Analysis On Vibration Characteristics Of Two-staged Planar Movable Tooth Transmission

The planar movable teeth transmission is a basic form of the movable teeth transmission.This paper presents a two-stage planar movable teeth transmission structure coupled with a hollow movable tooth frame,which has the characteristics of smooth transmission,large speed ratio,high stiffness and compact axial structure.In this paper,the force analysis,meshing stiffness analysis,free vibration analysis,modal analysis and sensitivity analysis are carried out,a two-stage planar movable teeth reducer prototype coupled with hollow movable tooth frame is designed and developed,and its vibration characteristics are tested.According to the theory of movable teeth transmission,the calculation model of force and time-varying meshing stiffness of the two-stage planar movable teeth system coupled with hollow movable teeth frame is established.The calculation formulas of the force,time-varying meshing stiffness of meshing pair and output torque of the first and second stage subsystems are derived.The influences of the various transmission parameters on force and meshing stiffness of meshing pair are analyzed.The free vibration analysis of the transmission system is carried out.The dynamic model of the transmission system and the calculation model of each subsystem are established.The motion differential equations of each subsystem are derived.The dynamic differential equations of the whole transmission system are obtained by the motion differential equations of each subsystem in the system.The natural frequencies of the system under different contact surface angles and different bearing stiffness are calculated,The main vibration modes of the system are analyzed.The free vibration mode of the movable tooth transmission system is divided into the movable tooth mode and the non movable tooth mode.The influences of various physical characteristic parameters on the natural frequency of the system are studied.The sensitivity of the transmission system is analyzed,the calculation formula of the system sensitivity corresponding to each transmission parameter is derived,and the influences of drive parameters on the sensitivity are analyzed.The modal analysis and harmonic response analysis of the two-stage planar movable teeth transmission system coupled with hollow movable teeth frame are carried out by using ANSYS Workbench finite element software.The natural frequency of the system and its corresponding main vibration modes are abtained,and the harmonic response of the components displacement easy to deformation is analyzed.The three-dimensional model of the movable tooth transmission system is established by using UG10.0,and the motion simulation is carried out.The vibration characteristic test of the prototype is carried out,and the amplitude frequency characteristic curve of the prototype is obtained.The measured natural frequency is close to the theoretical calculation.It illustrate the analysis in the paper is accurate.