Electrodynamometer, 178
Electromagnetic spectrum, 297, 297
Electromagnetic techniques, 443–444
Electronic reference junction compensation, 280
Elemental errors
combining, RSS method, 137
propagation of, 157–163
Emissive power, 297–298, 303
Energy, 26
joule, 26
Epistemic uncertainty, 144
Error(s), 16
calibration errors, 141, 141
conversion error, 230–232
data-acquisition errors, 141, 141
data-reduction errors, 142, 142
error fraction, 71
hysteresis error, 19, 20
overall instrument error, 22
propagation of error, 145–146
random errors, 16–17, 17, 143–144
repeatability error, 19, 20
saturation error, 229–230
sensitivity error, 20, 21
sources, identifying, 141
systematic errors, 16, 17, 17
zero shift (null) error, 20, 21
Euler, Leonhard, 358
Euler formulas, 49
Even functions, 49–54
Expanded uncertainty, 159, 164
Expansion factor, 363–364, 366
Experimental test plan, 5–14. See also Randomization; Variables
concomitant methods, 14
data reduction design plan, 5
interference, 8–9, 9
noise, 8–9, 9
parameter design plan, 5
repetition, 13
replication, 13
steps in, 5
system and tolerance design plan, 5
Extraneous variables, 6
F
Fahrenheit (∘F), 25
Fahrenheit, Gabriel D., 259
Farad (F), 26
Faraday, Michael, 377, 428
Fast Fourier transform (FFT), 57
Feedback control, 4, 458
Fiber Bragg strain measurement, 422, 422–423
Filter band, 85
Filters, 201–211, 238–240. See also Bessel filters; Butterworth
filters
active filters, 201, 209–211
analog, 238
bandpass filter, 201
Butterworth filters, 202, 202
cascading filters, 203
characteristics, 201, 201
digital, 238–239
high-pass filter, 201
low-pass filter, 201
notch filter, 201
passband, 201
passive analog filter circuits, 201
roll-off, 202
stopband, 201
Final value theorem, 483
Finite-sized data sets, statistics of, 107–114
finite statistics, 108
inferential statistics, 107
repeated tests and pooled data, 113–114
standard deviation of the means, 110–113
Finite statistics, 108
First-order systems, 69–79
frequency response, 77
determination, 79
magnitude ratio, 77, 78
phase shift, 77, 78
simple periodic function input, 76–79
step function input, 70–76
time constant, 70I-6 INDEX
First-order uncertainty, 152, 153
Fixed point temperatures, 259–260
Flip-flop circuits, 199–201
Flip-flop multivibrator, 200, 200
Flow coefficient, 363–364, 365, 457
Flow-control valves, 455–457, 456
Flow measurements, 357–393. See also Insertion volume
flow meters; Mass flow meters; Pressure differential
meters
Bernoulli effect, 361
flow meter calibration and standards, 391–392
historical background, 357–358
mass flow rate, 357
standard flow rate, estimating, 392–393
volume flow rate, 357
through velocity determination, 359–361
Flow nozzle, 361, 363–373
Flow rate concepts, 358–359
Fluid velocity measuring systems, 345–354
particle image velocimetry (PIV), 352, 352–353
pitot–static pressure methods, 353
pitot-static pressure probe, 346, 346–348
thermal anemometry, 348, 348–350
velocity measuring methods, 353–354
Folding diagram, 219, 219
Force, 25–26
load cells, 444–447
measurement, 444–447
Newton, 25
Fortin barometer, 319, 319
Fourier analysis, 43
Fourier coefficients, 48
Fourier series, 48
cosine series, 49
fundamental, 48
sine series, 50–54
Fourier transform, 55–62
discrete Fourier transform, 56–60
inverse Fourier transform, 56
Francis, James, 368
Freeman, John Ripley, 369
Frequency, 24, 35. See also Nyquist frequency
analysis, 45–48
bandwidth, 78
distribution, 99
response, 77
of signal, 42–54
spectrum, 55–62
Frontinius, Sextus, 357
Full field IR imaging, 303–304
Full-log coordinate format, 30, 31
Full scale operating range (FSO), 15
Functions
even functions, 49–54
odd functions, 49–54
with T = 2π, 49
Fundamental Fourier series, 48
Fundamental frequency, 48
G
Galvanometer, 177, 181, 182
Gases, transmission effects, 339–340
Gauge factor, 401–403
Gauge length, 400, 404
