1st Edition

# Rotor Systems Analysis and Identification

1092 Pages 45 Color & 740 B/W Illustrations
by CRC Press

1092 Pages 45 Color & 740 B/W Illustrations
by CRC Press

Also available as eBook on:

The purpose of this book is to give a basic understanding of rotor dynamics phenomena with the help of simple rotor models and subsequently, the modern analysis methods for real life rotor systems. This background will be helpful in the identification of rotor-bearing system parameters and its use in futuristic model-based condition monitoring and, fault diagnostics and prognostics. The book starts with introductory material for finite element methods and moves to linear and non-linear vibrations, continuous systems, vibration measurement techniques, signal processing and error analysis, general identification techniques in engineering systems, and MATLAB analysis of simple rotors.

Key Features:

• Covers both transfer matrix methods (TMM) and finite element methods (FEM)

• Discusses transverse and torsional vibrations

• Includes worked examples with simplicity of mathematical background and a modern numerical method approach

• Explores the concepts of instability analysis and dynamic balancing

• Provides a basic understanding of rotor dynamics phenomena with the help of simple rotor models including modern analysis methods for real life rotor systems.

CHAPTER 1 A BRIEF HISTORY OF ROTOR DYNAMICS AND RECENT TRENDS

1.1 From the Rankine to Jeffcott Rotor Models

1.2 Rotor Dynamics Phenomena Studies from Stodola to Lund

1.3 Development of Rotor Dynamics Analysis Tools

1.4 Software for Rotor Dynamics Analysis

1.5 Dynamic Balancing of Rotors

1.6 Condition Monitoring of Rotating Machineries

1.7 Conferences on Rotordynamics

1.8 Concluding Remarks

Exercise Problems

References

CHAPTER 2

ANALYSIS OF SIMPLE ROTOR SYSTEMS

2.1 Single-DOF Undamped Rotor Model

2.2 A Single-DOF Damped Rotor Model

2.3 Rankine Rotor Model

2.4 Jeffcott Rotor Model

2.5 A Jeffcott Rotor Model with an Offset Disc

2.6 Suppression of Critical Speeds

Concluding Remarks

Exercise Problems

References

CHAPTER 3

ROTORDYNAMIC PARAMETERS OF BEARINGS, SEALS AND DAMPERS

3.1 Rolling Element Bearings

3.2 Hydrodynamic Fluid-Lubricated Journal Bearings

3.3 Dynamic Seals

3.4 Squeeze-Film Dampers

Concluding remarks

Exercise Problems

References

CHAPTER 4

TRANSVERSE VIBRATIONS-II: SIMPLE ROTOR-BEARING-FOUNDATION SYSTEMS

4.1 Symmetrical Long Rigid Shaft on Flexible Anisotropic Bearings

4.2 A Symmetrical Long Rigid Shaft on Anisotropic Bearings

4.3 A Symmetrical Flexible Shaft on Anisotropic Bearings

4.4 A Rotor on Flexible Bearings and Foundations

4.5 A Turbine-Coupling-Generator Rotor on Flexible Bearings

Concluding Remarks

Exercise Problems

References

5. TRANSVERSE VIBRATIONS-III: SIMPLE ROTOR SYSTEMS WITH GYROSCOPIC EFFECTS

5.1 Angular Momentum

5.2 Gyroscopic Moments in Rotating Systems

5.3 Synchronous Motion of Rotors

5.4 Asynchronous Rotational Motion of Rotor System

5.5 Asynchronous General Motion of Rotor Systems

5.6 Gyroscopic Effects by the Dynamics Approach

5.7 Analysis of Gyroscopic effects with Energy Methods

5.8 Pure Transverse Rotational Vibrations of a Jeffcott Rotor Model with Moment Unbalance

Concluding Remarks

Exercise Problems

References

CHAPTER 6

TORSIONAL VIBRATIONS OF ROTORS-I: THE DIRECT AND TRANSFER MATRIX METHODS

6.1 A Simple Torsional Rotor System with a Single Disc

6.2 A Two-Disc Torsional Rotor System

6.3 A Two-Disc Torsional Rotor System with a Stepped Shaft

6.4 Three-Disc Torsional Rotor System

6.5 Transfer Matrix Methods

6.6 Simple Geared Rotor Systems

6.7 TMM for Branched Gear Systems

6.8 TMM for Damped Torsional Vibrations

6.9 Modelling of Reciprocating Machine Systems

Concluding remarks

Exercise Problems

References

7 TORSIONAL VIBRATIONS OF ROTORS-II:

