PART I: PRINCIPLES AND METHODS OF FORCE MEASUREMENT
1 INTRODUCTION TO FORCE MEASUREMENT ............................ 3
1.1 Various Approaches to Force Transduction ................ 3
1.2 Newton - Measurement Unit of Force ...................... 6
1.3 Mechanical Measurements of Forces & Tribology ........... 8
1.4 Force Transducers Other than Electrical ................ 10
1.5 Terminology: Sensors or Transducers? ................... 13
1.6 Force Measurement Systems .............................. 16
REFERENCES .................................................. 20
2 ELECTRICAL METHODS OF FORCE MEASUREMENT ..................... 23
2.1 Energetical Aspects in Force Transduction .............. 24
2.2 Examples of Force Measurement in Thermal Processes ..... 27
2.3 Typical Requirements for Force Transducers ............. 29
2.4 Force Transducers (FTs) Classifications ................ 30
2.4.1 First Attempts of Force Transducers
Systematization ................................. 30
2.4.2 German FT Classifications ....................... 32
2.4.3 Dutch FT Classifications ........................ 34
2.4.4 English FT Classifications ...................... 35
2.5 Nonconventional Types of Force Transducers ............. 37
2.5.1 Electrodynamic Force Transducers ................ 37
2.5.2 Galvanomagnetic Force Transducers (Based on
Hall Effect) .................................... 37
2.5.3 Acoustic Force Transducers (SAWs) ............... 38
2.6 An Enlarged Classification of Force Transducers ........ 40
REFERENCES .................................................. 44
3 RESISTIVE FORCE TRANSDUCERS ................................. 49
3.1 Resistive Force Transducers Types ...................... 50
3.2 Potentiometers ......................................... 52
3.3 Pretensioned Wires ..................................... 53
3.4 Strain Gauges .......................................... 54
3.5 Piezoresistive Sensors ................................. 56
3.5.1 Silicon Devices ................................. 57
3.5.2 Carbon Film Coatings and Carbon Nanotubes
(CNTs) .......................................... 59
3.6 Force Sensing Resistors (FSRs) ......................... 62
3.7 Force Sensing Resistive Networks ....................... 65
REFERENCES .................................................. 68
4 INDUCTIVE FORCE TRANSDUCERS ................................. 73
4.1 LVDT (Linear Variable Differential Transformer) ........ 74
4.2 Variable Reluctance Transducers ........................ 78
4.3 Mutual Inductance Variation Force Transducers .......... 79
4.4 Inductive Eddy Current Transducer ...................... 81
4.5 Biparametric Inductive Force Transducers ............... 81
4.5.1 Biparametric LR ................................. 81
4.5.2 Biparametric LC ................................. 82
REFERENCES .................................................. 85
5 CAPACITIVE FORCE TRANSDUCERS ................................ 87
5.1 Capacitive Force Transducers Classification ............ 87
5.2 Capacitive Force Transducers (CFTs) with Plates ........ 88
5.2.1 CFT with Variable Thickness of the Dielectric
Pad ............................................. 88
5.2.2 CFT with Variable Distance between Plates ....... 90
5.2.3 CFT with Plates Arranged under a Certain
Angle ........................................... 91
5.3 Multiple Plates Capacitive Force Transducers ........... 92
5.4 Interdigitated and Matrix of Capacitive Sensors ........ 94
5.4.1 CFT with Interdigitated Electrodes .............. 94
5.4.2 CFT Using a Matrix of Capacitive Sensing
Elements ........................................ 96
5.5 Cylindrical Capacitive Force Transducers ............... 97
5.6 Applications Based on Electrostatic Forces ............ 100
5.6.1 Electrostatic Force Balances ................... 100
5.6.2 Other Applications of Electrostatic Forces
for the Measurement of Mechanical Quantities ... 102
5.7 Electronic Circuits for Capacitive Transducers ........ 103
REFERENCES ................................................. 105