General measurement system, 2–5
components, 4
General model for measurement system, 64–68
General purpose interface bus (GPIB), 248, 249
General system model, 68–88
first-order systems, 69–79. See also individual entry
second-order systems, 79–88. See also individual entry
static sensitivity (K), determination, 68–69
zero-order systems, 68–69
General template for measurement system, 4–5
General versus detailed uncertainty analysis, 136
Goodness-of-fit test, 119–121
Gosset, William S., 109, 109n5
GPIB. See General purpose interface bus (GPIB)
Ground loops, 212
Grounds, 211–212
H
Hall effect, 178
Handshake, 247
Harmonics, 48
Heat flux, 291–294
heat flux sensor, 291
Heat flux sensor, 291
construction of, 291, 291
thin-film heat flux sensor, 292, 292
Heavily damped systems, 340–341
Hero of Alexandria, 357
Herschel, Clemens, 366
Herschel venturi meter, 366, 367
Hierarchy of standards, 28–29
Higher-order uncertainty, 152
High-pass filter, 201
Histogram, 99
Hooke’s law, 396
Hot-film sensor, 348, 354
Hot-wire sensor, 348, 350, 354
Hydraulic actuators, 452–455
Hypothesis testing, 114–117
p-value, 115
t-test, 115
z-test, 115
Hysteresis, 19
error, 19, 20
I
Image acquisition, 252, 252–253, 253
Image processing, 253–256Index I-7
Impact cylinder, 334, 335
Impedance matching, 188–192
Imread function, 253
Imshow function, 253
Inch-pound (I-P) unit system, 23
Inclined tube manometer, 321, 321
Independent variables, 6
Inertance, 336
Inferential statistics, 107
Infinite statistics, 108
Input, 35
Input/output signal concepts, 35–39
generalized behavior, 36
measurement system selection, 35, 36
signal waveforms, 38–39
waveforms classification, 36–38
Insertion errors, 305
Insertion volume flow meters, 377–386
diaphragm meters, 385
Doppler (ultrasonic) flow meters, 383–384
electromagnetic flow meters, 377–379
positive displacement meters, 382–384
rotameters, 381–382, 382
rotating vane meters, 385
transit time flow meters, 383–384
turbine meters, 382–383
vortex shedding meters, 379–381, 380
wobble meters, 385
Instrument error
common elements of, 20
hysteresis error, 20
linearity error, 20
repeatability error, 20
sensitivity error, 20
zero shift (null) error, 20
Instrument precision, 21
Instrument repeatability, 21
Instrument uncertainty, 22, 137
Interference, 8–9, 9
International Bureau of Weights and Measures (BIPM), 23
International Organization for Standardization (ISO), 29, 134, 144
International Temperature Scale of 1990 (ITS-90), 260
Interpolation, 260
standards for, 261
Interstage loading errors, 190–192
Inverse Fourier transform, 56
Inverting bandpass active filter, 209, 210
Inverting high-pass active filter, 209, 210
Inverting low-pass active filter, 209, 209
J
Joule, 26
K
Kelvin (K) scale, 24, 260
K-factor, 380
Kiel probe, 334, 335
Kinematic viscosities, 481
King’s law, 348
L
Laminar flow elements, 376–377
Laplace transforms, 460–462
analysis, 466
basics, 482–483
pairs, 483
Laser Doppler anemometer (LDA), 350, 351, 354
Lateral strains, 397–398
Law of homogeneous materials, 278
Law of intermediate materials, 278–279
Law of successive or intermediate temperatures, 279
LDA. See Laser Doppler anemometer (LDA)
Leakage, 221–223
Least significant digit, 31
Least-squares regression analysis, 121–124
Leibniz, Gottfried Wilhelm, 51n5
Length, 24
Level of significance, 115
Light, characteristics, 418–419
Linear actuators, 450
screw-drive linear motion, 450, 452
slider–crank mechanism, 450
using lead screw, 450, 452
Linearity error, 19–20, 20
Linear polynomials, 124–126
Linear variable differential transformer (LVDT), 327, 428,
428–429
LVDT gauge head, 429, 430
Linear velocity measurements, 437
Linkwitz–Riley high-pass or low-pass filter, 207, 207
Linnaeus, Carolus, 259
Liquid-in-glass thermometer, 260, 260, 262, 262
complete immersion thermometer, 262
partial immersion thermometer, 262
total immersion thermometer, 262
