Research On Dynamics Of Cycloid Ball Transmission With Thermal Deformation

Cycloid ball transmission is a new type of precision transmission,which has the advantages of no backlash,high bearing capacity and high transmission accuracy.So It has a good application prospect in the field of precision mechanical transmission.The friction heat generated by meshing of ball and cycloid groove cause the meshing temperature rise and thermal deformation,seriously affecting the system transmission performance.So it has important significance for the study of cycloid ball transmission dynamics considering the influence of thermal deformation.Based on the transmission principle and structure characteristics of cycloid ball transmission,the load characteristics,geometric characteristics,motion characteristics and contact characteristics of the cycloid ball meshing pair are analyzed.According to the principle of tribology and heat transfer theory,the variation law of friction heat of cycloid ball meshing pair is analyzed.The effects of various parameters on heat generation rate are investigated.Based on the theory of differential operator,the general solution of the basic equations of thermoelasticity and the green function of point heat source on the surface of half space are derived.The single tooth model and the thermoelastic analysis model are established,and the thermal deformation of the meshing pair is calculated by the superposition principle of the Green function method.The finite element simulation of the thermal deformation of the meshing pair is carried out by using thermal structure coupling module of the Workbench software,which verifies the validity of the Green function method.The influence of system parameters on the thermal deformation is analyzed.According to the point contact Hertz theory,the contact model of meshing pair is established and the expression of meshing stiffness coefficient is deduced.The influence of each parameter on the meshing stiffness coefficient is analyzed.In order to facilitate the dynamic analysis,based on the rotation of the planetary disk,the nonlinear and linear equivalence of meshing stiffness are derived.The thermal deformation is used to calculate the deflection of the planetary disk caused by the thermal effect,and the thermal stiffness coefficient is obtained.The translation torsion coupling vibration model for reducing mechanism of cycloid ball transmission is established.The dynamic differential equation of vibration system is derived according to the force balance and torque balance.Equivalent analysis of meshing stiffness excitation is made.The natural frequency and main vibration mode of the system are analyzed based on the derived system.The dynamic response of the system is solved by Runge Kutta numerical method,and the influence of the thermal deformation of the meshing pair on the dynamic performance of the system is analyzed.