# Research status of spiral bevel gear technology

In terms of the basic theory of spiral bevel gear, the French geometer T. Olivier proposed the envelope method for solving conjugate gear and the concept of spiral bevel gear in 1820. Different from the traditional analytical principle, he used the pure geometric principle to solve the conjugate surface. With the application of computer technology in gear engineering theory, T. Olivier’s geometric calculation method has been proved to be more suitable for program design. At the beginning of the 20th century, Paul B Ê ttcher invented the method of machining spiral bevel gear with single indexing and continuous indexing by using milling cutter disc, applied for invention patent, and developed the first gear milling machine for machining equal height conjugate spiral bevel gear according to the patent.

Ernst wildhaber and Meriwether L. Baxter were gear scientists who studied the theory of spiral bevel gears earlier. Wildharper first studied the geometric relationship of the transmission pitch cone of hypoid gear pair, and its research results became the basis for later scholars to study the theory of hypoid gear. He also put forward the differential geometry principle of spiral bevel gear transmission and the concepts of limit pressure angle and limit normal radius of curvature, which has important guiding significance for the study of indirect generation of local meshing tooth surface. Baxter also proposed a method to directly solve the curvature of the second surface according to the curvature of the first surface and the relative motion between the first surface and the second surface, and deduced its calculation formula. This formula is called Baxter formula, which greatly simplifies the solution process of conjugate surface curvature. At the same time, he also improved the method of wheel surface contact analysis of spiral bevel gear and put forward the principle of second-order surface generation of spiral bevel gear. The two gear scientists have worked with Gleason company in the United States, which also makes Gleason company in the forefront of the world in the theoretical research of spiral bevel gears.

The traditional Gleason’s spiral bevel gear cutting adjustment calculation and contact area guarantee are based on the local conjugate principle. The basic idea is to determine the gear tooth surface randomly according to the geometric parameters of the gear pair, and obtain the curvature parameters of the reference point of the gear tooth surface calculation. In order to obtain the local contact characteristics of large and small tooth surfaces, the curvature of the calculation point of pinion gear is corrected according to the principle of relative curvature. When calculating the machine adjustment parameters of the small wheel, the goal is to ensure the curvature of the corrected calculation point of the small wheel. Based on this advanced theory, Gleason’s spiral bevel gear geometric design, cutting adjustment calculation of machining machine tool, tooth surface contact analysis and other technologies have gradually developed, forming a perfect design and machining technology system.

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