Liquids, transmission effects, 338
Load cells, 444–447
bending beam load cell, 444, 445
elastic load cell designs, 444, 445
piezoelectric load cells, 444–447
design, 446, 446
proving ring, 446–447, 447
shear beam load cell, 444, 445
strain gauge load cells, 444
Loading errors, 188–192
interstage loading errors, 190–192
for voltage-dividing circuit, 189, 189–190
Log normal distribution, 102
Lowpass Butterworth Active Filter program, 210
Low-pass filter, 201
low-pass Butterworth filter, 202, 202I-8 INDEX
Luminous intensity, 25
candela, 25
LVDT. See Linear variable differential transformer (LVDT)
M
Mach number, 311–312, 332
Magnitude, 35
magnitude ratio, 77, 78
Manometer, 320–323
inclined tube manometer, 321, 321
micromanometer, 321, 321
U-tube manometer, 320, 321
Mass, 23–24
Mass flow meters, 386–391
Coriolis flow meter, 387–391, 388–389
thermal flow meter, 386–387
McLeod gauge, 318, 318–319
Mean value, 39, 97–99, 101, 103, 108, 111–114, 126, 135, 145,
146, 150, 164–167, 239
digital signal, 41
discrete time signal, 41
sample mean, 98, 108, 111, 126, 135, 145
true mean, 6, 99, 103, 108, 111–114
Measurand, 98
Measured value, 2, 16
Measured variable, 98
Measurement errors, 134–136
repeated measurements, distribution of errors on, 134, 135
Measurement methods, 1–33. See also Calibration;
Experimental test plan; Standards
basic concepts, 1–33
experimental test plan, 5–14
feedback-control stage, 4
general measurement system, 2–5
general template for, 4–5
output stage, 4
sensor, 2–3
signal-conditioning stage, 3–4
transducer, 2–3
Measurement random standard uncertainty, 158
Measurement systematic standard uncertainty, 158
Measurement system behavior, 64–95. See also General system
model
coupled systems, 93–95, 94
dynamic measurements, 65–66
general model for, 64–68
multiple-function inputs, 91–93
phase linearity, 90–91
transfer functions, 88–89
Mechanical measurement techniques, 441, 442
Mechanical power measurements, 448–450
cradled dynamometers, 449–450
prony brake, 448, 449
rotational speed, 448–449
shaft power, 448–449
torque, 448–449
Mechatronics, 426–473. See also Actuators; Controls; Force,
measurement; Sensors; Velocity measurements
Metallic gauges, 398–400
metallic foil strain gauge, 400, 400
Method of least-squares, 122
Metrology, 134
Micromanometer, 321, 321
Microphones, 342–345
Modified three-sigma test, 126
Moiré methods, 421, 421–422
Mole, 25
Monostable multivibrator, 200
Monte Carlo simulations, 129, 129–131, 151
Most significant digit, 30
Moving coil transducers, 441, 441
Moving fluids, 333–336. See also Pressure measurements, in
moving fluids
Mueller 4-wire bridge, 267
Multiple-function inputs, 91–93
Multiple gauge bridge, 407–408
Multiple-junction thermocouple circuits, 289–291
Multiple-measurement uncertainty analysis, 157–168, 158
combined standard uncertainty, 159, 164
elemental errors, propagation of, 157–163
expanded uncertainty, 159, 164
propagation of elemental systematic uncertainties, 157–159
propagation of uncertainty to a result, 163–168
Welch–Satterthwaite formula, 164
Multiplexer, 241, 241
Multi-variable error propagation, 144–151
Monte Carlo method, 151
propagation of error, 145–146
sensitivity index, approximating, 146–148
sequential perturbation, 149–150
Multivibrator, 199, 199–201
astable, 199
flip-flop/bistable multivibrator, 200, 200
monostable, 200
TTL signal, 199
N
Narrow band infrared temperature measurement, 302–304
full field IR imaging, 303–304
fundamental principles, 302–303
two-color thermometry, 303
National Institute of Standards and Technology (NIST), 261, 280,
282, 287, 295, 296, 392
Natural frequency, 82
Negative temperature coefficient (NTC), 263
Newton, 25
Newton, Sir Isaac, 358
NIST. See National Institute of Standards and Technology (NIST)
Noise, 8–9, 9
Nondeterministic signal, 38–39
Nonsymmetrical systematic uncertainty interval, 170–171
