Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics & Laser Vibrometry, Volume 8

Preface	6
Contents	8
1 Practical Techniques for Scaling of Optically Measured Operating Deflection Shapes	11
Nomenclature	11
1.1 Introduction	12
1.2 Theoretical Background	13
1.2.1 Drive Point Scaling Technique	13
1.2.2 Mass Sensitivity Scaling Technique	14
1.2.3 Structural Dynamic Modification	15
1.3 Experimental Test Setup	17
1.4 Test Cases Studied	19
1.4.1 Case A: Drive Point Measurement	19
1.4.2 Case B: Mass Sensitivity Scaling Technique	19
1.4.3 Case B.1: Estimating Mode Shapes of the Modified Structure Using Unscaled Deflection Shapes	21
1.4.4 Case B.2: Mass Sensitivity Scaling Technique	23
1.4.5 Case B.3: SDM Using Scaled Operating Deflection Shapes	23
1.5 Conclusion	24
References	26
2 Prediction of the Coupled Impedance from Frequency Response Data	28
2.1 Introduction	28
2.2 FRF Coupling	29
2.3 Experimental Setup	30
2.3.1 Experimental Case Study	31
2.4 Numerical Model	32
2.5 Conclusions	33
References	33
3 Real-Time State Detection in Highly Dynamic Systems	35
3.1 Introduction	35
3.2 EMI Method and Current State of Real-Time SHM	36
3.3 Adaptation of SHM Impedance Method and Equipment	36
3.4 Preliminary Timing Study	37
3.5 Design of Experimental Setup	38
3.6 Non-Real-Time Data Acquisition	40
3.7 Conclusions	40
3.8 Future Work	40
References	41
4 Stereo-DIC Measurements of Thermal Gradient Effects on the Vibratory Response of Metals	43
4.1 Introduction	43
4.2 Experimental Method	44
4.3 Results and Discussion	45
4.4 Conclusions	49
References	49
5 Modal Testing of a Nose Cone Using Three-Dimensional Scanning Laser Doppler Vibrometry	50
5.1 Introduction	50
5.2 Test Descriptions	50
5.2.1 Baseline Test	52
5.2.2 1D Test with New System	53
5.2.3 3D Test with New System	55
5.3 Analysis and Comparisons	56
5.3.1 Frequency Response Function Comparisons	57
5.3.2 Mode Shape Comparisons	58
5.4 Lessons Learned	59
5.5 Conclusions	62
References	62
6 A Mathematical Model for Determining the Pose of a SLDV	63
6.1 Introduction	63
6.2 Mathematical Model of a SLDV	64
6.2.1 Case When Only X Mirror Rotates	65
6.2.2 Case When Only Y Mirror Rotates	66
6.2.3 General Case	67
6.3 Rigid Transformation from the SMCS to SCS	67
6.4 Procedure to Determine the Orientation and Position of a SLDV	69
6.5 Experimental Validation	70
6.5.1 3D Structure Scanning	70
6.5.2 2D Clamped Plate Scanning	76
6.6 Conclusion	77
References	78
7 Operational Modal Analysis with a 3D Laser Vibrometer Without External Reference	80
7.1 Introduction	80
7.2 Theory	81
7.2.1 3D SLDV: Mode Shape Coordinate Transformation	81
7.2.2 Operational Modal Analysis: Stochastic Subspace Identification	82
7.2.3 Multi-setup Merging Strategies	83
7.3 Proposed Approach	85
7.4 Application	86
7.4.1 Experimental Setup	86
7.4.2 Discussion of Results	88
7.5 Conclusion	89
References	90
8 Scanning LDV Measurement Technology for Vibration Fatigue Testing	91
8.1 Introduction	91
8.2 Material and Methods	92
8.3 Results	94
8.4 Conclusions	98
References	98
9 Optically Detecting Wavefronts and Wave Speeds in Water Using Refracto-Vibrometry	99
9.1 Introduction	99
9.2 Theory	100
9.2.1 Refracto-Vibrometry	100
9.2.2 Speed of Sound Measurement	100
9.3 Experimental Setup	101
9.3.1 Optical Detection of 1 MHz Acoustic Wave and Its Reflections	102
9.3.2 Speed of Sound Measurement Through Lead and Bone	102
9.4 Results	103
9.4.1 Wavefront Transmission and Reflection	103
9.4.2 Speed of Sound Measurement in Lead	104
