Gupta IUTAM Symposium on Emerging Trends in Rotor Dynamics

Proceedings of the IUTAM Symposium on Emerging Trends in Rotor Dynamics, held in New Delhi, India, March 23 - March 26, 2009
1. Auflage 2011
ISBN: 978-94-007-0020-8
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 25, 555 Seiten

Reihe: IUTAM Bookseries

Rotor dynamics is an important branch of dynamics that deals with behavior of rotating machines ranging from very large systems like power plant rotors, for example, a turbogenerator, to very small systems like a tiny dentist's drill, with a variety of rotors such as pumps, compressors, steam/gas turbines, motors, turbopumps etc. as used for example in process industry, falling in between. The speeds of these rotors vary in a large range, from a few hundred RPM to more than a hundred thousand RPM. Complex systems of rotating shafts depending upon their specific requirements, are supported on different types of bearings. There are rolling element bearings, various kinds of fluid film bearings, foil and gas bearings, magnetic bearings, to name but a few. The present day rotors are much lighter, handle a large amount of energy and fluid mass, operate at much higher speeds, and therefore are most susceptible to vibration and instability problems. This have given rise to several interesting physical phenomena, some of which are fairly well understood today, while some are still the subject of continued investigation. Research in rotor dynamics started more than one hundred years ago. The progress of the research in the early years was slow. However, with the availability of larger computing power and versatile measurement technologies, research in all aspects of rotor dynamics has accelerated over the past decades. The demand from industry for light weight, high performance and reliable rotor-bearing systems is the driving force for research, and new developments in the field of rotor dynamics.  The symposium proceedings contain papers on various important aspects of rotor dynamics such as, modeling, analytical, computational and experimental methods, developments in bearings, dampers, seals including magnetic bearings, rub, impact and foundation effects, turbomachine blades, active and passive vibration control strategies including control of instabilities, nonlinear and parametric effects, fault diagnostics and condition monitoring, and cracked rotors. This volume is of immense value to teachers, researchers in educational institutes, scientists, researchers in R&D laboratories and practising engineers in industry.

Autoren/Hrsg.

Gupta, K.

Inhaltsverzeichnis

1;Foreword;6
2;Preface;8
3;List of Speakers;18
4;Contents;24
5;Rotordynamics Research: Current Interests and Future Directions;30
5.1;1 Introduction;30
5.2;2 Labyrinth Seal Excitation;32
5.2.1;2.1 Background;32
5.2.2;2.2 Summary of Prior Work;33
5.3;3 Synchronous Thermal Instability;36
5.4;4 Conclusions;38
5.5;5 Recommendations;38
5.6;References;39
6;Optimized Life Using Frequency and Time Domain Approaches;41
6.1;1 Introduction;41
6.2;2 Time Domain;42
6.2.1;2.1 Some Observations on Time Domain Method;44
6.3;3 Frequency Domain;45
6.3.1;3.1 Structural Components Crossing Critical Speeds;45
6.3.2;3.2 Friction Damping;47
6.3.3;3.3 Identification of Critical Speed;48
6.3.4;3.4 Resonant Response;49
6.3.5;3.5 Cumulative Damage Through Resonance;50
6.3.6;3.6 Example of Propeller Shaft Life in Frequency Domain;50
6.4;4 Lifing and Optimization;51
6.5;5 Concluding Remarks;53
6.6;References;53
7;Dynamic Modeling of Rotors: A Modal Approach;55
7.1;1 Introduction;55