6 PIEZOELECTRIC FORCE TRANSDUCERS (PZFTs) .................... 109
6.1 Piezoelectric Materials ............................... 110
6.1.1 Quartz Crystals ................................ 110
6.1.2 Sensors with Organic Polymers .................. 111
6.1.3 Solid State Devices ............................ 113
6.2 Unidirectional Piezoelectric Force Transducers ........ 114
6.3 Tridirectional Piezoelectric Force Transducers ........ 117
6.4 Piezoelectric Bimorph as Force Transducer ............. 120
6.5 Electronic Circuits for Piezo Force Transducers ....... 123
6.6 Complex Applications with Piezoelectric Devices ....... 125
REFERENCES ................................................. 126
7 ELECTROMAGNETIC FORCE TRANSDUCERS .......................... 131
7.1 Classification ........................................ 131
7.2 Magnetoresistive Force Transducers .................... 135
7.3 Force Measurements in Magnetic Field .................. 138
7.3.1 Resistive Force Transducers in Magnetic
Field .......................................... 139
7.3.2 Capacitive Force Transducers in Magnetic
Field .......................................... 140
7.3.3 Pressure Transducers Based on Magnetic
Higher-Order Harmonic Fields ................... 141
7.4 Electromagnetic Weighing by Force Compensation ........ 142
7.5 Electromagnetic Devices for Small Forces .............. 144
7.5.1 Electromagnetic Probes for Micro- and Nano-
force Measurements ............................. 144
7.5.2 Magnetic Flux Quantum as a Sub-pico-newton
Weight ......................................... 146
7.5.3 Casimir Forces and Levitation Pressures
Measurement .................................... 148
REFERENCES ................................................. 149
8 ELECTRODYNAMIC FORCE TRANSDUCERS ........................... 153
8.1 Electrodynamic Force Compensation Principle ........... 155
8.2 Load Cells with Electrodynamic Feedback ............... 156
8.3 Electrodynamic Force Compensation Balances ............ 157
8.3.1 Hydrodynamic Gravimetric Balance ............... 157
8.3.2 Electrodynamic Vacuum Microbalance ............. 158
8.3.3 Electrodynamic Devices for Small Particles
Experiments .................................... 159
8.4 Micromechanical Testers with Moving Coils ............. 160
8.5 Multifunctional Transducers with Moving Coils ......... 161
REFERENCES ................................................. 163
9 MAGNETOELASTIC FORCE TRANSDUCERS ........................... 165
9.1 The Magnetostrictive Principle ........................ 166
9.2 Classification of Magnetoelastic FTs .................. 168
9.3 Axial Magnetoelastic Force Transducers ................ 170
9.3.1 Magnetostrictive Strips and Bars ............... 170
9.3.2 Magnetostrictive Amorphous Wires ............... 172
9.4 Frame-Shaped Magnetoelastic Force Transducers ......... 173
9.5 Tubular Magnetoelastic Force Transducers .............. 174
9.6 Circular Magnetoelastic Force Transducers ............. 176
9.7 Block-Shaped Magnetoelastic Force Transducers ......... 178
9.8 Magnetoelastic Shafts for Torque Transducers .......... 180
9.9 Magnetoelastic FTs Electronic Circuitry ............... 181
REFERENCES ................................................. 183
10 GALVANOMAGNETIC FORCE TRANSDUCERS .......................... 185
10.1 Hall Effect and Its Applications ...................... 186
10.2 Force Transducers Based on the Hall Effect ............ 189
10.2.1 Hall Effect in Geotechnical Engineering ........ 189
10.2.2 Medical Applications with Hall Sensors ......... 190
10.3 Hall Devices for Other Mechanical Quantities .......... 191
10.3.1 Displacement and Position Measurements Using
Hall Sensors ................................... 191
10.3.2 Weighing Based on Hall Devices ................. 192
10.3.3 Pressure and Row Measurements by Means of
Hall Sensors ................................... 193
10.3.4 Shock Measurements Using Hall Devices .......... 194
10.3.5 Penetration Velocity and Rotational Speed
Measured with Hall Sensors ..................... 195
10.4 Galvanomagnetic FTs in Complex Measurement Chains ..... 196