9.4.3 Speed of Sound Measurement in Synthetic Bone	105
9.5 Conclusions	106
References	107
10 Stochastic Wavenumber Estimation: Damage Detection Through Simulated Guided Lamb Waves	108
10.1 Introduction and Background	108
10.2 Inverse Modeling of Lamb-Wave Propagation	110
10.2.1 Rayleigh-Lamb Wave Equations	110
10.2.2 Feasibility for Inverse Modeling	111
10.3 Sources of Uncertainty in AWS	111
10.4 Methodology	113
10.4.1 Damage Detection Through Inverse Analysis	113
10.4.2 Bayesian Inference for Inverse Problems	114
10.4.3 Application to AWS: Stochastic Wavenumber Estimation	115
10.4.3.1 Parametric Uncertainty	116
10.4.3.2 Experimental Uncertainty	117
10.5 Case Study Application: Quantifying Severity of Damage in an Aluminum Plate Under Uncertainty	119
10.5.1 Model Development	119
10.5.2 Parametric Uncertainty	119
10.5.2.1 Experimental Campaign	119
10.5.2.2 Results and Discussion	121
10.5.3 Experimental Uncertainty	123
10.5.3.1 Experimental Campaign	123
10.5.3.2 Results and Discussion	124
10.6 Conclusion	126
References	128
11 Use of Continuous Scanning LDV for Diagnostics	130
11.1 Introduction	130
11.1.1 Background	131
11.2 Design of Experiment	132
11.2.1 Design of Damage by Finite Element	132
11.2.2 Virtual Test Simulation	135
11.3 Conclusions	138
References	140
12 A Cost Effective DIC System for Measuring Structural Vibrations	141
12.1 Introduction	141
12.2 Theoretical Background	142
12.3 Proposed Setup	145
12.4 Experimental Results	146
12.5 Conclusions	147
References	148
13 Teaching DSP and Dynamic Measurements at the Graduate Level at Michigan Technological University	149
13.1 Introduction	149
13.2 Teaching Approach	149
13.3 Topics Presented	150
13.4 Assignments	150
13.4.1 Basic Data Acquisition	151
13.4.2 Sampling and Quantization	151
13.4.3 Leakage, Windows, and FFT	151
13.4.4 FRF and Coherence	151
13.4.5 Digital Filtering	152
13.4.6 Order Tracking	152
13.5 Instrumentation	153
13.6 Distance Learning and Class Size	153
13.7 Grading	154
13.8 Conclusions	154
References	155
14 Flipping the Classroom for a Class on Experimental Vibration Analysis	156
14.1 Introduction	156
14.2 Motivation	157
14.3 Organization	157
14.4 Lecturer's Experience	158
14.5 Students' Experience	158
14.5.1 The Students' Experience with the Videos	158
14.5.2 How Did the Students Work with the Videos?	159
14.5.3 How Did the Students Experience the Classes in This New Teaching Style?	159
14.6 Conclusions	159
References	160
15 Lessons Learned from Operational Modal Analysis Courses at the University of Molise	161
15.1 Introduction	161
15.2 Teaching Methodology and Objectives	162
15.3 Organization of the Course	162
15.4 Conclusions	166
References	167
16 Authentic Engineering Assignments for an Undergraduate Vibration Laboratory Class	168
16.1 Introduction	168
16.2 Redesign of Laboratory Experiments as Authentic Assignments	168
16.3 Lab Activity 1: Free Response of an Aircraft Wing	169
16.4 Lab Activity 2: Spin Speed for Washing Machine	170
16.5 Lab Activity 3: Tuned Absorber to Reduce Steering Wheel Vibration	173
16.6 Conclusions	174
References	174
17 Vibration and Acoustic Analysis of Acoustic Guitar in Consideration of Transient Sound	175
17.1 Introduction	175
17.2 Vibration and Acoustic Characteristic of Guitar	175
17.2.1 Structure of Guitar	175
17.2.2 Measurement of Vibration and Sound	176
17.2.3 Steady State Characteristic	176
17.2.4 Transient Characteristic	176
17.3 Sound Quality Change	177
