IUTAM Symposium on Emerging Trends in Rotor Dynamics (eBook)

Foreword 6
Preface 8
List of Speakers 18
Contents 24
Rotordynamics Research: Current Interests and Future Directions 30
1 Introduction 30
2 Labyrinth Seal Excitation 32
2.1 Background 32
2.2 Summary of Prior Work 33
3 Synchronous Thermal Instability 36
4 Conclusions 38
5 Recommendations 38
References 39
Optimized Life Using Frequency and Time Domain Approaches 41
1 Introduction 41
2 Time Domain 42
2.1 Some Observations on Time Domain Method 44
3 Frequency Domain 45
3.1 Structural Components Crossing Critical Speeds 45
3.2 Friction Damping 47
3.3 Identification of Critical Speed 48
3.4 Resonant Response 49
3.5 Cumulative Damage Through Resonance 50
3.6 Example of Propeller Shaft Life in Frequency Domain 50
4 Lifing and Optimization 51
5 Concluding Remarks 53
References 53
Dynamic Modeling of Rotors: A Modal Approach 55
1 Introduction 55
2 Analysis 57
2.1 Generalized Coordinates 57
2.2 Formulation of the Rotor Model 58
3 Modal Reduction 59
3.1 First Approach 59
3.2 Second Approach 60
4 The Rotor Superelement 61
5 Example 62
6 Conclusions 65
References 66
Evolution of Frequency-Speed Diagram in Rotating Machinery 67
1 Introduction 67
2 Campbell Diagram 68
3 Enhanced Frequency-Speed Diagrams 69
4 Separation of Forward and Backward Modes 70
5 Modal Analysis and Commercial Software 72
6 New Whirl Speed Chart 73
7 Illustrative Examples 74
8 Conclusions 77
References 78
Developments in Rotor Dynamical Modeling of Hydropower Units 79
1 Introduction 79
2 Magnetic Pull Force 80
3 Stability due to Magnetic Pull 84
4 Influence of Shape Deviations 85
5 Tangential Forces 87
6 Conclusions 89
References 89
Control-Oriented Approach to the Rotor Dynamics 91
1 Introduction 91
2 Mathematical Model 92
3 Classical Analysis of Free Torsional/Lateral Rotor Vibrations 93
4 Control Theory Approach to the Vibration Analysis 95
4.1 Undamped Free Vibrations of Isotropic Rotor 95
4.2 Damped Lateral Vibrations of Anisotropic Rotor 97
5 Control of Damped Lateral Vibrations of Anisotropic Rotor 97
6 Chosen Strategies of Rotor Lateral Vibration Control 98
7 Control of Full Torsional/Lateral Model 101
8 Summary 103
References 103
New Approach to the Analysis of the Dynamics Behavior of a Fluid Structure Interaction 104
1 Introduction 104
2 Mathematical Model for Fluid Analysis 106
3 Model Sample 108
4 Conclusion 114
References 114
On the Analysis of Rotor-Bearing-Foundation Systems 115
1 Introduction 115
2 Theoretical Model 117
3 Test-Rig Modelling 122
4 Experimental Set-up 122
5 Results 123
6 Conclusions 125
References 126
A Multiple Whirls Phenomenon and Heuristic Problems in Rotor-Bearing Systems 128
1 Research Tools and Their Verification 128
2 Stability Testing of High-Speed Rotors Phenomenon of Multiple Whirls
3 Stochastic Variability of Input Data in Heuristic Modeling of Rotors 133
4 Final Conclusions 137
References 137
Experimental Decomposition of Vibration, Whirl and Waves in Rotating and Non-rotating Parts 138
1 Introduction 138
2 Separation of Measured Signals in Rotating Machines 140
2.1 Shaft Dynamics – Decomposition and Transformation 140
2.1.1 Experimental Demonstration of Real Time Decomposition of Shaft Vibrations 141
2.2 Disc and Blade Dynamics: Decomposition and Transformation 144
3 Concluding Remarks 147
