| Planar sinusoidal ball reducer is a new type of coaxial deceleration transmission mechanism.It has the advantages of small size,simple structure,high coincidence,compact structure,convenient processing and simple installation.It is used in the case of limited space and coaxial transmission.Due to the lack of in-depth theoretical research,it has not yet entered the practical application.The research object of this paper is plane sinusoidal ball reducer,which will be systematically studied from the aspects of motion law,meshing characteristics of tooth profile,mechanical model,contact characteristics and system stiffness.The assembly relationship of the mechanism is studied and the degree of freedom is analyzed.At the same time,the method of judging the output rotation direction of the mechanism corresponding to the number of steel balls is studied,and the expression of the transmission ratio of the same or reverse transmission of the transmission mechanism is deduced by using the plane expansion method,which is used for structural design calculation.At the same time,the transmission ratio formula of the mechanism is validated by means of motion simulation.The conjugate tooth profile meshing equation between steel ball and active or driven disk is deduced by using space coordinate transformation method,relative motion velocity analysis and basic principle of gear meshing.The equation is used to construct the mechanical model of steel ball.At the same time,the equation is simulated by using MATLAB.Considering the influence of steel ball inertia force,the force equation,deformation compatibility equation and geometric relationship are analyzed.The spatial mechanical model of steel ball is established by combining transmission ratio formula and conjugate tooth profile equation.The model is solved and analyzed by appropriate algorithm,and the influence law of contact force is obtained.At the same time,the influence of the main structural parameters of the reducer on the contact force is analyzed,and the general design method of the reducer is obtained.According to Hertz elastic contact theory,the contact quantity of meshing pair is analyzed,and the changing rules of elliptical half-long axis,half-short axis and elastic approach quantity in contact area are obtained by calculating the parameters of mechanical model.Then the changing rules of contact stress of meshing parts are obtained,which can be used to optimize the structure of mechanism and study the vibration of system.The contact stiffness of the meshing area of the steel ball is analyzed,the torsional vibration model of the system is established,and the equivalent torsional stiffness of the steel ball with the active disc,cage and driven disc is deduced.By solving the vibration equation of the system,the variation of natural frequency with the rotation angle of the active disk is obtained,which provides a basis for the dynamic load analysis and dynamic response analysis of the mechanism. |
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