Normal distribution, 102Index I-9
Normal (or Gaussian) distribution, 103
Normal error function, 104
Normal stress, 395
Notch filter, 201
NTC. See Negative temperature coefficient (NTC)
Nth-order uncertainty, 152–157
Null method, 184
Numerical operations, 32
Nyquist frequency, 218, 238
O
Obstruction meters, 361–364
compressibility effects, 363
selection, 374–376
accuracy, 375
costs, 374–375
placement, 374
pressure loss, 374
turndown, 375–376
square-edged orifice plate meter, 361, 362
standards for, 364
Odd functions, 49–54
Offset binary, 224
Offset nulling circuit, 240
Ohm (Ω), 26, 27
Ohmmeter circuits, 182, 183
multirange ohmmeter circuits, 182, 183
Ones-complement binary codes, 224
One-shot circuit, 200
One-sided or half-transform, 57
On–off control, 458, 459–460
Open-loop control, 458, 458
Operational amplifier, 193, 194–195
Operational blocks, 463
single-input, single-output amplifier block, 463
temperature-input, voltage-output amplifier block, 463
Optical cable, 213
Optical fiber thermometer, 301, 301
Optical strain measuring techniques, 418–423
Orifice meter, 364–366
square-edged orifice meter, 364, 364–365
Orifice plate, 361
Oscilloscope, 179–181
Outlier, 126–127
Chauvenet’s criterion, 126–127
three-sigma test, 126
Output, 35
stage, 4
Oven control model, 464–467, 465, 467
controller model, 465
Laplace transform analysis, 466
plant model, 464–465
step response, 466–467
Overall instrument error, 22
Overdamped system, 80
P
Parallel communications, 249–252
Parallel converters, 235, 236
Parameter, 6
Parity, 247
Partial immersion thermometer, 262
Particle image velocimetry (PIV), 352, 352–354
Pascal (Pa), 26
Passband, 201
Passive analog filter circuits, 201
Peltier, Jean Charles Athanase, 277
Peltier coefficient, 277
Peltier effect, 277
Period, 44
Periodic signals, 43–45
spring-mass system, 43, 44
Perturbation, sequential, 149–150
Phase Doppler anemometry, 351
Phase linearity, 90–91
Phase shift, 77, 78
Photoelastic measurement, 419–421
plane polariscope, 420, 420–421
Physical errors in temperature measurement, 304–312
conduction errors, 305–308
errors associated with temperature sensors, 305
insertion errors, 305
probe design, 307–308
radiation errors, 308–309
radiation shielding, 310
random errors, 305
recovery errors, 311–312
systematic errors, 305
PI. See Proportional-integral (PI) control
PID. See Proportional integral–derivative (PID) control
Piezoelectric accelerometer, 436, 436
Piezoelectric crystal elements, 330, 330–331
Piezoelectric load cells, 444–447, 446
Pitot–static pressure methods, 353
Pitot-static pressure probe, 346, 346–348
Pitot tube, 334, 335
PIV. See Particle image velocimetry (PIV)
Place value, 30
Planck’s constant, 298
Plane polariscope, 420, 420–421
Plant model, 464–465
Platinum resistance temperature device (RTD), 266
PLC. See Programmable logic controller (PLC)
Plotting formats, 30, 31
full-log coordinate format, 30, 31
rectangular coordinate format, 30, 31
semilog coordinate format, 30, 31
Pneumatic actuators, 452–455, 454
Poiseulle, Jean, 376
Poisson distribution, 102
Poisson’s ratio, 328, 397, 398, 401
Polarization of light, 419, 419I-10 INDEX
Pooled data, 113–114
Pooled mean, 113
Pooled standard deviation, 114
Pop test, 332
Population behavior, 103–107
Positive displacement meters, 377, 384–386
Positive temperature coefficient (PTC), 263
Potentiometer, 181–182
instruments, 181–182
voltage divider circuit, 181, 181
Potentiometer pressure transducer, 327, 327
Power, 26
watt (W), 26
Prandtl tube for static pressure, 335, 336, 336
Precision interval in a sample variance, 118–119
Pressure, 26
absolute, 68, 315–317, 319, 325, 332
pascal (Pa), 26
Pressure concepts, 315–317
relative pressure scales, 316, 316
Pressure differential meters, 361–377
flow nozzles, 368–373
laminar flow elements, 376–377
obstruction meters, 361–364
selection, 374–376
orifice meter, 364–366