References 147
Rotating Internal Damping in the Case of Composite Shafts 149
1 Introduction 149
2 Equations of Motion: Composite Rotor 150
3 Application 151
3.1 Thin Walled Composite Shaft 152
3.2 Composite Rotor with Two Discs 153
4 Experimental Analyses 155
5 Conclusion 157
References 157
Unbalance Response Analysis of a Spinning Rotor Mounted on a Precessing Platform 159
1 Introduction 159
2 Analysis 160
2.1 Governing Equations of Motion 160
3 Numerical Example 164
4 Conclusion 166
References 166
A Simple Viscoelastic Model of Rotor-Shaft Systems 167
1 Introduction 167
2 Analysis 168
3 Results and Discussion 172
4 Conclusions 174
References 174
Rotor Dynamic Analysis Using ANSYS 176
1 Introduction 176
2 Theoretical Background 177
2.1 The Fundamental Equations 177
2.2 Supported Element Types 179
2.3 Modeling Bearings and Seals 179
3 Free Vibration (Modal) Analysis 180
4 Harmonic Analysis 182
5 Transient Analysis 183
6 Conclusion 184
References 185
Vibration of Rotating Bladed Discs: Mistuning, Coriolis, and Robust Design 186
1 Definition of the Problem 186
2 The Practical Problem 187
3 Brief Review of Major Features from Previous Studies 189
4 Some Recent Developments 191
4.1 Coriolis Effects 191
4.2 Combined Aero/Structural Effects 192
4.3 Intentional Mistuning 193
4.4 Determination of Specific Mistune Pattern from Bladed Disc Modes 193
5 A New Mistuning Strategy (NMS) 194
5.1 Step 1 194
5.2 Step 2 194
5.3 Step 3 196
6 Concluding Discussion 197
References 197
Modeling Geometric Mistuning of a Bladed Rotor: Modified Modal Domain Analysis 199
1 Introduction 199
2 Modified Modal Domain Analysis (MMDA) 200
2.1 Computation of iHMtj via ANSYS Sector Analyses 201
2.2 Computation of iHMtj via ANSYS Sector Analyses 202
2.3 Connection with ANSYS Sector Analysis 203
3 Numerical Results 203
4 Conclusions 206
References 206
Trends in Controllable Oil Film Bearings 207
1 Introduction 207
2 Designing and Testing Controllable Oil Film Bearings 209
3 Controllable Elastohydrodynamic Bearings 212
4 Control Design Strategies 213
5 Modification of Oil Film Dynamic Coefficients and Active Vibration Control of Rotors 214
6 Smart Bearings – Rotordynamic Testing and Parameter Identification 216
7 Feasibility of Industrial Application 217
8 Concluding Remarks 218
References 219
Developments in Fluid Film Bearing Technology 222
1 Introduction 222
2 Experimental and Numerical Investigation of Misalignment 223
2.1 Experiments with Coupling Misalignment 223
2.1.1 Data 224
2.1.2 Case 1 225
2.1.3 Case 2 226
2.1.4 Case 3 226
2.1.5 Discussion 227
2.2 Numerical Results for Bearing Misalignment 227
2.3 Experiments with Bearing Misalignment 230
3 Possible New Bearing Designs 233
4 Integrated Journal and Active Magnetic Bearing 234
5 Conclusion 235
References 236
Numerical Model of the High Speed Rotors Supported on Variable Geometry Bearings 237
1 Introduction 237
2 Gas Bearing Technology: Tilting Pad Bearing Model 240
3 Hydrodynamic Bearing Technology: Foil Bearing Model 243
4 Conclusions 246
References 247
Effect of Unbalance on the Dynamic Response of a Flexible Rotor Supported on Porous Oil Journal Bearings 248
1 Introduction 248
2 Mathematical Model 249
2.1 Finite Element Equation of Motion of the Rotor-Disk System 249
2.2 Hydrodynamic Porous Bearing 251
3 Solution Procedure 252