7.2;2 Analysis;57
7.2.1;2.1 Generalized Coordinates;57
7.2.2;2.2 Formulation of the Rotor Model;58
7.3;3 Modal Reduction;59
7.3.1;3.1 First Approach;59
7.3.2;3.2 Second Approach;60
7.4;4 The Rotor Superelement;61
7.5;5 Example;62
7.6;6 Conclusions;65
7.7;References;66
8;Evolution of Frequency-Speed Diagram in Rotating Machinery;67
8.1;1 Introduction;67
8.2;2 Campbell Diagram;68
8.3;3 Enhanced Frequency-Speed Diagrams;69
8.4;4 Separation of Forward and Backward Modes;70
8.5;5 Modal Analysis and Commercial Software;72
8.6;6 New Whirl Speed Chart;73
8.7;7 Illustrative Examples;74
8.8;8 Conclusions;77
8.9;References;78
9;Developments in Rotor Dynamical Modeling of Hydropower Units;79
9.1;1 Introduction;79
9.2;2 Magnetic Pull Force;80
9.3;3 Stability due to Magnetic Pull;84
9.4;4 Influence of Shape Deviations;85
9.5;5 Tangential Forces;87
9.6;6 Conclusions;89
9.7;References;89
10;Control-Oriented Approach to the Rotor Dynamics;91
10.1;1 Introduction;91
10.2;2 Mathematical Model;92
10.3;3 Classical Analysis of Free Torsional/Lateral Rotor Vibrations;93
10.4;4 Control Theory Approach to the Vibration Analysis;95
10.4.1;4.1 Undamped Free Vibrations of Isotropic Rotor;95
10.4.2;4.2 Damped Lateral Vibrations of Anisotropic Rotor;97
10.5;5 Control of Damped Lateral Vibrations of Anisotropic Rotor;97
10.6;6 Chosen Strategies of Rotor Lateral Vibration Control;98
10.7;7 Control of Full Torsional/Lateral Model;101
10.8;8 Summary;103
10.9;References;103
11;New Approach to the Analysis of the Dynamics Behavior of a Fluid Structure Interaction;104
11.1;1 Introduction;104
11.2;2 Mathematical Model for Fluid Analysis;106
11.3;3 Model Sample;108
11.4;4 Conclusion;114
11.5;References;114
12;On the Analysis of Rotor-Bearing-Foundation Systems;115
12.1;1 Introduction;115
12.2;2 Theoretical Model;117
12.3;3 Test-Rig Modelling;122
12.4;4 Experimental Set-up;122
12.5;5 Results;123
12.6;6 Conclusions;125
12.7;References;126
13;A Multiple Whirls Phenomenon and Heuristic Problems in Rotor-Bearing Systems;128
13.1;1 Research Tools and Their Verification;128
13.2;2 Stability Testing of High-Speed Rotors; Phenomenon of Multiple Whirls;130
13.3;3 Stochastic Variability of Input Data in Heuristic Modeling of Rotors;133
13.4;4 Final Conclusions;137
13.5;References;137
14;Experimental Decomposition of Vibration, Whirl and Waves in Rotating and Non-rotating Parts;138
14.1;1 Introduction;138
14.2;2 Separation of Measured Signals in Rotating Machines;140
14.2.1;2.1 Shaft Dynamics – Decomposition and Transformation;140
14.2.1.1;2.1.1 Experimental Demonstration of Real Time Decomposition of Shaft Vibrations;141
14.2.2;2.2 Disc and Blade Dynamics: Decomposition and Transformation;144
14.3;3 Concluding Remarks;147
14.4;References;147
15;Rotating Internal Damping in the Case of Composite Shafts;149
15.1;1 Introduction;149
15.2;2 Equations of Motion: Composite Rotor;150
15.3;3 Application;151
15.3.1;3.1 Thin Walled Composite Shaft;152
15.3.2;3.2 Composite Rotor with Two Discs;153
15.4;4 Experimental Analyses;155
15.5;5 Conclusion;157
15.6;References;157
16;Unbalance Response Analysis of a Spinning Rotor Mounted on a Precessing Platform;159
16.1;1 Introduction;159
16.2;2 Analysis;160
16.2.1;2.1 Governing Equations of Motion;160
16.3;3 Numerical Example;164
16.4;4 Conclusion;166
16.5;References;166
17;A Simple Viscoelastic Model of Rotor-Shaft Systems;167
17.1;1 Introduction;167
17.2;2 Analysis;168
17.3;3 Results and Discussion;172
17.4;4 Conclusions;174
17.5;References;174
18;Rotor Dynamic Analysis Using ANSYS;176
18.1;1 Introduction;176
18.2;2 Theoretical Background;177
