Research On Axial Preloaded Cycloid Ball Planetary Transmission

The cycloid ball planetary transmission has the advantages of high transmission accuracy and positioning accuracy.It also has the advantages of small volume,compact structure and fast response.Besides,it has the characteristics of real-time maintaining precision.Cycloid ball planetary transmission is widely applied in many fields,such as robot,CNC machine,aerospace,defense industry,transportation,servo drive,chemical machinery and so on.Through the analysis of the actual tooth profile of the cycloid groove,the actual tooth shape equation of the cycloid groove is given.The influence of the variation of the steel ball radius on the actual tooth formation is analyzed.On the basis of the analysis of the traditional ring groove tooth profile,a double circular arc groove is given,which composed of the outer arc,the inner arc and the bottom line.It is found that the size of the double circular arc ring groove is not affected by the eccentricity and the diameter of the steel ball.For the each meshing state of each meshing pair under axial pretension,the mechanics model of each meshing pair is established.The formula of the elastic angle of each meshing pair is established.The change law of the elastic angle of the constant speed meshing pair and the cross slide groove are analyzed.The influence of the change of the system parameters on the elastic error of the transmission mechanism is studied.For the meshing state of each meshing pair under axial micro movement conditions,the mechanics model of each meshing pair is established.The relationship between the force and the axial momentum is derived,and the critical compression coefficient for real time four point contact is obtained by the meshing pair.The sliding velocity model of the meshing point is established.The equivalent wear function of the meshing pair is obtained.The wear law of the meshing point is analyzed.It is found that the transmission precision of the ring groove constant speed mechanism is higher.When the compression coefficient is greater than the critical value,the meshing pair can realize the anti-backlash meshing transmission.Under the axial pretightening condition,the deceleration meshing pair compensates the wear and tear in real time.For a variety of nonlinear factors,the pure torsional nonlinear dynamic models of the ring groove and the cross sliding slot equal speed mechanism are established.The pretightening nonlinear function is expressed as a polynomial form.The clearance nonlinear function is expressed as the form of description function.A set of nonlinear dynamic differential equations for an equal speed mechanism are established.The differential equations are transformed into nonlinear algebraic equations by the harmonic balance method.The fundamental frequency steady-state response of the system is obtained by the numerical analysis software.The influence of the variation of different parameters on the nonlinear characteristics of the system is analyzed.The results show that the nonlinear degree of the pretightening system of ring groove constant speed mechanism increases with the increase of T_s,and decreases with the gradual increase of axial pretightening,mesh stiffness and slewing radius.The vibration stability of the ring groove equal speed mechanism is stronger.Under consideration of meshing point damping conditions,a pure torsional nonlinear dynamic model for a ring groove mechanism with damping is established.The amplitude frequency response of the main vibration,subharmonic vibration and super harmonic vibration of a ring groove equal speed mechanism is studied by using the multi-frequency expansion method.The influence of damping coefficient,preload and meshing stiffness on the amplitude frequency characteristics is analyzed.It is found that the preload has a great influence on the vibration stability of the system.The increase of damping coefficient and preload can improve the vibration stability of the mechanism.The increase of stiffness coefficient can improve the vibration stability of the mechanism in the low frequency range.According to the results of statics analysis,a purely torsion strong and nonlinear coupled dynamics model of a cycloid ball planetary transmission including external excitation,meshing pair deformation and meshing stiffness is established.The differential equations of nonlinear dynamics are derived.The bifurcation diagram of the system is obtained by using the numerical analysis method.The time domain response and other graphs are plotted.The influence of the variation of different parameters on the dynamic characteristics of the system is analyzed.The results show that the cycloid ball planetary transmission shows very rich nonlinear dynamic characteristics under the comprehensive influence of various nonlinear factors.The change of axial preload has a great influence on the stability of the system.The vibration stability of the system is gradually increased with the increase of damping.Under different axial forces,the change rule of the elastic error of the transmission mechanism with the increase of torque is tested,and the test value is compared with the theoretical calculation value.Under the conditions of different axial movement,the meshing state of the deceleration meshing pair is tested,and the test value is compared with the theoretical value.The theoretical profile of the cycloid grooves after repair are measured,and the results of the measurement and the theoretical calculation are compared and analyzed.It is found that the results of the test are in good agreement with the theoretical calculation.The theoretical deduction is correct and the tooth shape repair method is feasible.