17.3.1 Evaluation on Modified Sound	178
17.3.2 Evaluation Result	178
17.4 Operational Deflection Shape, ODS	178
17.4.1 ODS Measurement	178
17.4.2 Front Plate ODS	179
17.4.3 Relation Between ODS and Sound Quality	179
17.5 ODS Design	180
17.5.1 Front Plate FE Model	180
17.5.2 Frequency ODS Formulation	180
17.5.3 Mode Shape Sensitivity	180
17.5.4 ODS Design by Non-Linear Programing	181
17.5.5 Optimized Design	181
17.5.6 Experimental Verification	183
17.6 Conclusion	183
References	184
18 Demarcation for the Coupling Strength in the MODENA Approach	185
18.1 Introduction	185
18.2 Theoretical Basis of MODENA	186
18.2.1 Dual modal formulation (DMF)	186
18.2.2 Power Balance Between Two Coupled Oscillators at Pure Tone	186
18.2.3 Power Balance of Multi-Modal Coupling System	188
18.3 Numerical Example 1: A Two-Oscillator Coupling Case	188
18.3.1 Definition of the Coupling Strength Factor	188
18.3.2 Error Analysis	189
18.3.3 Criterion for Determining the Level of Coupling Strength	190
18.4 Numerical Example 2: A Multi-Modal Coupling Case	191
18.4.1 System Definition and External Excitation	191
18.4.2 Energy Response of the Multi-Modal Coupling System	191
18.5 Conclusions	192
References	193
19 Vibro-Acoustic Modal Model of a Traction Motor for Railway Applications	194
19.1 Introduction	194
19.2 Experimental Modal Analysis	195
19.2.1 Mode Shape	195
19.2.2 Modal Parameter Extraction	196
19.2.3 Test Setup	196
19.2.4 Result	197
19.2.5 Discussion	197
19.3 Reduced Order Modal Model	200
19.3.1 Maxwell Forces	200
19.3.2 Spatial Force Distribution	200
19.3.3 Structural Model	201
19.4 Simulation Results	203
19.4.1 Simulation Setup	203
19.4.2 Results	203
19.4.3 Discussion	203
19.5 Conclusion	205
References	205
20 Operational Deflection Shapes of a PWM-Fed Traction Motor	206
20.1 Introduction	206
20.2 Magnetic Noise Characterization at PWM Operation	207
20.2.1 Slotting Vibrations	207
20.2.2 PWM Vibrations	208
20.2.3 Slotting PWM Vibrations	208
20.3 Experimental Set-Up	209
20.4 Results	210
20.5 Discussion	211
20.6 Conclusions	213
References	213
21 Acoustic Fatigue and Dynamic Behavior of Composite Panels Under Acoustic Excitation	215
21.1 Introduction	215
21.2 Model	216
21.3 Modal Analysis	220
21.4 Random Response Analysis	221
21.5 Conclusion	223
References	225
22 Evaluation of Microphone Density for Finite Element Source Inversion Simulation of a Laboratory Acoustic Test	226
Nomenclature	226
22.1 Introduction	226
22.2 Description of the Direct Field Acoustic Test	227
22.3 Model of a Flight System DFAT Test	227
22.4 Acoustic Source Inversion in Sierra/SD	229
22.5 Target Node Study Description	230
22.6 Results	231
22.6.1 Comparison of Target Node Pressure	231
22.6.2 Comparing Mean Sound Pressure Level	232
22.6.3 Comparing Mean Percent Difference in the Real and Imaginary Parts of Pressure	232
22.6.4 Comparing MAC of the Pressure Shape on the Wetted Surface	233
22.6.5 Visualizing the SPL	235
22.7 Conclusions and Future Work	237
References	237
23 Experimental Mapping of the Acoustic Field Generated by Ultrasonic Transducers	238
23.1 Introduction	238
23.2 Theoretical Background	239
23.3 Testing Performed	240
23.4 Results and Discussion	241
23.5 Conclusion	244
References	249
24 Enhanced Spin-Down Diagnostics for Nondestructive Evaluation of High-Value Systems	250
24.1 Introduction	250
24.2 Experimental Procedures	251
24.2.1 Experimental Setup	251
24.2.2 Analysis Methods	252
24.2.3 Linear Predictive Coding for Detection and Localization	253