sonic nozzles, 373–374
venturi meter, 366–368
Pressure-fluid systems, modeling, 336–337
Pressure measurements, 315–354. See also Transmission effects
in moving fluids, 333–336
dynamic pressure, 334
stagnation, 334
static pressure, 334–336
total pressure, 334
total pressure measurement, 334–335
Pressure reference instruments, 318–325
barometer, 319–320
deadweight testers, 324, 324–325
inclined tube manometer, 321, 321
manometer, 320–323
McLeod gauge, 318, 318–319
micromanometer, 321, 321
U-tube manometer, 320, 321
Pressure sensors, elastic elements as, 325, 326
Pressure transducers, 325–331. See also Diaphragms
bellows, 326–327
Bourdon tube, 326
calibration, 331–333
dynamic calibration, 331–333
static calibration, 331
capsule elements, 326–327
diaphragms, 327–330
potentiometer pressure transducer, 327, 327
pressure sensors, elastic elements as, 325, 326
Primary standard, 23
Primary unit standards, 23
Principle of superposition, 91
Probability, 97–131. See also Chi-squared (χ2) distribution;
Probability density functions; Regression analysis
Monte Carlo simulations, 129, 129–131
number of measurements required, 127–129
Probability density functions, 98–103
standard statistical distributions, 102
binomial, 102
log normal, 102
normal, 102
Poisson, 102
rectangular, 102
triangular, 102
Programmable logic controller (PLC), 5
Prony brake, 448, 449
Propagation
of elemental systematic uncertainties, 157–159
of uncertainty to a result, 163–168
Property data, 475–481
thermophysical properties, 476–477
Proportional-integral (PI) control, 468, 468–469
integral control, 468
time response, 469
Proportional integral–derivative (PID) control, 469–473, 473
proportional control, 472–473
of a second-order system, 469–473, 471
Provers, 391
Proving ring, 446–447, 447
P-value, 115
Pyranometer construction, 300
Pyrometry, 300–301
Q
Quantization, 37, 228
quantization error, 228–229
R
Radiation
blackbody, 261, 297
detectors, 299
emissive power, 297, 303
errors, 308–309
shielding, 310
temperature measurement, 297–304
wavelength distribution, 298
Radiative temperature measurements, 297–304
narrow band infrared temperature measurement, 302–304
optical fiber thermometer, 301, 301
pyrometry, 300–301
radiation detectors, 299
radiation fundamentals, 297–299
radiometer, 299, 299–300
Radiometer, 299, 299–300
pyranometer construction, 300Index I-11
Ramp (integrating) converters, 233–235, 234, 235
Random errors, 16–17, 17, 143–144, 305
Randomization, 9–13
Random standard uncertainty, 143
Random test, 19
Random uncertainty, 98, 112, 143, 144
Random variable, 98, 99
Range, 15, 35
Rayleigh relation, 348
Recovery errors in temperature measurement, 311–312
Rectangular coordinate format, 30, 31
Rectangular distribution, 102, 129, 135, 151, 157, 171
standard uncertainty, 151
Reference junction, 280
Regression analysis, 121–126
least-squares regression analysis, 121–124
linear polynomials, 124–126
Relative pressure scales, 316, 316
Repeatability, 21
Repeatability error, 20, 21
Repeated measurements, distribution of errors on, 134, 135
Repeated tests, 113–114
Repetition, 13
Replication, 13
Reproducibility, 21
Resistance, 26, 336
Ohm (Ω), 26, 27
Resistance measurements, 182–188
bridge circuits, 182–184
deflection method, 185–188
null method, 184
ohmmeter circuits, 182, 183
Resistance strain gauges, 398–404
configurations, 401
delta rosette, 401
diaphragm pattern, 401
linear pattern, 401
rectangular rosette, 401
residual stress pattern, 401
stacked rosette, 401
tee pattern, 401
torque rosette, 401
gauge factor, 401–403
metallic gauges, 398–400
semiconductor strain gauges, 403–404
strain gauge construction and bonding, 400–403
Resistance temperature detectors (RTDs), 263–266, 265,
348, 387
platinum RTDs, 266
Resistance temperature device resistance measurement, 266–270
Resolution, 16, 228
conversion resolution, 229, 230
Resonance band, 84–85