10.4.1 Combined Measurands in Galvanomagnetic Force
Transducers .................................... 196
10.4.2 Triaxial Galvanomagnetic Force Transducers ..... 198
10.5 Other Electromagnetic Principles in Force
Measurement ........................................... 199
REFERENCES ................................................. 200
11 VIBRATING-WIRE FORCE TRANSDUCERS ........................... 203
11.1 Vibrating Wire as Force Measurement Principle ......... 203
11.2 VWFTs' Structures and Characteristics ................. 206
11.3 Electronic Circuits for VWTs .......................... 209
11.3.1 Vibrating-Wire Excitation Methods .............. 209
11.3.2 Measuring Circuits for Vibrating-Wire
Transducers .................................... 211
11.3.3 Digital Weighing В ased on Vibrating-Wire
Transducers .................................... 211
11.3.4 Virtual Musical Instruments Investigated by
Means of VWFTs ................................. 212
11.4 Different Types of Vibrating-Wire Transducers ......... 213
11.5 VWTs' Applications for Other Physical Quantities ...... 217
11.5.1 Viscometers and Densimeters .................... 217
11.5.2 "Piezometers" (for Underground Water
Pressure) ...................................... 219
11.5.3 Tiltmeters / Inclinometers and Slope
Indicators ..................................... 220
11.6 VWTs' Progress and Their Extended Utilization ......... 220
REFERENCES ................................................. 223
12 RESONATOR FORCE TRANSDUCERS ................................ 227
12.1 Resonator Principle in Force Measurement .............. 228
12.2 Materials for Resonators and Their Q-Factors .......... 230
12.2.1 Quartz Resonators for Force Transducers ........ 231
12.2.2 Silicon Resonators for Force Transducers ....... 232
12.3 Various Shapes of Resonators .......................... 235
12.3.1 Resonating Beams for Force Transducers ......... 235
12.3.2 Resonating Diaphragms / Membranes for Force /
Pressure Transducers ........................... 237
12.3.3 Resonating Tubes for Force Transducers ......... 238
12.4 Single Beam (Micro)Resonators ......................... 238
12.5 Double Beam (Micro)Resonators ......................... 240
12.5.1 Classical Double-Ended Tuning Forks (DETFs) .... 240
12.5.2 Modern Solutions for DETF Resonators ........... 242
12.6 Metallic Triple Beam Resonators (MTBRs) ............... 244
12.6.1 Force Transducers with MTBRs ................... 244
12.6.2 Torque Transducers with MTBRs .................. 246
REFERENCES ................................................. 247
13 ACOUSTIC FORCE TRANSDUCERS ................................. 251
13.1 Interdigital Transducers (IDTs) ....................... 252
13.2 Acoustic Emission and Waveguides ...................... 254
13.2.1 Acoustic Emission Applications ................. 254
13.2.2 Acoustic Waveguides Applications ............... 254
13.3 Ultrasound Force Transducers .......................... 256
13.3.1 Industrial Applications of Ultrasound Force
Transducers .................................... 256
13.3.2 Ultrasound Force Transducers for Food and
Farmacology .................................... 259
13.3.3 Medical Applications of Ultrasound Force
Transducers .................................... 260
13.4 Acoustic Radiation Force Transducers .................. 261
13.4.1 Acoustic Radiation Force Transducers in
Medicine ....................................... 261
13.4.2 Acoustic Radiation Force Transducers in
Metrology ...................................... 262
13.5 Surface Acoustic Wave (SAW) Transducers ............... 264
13.5.1 SAW Force Transducers .......................... 265
13.5.2 SAW Torque Transducers ......................... 266
13.5.3 SAW Pressure Transducers ....................... 267
13.5.4 SAW Fluidic Transducers ........................ 267
13.6 SAW Electronic Circuits ............................... 268
REFERENCES ................................................. 272
14 GYROSCOPIC FORCE TRANSDUCERS ............................... 275