THE CONTINUOUS SYSTEM AND FINITE ELEMENT METHODS

7.1 Torsional Vibrations of Continuous Shaft Systems

7.2 Applications of Finite Element Methods

7.3 Development of the Finite Element for a Simple Gear-pair

Concluding Remarks

Exercise Problems

References

8 TRANSVERSE VIBRATIONS-IV: MULTI-DOFs ROTOR SYSTEMS

8.1 Influence Coefficient Method

8.2 Transfer Matrix Method

8.3 Dunkerley’s Formula

Concluding Remarks

Exercise Problems

Figure 8.8

References

9 CONTINUOUS AND FINITE ELEMENT TRANSVERSE VIBRATION ANALYSES OF SIMPLE ROTOR SYSTEMS

9.1 Governing Equations in Continuous Systems

9.2 Natural Frequencies and Mode Shapes

9.3 Forced Vibrations

9.4 A Brief Review on Application of FEM in Rotor-Bearing Systems

9.5 A Finite Element Formulation

9.6 Proportional Damping

9.7 The Static and Dynamic Reductions

Concluding Remarks

Exercises

References

10. TRANSVERSE VIBRATIONS-VI: FINITE ELEMENT ANALYSIS OF ROTORS WITH GYROSCOPIC EFFECTS

10.1 Rotor Systems with a Single Rigid-Disc

10.2 Timoshenko Beam Theory

10.3 Finite Element Formulations of the Timoshenko Beam

10.4 Whirling of Timoshenko Shafts

Concluding Remarks

Appendix 10A Timoshenko Beam Model

Appendix 10B Rotating Timoshenko Beam Model

Exercise Problems

References

11. INSTABILITY IN ROTATING MACHINES

11.1 Self Excited Vibrations

11.2 Phenomenon of the Oil-Whirl

11.3 Stability Analysis using Linearized Stiffness and Damping Coefficients

11.4 Instability Analysis with Fluid-Film Non-Linearity

11.5 Phenomenon of the Oil-Whip

11.6 Internal Damping in Rotors

11.7 Effect of Rotor Polar Asymmetry

11.8 An Asymmetric Rotor with Uniformly Distributed Mass

11.9 System with Variable or Nonlinear Characteristics

11.10 Sub-Critical Vibrations of a Jeffcott Rotor

11.11 Stream Whirl Instability

11.12 Instability due to Rotary Seals

11.13 Non-linear Equations of Motion of the Jeffcott Rotor (Run-up and run-down)

Concluding Remarks

Exercise Problems

References

12. INSTABILITY OF MULTI-DOF ROTORS MOUNTED ON FLEXIBLE BEARINGS

12.1 Rotors Mounted on Flexible Bearings

Coupling

Concluding Remarks

References

Exercise Problems

13. DYNAMIC BALANCING OF ROTORS

13.1 Unbalances in the Rigid and Flexible Rotors

13.2 Principles of the Rigid Rotor Balancing

13.3 Balancing of Practical Rigid Rotor

13.4 Balancing of Flexible Rotors

Concluding Remarks

Exercise Problems

References

14. EXPERIMENTAL ESTIMATION OF DYNAMIC PARAMETERS OF BEARINGS, DAMPERS AND SEALS

14.1 Past Reviews and Surveys on Dynamic Parameters of Bearings

14.2 Hypothesis of Bearing Descriptions and its Basic Concepts

14.3 General Description of the Dynamic System Identification

14.6 Derivation of a Unified Estimation Procedure in Linear Rotor-Bearing Systems

14.7 Estimation with the Help of Electromagnetic Exciters

14.8 Application of Unbalance Forces

14.9 Transient Methods

14.10 Output-Only Estimation Methods

14.11 Procedures for Estimation of Dynamic Parameter of Seals

14.12 Concurrent Estimation of Residual Unbalances and Bearing Dynamic Parameters

Concluding Remarks

Exercise Problems

References

15. MEASUREMENTS IN ROTATING MACHINERIES

15.1 Features of Measuring Units

15.2 Uncertainty Analysis of Estimated Parameters

15.3 Transducers

15.4 Signal Conditioning and Analysis Equipments

15.5 Vibration Exciter Systems

15.6 Sound Measurements

Final Remarks

Exercise Problems

16. SIGNAL PROCESSING IN ROTATING MACHINERIES

16.1 Visual Presentation of Vibration Measurements

16.2 Errors in Vibration Acquisitions

16.3 Basic Concepts of Fourier Series

16.4 Basics of Fourier Transform and Fourier Integral

16.5 Basics of the Discrete Fourier Transform

16.6 Basics of the Fast Fourier Transform

16.7 Leakage Error and its Remedial

16.8 Full-Spectrum and its Applications to Rotor Vibration Analysis

16.9 Statistical Properties of Random Discrete Signals

