Research On Meshing Theory And Meshing Characteristics Of Toroidal Surface Enveloping Spiroid Drive

In this paper,a new type of the spiroid drive is put forward,which may be called the toroidal surface enveloping spiroid drive.The conical worm is ground by a disk-shaped toroidal grinding wheel.And mating conical worm gear is generated by a conical hob,whose generating surface is the same as the helicoidal surface of the toroidal surface enveloping spiroid.the toroidal surface enveloping spiroid drive is selected to be the research object,and its mathematical model is established.What’s more,the numerical example study is performed to investigate the meshing principle and meshing characteristics.The main content of this article is as follows:(1)The mathematical model of the toroidal surface enveloping spiroid drive is established.According to Differential Geometry and Meshing Theory,the meshing functions of cutting engagement of enveloping spiroid and engagement of enveloping spiroid gearing are deduced respectively.Then,the equations of the helicoidal surface of the enveloping spiroid and the tooth surfaces of the worm gear are given,and the formulas of the meshing performance parameters are listed.(2)Combine the equation of the helicoidal surface with meshing function of the enveloping spiroid,a method is put forward to draw the tooth profile of the enveloping spiroid in its shaft section.Meanwhile,an approach to calculate the slope in the middle of the tooth profile is suggested.Futher more,the tooth profile angle of the enveloping spiroid in its shaft section is figured out.(3)The spiroid theory based on the operating pitch cone is applied to the toroidal surface enveloping spiroid drive.The installation position of the enveloping spiroid is determined though the formulas of operating pitch cone parameters.(4)According to the parameters of the operating pitch cone,the blank dimensions of the conical worm gear and boundary equations of tooth surface for enveloping spiroid drive are ascertained.(5)The numerical example study is performed to illustrate the way to determine the key points of conjugate zone.The methodology to compute the conjugate zone and the contact line is set forth.In the end,the meshing performance parameters,including the induced normal curvature and the sliding angle,and the Gaussian curvature are obtained.The results prove that both the global and the local meshing characteristics of the toroidal surface enveloping spiroid drive are favorable.(6)With the aid of numerical example studies,the influences that the design parameters made on the meshing performance parameters are investigated.The rearch results prove that the meshing asymmetry of the enveloping spiroid gear set could be reduced via parameter adjustment.Besides,the toroidal surface enveloping spiroid drive also performs well in some special cases.