Rotor Systems Analysis and Identification

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 14.4 Static Load Procedure 14.5 Methods Using Dynamic Loads 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

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.