Design And Performance Analysis Of The Profile Tooth Profile Of Cycloidal Steel Ball Planetary Transmission

The cycloid steel ball planetary transmission is a precision transmission device developed by the K-H-V type planetary transmission,it brings several advantages,such as,large gear ratio,no backlash,high transmission efficiency,etc.In this paper,the profile of the slot section is the main research object,it is designed geometrically.And the performance of cycloid ball planetary drive with different groove profile are analyzed.According to the formation principle of cycloid steel ball planetary gear shaping,The three-dimensional profile equations of the section of the elliptical groove and the parabolic groove are derived respectively.The meshing point coordinates of the steel ball and the actual tooth profile are deduced based on the four-point contact model.According to the knowledge of differential geometry,the curvature and radius equation of the actual tooth profile are derived,and the influence of parameters on curvature is studied.In this paper,the reasonable range of the radius of the steel sphere and the depth of the slot groove and the depth of the cycloid groove in the cycloidal groove are obtained.The mechanism of the top cutting of cycloidal tooth profile is analyzed,the condition type and the location of the top cutting are deduced respectively,the influence of parameters on top cutting and the range of design parameters are analyzed by using fixed variable method.Finally,the geometrical design flow of the cross section tooth profile of cycloid steel ball is developed.The principal curvature and principal curvature radius equation of each cycloidal tooth profile are derived.According to the Hertz contact theory,the contact stress of the tooth profile meshing of each groove is calculated.And the contact stress of the gear profile meshing pair with the linear groove section are compared and analyzed.The influence of the parameters on the contact stress of meshing pairs of each groove are analyzed.ABAQUS is used for the finite element simulation of three kinds of profile meshing.According to the Hertz contact theory and the four-point contact model,the meshing stiffness equations of each meshing position are deduced.The dynamics model of acycloidal ball planetary drive deceleration mechanism with four degrees of freedom translation-torsional coupling is established,the dynamical differential equations of the system are derived.The natural frequency of the system is obtained by solving the eigenvalue of the dynamical differential equation of the derived system.The influence of parameters on natural frequency is analyzed.By using Runge-Kutta method,the vibration steady-state response of the profile meshing system of the elliptical groove section are solved,and a comparative analysis is made with the tooth profile engagement system of the linear groove section.