Research On Nonlinear Dynamics Of Cycloid Ball Transmission Based On Lumped Stiffness Method

Precision and low vibration mechanical precision transmission is the practical requirement for precision equipment such as industrial robot,cycloid ball transmission is a typical research object.The relationship between dynamic accuracy and dynamic characteristics of the system is clearly analyzed by revealing the dynamic behaviors.The related researches are helpful to establish the evaluation system of dynamic accuracy and form the evaluation method.So as to provide guidance for the control strategy of dynamic precision of the system.At the same time,the research results are expected to provide reference for the design and manufacture of similar precision gear transmission.Therefore,it is also of importance to the engineering application.In this paper,the dynamic problem of cycloid ball transmission is deeply studied,including the lumped stiffness modeling method,inherent characteristics,parametric vibration stability and nonlinear vibration characteristics.The main contents of this paper are as follows:Firstly,the basic structure and working principle of cycloid ball transmission are introduced.The meshing force of cycloid ball meshing pair and cross ball equal-speed meshing pair is analyzed respectively.The idea of lumped stiffness modeling is proposed.The meshing stiffness of single cycloid ball meshing pair and single cross ball equal-speed meshing pair is deduced respectively.Then,The lumped stiffness model of cycloid steel ball meshing pair and cross ball equal-speed meshing pair is established respectively.Brief analyses on lumped stiffness are provided as wellSecondly,the basic parameters of cycloid ball transmission system are calculated.A seven degree of freedom translational-rotation coupling dynamic model of system is established.The factors such as average meshing stiffness,bearing support stiffness,and so on are considered.The linear dynamic differential equation of system is derived using Newton's second law.By solving the eigenvalue problem,the natural frequency and the main vibration mode of system are obtained,and the main formation is analyzed.The influence of main parameters on the natural frequency of system is analyzed using variable-controlling approach,and corresponding frequency variation curves are drawn.Thirdly,the time-varying meshing stiffness and meshing error are analyzed.The nonlinear differential equations of cycloid ball transmission are derived considering the factors such as time-varying meshing stiffness,damping and meshing error.Thebasic knowledge of dynamic equation decoupling is introduced.Then the regular modal matrix is used to decoupling the dynamic equations of system.The regular modal equation is obtained.The dynamic stability of the system is solved by multi-scale method.The combination resonance frequencies of the system are calculated,the corresponding stability boundary curves are obtained,and the stability diagrams are drawn using Matlab.The influence of the main parameters on the dynamic stability of the system is analyzed.Then,the nonlinear dimensionless motion equations are deduced by using the nondimensional parameters.The problem of selecting the initial value of integral is discussed.The static deformation of the system is calculated.The variable dimension Runge-Kutta is used to solving the dimensionless differential equations of system.The vibration displacement,velocity,phase diagram and Poincaré section are systematically analyzed.The nonlinear dynamic characteristics of the system are analyzed,and the influence of main parameters on the nonlinear characteristics of system are analyzed.Finally,the design idea of cycloid ball transmission mechanism is introduced,which takes into account the factors such as precision,strength and manufacturing technology.The design process of cycloid ball transmission mechanism is given,and the design steps are introduced in detail.The 3D modeling of key parts is carried out through Solidworks.The prototype is successfully designed according to the design idea and process,and the trial-manufacture is successful.