24.2.4 “Binning Method” for Localization	253
24.2.5 Cross-Correlation of Laser Displacement Sensors	254
24.2.6 General Notes	254
24.3 Results	255
24.3.1 Linear Predictive Coding	255
24.3.2 Damage Location Binning	256
24.3.3 Out-of-Plane Displacement	258
24.4 Conclusions	259
References	260
25 Performing Direct-Field Acoustic Test Environments on a Sandia Flight System to Provide Data for Finite Element Simulation	261
25.1 Introduction	261
25.2 DFAT with MIMO Control	262
25.3 Test Design	262
25.4 Test Setup	263
25.5 Test Environment	265
25.6 Test Results: Truth Test #2	267
25.7 Test Results: Truth Test #4	268
25.8 Test Data Applied to Acoustic Finite Element Simulation	271
25.9 Response Microphone Examination	272
25.10 Conclusions	272
References	273
26 Smooth Complex Orthogonal Decomposition Applied to Traveling Waves in Elastic Media	274
26.1 Introduction	274
26.2 Mathematical Development for Smooth Complex Orthogonal Decomposition	275
26.3 Simulated Infinite Euler-Bernoulli Beam	278
26.3.1 Data Processing	279
26.3.2 Results	280
26.4 Experimental Beam	280
26.4.1 Setup	280
26.4.2 Data Processing	281
26.4.3 Results	282
26.5 Conclusions	282
Appendix: Primer of Smooth Orthogonal Decomposition	284
References	286
27 Subspace Algorithms in Modal Parameter Estimation for Operational Modal Analysis: Perspectives and Practices	287
Abbreviations	287
Nomenclature	287
27.1 Introduction	288
27.2 Stochastic Subspace Identification Algorithm	288
27.2.1 Covariance Driven Stochastic Subspace Identification Algorithm	289
27.2.1.1 SSI-Cov Based on Traditional Formulation	289
27.2.1.2 Alternate Formulation	290
27.2.2 Data Driven Stochastic Subspace Identification Algorithm	291
27.3 Conclusions	292
References	293
28 An Application of Multivariate Empirical Mode Decomposition Towards StructuralModal Identification	294
28.1 Introduction	294
28.2 Multivariate EMD	295
28.3 A Hybrid MEMD Method	296
28.4 Numerical Illustration	298
28.5 Conclusions	299
References	300
29 Dynamic Characterization of Milling Plant Columns	301
29.1 Introduction	301
29.2 Column Description and Setup of Experimental Tests	302
29.3 Experimental Set-Up	302
29.3.1 Sensors and Data Acquisition System	303
29.3.2 Signal Processing	305
29.4 Results	306
29.5 Concluding Remarks	309
References	310
30 Mixed Force and Displacement Control for Base-Isolation Bearings in RTHS	312
30.1 Introduction	312
30.2 Experimental Setup	313
30.2.1 Loading Frame and Base Isolation Bearings	313
30.2.2 Control, Instrumentation and Data Acquisition Systems	314
30.3 Preliminary Investigation of the Bearing Behavior	314
30.4 Mixed Force and Displacement Control Design	316
30.4.1 Decentralized Control Approach with Loop Shaping in the Vertical Actuator	316
30.4.2 Loop-Shaping Controller Design for the Force Controlled Actuator	317
30.5 Experimental Verification of Mixed-Mode Control	317
30.5.1 Verification of Constant Vertical Force Control Under Harmonic Lateral Loading	318
30.5.2 Verification of Varying Vertical Force Control Under Earthquake Lateral Loading	318
30.6 Real-Time Hybrid Simulation of Base Isolation Bearings	319
30.7 Conclusions	320
References	321
31 Leveraging Hybrid Simulation for Vibration-Based Damage Detection Studies	322
31.1 Introduction	322
31.2 Hybrid Simulation of Vibration Testing and Damage Progression	324
31.2.1 Description of Case Study Structure	324
31.2.2 Overview of Hybrid Simulation Methodology Employed	325
31.2.3 Details of Experimental Test Program	326