16.10 Vibration Signal Conditioning

Final Remarks

Exercise Problems

17. VIBRATION BASED CONDITION MONITORING IN ROTATING MACHINERIES

17.1 Unbalances in Rotor Systems

17.2 Shaft Bow or Thermal Bow

17.3 Misalignment

17.4 Rubs

17.5 Slackness of Rotor Elements

17.6 Shaft Flaws

17.7 Rolling Bearing Defects

17.8 Faults in Gears

17.9 Faults in Centrifugal Pumps

17.10 Faults in Induction Motors

Fault Signature of Induction Motor

Final Remarks

Exercise Problem

References

18 ROTOR SYSTEMS WITH ACTIVE MAGNETIC BEARINGS

18.1 Introduction

18.2 Literature Survey on Design and Analysis of AMBs

18.3 Basics of Active Magnetic Bearings

18.4 Block Diagrams and Transfer Functions

18.5 Tuning of the Controller Parameters

18.6 A Single-DOF Rotor System 4

18.7 Two-DOF Rotor Systems

18.8 Four-DOFs Rigid-Rotor Flexible-Bearing Systems

18.8.1 Rotor System Model

18.9 Flexible Rotor-Bearing Systems

General Remarks

Exercise Problems

REFERENCES

### Biography

Dr. Rajiv Tiwari was born in 1967 at Raipur in Madhya Pradesh. India. He graduated in B.E. in 1988 (Mechanical Engineering) from Ravishankar University, Raipur and M. Tech. (Mechanical Engineering) in 1991 and Ph. D. (Mechanical Engineering) in 1997 from Indian Institute of Technology (IIT) Kanpur, India.

He started his career as Lecturer in 1996 at Regional Engineering College, Hamirpur (Himachal Pradesh), India and worked for one year. From beginning of 1997, he joined Indian Institute of Technology Guwahati as Assistant Professor in the Department of Mechanical Engineering. He worked as Research Officer at University of Wales, Swansea, UK for one year in 2001 on deputation. He was elevated to Associate Professor in 2002 and to Professor in 2007 at IIT Guwahati. He was the Head of the Center of Educational Technology and Institute Coordinator of the National Programme on Technology Enhanced Learning (NPTEL) during 2005 to 2009, and the National Coordinator of the Quality Improvement Programme (QIP) for engineering college teachers during 2003-2009.

He has been deeply involved in research area of Rotor Dynamics (i.e. especially on Identification of mechanical system parameters, e.g. the bearings, seals and rotor crack dynamic parameters, Fault diagnosis of machine components like bearings, gears, pumps, and induction motor and application of active magnetic bearings in condition monitoring of rotating machinery). His research area also includes rolling element bearing design and analysis for high-speed applications. He has completed three projects from Aeronautical Research & Development Board (ARDB), India on these topics. He has been offering consultancy for last several years to Indian industries like Indian Space Research Organisation (ISRO), Trivendrum; Combat Vehicle R&D Establish (CVRDE) Chennai; Tata Bearings, Kharagpur; apart from other local industries in the northeast of India. One of the European power industries the Skoda Power, Czech Republic has also taken consultancy of seal dynamic parameter estimation for steam turbine applications.

Dr. Tiwari has been author of over 130 Journal and Conference papers. He has guided Thirty Eight M. Tech. students and has guided Seven Ph.D. students and Eight more are pursuing their research at present.

He has organized successfully a national level Symposium on Rotor Dynamics (NSRD-2003), four short term courses on Rotor Dynamics (2004, 2005, 2008, 2015) and National Workshop on Use and Deployment of Web and Video Courses for Enriching Engineering Education (2007) at IIT Guwahati, India. He has jointly organized an International Conference on Vibration Problems ICOVP 2015 at IIT Guwahati. He has developed two web and video based course under NPTEL (i) Mechanical Vibration and (ii) Rotor Dynamics, and under MHRD sponsored Virtual lab on Mechanical Vibration Virtual Lab.