Dynamic Analysis Of Swing-rod Movable Tooth With Considering The Influence Of Thermal Deformation

Swing-rod movable teeth transmission is a kind of planetary drive with small tooth difference by using the meshing pair between movable tooth and wave generator to equispeed inputting and using the meshing pair between the movable tooth and ring gear to reducation outputting,has the advantages of multi-tooth meshing,high transmission efficiency by full rotation,good dynamic balance performance and large output stiffness etc,is widely used into robot and petroleum machinery.Because radiation space of the meshing pair with the swing rod movable teeth transmission is compact under high load condition,the heat generated by the rolling and sliding friction is difficult to dissipate and is transfered into thermal energy,which causes temperature rise and thermal deformation of the meshing pair.It causes the meshing stiffness to change and affects the dynamic characteristics of the system.Therefore,it is of great significance to study of the swing-rod movable teeth transmission dynamics considering the influence of thermal deformation.In this paper,according to the transmission principle and structure characteristics of swing-rod movable teeth transmission.The normal force,contact stress and motion state of the meshing pair are analyzed.Based on the principle of tribology and heat transfer theory,the variation law and its influence factors of the friction heat flux density of the meshing pair are analyzed.Thermal structure coupling simulation of the meshing pair is carried out by using the ANSYS Workbench.Then the thermal characteristics of the ring gear are studied and its influence factors are analyzed.According to the differential operator theory and linear algebra related knowledge,the general solution of the basic equation of the thermal elasticity of the ring gear is deduced.The Green’s function of the line heat source acting on the surface of the half-space is obtained.The normal thermal deformation and thermal stress of the ring gear are obtained by the Green’s function method,which verifies the validity of the simulation results.According to the structure characteristics of swing-rod movable teeth transmission,the contact model of the meshing pair is founded.Based on Hertz line contact theory,the formula of meshing stiffness of the meshing pair is deduced.The thermal mesh stiffness of the meshing pair is calculated by taking the thermal deformation into consideration.The meshing stiffness is equivalent to “series spring” model,and the formula of the comprehensive meshing stiffness with thermal deformation is derived.A purely torsional vibration model of the swing-rod movable teeth transmission system considering the meshing stiffness is established by the lumped parameter method.According to Newton’s second law and the relative elastic displacement equation,the dynamic equation of the swing-rod movable teeth transmission system is established.The natural frequency and main vibration of the system are analyzed.The dynamic response is solved by mode superposition method,and the effect of thermal deformation on the system dynamics is studied.