31.3 Discussion of Results	327
31.3.1 Hybrid Simulation in the Healthy Condition	327
31.3.2 Hybrid Simulation in the Damaged Condition	328
31.4 Summary	330
References	330
32 Real Time Hybrid Simulation with Online Model Updating on Highly Nonlinear Device	331
32.1 Introduction	331
32.2 Real Time Hybrid Simulation with Model Updating	332
32.2.1 Constrained Unscented Kalman Filter	333
32.3 Experimental Validation	334
32.3.1 Model Updating Results	335
32.3.2 RTHSMU Local and Global Results	335
32.4 Conclusion	337
References	338
33 Discrete-Time Compensation Technique for Real-Time Hybrid Simulation	339
33.1 Introduction	339
33.2 Discrete-Time Compensator	340
33.3 Optimization Schemes	341
33.4 Implementation of the Compensator	342
33.5 Experimental Study	343
33.6 Summary and Conclusion	344
References	346
34 Evaluating the Effectiveness of a Lodengraf Damping Approach for String Trimmers	347
34.1 Introduction	347
34.2 Materials and Methods	348
34.2.1 Handles	348
34.2.2 String Trimmers	348
34.2.3 Accelerometers and Data Acquisition System	350
34.2.4 Handle Shaker Tests and Modal Analysis	351
34.2.5 Shafts	352
34.3 Experimental	352
34.4 Results	353
34.4.1 Handle Shaker Tests	353
34.4.2 Modal Analysis	353
34.4.3 Suspended String Trimmer Trials	353
34.5 Discussion, Conclusions and Future Work	354
34.5.1 Modal Response of 3D-Printed ABS Handles, and Effect of Perlite	354
34.5.2 Effectiveness of Various Vibration Damping Approaches in Operating String Trimmers	355
References	362
35 Using Operating Data to Locate and Quantify Unbalance in Rotating Machinery	363
35.1 Introduction	363
35.1.1 Output-Only Frequency Spectra	364
35.1.2 Operating Deflection Shape	364
35.1.3 Time-Based ODS	364
35.1.4 Frequency-Based ODS	365
35.1.5 Order-Based ODS	365
35.2 Data Acquisition from a Rotating Machine	365
35.3 Seven Unbalance Cases	365
35.4 Modal Assurance Criterion	367
35.5 Shape Difference Indicator	368
35.6 Applying MAC and SDI to Order-Based ODS'S	368
35.7 SDI Sensitivity	370
35.8 Fault Correlation Tools	373
35.9 Conclusion	374
References	374
36 Gear Dynamics Characterization by Using Order-BasedModal Analysis	375
36.1 Introduction	375
36.2 Order Tracking Techniques	376
36.2.1 Angle Domain Computed Order Tracking (AD)	376
36.2.2 Time Variant Discrete Fourier Transform (TVDFT)	377
36.2.3 Vold-Kalman Filter Based Order Tracking (VK)	377
36.3 Order-Based Modal Analysis	378
36.4 Test Rig Description	379
36.5 Results	380
36.5.1 Experimental Modal Analysis	380
36.5.2 Order-Based Modal Analysis: Order Tracking Step	381
36.5.3 Order-Based Modal Analysis: Operational Modal Analysis Step	385
36.6 Conclusions	387
References	391
37 A Design Framework to Improve the Dynamic Characteristics of Double Planet Planetary Gearsets	393
37.1 Introduction	393
37.2 Selection of the DOE Technique	394
37.3 Layout of Design Space	395
37.4 A Computational Case Study	396
37.5 Results and Discussion	397
37.6 Conclusions	401
References	404
38 Dynamics and Pareto Optimization of a Generic Synchronizer Mechanism	405
38.1 Introduction	405
38.2 Generic Synchronizer	405
38.3 Measures of Synchronizer Performance	409
38.4 Optimization Problem Statement	410
38.5 Conclusion and Outlook	412
References	413
39 Modeling and Characterization of a Flexible Rotor Supported by AMB	414
39.1 Introduction	414
39.2 Active Magnetic Bearings (AMB)	415
39.3 Model and Numerical Results	416
39.4 Conclusion	422
References	422