4 Results and Discussion 253
5 Conclusions 257
References 258
Analysis of Capillary Compensated Hole-Entry Hydrostatic/Hybrid Journal Bearing Operating with Micropolar Lubricant 259
1 Introduction 259
2 Analysis 260
2.1 Fluid-Film Thickness 262
3 Results and Discussion 262
4 Conclusions 268
References 270
Rotordynamic Analysis of Carbon Graphite Seals of a Steam Rotary Joint 271
1 Introduction 271
2 Working of Steam Rotary Joint 273
3 Experimental Setup 274
4 Theoretical Modeling 276
5 Experimental Study on Modified Seal Ring 279
6 Conclusions 280
References 280
Applications and Research Topics for Active Magnetic Bearings 281
1 Introduction 281
2 A Glance on History 282
3 Industrial Applications 283
4 Research Topics 286
5 Conclusions 290
References 291
Accurate Analytical Determination of Electromagnetic Bearing Coefficients 292
1 Introduction 292
2 Mathematical Development 293
3 Numerical Results 298
4 Conclusions 301
References 302
Sensitivity Analysis of the Design Parameters in Electrodynamic Bearings 303
1 Introduction 303
2 Modeling of Electrodynamic Bearings 305
2.1 Modeling of the Forces Generated by a Conductor Rotating in a Magnetic Field 305
2.2 Characterization of the Bearing Through a Quasi-Static Analysis 307
3 Finite Element Model and Sensitivity Analysis 308
3.1 FEM Model 308
3.2 Sensitivity Analysis 309
4 Conclusions 310
References 311
Advanced Analysis and Optimization of Nonlinear Resonance Vibrations in Gas-Turbine Structures with Friction and Gaps 313
1 Introduction 313
2 Method for Analysis of Resonance Peak Forced Response 314
2.1 Frequency-Domain Equation for Resonance Peak Forced Response 314
2.2 Calculation and Tracing of the Resonance Peaks Under Parameter Variation 316
3 Optimization of Resonance Peak Responses 317
4 Numerical Examples 319
5 Conclusions 323
References 323
Non-Parametric Identification of Rotor-Bearing System through Volterra-Wiener Theories 324
1 Introduction 324
2 Volterra Series 325
3 Wiener Series 326
4 Nonlinear Stiffness Modeling in a Rotor-Bearing System 328
5 Parameter Estimation Using Volterra Theory and Harmonic Probing 330
5.1 Experimentation and Parameter Estimation 330
6 Wiener Series Application 333
7 Conclusion 335
References 335
Nonlinear Dynamics and Chaos of an Unbalanced Flexible Rotor Supported by Deep Groove Ball Bearings with Radial Internal Clearance 336
1 Introduction 337
2 Problem Formulation 337
2.1 Rotor Model 338
2.2 Ball Bearing 339
2.3 Methods of Solution and Analysis 340
3 Validation 340
4 Results and Discussion 341
5 Conclusion 347
References 348
Bifurcation Analysis of a Turbocharger Rotor Supported by Floating Ring Bearings 349
1 Introduction 350
2 Mechanical Model of the Turbocharger Rotor 351
3 Bifurcation Analysis 354
3.1 Rigid Rotor 355
3.2 Flexible Rotor 357
4 Conclusion 360
References 360
Vibration Analysis of High Speed Rolling Element Bearings due to Race Defects 362
1 Introduction 362
2 Problem Formulation 364
2.1 Mathematical Modeling 364
2.2 Race Waviness 365
2.3 Formulation of Equations of Motion 366
2.3.1 Energy Expression of the Rolling Element Bearings 366
2.4 Equations of Motion 367
3 Methods of Solution 368
3.1 Numerical Integration 369
4 Results and Discussion 369
5 Conclusions 371
References 372
Beneficial Effects of Parametric Excitation in Rotor Systems 373