14.1 The Gyroscopic Principle in Force Measurement ......... 275
14.2 Conventional Gyroscopic Force Transducers ............. 277
14.3 Types of Micro-Gyroscopic Force Transducers ........... 279
14.3.1 Inertial Gyroscopes ............................ 279
14.3.2 Piezoelectric Gyroscopes ....................... 281
14.3.3 Resonator / Vibrating Gyroscopes ............... 282
14.3.4 Acoustic (and SAW) Gyroscopes .................. 284
14.3.5 Coriolis Force Transducers in Medical
Applications ................................... 285
14.4 Optical Gyroscopes .................................... 286
14.4.1 Fiber Optic Gyroscopes (FOGs) .................. 286
14.4.2 Laser Gyroscopes ............................... 288
14.4.3 MOEMS (Micro-Opto-Electro-Mechanical System)
Gyroscope ...................................... 288
14.5 A Topical Review of Gyroscopes ........................ 288
REFERENCES ................................................. 290
15 FORCE BALANCE TECHNIQUES ................................... 293
15.1 Force Balance Principle Applied to Transducers ........ 294
15.2 Electromagnetic Force Compensation (EMFC) ............. 297
15.3 Electrostatic Force Compensation ...................... 299
15.4 Optical Devices Based on Force Feedback ............... 302
REFERENCES ................................................. 304
16 MIXED METHODS IN FORCE MEASUREMENTS ........................ 307
16.1 Force Transducers Using Advanced Electronics .......... 308
16.2 Cantilever Beams for Various Force Transducers ........ 310
16.3 CNTs for Measuring Mechanical Quantities .............. 312
16.4 Combined Methods of Force Transduction ................ 316
16.4.1 Force Transducers in Medical Instruments ....... 316
16.4.2 EMAT (Electro-Magnetic Acoustic Transducer)
and Lorentz Force .............................. 318
16.4.3 Multitransducer Equipment ...................... 320
16.4.4 Force Transducers Involving Optical
Techniques ..................................... 321
REFERENCES ................................................. 324
PART II: FORCE TRANSDUCERS COMPONENTS
17 THE FORCE MEASUREMENT CHAIN ................................ 331
17.1 Force Measurement Chain Components .................... 331
17.2 Strain Gauge Sensing .................................. 334
17.3 Strain Gauges Signal Conditioning ..................... 337
17.4 Strain Gauges Signal Processing ....................... 340
17.5 Data Presentation for Force Transducers ............... 343
REFERENCES ................................................. 345
18 WHEATSTONE BRIDGE - THE BASIC CIRCUIT FOR STRAIN GAUGE
FORCE TRANSDUCERS .......................................... 347
18.1 Wheatstone Bridge - General Presentation .............. 347
18.2 Wheatstone Bridge - Fundamental Properties ............ 348
18.3 Bridge Compensation and Adjusting Resistors ........... 350
18.4 Supply Possibilities for Wheatstone Bridges ........... 352
18.5 Different Applications with Measuring Bridges ......... 353
18.6 Further Connections for Wheatstone Bridges ............ 356
REFERENCES ................................................. 358
19 STRAIN GAUGES ELECTRONIC CIRCUITS .......................... 361
19.1 Signal Conditioning for Force Transducers ............. 361
19.2 Signal Conditioners ................................... 362
19.2.1 Pre- and Post-Conditioning ..................... 362
19.2.2 High-Gain Signal Conditioning .................. 363
19.2.3 "QuantumX" Universal Conditioner ............... 363
19.3 Analog-to-Digital Converters .......................... 365
19.3.1 Different Conversions to Frequency ............. 365
19.3.2 Resistance-to-Time Converter ................... 365
19.3.3 Sigma-Delta Converter .......................... 366
19.4 Bridge Oscillators .................................... 367
19.4.1 Wien Bridge Based Oscillator ................... 367
19.4.2 Wheatstone Bridge Based Oscillator ............. 368
19.5 AC Generators ......................................... 369
19.5.1 Sine Wave Generator ............................ 369