Resonance frequency, 85
Reynolds number, 6
Ringing frequency, 81–82
Rise time of system, 71, 81
Roll-off, 202
Root-mean-square, analog signal, 40
Root-sum-squares (RSS) method, 137
Rotameters, 381–382, 382
Rotary actuators, 455
stepper motors, 455, 455
Rotary variable differential transformer (RVDT), 430, 431
Rotating vane meters, 385
Rotational speed, 448–449
Rounding, 32
RS-232C protocol, 249
RTDs. See Resistance temperature detectors (RTDs)
Ruge, Arthur, 398
RVDT. See Rotary variable differential transformer (RVDT)
S
Sallen–Key unit-gain filter, 210
Sample-and-hold circuit (SHC), 197, 197
Sample mean value (), 108
Sample standard deviation (sx), 108
Sample variance (sx2), 108
Sampling, 215–256
alias frequencies, 218–221
amplitude ambiguity, 221
anti-aliasing filter, 219
concepts, 216–223
leakage, 221–223
sample rate, 216–217, 216–218
waveform fidelity, 223
Sampling theorem, 217
Saturation error, 229–230
Screw-drive linear motion, 450, 452
Second-order systems, 79–88
ringing frequency, 81–82
rise time, 81
settling time, 81
simple periodic function input, 83–84
step function input, 80–83
system characteristics, 84–88
Seebeck, Thomas Johann, 276
Seebeck effect, 276–277
Seismic transducer, 430–435, 432, 434
Semiconductor strain gauges, 403–404
Semilog coordinate format, 30, 31
Sensitivity error, 20, 21
Sensitivity index, approximating, 146–148
Sensors, 2–3, 426–450. See also Displacement sensors; Load cells
acceleration measurement, 430–435
atomic force microscope, sensor stage of, 2–3
displacement sensors, 426–430
potentiometer construction, 427, 427
rotary variable differential transformer, 430, 431
seismic transducer, 430–435
torque measurements, 447–448
vibration measurement, 430–435I-12 INDEX
Sequential perturbation, 149–150
Sequential test, 19
Settling time, 81
Shaft power, 448–449
SHC. See Sample-and-hold circuit (SHC)
Shear beam load cell, 444, 445
Shielding, 212–213
Shields, 212–213
Shock tube facility, 331, 332
Shunt resistor circuits, 240, 240
Signal, 35–62. See also Input/output signal concepts
amplitude, 42–54
analysis, 39–42
digital signals, 40–41
direct current offset, 41–42
discrete time signals, 40–41
in frequency space, 60–62
signal root-mean-square value, 40
conditioning, 3–4
strain measurement and, 416–418
definition, 36
dynamic characteristics, 35–62
frequency, 42–54
periodic signals, 43–45
signal-conditioning, 3–4
static characteristics, 35–62
Signal root-mean-square value, 40
Signal waveforms, 38–39
aperiodic, 38
deterministic signal, 38
dynamic signal, 38, 39
nondeterministic signal, 38–39
simple periodic waveform, 38
static signal, 38
steady periodic signal, 38
Signal weighting, 341–342
A-weighting scale, 342, 342
condenser microphone, 343, 343
C-weighting scale, 342, 342
Significant digits, 30–33
Simmons, Edward, 398
Simple multirange ammeter, 176
Simple periodic function input, 76–79, 83–84
Simple periodic waveform, 38
Single cable, 213
Single-ended connection, 245, 245–246
Single-measurement uncertainty analysis, 151, 153
Single-tailed test, 115
Slider–crank mechanism, 450
Sobel method, 253, 254, 255
Solenoids, 453, 454, 455
Sonic nozzles, 373–374
Sound level meter (SLM), 344, 344
Span, 15–16
Special-purpose circuits, 196–201
analog voltage comparator, 196–197, 197
astable multivibrator, 199
charge amplifier, 197, 198, 199
4–20mA current loop, 199
flip-flop circuits, 199–201
multivibrator, 199–201
sample-and-hold circuit (SHC), 197, 197
Special signal conditioning modules, 246
Square-edged orifice plate meter, 361, 362, 364, 364–365
Stagnation in moving fluids, 334
Standard, 14
Standard cubic feet per minute (SCFM), 392
Standard deviation, 21, 103
of the means, 110–113
Standard error of the fit, 122
Standard flow rate, estimating, 392–393
Standardized normal variate, 104
Standards, 22–30. See also Base dimensions and units; Derived
dimensions and units