40 Nonlinear Reduced Order Modeling of a Curved Axi-Symmetric Perforated Plate: Comparison with Experiments	423
40.1 Introduction	423
40.2 Numerical Model and Experimental Structure	424
40.2.1 Finite Element Model	424
40.2.2 Experimental Structure	425
40.3 Results	426
40.3.1 Model NNMs	426
40.3.2 Experimental NNMs	428
40.4 Conclusion	431
References	431
41 Reduced Order Models for Systems with Disparate Spatial and Temporal Scales	432
41.1 Introduction	432
41.2 Nonlinear Model Reduction	433
41.2.1 Proper and Smooth Orthogonal Decomposition	433
41.2.2 Separated Multivariate Analysis for Reduced Order Models	434
41.3 Nonlinear Mass-Spring-Damper System	435
41.4 Results	436
41.5 Conclusions	439
References	439
42 Using NNMs to Evaluate Reduced Order Models of Curved Beam	441
42.1 Introduction	441
42.2 Theory	442
42.2.1 Enforced Displacement (ED)	443
42.2.2 Implicit Condensation and Expansion (ICE)	443
42.2.3 Nonlinear Normal Modes	444
42.2.4 Proposed Methodology for Creating a Valid ROM	444
42.3 Numerical Results of an Asymmetric Curved Beam	445
42.3.1 Pre-Processing	446
42.3.2 Computed NNMs	446
42.3.3 Load Scaling Sensitivity Analysis	450
42.4 Conclusion	452
References	453
43 Simulation of Rotor Damping Assembled by Disc Shrink Fits	454
43.1 Introduction	454
43.2 The Two Disc Rotor as a Test Structure	454
43.3 Layout of the Generic Joint Experiment	455
43.4 Determination of Isolated Joint's Parameters	456
43.5 Two-Disc Rotor Measurements	459
43.6 FE-Modeling	460
43.7 FE Simulation	462
43.8 Summary	463
References	463
44 Developments in the Prediction of Full Field Dynamics in the Nonlinear Forced Response of Reduced Order System Models	464
44.1 Introduction	464
44.2 Theoretical Background	465
44.2.1 Equations of Motion for Multiple DOF System	465
44.2.2 System Modeling and Mode Contribution	465
44.2.2.1 Physical Space System Modeling	466
44.2.2.2 Structural Dynamic Modification	467
44.2.3 General Reduction and Expansion Methodology	467
44.2.3.1 Guyan Reduction	468
44.2.3.2 SEREP	468
44.2.3.3 KM_AMI	468
44.2.4 Expansion of System Modes from Uncoupled Component Modes	469
44.2.5 Expansion of Reduced Order Real Time Response	469
44.2.6 Timer Response Correlation Tools	472
44.2.6.1 Modal Assurance Criteria (MAC)	472
44.2.6.2 Time Response Assurance Criteria (TRAC)	472
44.2.7 Numerical Computations	473
44.3 Analytical Case Studies	474
44.3.1 Nonlinear Solution with Reduced Model from Beam/Line Elements	477
44.3.2 Expansion of Beam/Line Elements to a Full 3D Finite Element Model	478
44.3.3 Ancillary Subcomponent Response from Embedded Reduced Order Model	479
44.4 Conclusion	487
References	490
45 On the Behaviour of Structures with Many Nonlinear Elements	492
45.1 Introduction	492
45.2 Framework for Simulation	493
45.3 Effect of Nonlinear Elements	494
45.3.1 Single Element Location	497
45.3.2 Multiple Nonlinearites	498
45.4 Conclusions	501
References	503
46 Estimation of Instantaneous Speed for Rotating Systems: New Processing Techniques	504
Nomenclature	504
46.1 Introduction	505
46.2 Smart Bayesian Algorithm	505
46.3 New Technique: Adaptive nth Pulse Algorithm	507
46.4 Comparison and Other Examples	515
46.5 Conclusion	515
References	518
47 Identification of Breathing Cracked Shaft Models from Measurements	519
47.1 Introduction	519
47.2 Equations of Motion and Breathing Crack Models	520
47.3 Rotor Response to Breathing Crack Models	521
47.4 Experimental Test Rig and Results	522
47.5 Conclusions	524
References	525

RkJQdWJsaXNoZXIy MTMzNzEzMQ==