Research On Meshing Theory And Meshing Characteristics Of Non-orthogonal Planar Enveloping Spiroid Drive

In this paper,a new type of conical drive is put forward,which be named the non-orthogonal planar enveloping conical worm drive.Spiral surface of the planar enveloping conical worm is shaped by grinding of the 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 planar surface enveloping spiroid,and the axis of the cone worm and worm gear is no orthogonal.After grinding,the tooth surface accuracy and finish are significantly improved.Besides,planar enveloping conical worm drive also has the following advantages:large carrying capacity,good lubrication condition,and the backlash are easy to adjust.etc.In this paper,a mathematic model of meshing analysis of non-orthogonal planar enveloping coning worm drive is established,and the influence of different parameters on the performance of the meshing of the worm is analyzed through numerical examples.The main contents of this paper include:(1)The mathematic model of the non-orthogonal plane enveloping coning worm drive is established.According to Differential Geometry and Meshing Theory,the meshing functions of cutting engagement of enveloping spiroidand engagement of enveloping spiroid gear 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.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,the tooth profile angle of the enveloping spiroid in its shaft section is figured out.(2)The spiroid theory based on the new operating pitch cone is applied to the planar surface enveloping spiroid drive.The installation position of the enveloping spiroid is determined though the formulas of operating pitch cone parameters.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.(3)A large number of numerical example studies are 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 are obtained.Meanwhile,with the aid of numerical example studies,the influences that the design parameters made on the parameters meshing performance are investigated.