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The Resource Vibrations in Rotating Machinery : Fundamental Rotordynamics

Vibrations in Rotating Machinery : Fundamental Rotordynamics

Label
Vibrations in Rotating Machinery : Fundamental Rotordynamics
Title
Vibrations in Rotating Machinery
Title remainder
Fundamental Rotordynamics
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Language
eng
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MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Mathematics for Industry Ser.
Series volume
v.16
Vibrations in Rotating Machinery : Fundamental Rotordynamics
Label
Vibrations in Rotating Machinery : Fundamental Rotordynamics
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=4864683
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface -- Contents -- 1 Introduction of Rotordynamics -- Abstract -- 1.1 Vibration Problems in Rotating Machinery -- 1.1.1 Varieties of Rotating Machinery -- 1.1.2 Bearings -- 1.1.3 Defects in Various Elements and Induced Vibration -- 1.1.4 Rotordynamics -- 1.2 Types of Vibration in Rotating Machinery -- 1.3 Classification of Vibration by Mechanism of Occurrence -- 1.4 Simplifying Complicated Phenomena -- 2 Basics for a Single-Degree-of-Freedom Rotor -- Abstract -- 2.1 Free Vibrations -- 2.1.1 Natural Frequency -- 2.1.2 Calculation of Spring Constant -- 2.1.3 Conservation of Energy -- 2.1.4 Mass Effects of Spring on Natural Frequency -- 2.2 Damped Free Vibration -- 2.2.1 Mass-Spring-Viscous Damped System -- 2.2.2 Measurement of Damping Ratio -- 2.2.3 Phase Lead/Lag Corresponding to Damping Ratio -- 2.3 Unbalance Vibration of a Rotating Shaft -- 2.3.1 Complex Displacement and Equation of Motion -- 2.3.2 Complex Amplitude of Unbalance Vibration -- 2.3.3 Resonance Curves -- 2.3.4 Nyquist Plot -- 2.3.5 Bearing Reaction Force at Resonance -- 2.3.6 Transmissibility of Unbalance Vibration to Foundation -- 2.4 Evaluation of Q-Value -- 2.4.1 Q-Value Criterion -- 2.4.2 Measurement of Q-Value by the Half Power Point Method -- 2.4.3 Measurement of Q-Value Using a Nyquist Plot -- 2.4.4 Re-evaluation of Q-Value for Rapid Acceleration -- 2.4.5 Vibration in Passing Through a Critical Speed -- 3 Modal Analysis of Multi-Degree-of-Freedom Systems -- Abstract -- 3.1 Equation of Motion for a Multi-dof System -- 3.1.1 Multiple Mass Systems -- 3.1.2 Equation of Motion for a Two-dof System -- 3.1.3 Equation of Motion for a Multi-dof System -- 3.2 Modal Analysis (Normal Mode Method) -- 3.2.1 Eigenvalue Analysis -- 3.2.2 Orthogonality -- 3.2.3 Reduced Order Modal Model -- 3.2.4 Vibration Response -- 3.3 Modal Analysis of Beams -- 3.3.1 Natural Frequencies and Eigenmodes
  • 3.3.2 Correspondence of the Modal Analyses for Multi-dof Systems and Continua -- 3.3.3 Reduced Modal Models -- 3.3.4 Modal Eccentricity -- 3.4 Physical Models from Reduced Modal Models -- 3.4.1 Modal Mass -- 3.4.2 Equivalent Mass Method -- 3.5 Approximation of Natural Frequencies -- 3.5.1 Rayleigh's Method -- 3.5.2 Method Using Influence Coefficients -- 3.5.3 Dunkerley's Formula -- 3.5.4 Iterative Method (Power Method) [B4] -- 3.5.5 Stiffness Matrix Method -- 3.5.6 Transfer Matrix Method -- 4 Mode Synthesis and Quasi-modal Method -- Abstract -- 4.1 Mode Synthesis Models -- 4.1.1 Why Mode Synthesis? -- 4.1.2 Guyan Reduction Method -- 4.1.3 Mode Synthesis Models -- 4.2 Quasi-modal Models -- 4.2.1 Principle of the