Study On Dynamic Performances Of Sleeve Movable Teeth Transmission

Sleeve movable teeth transmission system has the advantages of transmitting power through line contact,high transmission efficiency and so on.But the excitation in the transmission may make mechanism produce vibration and noise.Therefore,this paper focuses on the dynamic performances of sleeve movable teeth transmission.According to the structure composition and transmission principle of sleeve movable teeth transmission,the analytical formula of center wheel profile is obtained through Coordinate transformation.Based on the assumption that the normal deformation of the sleeve movable teeth on the shock wave is distributed in the form of sine function,the formula of calculating the normal force of the traditional algorithm is obtained.According to the nonlinear relationship between the normal force and the contact deformation,a new algorithm of calculating normal force is put forward,then the result of the normal force of the two algorithms is compared.The mechanism’s transmission ratio and the stress and strain of each component are simulated.Based on the theory of line contact between hollow cylinder and solid cylinder,the meshing stiffness of the meshing pair between sleeve movable teeth and shock wave and the meshing pair between sleeve movable teeth and center wheel is analyzed.Based on the theory of line contact between two solid cylinders,the meshing stiffness of the meshing pair between the sleeve movable teeth and the column pin of movable teeth frame is analyzed.The influence of the parameters on the meshing stiffness is also analyzed.By means of the fitting expression of meshing stiffness and Fourier transform,the sum of the average value and the increment of meshing stiffness is obtained,then the frequency analysis of the increment part of meshing stiffness is carried out.Taking the time-varying meshing stiffness and the meshing damping into account,a coupled translational torsion dynamic model of sleeve movable teeth transmission is established.Through the relative motion relationship of each mechanism component,the nonlinear dynamic equation of the transmission system is derived.Through linearization of nonlinear equation set,the characteristic equation of the vibration system is solved,andthe natural frequencies of the transmission system are obtained.By solving characteristic equation of the derived system,the natural frequencies of the derived system is gotten and the influence of the parameters on each natural frequency is analyzed.Depended on the translation shift factor torsional coupling dynamic model of sleeve movable teeth transmission,the reduced-order equations of the second-order non-linear equations are carried out by introducing the state variables.The Runge-Kutta method is used to solve the reduced-order equation,and the time domain response curves of each component are obtained.By using the Linzi Ted-Poincaré perturbation theory,the steady-state response of the transmission system is analyzed.