Rotor Systems: Analysis and Identification

Description

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. Content: CHAPTER 1 A BRIEF HISTORY OF ROTOR DYNAMICS AND RECENT TRENDS1.1 From the Rankine to Jeffcott Rotor Models1.2 Rotor Dynamics Phenomena Studies from Stodola to Lund1.3 Development of Rotor Dynamics Analysis Tools1.4 Software for Rotor Dynamics Analysis1.5 Dynamic Balancing of Rotors1.6 Condition Monitoring of Rotating Machineries1.7 Conferences on Rotordynamics1.8 Concluding RemarksExercise ProblemsReferencesã CHAPTER 2ANALYSIS OF SIMPLE ROTOR SYSTEMS2.1 Single-DOF Undamped Rotor Model2.2 A Single-DOF Damped Rotor Model2.3 Rankine Rotor Model2.4 Jeffcott Rotor Model2.5 A Jeffcott Rotor Model with an Offset Disc2.6 Suppression of Critical SpeedsConcluding RemarksExercise ProblemsReferencesã ã CHAPTER 3ROTORDYNAMIC PARAMETERS OF BEARINGS, SEALS AND DAMPERS3.1 Rolling Element Bearings3.2 Hydrodynamic Fluid-Lubricated Journal Bearings3.3 Dynamic Seals3.4 Squeeze-Film DampersConcluding remarksExercise ProblemsReferencesã CHAPTER 4TRANSVERSE VIBRATIONS-II: SIMPLE ROTOR-BEARING-FOUNDATION SYSTEMS4.1 Symmetrical Long Rigid Shaft on Flexible Anisotropic Bearings4.2 A Symmetrical Long Rigid Shaft on Anisotropic Bearings4.3 A Symmetrical Flexible Shaft on Anisotropic Bearings4.4 A Rotor on Flexible Bearings and Foundations4.5 A Turbine-Coupling-Generator Rotor on Flexible BearingsConcluding RemarksExercise ProblemsReferences5. TRANSVERSE VIBRATIONS-III: SIMPLE ROTOR SYSTEMS WITH GYROSCOPIC EFFECTS5.1 Angular Momentum5.2 Gyroscopic Moments in Rotating Systems5.3 Synchronous Motion of Rotors5.4 Asynchronous Rotational Motion of Rotor System5.5 Asynchronous General Motion of Rotor Systems5.6 Gyroscopic Effects by the Dynamics Approach5.7 Analysis of Gyroscopic effects with Energy Methods5.8 Pure Transverse Rotational Vibrations of a Jeffcott Rotor Model with Moment UnbalanceConcluding RemarksExercise ProblemsReferencesã CHAPTER 6TORSIONAL VIBRATIONS OF ROTORS-I: THE DIRECT AND TRANSFER MATRIX METHODS6.1 A Simple Torsional Rotor System with a Single Disc6.2 A Two-Disc Torsional Rotor System6.3 A Two-Disc Torsional Rotor System with a Stepped Shaft6.4 Three-Disc Torsional Rotor System6.5 Transfer Matrix Methods6.6 Simple Geared Rotor Systems6.7 TMM for Branched Gear Systems6.8 TMM for Damped Torsional Vibrations6.9 Modelling of Reciprocating Machine SystemsConcluding remarksExercise Problems References7 TORSIONAL VIBRATIONS OF ROTORS-II:THE CONTINUOUS SYSTEM AND FINITE ELEMENT METHODS7.1 Torsional Vibrations of Continuous Shaft Systems7.2 Applications of Finite Element Methods7.3 Development of the Finite Element for a Simple Gear-pairConcluding RemarksExercise ProblemsReferences8 TRANSVERSE VIBRATIONS-IV: MULTI-DOFs ROTOR SYSTEMS8.1 Influence Coefficient Method8.2 Transfer Matrix Method8.3 Dunkerley's FormulaConcluding RemarksExercise ProblemsFigure 8.8Referencesã 9 CONTINUOUS AND FINITE ELEMENT TRANSVERSE VIBRATION ANALYSES OF SIMPLE ROTOR SYSTEMS9.1 Governing Equations in Continuous Systems9.2 Natural Frequencies and Mode Shapes9.3 Forced Vibrations9.4 A Brief Review on Application of FEM in Rotor-Bearing Systems9.5 A Finite Element Formulation9.6 Proportional Damping9.7 The Static and Dynamic ReductionsConcluding RemarksExercisesReferences10. TRANSVERSE VIBRATIONS-VI: FINITE ELEMENT ANALYSIS OF ROTORS WITH GYROSCOPIC EFFECTS10.1 Rotor Systems with a Single Rigid-Disc10.2 Timoshenko Beam Theory10.3 Finite Element Formulations of the Timoshenko Beam10.4 Whirling of Timoshenko ShaftsConcluding