Gleason company of the United States was the first to put forward the hypoid gear transmission, and it was only some theoretical descriptions at first. After nearly a hundred years of accumulation and development, the design theory and processing and manufacturing technology of hypoid gear have developed into a set of relatively mature and widely used technology. With the continuous development of computer simulation technology, automatic control technology and precision machinery technology. The traditional design theory and machining process can not meet the design and manufacturing requirements of hypoid gears in the current machinery industry. At present, hypoid gears are developing in the direction of large transmission ratio, miniaturization, high bearing capacity, low noise and high transmission efficiency.
Abroad, first, M.L. Baxter of Gleason company of the United States published some contents about the point meshing theory and gear cutting processing method in gear transmission technology. Then, M.L. Baxter first cut out the gear teeth of the big wheel according to an effective and simple method by using the method of “local conjugate of gear surface”, and then select a point on the cut out gear surface and take this point as the reference point. Then, according to the coordinate position of the reference point on the tooth surface, the normal vector and curvature value of the corresponding point on the pinion tooth surface in line contact with the gear tooth surface are obtained through a series of mathematical operations. According to the calculated normal vector and curvature, and then according to the size of the contact area when the two tooth surfaces mesh, the calculation points of the small wheel tooth surface are corrected to determine the machine tool processing parameters of the small wheel, so that the small wheel can meet the requirements of the above design. It can be seen that the correction of the normal curvature of the corresponding point of the small gear tooth surface corresponding to the reference point of the large gear tooth surface is the key and difficult point of the hypoid gear design technology. After the correction of the normal curvature of the tooth surface of the small wheel, the meshing performance of a pair of gears can be checked through the roll inspection experiment.
On the other hand, three-dimensional simulation experiments can also be carried out on the designed large and small wheels by using three-dimensional software. The simulated large and small wheels can be assembled, and then the meshing performance of large and small wheels can be analyzed by three-dimensional software. Therefore, in order to achieve the results required by the design, many repeated experiments are often required, and the testers need to have a certain accumulation of experience. Therefore, the design and calculation process is not only cumbersome, but also has certain approximation and experience, which is difficult for ordinary engineers and technicians to master. In order to be able to design and calculate quickly, Gleason company has compiled a set of computer programs to analyze the gear contact of the big wheel of hypoid gear designed by the authors. This analysis method selects a series of two contact parameters on the tooth surface to study it, then adjusts the cutting parameters, and finally obtains the hypoid gear with good contact performance.
After the point meshing technology of gear was put forward, this technology has been continuously improved and developed. The representative Professor Li Tewen of the United States has greatly expanded the point meshing spiral bevel gear theory. Professor Li Tewen made a comprehensive research on Gleason’s local conjugate principle technology, and then modified and improved this technology. In his book “gear meshing principle”, Professor Li Tewen proposed the “local synthesis” method of hypoid gear design.