19.5.2 Saw-Tooth Wave Generator ....................... 369
19.5.3 Rectangular Wave Generator ..................... 370
19.6 Strain Gauged Force Transducers Connected to PC ....... 371
19.6.1 Direct Resistance Change Measurement ........... 371
19.6.2 Strain Gauge Bridge Signal Processing .......... 371
REFERENCES ................................................. 373
20 CLASSIFICATION OF ELASTIC ELEMENTS ......................... 375
20.1 Elastic Elements Loading Modes ........................ 375
20.2 Examples of Elastic Elements Classifications .......... 378
20.3 Comprehensive Classification of Elastic Elements ...... 381
REFERENCES ................................................. 387
21 STRETCHED / COMPRESSED COLUMNS ............................. 389
21.1 Classical Columns ..................................... 389
21.2 Optimized Columns ..................................... 394
21.3 Increasing Sensitivity for Columnar Transducers ....... 394
21.4 Complex Structures Composed by Bars / Columns ......... 395
21.5 Dynamic Testing for Cylindrical Transducers ........... 396
REFERENCES ................................................. 397
22 STRETCHED / COMPRESSED TUBES ............................... 399
21.1 Classical Tubes ....................................... 399
22.1 Concentric Tubes ...................................... 403
22.2 Profiled Tubes ........................................ 404
22.3 Tubes with Holes or Slots ............................. 408
22.4 Tubular Structures under Complex Loading .............. 410
REFERENCES ................................................. 411
23 BENT LAMELLA (CANTILEVER BEAMS) ............................ 415
23.1 Various Applications with Cantilever Beams ............ 415
23.2 Cantilever Beams for Lower Forces ..................... 419
23.3 (Bio)Chemical Cantilevers ............................. 424
23.4 Several Shapes of Cantilever Beams .................... 428
23.5 Cantilever Beams in Multicomponent FTs ................ 431
REFERENCES ................................................. 434
D.M. STEFANESCU
24 BENT AND / OR TORSION SHAFTS ............................... 437
24.1 Bending of Cantilever Tube or Cylinder ................ 437
24.2 Rotating Shafts ....................................... 439
24.3 Complex Loaded Shafts ................................. 441
REFERENCES ................................................. 443
25 MIDDLE BENT BARS WITH FIXED ENDS ........................... 445
25.1 Examples of Middle Bent Bars with Fixed Ends .......... 445
25.2 Slotted Structures for Middle Bent Bars with Fixed
Ends .................................................. 448
25.3 Dynamic Applications of Double Ended Beams ............ 450
25.4 Various Models of Four-Spoke Wheels ................... 452
REFERENCES ................................................. 455
26 SHEARING STRAINED ELASTIC ELEMENTS ......................... 457
26.1 'I'-Profiles Subjected to Shearing .................... 459
26.2 Load Measuring Pins / Bolts ........................... 460
26.3 Hollow Discs / Wheels ................................. 462
26.4 S (Z) Shaped Elastic Elements ......................... 464
26.5 Helix Load Cells ...................................... 465
REFERENCES ................................................. 466
27 BENT YOKES AND FRAMES ...................................... 469
27.1 Various Shapes of Bent Yokes and Frames ............... 471
27.2 Force-Measuring Clamps ................................ 474
REFERENCES ................................................. 475
28 BENT RINGS AND "GLASSES" ................................... 477
28.1 Various Shapes of Bent Rings .......................... 477
28.1.1 Circular Rings ................................. 477
28.1.2 "Square" Rings ................................. 480
28.1.3 Hexagonal Rings ................................ 481
28.1.4 Octagonal Rings ................................ 481
28.1.5 Other Shapes of Bent Rings ..................... 482
28.2 "Glasses"-Shaped Elastic Structures ................... 484
