Research On Meshing Principle Of ZC1 Worm Drive

This paper presents a new type of cylindrical worm gearing,that is,ZC1 worm drive.The worm is composed of helical ring disc grinding wheel and worm,called ZC1.The worm gear matched with the worm wheel is formed by hobbing the hob with the spiral surface of the enveloping worm.A mathematical model for meshing analysis of ZC1 worm pair is established in this paper.Through numerical examples,the influence of design parameters and process parameters on meshing performance of ZC1 worm pair are investigated.The main contents of this paper include:(1)The mathematical model of meshing analysis of ring shaped cylindrical worm and meshing analysis of ring shaped cylindrical worm pair and worm pair is established.Related knowledge of differential geometry and gear meshing theory,the meshing function of the enveloping worm and worm enveloping worm wheel of the grinding wheel is derived by using the vector rotation method,the equations of the spiral surface and the tooth surface of the worm wheel is derived,and the meshing parameters of enveloping worm pair are given.Combining the meshing function and the spiral surface equation of the enveloping worm pair,the calculation principle of the tooth profile of enveloping worm is given.(2)Combining the meshing function and the spiral surface equation of the enveloping worm pair,the expression of the tooth profile of the enveloping worm and the calculation principle of the parameter of the tooth shape are given.The size of the worm and worm wheel is determined according to the geometric parameters,and the boundary equation of the tooth surface is listed.(3)Combining with a specific numerical example,the nonlinear equations for calculating the critical points of the conjugate region boundary of the enveloping worm pair are given,then map out conjugate tooth surface area in the worm and ZC1 worm shaft section,and the drawing method of instantaneous contact line is given,the induced normal curvature and sliding angle of each contact point are calculated.(4)Through a large number of numerical examples,the influence of design parameters and process parameters on the meshing performance of ZC1 worm gearing is illustrated.It is found that the meshing performance of the ZC1 worm can be effectively improved by adjusting the parameters.