RemarksAppendix 10A Timoshenko Beam ModelAppendix 10B Rotating Timoshenko Beam ModelExercise ProblemsReferencesã ã 11. INSTABILITY IN ROTATING MACHINES11.1 Self Excited Vibrations11.2 Phenomenon of the Oil-Whirl11.3 Stability Analysis using Linearized Stiffness and Damping Coefficients11.4 Instability Analysis with Fluid-Film Non-Linearity11.5 Phenomenon of the Oil-Whip11.6 Internal Damping in Rotors11.7 Effect of Rotor Polar Asymmetry11.8 An Asymmetric Rotor with Uniformly Distributed Mass11.9 System with Variable or Nonlinear Characteristics11.10 Sub-Critical Vibrations of a Jeffcott Rotor11.11 Stream Whirl Instability11.12 Instability due to Rotary Seals11.13 Non-linear Equations of Motion of the Jeffcott Rotor (Run-up and run-down)Concluding RemarksExercise ProblemsReferencesã 12. INSTABILITY OF MULTI-DOF ROTORS MOUNTED ON FLEXIBLE BEARINGS12.1 Rotors Mounted on Flexible BearingsCouplingConcluding RemarksReferencesExercise Problemsã 13. DYNAMIC BALANCING OF ROTORS13.1 Unbalances in the Rigid and Flexible Rotors13.2 Principles of the Rigid Rotor Balancing13.3 Balancing of Practical Rigid Rotor13.4 Balancing of Flexible RotorsConcluding RemarksExercise ProblemsReferencesã 14. EXPERIMENTAL ESTIMATION OF DYNAMIC PARAMETERS OF BEARINGS, DAMPERS AND SEALS14.1 Past Reviews and Surveys on Dynamic Parameters of Bearings14.2 Hypothesis of Bearing Descriptions and its Basic Concepts14.3 General Description of the Dynamic System Identification14.4 Static Load Procedure14.5 Methods Using Dynamic Loads14.6 Derivation of a Unified Estimation Procedure in Linear Rotor-Bearing Systems14.7 Estimation with the Help of Electromagnetic Exciters14.8 Application of Unbalance Forces14.9 Transient Methods14.10 Output-Only Estimation Methods14.11 Procedures for Estimation of Dynamic Parameter of Seals14.12 Concurrent Estimation of Residual Unbalances and Bearing Dynamic ParametersConcluding RemarksExercise ProblemsReferencesã 15. MEASUREMENTS IN ROTATING MACHINERIES15.1 Features of Measuring Units15.2 Uncertainty Analysis of Estimated Parameters15.3 Transducers15.4 Signal Conditioning and Analysis Equipments15.5 Vibration Exciter Systems15.6 Sound MeasurementsFinal RemarksExercise Problems16. SIGNAL PROCESSING IN ROTATING MACHINERIES16.1 Visual Presentation of Vibration Measurements16.2 Errors in Vibration Acquisitions16.3 Basic Concepts of Fourier Series16.4 Basics of Fourier Transform and Fourier Integral16.5 Basics of the Discrete Fourier Transform16.6 Basics of the Fast Fourier Transform16.7 Leakage Error and its Remedial16.8 Full-Spectrum and its Applications to Rotor Vibration Analysis16.9 Statistical Properties of Random Discrete Signals16.10 Vibration Signal ConditioningFinal RemarksExercise Problems17. VIBRATION BASED CONDITION MONITORING IN ROTATING MACHINERIES17.1 Unbalances in Rotor Systems17.2 Shaft Bow or Thermal Bow17.3 Misalignment17.4 Rubs17.5 Slackness of Rotor Elements17.6 Shaft Flaws17.7 Rolling Bearing Defects17.8 Faults in Gears17.9 Faults in Centrifugal Pumps17.10 Faults in Induction MotorsFault Signature of Induction MotorFinal RemarksExercise ProblemReferencesã ã 18 ROTOR SYSTEMS WITH ACTIVE MAGNETIC BEARINGS18.1 Introduction18.2 Literature Survey on Design and Analysis of AMBs18.3 Basics of Active Magnetic Bearings18.4 Block Diagrams and Transfer Functions18.5 Tuning of the Controller Parameters18.6 A Single-DOF Rotor System 418.7 Two-DOF Rotor Systems18.8 Four-DOFs Rigid-Rotor Flexible-Bearing Systems18.8.1 Rotor System Model18.9 Flexible Rotor-Bearing SystemsGeneral RemarksExercise ProblemsREFERENCES