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
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.
