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