28.3 Multiple "Glasses"-Shaped Elastic Elements ............ 490
REFERENCES ................................................. 491
29 BENT MEMBRANES ............................................. 495
29.1 Various Types of Bent Membranes ....................... 495
29.2 Circular Membranes .................................... 500
29.3 Square Membranes ...................................... 505
29.4 Membranes with Various Shapes of Apertures ............ 509
29.5 Other Shapes of Membranes ............................. 511
REFERENCES ................................................. 514
30 COMPLEX LOADED TORUS ....................................... 517
30.1 Torus as Elastic Element for Force Transducers ........ 517
30.2 Toroidal Elastic Elements in Special Applications ..... 520
REFERENCES ................................................. 522
31 AXISYMMETRIC ELASTIC ELEMENTS .............................. 523
31.1 Various Axisymmetric EEs for Force Transducers ........ 523
31.2 Axisymmetrical EEs for Very Large Force
Transducers ........................................... 528
31.3 N-Shaped Axisymmetric Elastic Elements ................ 534
REFERENCES ................................................. 537
32 VOLUMETRIC ELASTIC ELEMENTS ................................ 539
32.1 Spheres ............................................... 539
32.2 Cubes ................................................. 542
32.2.1 Full Cubes ..................................... 542
32.2.2 Cubic Blocks with Slots ........................ 543
32.3 Complex Bodies with Oblique Slots ..................... 547
REFERENCES ................................................. 548
33 COMPLEX, COMPOSED AND COMBINED ELASTIC STRUCTURES .......... 549
33.1 Complex Elastic Structures ............................ 550
33.1.1 Plane Complex Structures ....................... 550
33.1.2 Spatial Complex Structures ..................... 552
33.2 Composed Elastic Structures ........................... 554
33.3 Combined Elastic Structures ........................... 558
33.3.1 Plane Combinations of Elastic Elements ......... 558
33.3.2 Axisymmetric Combinations of Elastic
Elements ....................................... 559
33.3.3 Spatial Combinations of Elastic Elements ....... 560
REFERENCES ................................................. 562
34 ELASTIC ELEMENTS SELECTION CRITERIA ........................ 563
34.1 Elastic Elements (EEs) Evaluation Criteria ............ 565
34.2 Elastic Elements Comparative Analysis ................. 566
34.3 ЕЕ Selection for Specific Applications ................ 569
34.3.1 From Single- to Multi-component Force
Transducers .................................... 569
34.3.2 Force Transducers in Mechatronics .............. 570
34.3.3 EEs for Very Large Forces ...................... 571
34.4 Elastic Elements Automatic Selection .................. 572
REFERENCES ................................................. 574
35 DIGITAL AND INTELLIGENT FORCE TRANSDUCERS .................. 577
35.1 Evolution from Analog to Digital ...................... 577
35.2 Automatic Recognition of Force Transducers ............ 579
35.3 Force Transducers in Dynamic Regime ................... 581
35.4 Intelligent (Smart) Force Transducers ................. 582
35.5 Further Prospects: Materials, Technologies, Ideas ..... 583
35.5.1 Smart Materials and Structures ................. 583
35.5.2 Intelligent Design and Smart Technology ........ 584
35.5.3 Neuro-Fuzzy Concepts ........................... 585
35.6 Updated Force Transducers + Data Communication ........ 585
35.6.1 Dual Output Force Transducers .................. 585
35.6.2 Data Display and Communication ................. 587
REFERENCES ................................................. 589
ANNEX 1. Rules for Strain Gauges Placement on the Elastic
Elements of Force Transducers ........................ 591
ANNEX 2. The Newton's Apple Tree in Korea ..................... 595
INDEX ......................................................... 597
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