1 Introduction 373
2 Stability of Parametrically Excited Rotor Systems 374
3 Vibration Suppression by PE in Rotor Systems 376
3.1 Rigid Rotor and Time-Periodic Bearing Mounts 377
3.2 Rotor with Flexible Shaft and Time-Periodic Bearing Stiffness 377
3.3 Flexible Multi-station Rotor with Local Time-Periodic Stiffness 379
3.4 Flexible Rotor Blade with Axial Time-Periodic Forcing 380
4 Conclusions 381
References 382
Simulation and Experiment of a Rotor with Unilateral Contacts and Active Elements 384
1 Introduction 384
2 Simulation Environment 385
3 Dynamics Between Impacts 386
4 Impact Dynamics 387
5 Elastic Components 387
6 Numerical Framework 388
7 Co-simulation with Simulink 388
8 Example: Rotor Test Rig with an Active Auxiliary Bearing 389
8.1 Feedback Control 389
8.2 Modeling 392
8.3 Test rig 392
8.4 Comparison: experiments-simulation 393
9 Conclusions 395
References 396
New Passive Control Methods for Reducing Vibrations of Rotors: Discontinuous Spring Characteristics and Ball Balancers 397
1 Introduction 397
2 Discontinuous Spring Characteristics 398
2.1 Theoretical Model 398
2.2 Discontinuous Spring Characteristics 399
3 Suppression of the Steady State Resonance of a Symmetrical Rotor by the Discontinuous Spring Characteristics 399
3.1 Equations of Motion 399
3.2 Principle of Vibration Suppression and Numerical Simulation 399
3.3 Experimental Set-up and Results 400
4 Elimination of an Unstable Range of an Asymmetrical Shaft Utilizing Discontinuous Spring Characteristics 401
4.1 Theoretical Model and Equations of Motion 401
4.2 Natural Frequency 402
4.3 Numerical Simulation 403
4.4 Experimental Set-up and Results 404
5 Elimination of an Unstable Range of a Hollow Rotor Partially Filled with Liquid Utilizing Discontinuous Spring Characteristics 405
5.1 Theoretical Model and Natural Frequency 405
5.2 Experimental Set-up and Experimental Results 406
6 Elimination of the Effect of Friction and the Self-Excited Oscillation in a Ball Balancer 407
6.1 Theoretical Analysis with No Friction 407
6.2 Experimental Set-up and Experimental Results 408
6.3 Elimination of the Effect of Friction and Self-excited Oscillation 410
7 Conclusion: Combination of Discontinuous Spring Characteristics and a Ball Balancer 412
References 413
Modeling and Diagnostics of Heavy Impeller Gyroscopic Rotor with Tilting Pad Journal Bearings 414
1 Introduction 414
2 Air Blower Rotor BR Condition Monitoring and Diagnostics 415
3 Vibration at Varying Loading 417
4 Vibration Severity at Resonance 417
5 Shaft Displacements (Gaps) in the Bearings 419
6 Mathematical Modeling and Simulation of Air Blower Machine 422
7 Tilting-Pad Journal Bearing Model 423
8 Simulation Results 424
9 Conclusions 427
References 427
A Mechanical Engine Simulator for Development of Aero Engine Failure Analysis Methods 428
1 Introduction 428
2 An Engine Mechanical Vehicle for CBO Event Simulation 431
3 Further Use of the Mechanical Engine Simulator 434
4 Conclusion 437
References 437
Signal Processing Tools for Tracking the Size of a Spall in a Rolling Element Bearing 438
1 Introduction 438
1.1 Signals from Entry into and Exit from a Spall 441
2 Test Equipment and Measurements 442
3 Measurement Results and Analysis 443
4 Discussion and Conclusion 448
References 448
Cracked Rotating Shafts: Typical Behaviors, Modeling and Diagnosis 450
