# Conjugate curve bevel gear transmission theory

This paper discusses the general principle of multi-point contact conjugate curve bevel gear, mainly discusses its design principle, calculation criteria and configuration method, and designs the actual parameters according to the proposed design method of multi-point contact conjugate curve bevel gear. On this basis, the three-dimensional solid models of two-point contact conjugate curve bevel gear and five point contact conjugate curve bevel gear are constructed, The finite element analysis of these models is carried out. The main work and conclusions are as follows:

① Considering that the spatial conjugate curve is actually the indirect contact line of the gear tooth surface, the multi-point contact bevel gear can be constructed by the following methods: designing multiple contact lines on a driving tooth surface, obtaining its spatial conjugate curve according to the spatial conjugate curve theory, and then constructing the driven tooth surface from these spatial conjugate curves, so as to realize multi-point contact.

② The tooth surface of multi-point contact bevel gear can be determined by section curve Γ 1s generated by coordinate transformation, Γ 1s shall be a regular curve and contact the tooth surface of bevel gear for X points Γ 1s also has the following limitations: Γ S1 needs to pass through P1, P2… PX points; At P1, Γ The tangent vector of S1 is α 11(t1P1) × n11(t1P1)； At point x, PX, Γ The tangent vector of S1 is α 11(t1P1) × n1x(txPx)。

③ Γ 1s can be composed of piecewise regular curves Γ 1s the part between the contact lines can be constructed by the third-order Bessel curve, which has the following properties: P0 = C (0), P3 = C (1); The tangent direction at the end point is parallel to p1-p0 and p3-p2; At the starting point (U = 0), the turning direction of the curve is the same as p0p1 P2, while at the end point (U = 1), it is the same as P1 P2 P3.

④ When the tooth surface of bevel gear is in single point contact, the contact area is an oval area. When the bevel gear tooth surface becomes multi-point contact, the contact area becomes multiple ellipses. When these ellipses are connected, the shape of the contact area becomes a long strip, which does not show the typical shape of the contact area of the point contact tooth surface.

⑤ When the instantaneous contact point increases from single point to two points, the contact stress decreases by 15%, and when the instantaneous contact point increases from two points to five points, the contact stress decreases by 10.1%. Therefore, it can be seen that with the increase of instantaneous contact points, the load between bevel gear tooth surfaces is shared by multiple contact points, which can significantly reduce the contact stress.

⑥ The third-order Bezier curve is used to construct the part of the section curve between the contact lines. In fact, other types of curves can also be used to construct this part of the section curve, but these curves must meet the node conditions.

Scroll to Top