18.2.1;2.1 The Fundamental Equations;177
18.2.2;2.2 Supported Element Types;179
18.2.3;2.3 Modeling Bearings and Seals;179
18.3;3 Free Vibration (Modal) Analysis;180
18.4;4 Harmonic Analysis;182
18.5;5 Transient Analysis;183
18.6;6 Conclusion;184
18.7;References;185
19;Vibration of Rotating Bladed Discs: Mistuning, Coriolis, and Robust Design;186
19.1;1 Definition of the Problem;186
19.2;2 The Practical Problem;187
19.3;3 Brief Review of Major Features from Previous Studies;189
19.4;4 Some Recent Developments;191
19.4.1;4.1 Coriolis Effects ;191
19.4.2;4.2 Combined Aero/Structural Effects ;192
19.4.3;4.3 Intentional Mistuning ;193
19.4.4;4.4 Determination of Specific Mistune Pattern from Bladed Disc Modes ;193
19.5;5 A New Mistuning Strategy (NMS);194
19.5.1;5.1 Step 1;194
19.5.2;5.2 Step 2;194
19.5.3;5.3 Step 3;196
19.6;6 Concluding Discussion;197
19.7;References;197
20;Modeling Geometric Mistuning of a Bladed Rotor: Modified Modal Domain Analysis;199
20.1;1 Introduction;199
20.2;2 Modified Modal Domain Analysis (MMDA);200
20.2.1;2.1 Computation of iHMtj via ANSYS Sector Analyses;201
20.2.2;2.2 Computation of iHMtj via ANSYS Sector Analyses;202
20.2.3;2.3 Connection with ANSYS Sector Analysis;203
20.3;3 Numerical Results;203
20.4;4 Conclusions;206
20.5;References;206
21;Trends in Controllable Oil Film Bearings;207
21.1;1 Introduction;207
21.2;2 Designing and Testing Controllable Oil Film Bearings;209
21.3;3 Controllable Elastohydrodynamic Bearings;212
21.4;4 Control Design Strategies ;213
21.5;5 Modification of Oil Film Dynamic Coefficients and Active Vibration Control of Rotors;214
21.6;6 Smart Bearings – Rotordynamic Testing and Parameter Identification ;216
21.7;7 Feasibility of Industrial Application;217
21.8;8 Concluding Remarks;218
21.9;References;219
22;Developments in Fluid Film Bearing Technology;222
22.1;1 Introduction;222
22.2;2 Experimental and Numerical Investigation of Misalignment;223
22.2.1;2.1 Experiments with Coupling Misalignment;223
22.2.1.1;2.1.1 Data;224
22.2.1.2;2.1.2 Case 1;225
22.2.1.3;2.1.3 Case 2;226
22.2.1.4;2.1.4 Case 3;226
22.2.1.5;2.1.5 Discussion;227
22.2.2;2.2 Numerical Results for Bearing Misalignment;227
22.2.3;2.3 Experiments with Bearing Misalignment;230
22.3;3 Possible New Bearing Designs;233
22.4;4 Integrated Journal and Active Magnetic Bearing;234
22.5;5 Conclusion;235
22.6;References;236
23;Numerical Model of the High Speed Rotors Supported on Variable Geometry Bearings;237
23.1;1 Introduction;237
23.2;2 Gas Bearing Technology: Tilting Pad Bearing Model;240
23.3;3 Hydrodynamic Bearing Technology: Foil Bearing Model;243
23.4;4 Conclusions;246
23.5;References;247
24;Effect of Unbalance on the Dynamic Response of a Flexible Rotor Supported on Porous Oil Journal Bearings;248
24.1;1 Introduction;248
24.2;2 Mathematical Model;249
24.2.1;2.1 Finite Element Equation of Motion of the Rotor-Disk System;249
24.2.2;2.2 Hydrodynamic Porous Bearing;251
24.3;3 Solution Procedure;252
24.4;4 Results and Discussion;253
24.5;5 Conclusions;257
24.6;References;258
25;Analysis of Capillary Compensated Hole-Entry Hydrostatic/Hybrid Journal Bearing Operating with Micropolar Lubricant;259
25.1;1 Introduction;259
25.2;2 Analysis;260
25.2.1;2.1 Fluid-Film Thickness;262
25.3;3 Results and Discussion;262
25.4;4 Conclusions;268
25.5;References;270
26;Rotordynamic Analysis of Carbon Graphite Seals of a Steam Rotary Joint;271
26.1;1 Introduction;271
26.2;2 Working of Steam Rotary Joint;273
26.3;3 Experimental Setup;274
26.4;4 Theoretical Modeling;276
26.5;5 Experimental Study on Modified Seal Ring;279
26.6;6 Conclusions;280
