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| موضوع: كتاب Theory and Design for Mechanical Measurements الأحد 21 مارس 2021, 11:41 am | |
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أخوانى فى الله أحضرت لكم كتاب Theory and Design for Mechanical Measurements Seventh Edition Richard S. Figliola Clemson University Donald E. Beasley Clemson University
و المحتوى كما يلي :
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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