The generation principle and mathematical model of a new involute-helix gear drive

Abstract

A new involute-helix gear drive, which is point contact with convex and concave circular-arc tooth profiles, is proposed in this article. The basic principle characterized by the advantages of involute and circular-arc gears is put forward. Based on the theory of conjugates curves, generation and mathematical model of this new transmission are presented. The separability of center distance on involute-helix gear is discussed and meshing characteristic of point contact is also analyzed. Finally, the three-dimensional solid model of a gear pair is developed to demonstrate the properties of this new transmission.

The geometric principles of general spiral bevel gears of local bearing contact from spatial conjugate curves

“…Notation i 21 gear ratio M ij coordinate transformation matrix from S j to S i (i,j ¼ 0,1,2, p,Fr1,Fr2) r j i position vector of known curve(j ¼ 1), its conjugate curve(j ¼ 2) and cross-section curve(j ¼ sec1,sec2) in coordinate system S i (i ¼ 0,1,2 or p) S i movable coordinate systems rigidly connected to pinion (i ¼ 1) and gear (i ¼ 2) S j fixed coordinate systems rigidly connected to absolute space at the revolve axis of pinion (j ¼ 0) and gear (j ¼ p) S j i position vector of tooth surface of pinion (j ¼ 1) and gear (j ¼ 2) in coor-…”

Theoretical and experimental analyses of spiral bevel gears with two contact paths

“…Mo and Zhang 16 investigated the influence of machining parameters on the tooth profiles of bevel gears and obtained the true tooth surfaces in their research. To simplify the designing process of point contact gears, Chen et al [17][18][19] presented the so-called spatial conjugate curve meshing theory. This theory uses curves instead of surfaces as the basic meshing elements.…”

Generation principle and meshing characteristics of conjugate-curve circular arc gears

“…With the developments of numerical control technology, the manufacture of complicated curve and surface can be realized easily (Fujimori, et al, 2012). So a new theory based on conjugate curves has been developed by authors, which is applied to carry out this research (Liang, et al, 2013), (Chen, et al, 2014a), (Chen, et al, 2014b).…”

“…So the new types of conjugate-curve gear drive are proposed and there are two aspects of applications: (1) The novel gear drive with ideal performance can be developed according to the given spatial curve. For example, the new involute-helix gear drive, which is point contact with convex and concave circular-arc tooth profiles, was proposed (Liang, et al, 2013). The contact line of gear tooth is an established involute-helix curve whose projection on the gear end-face is a segment of involute.…”