Machinery Dynamics

Part I: Rigid-body Dynamics

1 Kineto-Static Analysis

1.1 Introduction

1.2 Analysis of Planar Linkages

1.2.1 Inertial Force and Inertial Moment

1.2.2 Analysis of Planar Linkage

1.2.3 Shaking Force and Shaking Moment

1.3 Analysis of Sider-Crank Mechanism

1.4 Analysis of Planar Cam Mechanisms

2 Balancing of Planar Mechanisms and Engine Dynamics

2.1 Introduction

2.2 Equivalent Masses

2.2.1 Equivalent Criteria

2.2.2 Real Equivalent Mass

2.3 Partial Force Balancing of Slider-Crank Mechanisms

2.3.1 Dynamic Analysis

2.3.2 Partial Balancing of Inertial Force

2.4 Complete Balancing of Planar Mechanisms

2.4.1 Criteria of Complete Balancing

2.4.2 Complete Balancing of Shaking Force through Mass Redistribution

2.4.3 Complete Balancing of Shaking Force and Shaking Moment

2.4.4 Complete Balancing through Duplicated Mechanism

2.4.5 Limitation of Complete Balancing

2.5 Optimized Balancing

2.6 Dynamics of Engines

2.6.1 Inline Engines

2.6.2 V Engines

3 Dynamics of Single DOF Machines

3.1 Introduction

3.2 Forces on Machines

3.2.1 Classification of Forces

3.3 Characteristics of Induction Motors

3.4 Dynamics of Single DOF systems

3.4.1 Lagrange’s Equation

3.4.2 Governing Equation of Single DOF Systems

3.4.3 Equivalent Model

3.4.4 Equation of Energy Form

3.4.5 Discussion

3.5 Solution of Equation

3.5.1 Case 1: "e being function of @

3.5.2 Case 2: Constant e and "e depending on l

3.5.3 Case 3: "e being function of @ and @¤

3.6 Machine Speed in Steady Stage

3.6.1 Estimated Initial Conditions

3.6.2 Roots of Equations

3.7 Smoothening Velocity Fluctuation

3.7.1 Traditional Flywheel

3.7.2 Sizing Flywheels

3.7.3 An Innovative Mini-Flywheel

4 Dynamics of Machines with Multiple DOF

4.1 Introduction

4.2 Dynamics of Machines of Two DOF

4.2.1 Kinematics

4.2.2 Kinetic Energy

4.2.3 Generalized Forces

4.2.4 Governing Equation of Motion

4.3 Dynamics of Two Link Manipulators

4.4 Brief Introduction to Dynamics of Robotic Manipulators

4.4.1 Robots and Robotic Manipulators

4.4.2 Introduction to Robotic Kinematics

4.4.3 Introduction to Robotic Dynamics
Part II: Theory of Mechanical Vibration

5 Vibration of Systems with Single DOF

5.1 Introduction

5.2 Free Vibration

5.2.1 Undamped Free Vibration

5.2.2 Damped Free Vibration

5.3 Forced Vibration

5.3.1 Response to Harmonic Force Excitation

5.3.2 Response to Harmonic Base Motion Excitation

5.3.3 Response to Periodic Force Excitation

5.3.4 Response to Non-periodic Forces

6 Vibration of Systems with Multiple DOF

6.1 Introduction

6.2 Vibration of Two DOF Systems

6.2.1 Equation Derived through Newton’s Second Law

6.2.2 Equation Derived through Lagrange’s Equation

6.2.3 Vibration Absorbers

6.3 Vibration of Multiple DOF Systems

6.3.1 Discretization of Continuous Systems

6.3.2 Dynamic Equation of Multiple DOF System

6.3.3 Flexibility Matrix

6.4 Solution of Multiple DOF Vibration

6.4.1 Coordinate Coupling

6.4.2 Natural Frequency and Principal Mode

6.4.3 Orthogonality and Normalization of Principal Mode

6.5 Vibration Response of Systems with Multiple DOF

6.5.1 Damping Assumption

6.5.2 Modal Truncation Method

6.5.3 Free Vibration Response of Systems with Multiple DOF

6.5.4 Forced Vibration Response of Systems with Multiple DOF

7 Finite Element Method for Vibration Problems

7.1 Introduction

7.2 One Dimensional Element

7.2.1 Bar Element

7.2.2 Beam Element

7.3 Two Dimensional Element

7.3.1 Triangular Elements

7.3.2 Rectangular Elements

7.3.3 Isoparametric Element

7.3.4 Plane Problems of FEM

8 Nonlinear Vibration

8.1 Introduction

8.2 Examples of Nonlinear Systems

8.2.1 Single Pendulum

8.2.2 Large Deformation

8.2.3 Joint Clearance

8.2.4 Dry Friction

8.3 Approximate Analysis of Free Vibration

8.4 Approximate Analysis of Forced Vibration

8.4.1 Primary Resonance

8.4.2 Nonresonant Response

8.4.3 Superharmonic Resonances

8.4.4 Subharmonic Resonance

8.5 Numerical Analysis
Part III: Elasto-Dynamics

9 Vibration of Shafts and Shaft Systems

9.1 Introduction