26.7;References;280
27;Applications and Research Topics for Active Magnetic Bearings;281
27.1;1 Introduction;281
27.2;2 A Glance on History;282
27.3;3 Industrial Applications;283
27.4;4 Research Topics;286
27.5;5 Conclusions ;290
27.6;References;291
28;Accurate Analytical Determination of Electromagnetic Bearing Coefficients;292
28.1;1 Introduction;292
28.2;2 Mathematical Development;293
28.3;3 Numerical Results;298
28.4;4 Conclusions;301
28.5;References;302
29;Sensitivity Analysis of the Design Parameters in Electrodynamic Bearings;303
29.1;1 Introduction;303
29.2;2 Modeling of Electrodynamic Bearings;305
29.2.1;2.1 Modeling of the Forces Generated by a Conductor Rotating in a Magnetic Field;305
29.2.2;2.2 Characterization of the Bearing Through a Quasi-Static Analysis;307
29.3;3 Finite Element Model and Sensitivity Analysis;308
29.3.1;3.1 FEM Model;308
29.3.2;3.2 Sensitivity Analysis;309
29.4;4 Conclusions;310
29.5;References;311
30;Advanced Analysis and Optimization of Nonlinear Resonance Vibrations in Gas-Turbine Structures with Friction and Gaps;313
30.1;1 Introduction;313
30.2;2 Method for Analysis of Resonance Peak Forced Response;314
30.2.1;2.1 Frequency-Domain Equation for Resonance Peak Forced Response;314
30.2.2;2.2 Calculation and Tracing of the Resonance Peaks Under Parameter Variation;316
30.3;3 Optimization of Resonance Peak Responses;317
30.4;4 Numerical Examples;319
30.5;5 Conclusions;323
30.6;References;323
31;Non-Parametric Identification of Rotor-Bearing System through Volterra-Wiener Theories;324
31.1;1 Introduction;324
31.2;2 Volterra Series;325
31.3;3 Wiener Series;326
31.4;4 Nonlinear Stiffness Modeling in a Rotor-Bearing System;328
31.5;5 Parameter Estimation Using Volterra Theory and Harmonic Probing;330
31.5.1;5.1 Experimentation and Parameter Estimation;330
31.6;6 Wiener Series Application;333
31.7;7 Conclusion;335
31.8;References;335
32;Nonlinear Dynamics and Chaos of an Unbalanced Flexible Rotor Supported by Deep Groove Ball Bearings with Radial Internal Clearance;336
32.1;1 Introduction;337
32.2;2 Problem Formulation;337
32.2.1;2.1 Rotor Model;338
32.2.2;2.2 Ball Bearing;339
32.2.3;2.3 Methods of Solution and Analysis;340
32.3;3 Validation;340
32.4;4 Results and Discussion;341
32.5;5 Conclusion;347
32.6;References;348
33;Bifurcation Analysis of a Turbocharger Rotor Supported by Floating Ring Bearings;349
33.1;1 Introduction;350
33.2;2 Mechanical Model of the Turbocharger Rotor;351
33.3;3 Bifurcation Analysis;354
33.3.1;3.1 Rigid Rotor;355
33.3.2;3.2 Flexible Rotor;357
33.4;4 Conclusion;360
33.5;References;360
34;Vibration Analysis of High Speed Rolling Element Bearings due to Race Defects;362
34.1;1 Introduction;362
34.2;2 Problem Formulation;364
34.2.1;2.1 Mathematical Modeling;364
34.2.2;2.2 Race Waviness;365
34.2.3;2.3 Formulation of Equations of Motion;366
34.2.3.1;2.3.1 Energy Expression of the Rolling Element Bearings;366
34.2.4;2.4 Equations of Motion;367
34.3;3 Methods of Solution;368
34.3.1;3.1 Numerical Integration;369
34.4;4 Results and Discussion;369
34.5;5 Conclusions;371
34.6;References;372
35;Beneficial Effects of Parametric Excitation in Rotor Systems;373
35.1;1 Introduction;373
35.2;2 Stability of Parametrically Excited Rotor Systems;374
35.3;3 Vibration Suppression by PE in Rotor Systems;376
35.3.1;3.1 Rigid Rotor and Time-Periodic Bearing Mounts;377
35.3.2;3.2 Rotor with Flexible Shaft and Time-Periodic Bearing Stiffness;377
35.3.3;3.3 Flexible Multi-station Rotor with Local Time-Periodic Stiffness;379
35.3.4;3.4 Flexible Rotor Blade with Axial Time-Periodic Forcing;380