Quasi-modal Model -- 4.2.2 Examples of Quasi-modal Models -- 4.3 Plant Transfer Function -- 5 Unbalance and Balancing -- Abstract -- 5.1 Unbalance in a Rigid Rotor -- 5.1.1 Static Unbalance and Dynamic Unbalance -- 5.1.2 Static Unbalance and Couple Unbalance -- 5.1.3 Adverse Effects of Unbalance Vibration -- 5.1.4 Residual Permissible Unbalance in a Rigid Rotor -- 5.2 Field Single-Plane Balancing (Modal Balancing) -- 5.2.1 Relationships among Rotational Pulse, Unbalance and Vibration Vector -- 5.2.2 Linear Relationship -- 5.2.3 Identifying the Influence Coefficient -- 5.2.4 Correction Mass -- 5.3 Balancing by the Influence Coefficient Method -- 5.4 Modal Balancing -- 5.5 n-Plane Balancing or (n + 2)-Plane Balancing? -- 5.5.1 Comparison -- 5.5.2 Number of Correction Planes Needed for Universal Balancing -- 5.5.3 What Is the "2" in the (n + 2)-Plane Method? -- 5.6 Balancing of a Rotor Supported by Magnetic Bearings -- 5.6.1 Balancing by Feed-Forward (FF) Excitation -- 5.6.2 Case Study: Centrifugal Compressor Supported by AMBs [30, VB245] -- 5.7 Balancing without Rotational Pulses -- 5.7.1 Four Run Method [B22]
  • 5.7.2 Balancing by Placing a Trial Mass at a Regular Phase Pitch -- 5.8 Solution of Two-Plane Balancing -- 5.8.1 Principle of Calculation [B22] -- 5.8.2 In-Phase and Out-of-Phase Balancing -- 6 Gyroscopic Effect on Rotor Vibrations -- Abstract -- 6.1 Rotordynamics -- 6.2 Gyroscopic Moment and the Motion of a Top -- 6.2.1 Gyroscopic Moment -- 6.2.2 Equation of Motion of a Top and Whirling Solution -- 6.3 Natural Vibration of a Rotor System -- 6.3.1 Natural Frequency of Whirling -- 6.3.2 Influence of the Gyroscopic Factor -- 6.3.3 Calculation of the Natural Frequency of Whirling in Multi-dof Rotor System -- 6.4 Unbalance Vibration and Resonance -- 6.4.1 Condition for Unbalance Resonance and Critical Speed -- 6.4.2 Resonance Curves for Unbalance Vibration -- 6.4.3 Calculation of Critical Speed of a Multi-dof Rotor System -- 6.5 Vibration and Resonance with Base Excitation -- 6.5.1 Resonance Conditions -- 6.5.2 Forced Vibrational Solution for Base Excitation -- 6.5.3 Resonance Curves and Whirling Trajectories -- 6.5.4 Case Study: Aseismic Evaluation of a High-Speed Rotor [52] -- 6.6 Ball Passing Vibration and Resonance Due to Ball Bearing Defects -- 6.6.1 Ball Bearing Specifications -- 6.6.2 Excitation by a Recess on Outer Race -- 6.6.3 Excitation by a Recess on Inner Race -- 6.6.4 Resonance Conditions -- 6.6.5 Case Study: Hard Disk Drive (HDD) [59, VB218] -- 7 Approximate Evaluation for Eigenvalues of Rotor-Bearing Systems -- Abstract -- 7.1 Equation of Motion for a Single-Degree-of-Freedom Rotor System -- 7.2 Vibration Characteristics of a Symmetrically Supported Rotor System -- 7.2.1 Natural Frequencies of a Conservative System -- 7.2.2 Effects of Non-conservative System Parameters -- 7.2.3 Parameter Survey -- 7.3 Natural Frequencies of a Rotor Supported by Anisotropic Bearings -- 7.3.1 Natural Frequency of a Conservative System