1 Introduction 450
2 Typical Cracked Shaft Dynamical and Static Behavior 451
3 Modeling 454
4 Sensitivity Analysis 459
5 Conclusions 462
References 463
Fault Identification in Industrial Rotating Machinery: Theory and Applications 464
1 Introduction 464
2 Model Based Identification in Rotor Dynamics 465
2.1 Definition of the Equivalent Excitations 465
2.2 Algorithms: From Least Squares to Robust Estimation 467
3 Case Histories 471
3.1 Unbalance 471
3.2 Misalignment 471
3.3 Rotor to Stator Rub 472
3.4 Rotor Bow 474
4 Conclusions 475
References 475
Cracked Continuous Rotors Vibrating on Nonlinear Bearings 477
1 Introduction 477
2 Continuous Model of a Cracked Rotor 478
3 Journal Bearing Support – Worn Bearing 479
4 Rotor – Bearing System 481
5 Experimental Crack Identification using External Exciter 482
6 Wear Assessment 484
7 Conclusions 485
References 486
Identification of the Bearing and Unbalance Parameters from Rundown Data of Rotors 487
1 Introduction 487
2 Modeling of Rotor-Bearing Systems 488
3 Identification Algorithms 490
4 Results and Discussions 492
5 Conclusions 496
References 497
Some Recent Studies on Cracked Rotors 498
1 Introduction 498
2 Modeling Aspects 499
2.1 Breathing Mechanism 499
2.1.1 SERR Approach 499
2.1.2 3D-FEM Approach 499
2.1.3 Modified 3D FEM 500
2.1.4 Motion Coupled with Crack Opening 500
2.2 Wavelet Finite Element Method 500
2.2.1 Other Methods 501
3 Dynamic Analysis 501
3.1 Coupled Vibrations 501
3.2 Multiple Faults 501
3.2.1 Multiple Cracks 501
3.2.2 Cracks Together with Other Faults 502
3.2.3 Slant and Helicoidal Cracks 502
3.3 Nonlinear, Chaos and Bifurcation 502
4 Identification and Condition Monitoring 503
4.1 Use of High Precision Modal Parameters and Wavelet FEM 503
4.2 Model Based Methods 504
4.3 Advanced Signal Processing Techniques 504
4.3.1 Wavelet 504
4.3.2 HHT 504
4.4 Operational Deflection Shapes 505
4.5 Constitutive Relation Error Updating Method 505
4.6 Soft Computing Methods 506
5 Real Rotor Systems – Case Studies 506
6 Future Trends 507
References 507
A Multi-Crack Identification Algorithm Based on Forced Vibrations from a Shaft System 511
1 Introduction 511
2 System Modeling 512
2.1 Model of a Shaft Element with a Crack 512
2.2 System Equations of Motion 513
3 Crack Identification Algorithms 514
4 Numerical Experiments 516
5 Conclusions 519
References 519
Vibration Based Condition Monitoring of Rotating Machines: A Future Possibility? 520
1 Introduction 520
2 The Proposed Method 522
3 Example 1 523
4 Example 2 524
4.1 Results and Discussion 525
5 Conclusion 527
References 527
Feature Selection for Bearing Fault Detection Based on Mutual Information 528
1 Introduction 528
2 Methodology 529
3 Feature extraction 530
4 Feature ranking 532
4.1 Mutual information 533
5 Feature selection 535
6 Results 535
7 Conclusion 537
References 538
Application of Full Spectrum Analysis for Rotor Fault Diagnosis 539
1 Introduction 540
2 Experiment Set-up 541
3 Results and Discussion 542
3.1 Vibration Response of Cracked Rotor 542
3.2 Vibration Response of Rotor with rub 544
3.3 Vibration Response of Aligned Coupled Rotors 544
3.4 Vibration Response of Rotors with Parallel Misalignment 545
3.5 Vibration Response of Rotors with Angular Misalignment 546
4 Conclusions 548
References 549
Author Index 550