Analysis Of Coupled Thermoelastic Contact And Dynamic Performance Of Cycloid Ball Planetary Transmission

The cycloid ball planetary transmission is a kind of precision transmission mechanism.Because of its advantages of zero-backlash,compact structure,small size and high transmission accuracy,it has a good application prospects in the fields of the precision mechanism,such as robots,unmanned aerial vehicle,medical devices and aerospace.The relative motion characteristic of the transmission system is studied based on the Buckingham's semi-empirical formula of sliding friction coefficient in this paper.The relative sliding velocity and sliding friction coefficient between the ball and the cycloidal tooth surface are calculated.On this basis,the force analysis model of cycloid-ball meshing pair with considering friction is presented,the formula of meshing force is deduced by using contact stiffness coefficient method,and the effect of friction on meshing force and the variation of meshing force with the rotation angle of deceleration ball system are analyzed.According to the contact mechanics,the non-Hertz contact model of the cycloid-ball meshing pair is established.The analytical formulas such as semi-axis of contact elliptical,meshing stiffness and so on are derived,and the variation property of the contact characteristics is analyzed.The deceleration ball and cycloidal plate are treated as the semi-infinite solids,and the discrete convolution and fast Fourier transform techniques are used to compute the surface and subsurface non-Hertz stress fields of bodies.Based on the stress analysis,a approach for estimating the bearing capacity of cycloid ball planetary transmission is proposed according to Mises yield criterion,and its bearing capacity is analyzed based on the method.Aiming at the sliding contact problem in cycloid ball planetary transmission,a semi-analytical transient solution analysis model of coupled thermoelastic for sliding contact is established.The thermoelastic displacement potential method is conducted to decouple the governing equations of coupled thermoelastic,and the semi-analytical solution of transient contact temperature rise is obtained by using the heat source method;the calculation method of thermoelastic fields considering the frictional thermal behavior is proposed based on the thermoelastic displacement potential-central difference method.The effects of coupled term,sliding velocity,sliding frictional coefficient and initial temperature on temperature field and the effect of thermal behavior on elastic field are analyzed.Taking into account the factor of coupling thermoelasticity,the coupled thermoelastic point contact model is applied to cycloid ball planetary transmission,the coupled thermoelastic contact analysis model of the cycloid-ball meshing pair is established.The semi-analytical formulas of local transient contact temperature rise and nominal steady temperature rise between the ball and the cycloidal tooth are deduced by heat source method,on this basis,a semi-analytical method for calculating the thermoelastic meshing deformation and thermoelastic meshing stiffness of cycloid-ball meshing pair considering the frictional thermal behavior is presented.The effects of input shaft speed and load torque on the contact temperature rise and the effect of frictional heat on meshing stiffness are analyzed.According to the analysis results from the coupled thermoelastic contact characteristics of cycloid ball planetary transmission,the lumped parameter method is adopted when establishing the dynamic model,a 11-DOF translational-torsional coupling spatial dynamic model of cycloid ball planetary transmission system is constructed by considering the factors such as the frictional thermal behavior,time-varying meshing stiffness and support stiffness of bear.The Lagrange mechanics method is adopted to derive the dynamic equations of system,and analyzing the natural property;the Runge-Kutta numerical method is employed to solve the dynamic equations and obtain the time domain response,and the dynamic performance of transmission system is analyzed by the displacement time history curve,phase diagram,power spectrum and Poincarésection diagram.A prototype of cycloid ball planetary transmission system is designed and manufactured,and the design and selection method of cycloidal groove and ball is put forward.The non-top-cutting condition of cycloidal groove is given,and the correctness of the non-top-cutting condition is verified by actual processing.The natural frequency of theprototype is tested by the experimental modal analysis method.The measured values are in good agreement with the theoretical values,and the error is within a reasonable range,which verifies the rationality and feasibility of the system dynamic model.