  • 7.3.2 Elliptical Whirling of a Conservative System -- 7.3.3 Influence of Gyroscopic Effect -- 7.3.4 Shape of Elliptical Whirling Orbit -- 7.3.5 Effects of Non-conservative Parameters [60] -- 7.3.6 Parameter Survey -- 7.4 Vibration Characteristics of a Jeffcott Rotor -- 7.4.1 Equation of Motion -- 7.4.2 Vibration Characteristics -- 7.4.3 Real Mode Analysis -- 7.4.4 Complex Mode Analysis -- 7.5 Analysis of Characteristics of Unbalance Vibration -- 7.5.1 Equation of Motion -- 7.5.2 Unbalance Vibration of an Isotropically Supported Rotor System -- 7.5.3 Unbalance Vibration of a Rotor Supported by Anisotropic Bearings -- 7.6 Case Study: Vibrations of a Flexible Rotor with Cylindrical Bearings -- 7.6.1 Critical Speed Map -- 7.6.2 Calculation of Complex Eigenvalues and Q-Values -- 7.6.3 Root Loci -- 7.6.4 Resonance Curves for Unbalance Vibration -- 8 Rotor System Evaluation Using Open-Loop Characteristics -- Abstract -- 8.1 Open-Loop Analysis of a Single-dof System -- 8.1.1 Open-Loop Frequency Response of a Single-dof System -- 8.1.2 Measurement of Open-Loop Frequency Response -- 8.2 Modal Open-Loop Frequency Response -- 8.2.1 Modal Model -- 8.2.2 Modal Open-Loop Frequency Response -- 8.3 Open-Loop Frequency Response of a Jeffcott Rotor -- 8.3.1 Series Coupling and Phase Lead Function -- 8.3.2 Open-Loop Frequency Response -- 8.3.3 Gain Cross-Over Frequency and Phase Margin -- 8.3.4 Precision of Approximate Solutions -- 8.3.5 Optimal Damping -- 8.3.6 Frequency Response -- 9 Bridge Between Inertial and Rotational Coordinate Systems -- Abstract -- 9.1 Vibration Waveforms (Displacement and Stress Caused by Strain) -- 9.2 Natural Frequencies -- 9.3 Resonance Conditions -- 9.4 Representation of Equation of Motion -- 9.4.1 Gyroscopic Moment and Coriolis Force -- 9.4.2 Case Study: Multi-blade Fan (Sirocco Fan) [81, VB55]
  • 10 Vibration Analysis of Blade and Impeller Systems -- Abstract -- 10.1 Natural Frequencies of Rotating Structure Systems -- 10.1.1 Natural Frequencies of a Thin Disk [9] -- 10.1.2 Natural Frequencies of Blades [9] -- 10.1.3 Vibration Analysis of Cyclic Symmetry Structural Systems -- 10.1.4 General Vibration Analysis of Blades and Impellers in a Rotational Coordinate System -- 10.2 Vibration and Resonance of Blades and Impellers -- 10.2.1 Conditions for Blade-Shaft Coupled Vibration -- 10.2.2 Natural Vibration Modes of Blades and Blade Wheels -- 10.2.3 External Forces Acting on Blades and Impellers -- 10.2.4 Resonance Conditions of Blades -- 10.2.5 Criterion of Blade Resonance: Campbell Diagram -- 10.2.6 Case Study: Resonance in Impeller Blades of Centrifugal Compressor [VB958] -- 10.3 Blade/Impeller Vibrations Excited at Stationary Side -- 10.3.1 Difference in Excitation Methods and Resonance Conditions -- 10.3.2 Representation of Vibration of Blades and Impellers in an Inertial Coordinate System -- 10.3.3 Resonance Condition 1 -- 10.3.4 Resonance Condition 2 -- 11 Stability Problems in Rotor Systems -- Abstract -- 11.1 Unstable Vibration Due to Internal Damping of a Rotor [B5] -- 11.1.1 Equation of Motion -- 11.1.2 Stability Condition -- 11.1.3 Stability Analysis -- 11.2 Unstable Vibration of an Asymmetric Rotor System -- 11.2.1 Equation of Motion -- 11.2.2 Overview of Vibration in an Asymmetric Rotating Shaft -- 11.2.3 Simulation of Vibration of Asymmetric Rotor -- 11.3 Vibration Due to Thermal-Bow by Contact Friction -- 11.3.1 Thermal-Bow -- 11.3.2 Thermal-Bow Model -- 11.3.3 Stability Analysis -- 11.3.4 Physical Interpretation of Stability -- 11.3.5 Simulation of Thermal-Bow Induced Vibration -- 11.4 Thermal-Bow Induced Vibration of an Active Magnetic Bearing Equipped Rotor -- 11.4.1 Thermal-Bow Model -- 11.4.2 Stability Analysis
  • 11.4.3 Physical Interpretation of Stability
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