hierarchy, 28–29
primary, 23
temperature, 24–25
test, 29
Standard statistical distributions, 102
binomial, 102
log normal, 102
normal, 102
Poisson, 102
rectangular, 102
triangular, 102
Standard thermocouple voltage, 282–287, 283
Static calibration, 14, 15
Static pressure in moving fluids, 334, 334n2
Static pressure measurement in moving fluids, 335–336
Prandtl tube for static pressure, 335, 336
static pressure wall tap, 335, 335
Static pressure transducer calibration, 331
Static sensitivity (K), 15, 68–69
determination, 68–69
Static signal, 38
Statistical measurement theory, 98–103. See also Probability
Density Functions
Steady periodic signal, 38
Step function input, 70–76
Stepper motors, 455, 455
Stiffness, 337
Stopband, 201
Strain, 395–398. See also Resistance strain gauges
axial strain, 395
lateral strains, 397–398
Strain gauge
electrical circuits, 404–407
elements, 328
interface, 246, 247
load cells, 444
Wheatstone bridge circuit, 404, 404Index I-13
Strain measurement, 395–423
apparent strain, 409–418
biaxial strain gauge rosettes, 414, 415
bridge constant, 408–409
fiber Bragg strain measurement, 422, 422–423
Moiré methods, 421, 421–422
multiple gauge bridge, 407–408
optical strain measuring techniques, 418–423
photoelastic measurement, 419–421
practical considerations for, 407–409
signal conditioning, 416–418
strain gauge data, analysis, 413–416
temperature compensation, 410–412
Stream pressure, 334n2
Stress, 26, 395–398
biaxial state of stress, 397
normal stress, 395
pascal (Pa), 26
Stroboscopic angular velocity measurements, 442,
442–443
Student’s t distribution, 108, 109
Substance measure, 25
mole, 25
Successive approximation converters, 232, 232–237
digital voltmeters, 235–237
parallel converters, 235, 236
ramp (integrating) converters, 233–235, 234, 235
Synchronous transmission, 247
Systematic errors, 16, 17, 17, 142–143, 305
Systematic standard uncertainty, 142
Systematic uncertainty, 142
T
Temperature, 24–25
celsius (∘C), 25
and definition, 259–261
fahrenheit (∘C), 25
kelvin (K), 24
standards, 259–261
Temperature compensation
bridge arrangements for, 412, 412
common gauge mountings, 411
and strain measurement, 410–412
Temperature measurements, 258–312. See also Electrical
resistance thermometry
fixed point temperatures, 259–260
historical background, 258–259
interpolation, 260
liquid-in-glass thermometer, 260, 260
physical errors in, 304–312. See also individual entry
scales and standards, 260–261
t estimator, 108
Test plan, 5–14. See also Experimental test plan
Test standards and codes, 29–30
Thermal anemometer, 353–354
Thermal anemometry, 348, 348–350
hot-wire probe, 349, 349
operating modes, 348
Thermal flow meter, 386–387
Thermistors, 271–276, 272
circuits, 271, 272
Thermocouple, 276, 276
basic temperature measurement with, 279–280, 280
multiple-junction thermocouple circuits, 289–291
in parallel, 291, 291
Thermocouple voltage measurement, 287–289
thermocouple reference table, 283–285
Thermoelectric temperature measurement, 276–296
applications for, 291–294
data acquisition considerations, 294–296
fundamental thermocouple laws, 278–279
Peltier effect, 277
reference junction, 280
Seebeck effect, 276–277
standard thermocouple voltage, 282–287, 283
thermocouple standards, 280–287
Thomson effect, 277–278, 278
Thermometer
bimetallic, 262–263, 263
complete immersion, 262
electrical resistance, 263–276
liquid-in glass, 262
optical fiber, 301
partial immersion, 262
platinum resistance, 29, 261, 266
radiation, 297
total immersion, 262
Thermometry based on thermal expansion, 261–263
bimetallic thermometers, 262–263, 263
liquid-in-glass thermometers, 262
Thermophysical properties, 476–477
of air, 479
of metallic solids, 476–477
of saturated water (liquid), 478
Thermopiles, 289–291, 290
Thin-film heat flux sensor, 292, 292
Thomson, William (Lord Kelvin), 24, 277, 398
Thomson effect, 277–278, 278