9.2 Natural Frequency of TorsionalVibration

9.2.1 Dynamic Model of Torsional Vibration

9.2.2 Transfer Matrix Method for Torsional Vibration

9.3 Transfer Matrix Method for Critical Speed

9.3.1 Point and Field Transfer Matrix

9.3.2 Global Transfer Matrix

9.3.3 Frequency Equation and Solution

9.4 Finite Element Method for Critical Speed

9.4.1 Finite Element Model

9.4.2 Critical Speed

9.5 Introduction to Rotor Dynamics

10 Dynamics of Cam Mechanisms

10.1 Introduction

10.2 Follower Motions for High Speed Cam Mechanisms

10.2.1 Two Types of Motion Constraints

10.2.2 Normalization of Motion Parameters

10.2.3 Characteristic Quantities

10.2.4 Follower Motions

10.3 Dynamic Models of Cam Mechanisms

10.3.1 Dynamic Model

10.3.2 Reduction of Model

10.4 Dynamic Analysis of Cam Mechanisms

10.4.1 Analysis of Single DOF Systems

10.4.2 Analysis of Cycloidal Motion

10.4.3 Analysis of Constant Acceleration Motion

10.4.4 Analysis of Generic Combined Harmonic Motion

10.4.5 Effect of _ and Dynamic Response Spectrum

10.5 Dynamic Design of Cam Mechanisms

10.5.1 Introduction to Design of High-speed Cam Mechanism

10.5.2 Polydyne Cams

10.5.3 General Rules for Design of High-speed Cams

10.6 High Speed Indexing Cam Mechanisms

10.6.1 Rotary Table Driven by Globoidal Cam

10.6.2 Flexible Chain System Driven by Parallel Cam

10.6.3 Simulation and Analysis

11 Elasto-Dynamics of Linkage

11.1 Introduction

11.1.1 Brief Historic Review

11.1.2 Review on Elasto-dynamic Analysis

11.2 Equation of Elements

11.2.1 Generalized Coordinates

11.2.2 Kinematic Relations

11.2.3 Equation of Elements

11.3 Global Equation of Motion

11.3.1 Generalized Coordinates

11.3.2 Formation of Global Equation of Motion

11.4 Solution of Equation and Analysis

11.4.1 Solution of Equation

11.4.2 Result Analysis

11.5 Elasto-Dynamic Synthesis and Suppression of Vibration

11.5.1 Elasto-Dynamic Synthesis

11.5.2 Suppression of Elasto-Dynamic Response

12 Elasto-Dynamics of Gear Trains

12.1 Introduction

12.1.1 Historical Review

12.1.2 Features of Gear Dynamics

12.2 Excitation in Gear Dynamics

12.2.1 Stiffness Excitation

12.2.2 Error Excitation

12.2.3 Meshing Impact

12.3 Pure Rotational Models for Spur Gear Trains

12.3.1 Rotational Model for Gear Pairs

12.3.2 Rotational Model of Gear-rotor System

12.4 Translational-Rotational Model

12.4.1 Dynamic Model

12.4.2 Case Study

12.5 Short Review on Gear Dynamics

12.5.1 Linear Gear Dynamics

12.5.2 Nonlinear Gear Dynamics

12.5.3 Random Gear Dynamics

12.5.4 Fault Diagnosis and Condition Monitoring

12.5.5 Gear Tooth Profile Modification

13 Dynamics of Planetary Gear Trains

13.1 Introduction

13.2 Pure Rotational Model

13.2.1 Dynamic Model

13.2.2 Free Vibration Analysis

13.2.3 Analytical Analysis of Natural Frequencies

13.3 Translational-Rotational Dynamic Model

13.3.1 Dynamic Model

13.3.2 Acceleration Transformation

13.3.3 Excitation

13.3.4 Relative Displacements

13.3.5 Governing Equation of Motion

13.3.6 Free Vibration Analysis

13.4 Planet Phasing and Parameter Selection

13.4.1 Planet Phasing

13.4.2 Physical Illustration

13.4.3 Experimental Validation

13.4.4 Parameter Selection

14 Elasto-Dynamics of Mechanical Systems

14.1 Introduction

14.2 Bridge Crane Systems

14.2.1 Dynamic Model

14.2.2 Equation of Motion

14.2.3 Solution of Equation

14.3 Rolling Mill System

14.3.1 Dynamic Model

14.3.2 Equation of Motion

14.4 Polydyne Servo-Cam Design

14.4.1 Principle

14.4.2 Design Process

14.4.3 Design Example

15 Dynamics of Machinery with Joint Clearance

15.1 Introduction

15.2 Three Modes of Clearance

15.3 Linkage Mechanism

15.3.1 Two Mode Model

15.3.2 One Mode Model

15.4 Cam Mechanisms

15.4.1 Dynamic Model

15.4.2 Solution

15.5 Gears

15.5.1 Dynamic Model

15.5.2 Solution and Result Analysis

15.6 Features of Dynamics with Joint Clearance
Appendices
A Crossover Shock
B Common Motions of Harmonic Combination
C Calculation of Deformation of Gear Tooth
D Matrices in Gear Dynamics
E Meshing Stiffness Calculation of Planetary Gear Train