Machinery Dynamics

Description

Machinery Dynamics includes recent advancements in this quickly evolving area, while also analyzing real applications, analyzing integrated systems, and including further discussions on each mechanical component. The book treats mechanisms separately, with different methods depending on the level of accuracy required. The contents of this book is made to suit the needs of MsC and PhD students, researchers and engineers in the areas of design of high speed machinery, condition monitoring of machine operation, and vibration. Front Cover Machinery Dynamics Copyright Contents List of figures Biography Ce Zhang Jianming Yang Zongyu Chang Preface Part 1 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 the slider-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 2.2.1.1 Static equivalency 2.2.1.2 Dynamic equivalency 2.2.2 Real equivalent mass 2.2.2.1 Static equivalency 2.2.2.2 Dynamic equivalency 2.3 Partial force balancing of slider-crank mechanisms 2.3.1 Dynamic analysis 2.3.2 Partial balancing of inertial forces 2.4 Complete balancing of planar mechanisms 2.4.1 Criteria for 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 2.6.1.1 Shaking force FS 2.6.1.2 Shaking moment Mz 2.6.1.3 Shaking moment Mx 2.6.2 V engines 2.6.2.1 Shaking force FS 2.6.2.2 Shaking moment Mz 2.6.2.3 Shaking moment Mx 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 3.4.2.1 Kinetic energy 3.4.2.2 Potential energy 3.4.2.3 Generalized force 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: Me being function of q 3.5.2 Case 2: constants Je and Me depending on ω 3.5.2.1 Closed-form solution 3.5.2.2 Numerical solution 3.5.3 Case 3: Me being a function of q and q̇ 3.5.3.1 General method 3.5.3.2 Fast method 3.6 Machine speed in the 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 DOFs 4.1 Introduction 4.2 Dynamics of machines of two DOFs 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 the 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 2 Theory of mechanical vibration 5 Vibration of systems with a 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 5.3.3.1 Fourier series 5.3.3.2 Superposition principle 5.3.3.3 Response in frequency domain 5.3.4 Response to nonperiodic forces 6 Vibration of systems with multiple DOFs 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 systems 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 the principal mode 6.4.3.1 Orthogonality of the principal mode 6.4.3.2 Normalization of principal mode 6.4.3.3 Decoupling of vibration equation of multiple-DOF systems 6.5 Vibration response of systems with multiple DOFs 6.5.1 Damping assumption 6.5.2 Modal truncation method 6.5.3 Free-vibration response of systems with multiple DOFs 6.5.4 Forced-vibration response of systems with multiple DOFs 7 Finite element method for vibration problems 7.1 Introduction 7.2 One-dimensional elements 7.2.1 Bar elements 7.2.1.1 Shape function 7.2.1.2 Element equations 7.2.1.3 Global equations 7.2.2 Beam element 7.2.2.1 Shape function 7.2.2.2 Element equations 7.2.2.3 Global equations 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 7.3.4.1 Plane-stress and plane-strain problems 7.3.4.2 General rules for meshing 7.3.4.3 An example 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 3 Elasto-dynamics 9 Vibration of shafts and shaft systems 9.1 Introduction 9.2 Natural frequency of torsional vibration 9.2.1 Dynamic model of torsional vibration 9.2.1.1 Equivalent torsional stiffness 9.2.1.2 Dynamic model of serial systems 9.2.2 Transfer matrix method for torsional vibration 9.2.2.1 State vector 9.2.2.2 Point transfer matrix 9.2.2.3 Field transfer matrix 9.2.2.4 Frequency equation 9.2.2.5 Solving the frequency equation 9.3 Transfer matrix method for critical speeds 9.3.1 Point and field transfer matrix 9.3.1.1 Point transfer matrix of masses 9.3.1.2 Field transfer matrix 9.3.1.3 Point transfer matrix of supports 9.3.2 Global transfer matrix 9.3.3 Frequency equation and solution 9.4 Finite element method for critical speeds 9.4.1 Finite element model 9.4.1.1 Discretization of shaft 9.4.1.2 Element matrices 9.4.1.3 Global matrices 9.4.1.4 Supports 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 10.2.4.1 Combined harmonic motions 10.2.4.2 Polynomial motions 10.3 Dynamic models of cam mechanisms 10.3.1 Dynamic model 10.3.1.1 Cam-pushrod subsystem 10.3.1.2 Camshaft–cam subsystem 10.3.1.3 Governing equations 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 λ and dynamic response spectrum 10.5 Dynamic design of cam mechanisms 10.5.1 Introduction to design of high-speed cam mechanisms 10.5.2 Polydyne cams 10.5.2.1 Rationale 10.5.2.2 Polynomial dynamic cam curve 10.5.2.3 Discussion 10.5.3 General rules for design of high-seed cams 10.6 High-speed indexing cam mechanisms 10.6.1 Rotary table driven by globoidal cam 10.6.1.1 Dynamic model 10.6.1.2 Governing equation 10.6.1.3 Simulation and analysis 10.6.2 Flexible chain system driven by a parallel cam 10.6.2.1 Dynamic model 10.6.2.2 Governing equation of motion 10.6.3 Simulation and analysis 11 Elasto-dynamics of linkage 11.1 Introduction 11.1.1 Brief historical review 11.1.2 Review on elasto-dynamic analysis 11.2 Equation of elements 11.2.1 Generalized coordinates 11.2.2 Kinematic relationships 11.2.3 Equation of elements 11.2.3.1 Kinetic energy 11.2.3.2 Potential energy 11.2.3.3 Equation of motion in rotating coordinate 11.2.3.4 Equation of motion in absolute coordinate 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 11.4.2.1 Error of motion 11.4.2.2 Dynamic stress 11.4.2.3 Analysis in different levels 11.5 Elasto-dynamic synthesis and suppression of vibration 11.5.1 Elasto-dynamic synthesis 11.5.2 Suppression of elasto-dynamic response 11.5.2.1 Composite materials 11.5.2.2 Active control 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 12.2.1.1 Gear-tooth deformation 12.2.1.2 Meshing stiffness 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 12.4.1.1 Basic assumption 12.4.1.2 Geometric and kinematic relationship 12.4.1.3 Force analysis 12.4.1.4 Equation of motion 12.4.2 Case study 12.4.2.1 Natural frequencies 12.4.2.2 Influence of meshing stiffness 12.4.2.3 Dynamic load factor 12.5 Short review of 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 13.2.3.1 Planet modes 13.2.3.2 Rotational modes 13.3 Translational–rotational dynamic model 13.3.1 Dynamic model 13.3.2 Acceleration transformation 13.3.3 Excitation 13.3.3.1 Time-varying meshing stiffness 13.3.3.2 Tooth profile error 13.3.4 Relative displacements 13.3.4.1 s-p mesh 13.3.4.2 r-p mesh 13.3.4.3 Between carrier and planet 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 the equation 14.2.3.1 Abrupt starting 14.2.3.2 Emergency braking 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 14.4.2.1 Cam profile designed at design speed in rise 14.4.2.2 Off-design speed in rise 14.4.2.3 Off-design speed in dwell 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 15.3.1.1 Equation of motion 15.3.1.2 Solution and result analysis 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 A Crossover shock B Common motions of harmonic combinations C Calculation of deformation of gear teeth D Matrices in gear dynamics E Meshing stiffness calculation of a planetary gear train References Index Back Cover