35.4;4 Conclusions;381
35.5;References;382
36;Simulation and Experiment of a Rotor with Unilateral Contacts and Active Elements;384
36.1;1 Introduction;384
36.2;2 Simulation Environment;385
36.3;3 Dynamics Between Impacts;386
36.4;4 Impact Dynamics;387
36.5;5 Elastic Components;387
36.6;6 Numerical Framework;388
36.7;7 Co-simulation with Simulink;388
36.8;8 Example: Rotor Test Rig with an Active Auxiliary Bearing;389
36.8.1;8.1 Feedback Control;389
36.8.2;8.2 Modeling;392
36.8.3;8.3 Test rig;392
36.8.4;8.4 Comparison: experiments-simulation;393
36.9;9 Conclusions;395
36.10;References;396
37;New Passive Control Methods for Reducing Vibrations of Rotors: Discontinuous Spring Characteristics and Ball Balancers;397
37.1;1 Introduction;397
37.2;2 Discontinuous Spring Characteristics ;398
37.2.1;2.1 Theoretical Model;398
37.2.2;2.2 Discontinuous Spring Characteristics;399
37.3;3 Suppression of the Steady State Resonance of a Symmetrical Rotor by the Discontinuous Spring Characteristics ;399
37.3.1;3.1 Equations of Motion;399
37.3.2;3.2 Principle of Vibration Suppression and Numerical Simulation;399
37.3.3;3.3 Experimental Set-up and Results;400
37.4;4 Elimination of an Unstable Range of an Asymmetrical Shaft Utilizing Discontinuous Spring Characteristics ;401
37.4.1;4.1 Theoretical Model and Equations of Motion;401
37.4.2;4.2 Natural Frequency;402
37.4.3;4.3 Numerical Simulation;403
37.4.4;4.4 Experimental Set-up and Results;404
37.5;5 Elimination of an Unstable Range of a Hollow Rotor Partially Filled with Liquid Utilizing Discontinuous Spring Characteristics ;405
37.5.1;5.1 Theoretical Model and Natural Frequency;405
37.5.2;5.2 Experimental Set-up and Experimental Results;406
37.6;6 Elimination of the Effect of Friction and the Self-Excited Oscillation in a Ball Balancer ;407
37.6.1;6.1 Theoretical Analysis with No Friction;407
37.6.2;6.2 Experimental Set-up and Experimental Results;408
37.6.3;6.3 Elimination of the Effect of Friction and Self-excited Oscillation;410
37.7;7 Conclusion: Combination of Discontinuous Spring Characteristics and a Ball Balancer;412
37.8;References;413
38;Modeling and Diagnostics of Heavy Impeller Gyroscopic Rotor with Tilting Pad Journal Bearings;414
38.1;1 Introduction;414
38.2;2 Air Blower Rotor BR Condition Monitoring and Diagnostics;415
38.3;3 Vibration at Varying Loading;417
38.4;4 Vibration Severity at Resonance;417
38.5;5 Shaft Displacements (Gaps) in the Bearings;419
38.6;6 Mathematical Modeling and Simulation of Air Blower Machine;422
38.7;7 Tilting-Pad Journal Bearing Model;423
38.8;8 Simulation Results;424
38.9;9 Conclusions;427
38.10;References;427
39;A Mechanical Engine Simulator for Development of Aero Engine Failure Analysis Methods;428
39.1;1 Introduction;428
39.2;2 An Engine Mechanical Vehicle for CBO Event Simulation;431
39.3;3 Further Use of the Mechanical Engine Simulator;434
39.4;4 Conclusion;437
39.5;References;437
40;Signal Processing Tools for Tracking the Size of a Spall in a Rolling Element Bearing;438
40.1;1 Introduction;438
40.1.1;1.1 Signals from Entry into and Exit from a Spall;441
40.2;2 Test Equipment and Measurements;442
40.3;3 Measurement Results and Analysis;443
40.4;4 Discussion and Conclusion;448
40.5;References;448
41;Cracked Rotating Shafts: Typical Behaviors, Modeling and Diagnosis;450
41.1;1 Introduction;450
41.2;2 Typical Cracked Shaft Dynamical and Static Behavior;451
41.3;3 Modeling;454
41.4;4 Sensitivity Analysis;459
41.5;5 Conclusions;462
41.6;References;463
42;Fault Identification in Industrial Rotating Machinery: Theory and Applications;464
42.1;1 Introduction;464