Three-sigma test, 126
Thresholding, 254
Time, 24
time constant, 70, 72
Torque, 448–449
measurements, 447–448
shaft instrumented for, 448, 448
Torricelli, Evangelista, 319, 366
Total immersion thermometer, 262
Total pressure in moving fluids, 334I-14 INDEX
Total pressure measurement, 334–335
impact cylinder, 334, 335
Kiel probe, 334, 335
Pitot tube, 334, 335
Transducers
atomic force microscope, transducer stage, 3
for shock and vibration measurement, 436–437
Transfer functions, 88, 88–89
operation of, 88, 88–89
Transit time flow meters, 383–384
Transmission band, 85
Transmission effects, 337–341
design and installation, 337–341
equivalent lumped parameter network, 337, 337
gases, 339–340
heavily damped systems, 340–341
liquids, 338
Triangular distribution, 102
Triaxial cable, 213
True mean value, 101
True value, 16
True variance, 103
T-test, 115
TTL signal, 199
Turbine meters, 382–383
Twisted pairs, 213
Two-color thermometry, 303
Twos-complement binary codes, 224
Two-tailed test, 115
Type A uncertainty, 144
Type B uncertainty, 144
U
Uncertainty, 17–18
propagation, 137
Uncertainty analysis, 133–171. See also Advanced-stage
uncertainty analysis; Multiple-measurement uncertainty
analysis; Multi-variable error propagation
advanced-stage, 151–157
aleatory uncertainty, 144
correction for correlated errors, 168–170
design-stage, 136–140
epistemic uncertainty, 144
error sources, identifying, 141
general versus detailed, 136
measurement errors, 134–136
multiple-measurement, 157–168
nonsymmetrical systematic uncertainty interval, 170–171
standard uncertainties, 142–144
systematic error, 142–143
type A uncertainty, 144
type B uncertainty, 144
Underdamped system, 80–82, 84, 85, 211, 331
Unit, 22
Unit step function, 70, 70
Universal Serial Bus (USB), 248
U.S. customary units, 23
U-tube manometer, 320, 321
V
Validation, 22
Valves, 455–457
Variables, 6–8
continuous, 6
controlled, 6
dependent, 6
discrete, 6
extraneous, 6
independent, 6
parameter, 6
Velocity measurements, 315–354, 437–438. See also Angular
velocity measurements; Fluid Velocity measuring
systems
Doppler anemometry, 354
laser Doppler anemometer (LDA), 354
linear velocity measurements, 437
particle image velocimetry (PIV), 354
pitot–static pressure methods, 353
selection of, 353–354
thermal anemometer, 353–354
velocity from displacement or acceleration, 437–441
Venturi, Giovanni, 368, 373
Venturi meter, 362, 366–368
Herschel venturi meter, 366, 367
Verification, 22
Vibration measurement, 430–435
transducers for, 436–437
Vibrometer, 433
Viscosity
absolute, 355, 432, 480
kinematic, 356, 359, 383, 481
Volt (V), 26, 27
Voltage
analog measurement, 179–182
digital measurement, 227–237
Voltage divider circuit, 181, 181
Voltage-divider principles, 427n2
Voltage-dividing circuit, loading errors for, 189, 189–190
Voltage measurements, 227–237
analog-to-digital converter, 228–232
digital-to-analog converter, 227, 227–228
quantization, 228
using analog devices, 179–182
Voltmeters, 179
Volt-ohmmeters (VOMs), 179
Volume flow rate through velocity determination, 359–361
von Karman, Theodore, 379
Vortex shedding meters, 379–381, 380–381Index I-15
W
Waterbrake dynamometers, 450, 451–452
Water, thermophysical properties, 478
Watt (W), 26
Waveforms, 35
classification, 36–38, 38. See also Signal waveforms
analog signal, 36, 36
analog-to-digital (A/D) converter, 37
digital signals, 37, 37
discrete time signal, 36, 37
fidelity, 223
Weisbach, Julius, 373
Welch–Satterthwaite formula, 164
Wheatstone bridge, 182–183, 184
voltage-sensitive Wheatstone bridge, 185, 185
Wobble meters, 385
Words, 223–225
Y
Young’s modulus, 396
Z
Zero errors, 21
Zero-order systems, 68–69
Zero-order uncertainty, 136, 152
Zero shift (null) error, 20
Zeroth law of thermodynamics, 259
z-test, 115
z variable, 104, 108, 109, 115


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