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

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

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 Numerical Methods for Solving Ordinary Differential Equations

3.9 Summary, 95

References, 95

Nomenclature, 96

Subscripts, 96

 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, 170

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, 223

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

Summary, 256

References, 256

Nomenclature, 256

 8 TEMPERATURE MEASUREMENTS 258 0

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 Devices, 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, 299

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, 353

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 Sensiivity, 412 Practical Considerations, 413 Analysis of Strain Gauge Data, 413

Signal Conditioning, 416

11.7 Non-contact 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

 A PROPERTY DATA AND CONVERSION FACTORS 475

 B LAPLACE TRANSFORM BASICS 482

B.1 Final Value Theorem, 483

B.2 Laplace Transform Pairs, 483 Reference, 483

GLOSSARY 484

INDEX 000