42.2;2 Model Based Identification in Rotor Dynamics;465
42.2.1;2.1 Definition of the Equivalent Excitations;465
42.2.2;2.2 Algorithms: From Least Squares to Robust Estimation;467
42.3;3 Case Histories;471
42.3.1;3.1 Unbalance;471
42.3.2;3.2 Misalignment;471
42.3.3;3.3 Rotor to Stator Rub;472
42.3.4;3.4 Rotor Bow;474
42.4;4 Conclusions;475
42.5;References;475
43;Cracked Continuous Rotors Vibrating on Nonlinear Bearings;477
43.1;1 Introduction;477
43.2;2 Continuous Model of a Cracked Rotor;478
43.3;3 Journal Bearing Support – Worn Bearing;479
43.4;4 Rotor – Bearing System;481
43.5;5 Experimental Crack Identification using External Exciter;482
43.6;6 Wear Assessment;484
43.7;7 Conclusions;485
43.8;References;486
44;Identification of the Bearing and Unbalance Parameters from Rundown Data of Rotors;487
44.1;1 Introduction;487
44.2;2 Modeling of Rotor-Bearing Systems;488
44.3;3 Identification Algorithms;490
44.4;4 Results and Discussions;492
44.5;5 Conclusions;496
44.6;References;497
45;Some Recent Studies on Cracked Rotors;498
45.1;1 Introduction;498
45.2;2 Modeling Aspects;499
45.2.1;2.1 Breathing Mechanism;499
45.2.1.1;2.1.1 SERR Approach;499
45.2.1.2;2.1.2 3D-FEM Approach;499
45.2.1.3;2.1.3 Modified 3D FEM;500
45.2.1.4;2.1.4 Motion Coupled with Crack Opening;500
45.2.2;2.2 Wavelet Finite Element Method;500
45.2.2.1;2.2.1 Other Methods;501
45.3;3 Dynamic Analysis;501
45.3.1;3.1 Coupled Vibrations;501
45.3.2;3.2 Multiple Faults;501
45.3.2.1;3.2.1 Multiple Cracks;501
45.3.2.2;3.2.2 Cracks Together with Other Faults;502
45.3.2.3;3.2.3 Slant and Helicoidal Cracks;502
45.3.3;3.3 Nonlinear, Chaos and Bifurcation;502
45.4;4 Identification and Condition Monitoring;503
45.4.1;4.1 Use of High Precision Modal Parameters and Wavelet FEM;503
45.4.2;4.2 Model Based Methods;504
45.4.3;4.3 Advanced Signal Processing Techniques;504
45.4.3.1;4.3.1 Wavelet;504
45.4.3.2;4.3.2 HHT;504
45.4.4;4.4 Operational Deflection Shapes;505
45.4.5;4.5 Constitutive Relation Error Updating Method;505
45.4.6;4.6 Soft Computing Methods;506
45.5;5 Real Rotor Systems – Case Studies;506
45.6;6 Future Trends;507
45.7;References;507
46;A Multi-Crack Identification Algorithm Based on Forced Vibrations from a Shaft System;511
46.1;1 Introduction;511
46.2;2 System Modeling;512
46.2.1;2.1 Model of a Shaft Element with a Crack;512
46.2.2;2.2 System Equations of Motion;513
46.3;3 Crack Identification Algorithms;514
46.4;4 Numerical Experiments;516
46.5;5 Conclusions;519
46.6;References;519
47;Vibration Based Condition Monitoring of Rotating Machines: A Future Possibility?;520
47.1;1 Introduction;520
47.2;2 The Proposed Method;522
47.3;3 Example 1;523
47.4;4 Example 2;524
47.4.1;4.1 Results and Discussion;525
47.5;5 Conclusion;527
47.6;References;527
48;Feature Selection for Bearing Fault Detection Based on Mutual Information;528
48.1;1 Introduction;528
48.2;2 Methodology;529
48.3;3 Feature extraction;530
48.4;4 Feature ranking;532
48.4.1;4.1 Mutual information;533
48.5;5 Feature selection;535
48.6;6 Results;535
48.7;7 Conclusion;537
48.8;References;538
49;Application of Full Spectrum Analysis for Rotor Fault Diagnosis;539
49.1;1 Introduction;540
49.2;2 Experiment Set-up;541
49.3;3 Results and Discussion;542
49.3.1;3.1 Vibration Response of Cracked Rotor;542
49.3.2;3.2 Vibration Response of Rotor with rub;544
49.3.3;3.3 Vibration Response of Aligned Coupled Rotors;544
49.3.4;3.4 Vibration Response of Rotors with Parallel Misalignment;545
49.3.5;3.5 Vibration Response of Rotors with Angular Misalignment;546
49.4;4 Conclusions;548
49.5;References;549
50;Author Index;550