Research On Meshing Theory Of Cylindrical Worm Drive With Circle-Arc Tooth Enveloped By Torus

Cylindrical worm drive with circle-arc tooth enveloped by torus is grinded by torus grinding wheel.The instantaneous contact line between grinding wheel and worm during grinding is a circular arc.As a kind of cylindrical worm,it is classified as ZC2 worm drive in Chinese gear standard.The ZC2 worm pair is obtained by adjusting the grinding wheel parameters on the basis of the processing of ZC1 worm pair.The ZC2 worm pair needs to meet the requirement that the instantaneous contact line is a plane curve in the grinding process.In this case,the reduction of grinding wheel diameter and the shortest distance between grinding wheel and worm shaft caused by dressing grinding wheel will not change the shape of worm tooth surface.At the same time,compared with the ZC1 worm pair,the meshing performance of the ZC2 worm pair under the same conditions is slightly improved.In this paper,the meshing theory of ZC2 worm drive is studied,and the influence factors of its meshing characteristics are analyzed.The specific research contents are as follows:(1)The meshing theory of ZC2 worm cutting is established.Based on the knowledge of differential geometry and gear meshing theory,the curved surface equation and its characteristic parameters of the grinding wheel profile are derived.The cylindrical worm profile equation and meshing function of the cylindrical worm grinding wheel are obtained.It is proved that the instantaneous contact line should be satisfied when the grinding wheel is grinding the worm blank.The induced normal curvature and induced short-range torsion of the toroidal surface of the grinding wheel and the spiral surface of the worm are calculated respectively,and the expressions of the corresponding normal curvature and the induced short-range torsion of the spiral surface of the worm are derived.(2)The meshing principle of ZC2 worm pair is established.The meshing function of ZC2 worm pair is deduced by establishing relative motion coordinate system.Then the meshing tooth surface equation and corresponding worm gear tooth surface equation are obtained.The meshing boundary equation and curvature interference boundary equation of ZC2 worm pair are obtained.The formula of induced principal curvature and sliding angle are derived.(3)The calculation principle of meshing characteristic of ZC2 worm drive is given.The worm profile and tooth angle are calculated,and the numerical simulation is carried out.The boundary of conjugate zone between worm gear and worm tooth surface in ZC2 worm pair meshing is determined by iteration.Some instantaneous contact lines are solved in conjugate zone,and the induced principal curvature and sliding angle of points in conjugate zone are calculated.The meshing performance of ZC2 worm drive is analyzed.(4)The factors affecting the meshing performance of ZC2 worm drive are analyzed.The design parameters of grinding wheel and some design parameters of worm pair are changed.The simulation results of conjugate zone,instantaneous contact line direction,induced principal curvature and sliding angle are compared.Furthermore,the matching method of process parameters with better meshing performance is obtained.At the same time,the meshing performance of ZC1 and ZC2 worm pairs is compared under the same conditions.