Theory and Design for Mechanical Measurements

Theory and Design for Mechanical Measurements merges time-tested pedagogy with current technology to deliver an immersive, accessible resource for both students and practicing engineers. Emphasizing statistics and uncertainty analysis with topical integration throughout, this book establishes a strong foundation in measurement theory while leveraging the e-book format to increase student engagement with interactive problems, electronic data sets, and more. This new Seventh edition has been updated with new practice problems, electronically accessible solutions, and dedicated Instructor Problems that ease course planning and assessment.

Extensive coverage of device selection, test procedures, measurement system performance, and result reporting and analysis sets the field for generalized understanding, while practical discussion of data acquisition hardware, infrared imaging, and other current technologies demonstrate real-world methods and techniques. Designed to align with a variety of undergraduate course structures, this unique text offers a highly flexible pedagogical framework while remaining rigorous enough for use in graduate studies, independent study, or professional reference. 

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

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 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

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 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 Sensitivity 412

Practical Considerations 413

Analysis of Strain Gauge Data 413

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

Chapter Homework Problems 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 I-1

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