Research On Meshing Theory Of Nonorthogonal Conical Surface Enveloping Spiroid Pair

In this paper,a new type of spiroid drive is presented,which may be called the nonrthogonal conical surface enveloping spiroid pair.The spiral surface of enveloping spiroid is ground by a conical wheel.In this paper,the meshing theory of nonrthogonal conical surface enveloping spiroid pair is studied.What’s more,the influence of design parameters and technological parameters on the meshing performance of the nonrthogonal conical surface enveloping spiroid pair is analyzed.The main research contents of this paper include:(1)The equation of spiral surface of the enveloping cone worm is derived,the meshing function and the meshing characteristic parameters of the cone worm gear cutting are obtained.Meanwhile,the meshing function,the meshing characteristic parameters and the meshing performance parameters of the nonrthogonal conical surface enveloping spiroid pair are solved.(2)Combine with the meshing function of the enveloping cone worm gear cutting and the helical surface equation of the enveloping cone worm,a method is put forward to draw the tooth profile of the enveloping spiroid.Meanwhile,the tooth profile angle in the pitch cone of the axial section is calculated.(3)The curvature interference characteristics of the cone worm gear cutting and the meshing characteristics of the nonrthogonal conical surface enveloping spiroid pair is carried out.The basis of this study is to solve the multivariate nonlinear system,and the elimination method and the geometric figure method to obtain all the solutions in the given region are applied.(4)The analysis of meshing theory based on reference point is carried out,and the selection of reference points and the calculation principle of the position coordinates are described.(5)The calculation principle of the boundary of the tooth surfaces and instantaneous contact lines for the nonrthogonal conical surface enveloping spiroid pair is described.The local meshing property rule is obtained and the improved method of meshing asymmetry is proposed.Meanwhile,through numerical simulation study,the macroscopic and local meshing properties of the nonrthogonal conical surface enveloping spiroid pair are analyzed,and the influence of design parameters and technological parameters on it is revealed.Research results show that,there are some great advantages of this nonrthogonal conical surface enveloping spiroid pair,such as high precision of tooth surface,large carrying capacity,good lubrication condition,long working length of the conical surface enveloping spiroid,large conjugate zone of enveloping spiroid pair.And the phenomenon of undercutting will not appear.