Spiral bevel gear is an important transmission part widely used in vehicle, aircraft, machine tool, industrial reducer and other machine systems to transmit motion and power between intersecting and staggered shafts. According to the type of tooth line, this kind of gear can be divided into arc bevel gear (Fig. 1) and Cycloid Bevel Gear (Fig. 2). The two kinds of gears adopt two different machining methods: end face milling and end face hobbing.
For a long time, domestic enterprises have widely used the intermittent bevel gear end face milling method. Some universities and enterprises in China have conducted in-depth research on it, and have better solved the theoretical basic problems in the meshing geometry, design, gear cutting processing method, tooth surface contact analysis, tooth profile measurement and error correction, tool design, machine tool design and manufacturing, and developed a variety of gear cutting machine tools and corresponding calculation and analysis software, It is widely used in industrial practice. Therefore, there is a small gap between China and Gleason company, which represents the highest international technical level, in the processing of arc bevel gears.
The spiral bevel gear usually adopts shrinkage teeth, so the cutting surface of the cutter head for machining the pinion can not be made the same as that of the big gear, and the small wheel can not be machined by the direct generation method, nor can the cutting surface of the big wheel cutter head coincide with the cutting surface of the small wheel cutter head and be machined by the indirect generation method, but the “local conjugate principle” must be used for gear cutting. When the double-sided cutter head is used for processing, the tooth lines on both sides drawn by the cutter head on the pitch plane of the plane crown wheel are two concentric circles with different radii. The corresponding center angles of the concentric circles on different radii of the plane crown wheel are different, so it can not meet the principle that the tooth lines of gear transmission must be distributed according to the equal circumference angle. Although the compound double-sided cutting method of changing the root cone angle of a pair of gears can also be used to complete the rough and finish machining of both sides of the gear in one installation, this method is difficult to obtain good machining quality for gears with medium modulus or above. In order to meet this principle and obtain good machining quality, generally only three times of cutting is used to complete the rough and finish machining of a gear, that is, the double-sided cutter head for rough milling is installed at one time, and the single-sided cutter head for finish milling is installed and machined on both sides of the tooth surface in two times under the conditions of different machine tools and tool adjustment parameters. Therefore, the application of this method has low machining efficiency and high cost in machining machine tools. Generally, a production line needs at least five gear milling machines, and the gears with high operation accuracy and low operation noise need to be ground. The introduction of such a CNC gear milling machine tool (Figure 3 and Figure 4) costs about 450000 US dollars. Even if domestic gear milling machine tools are used, a CNC gear milling machine also costs 2 million yuan, while the introduction of such a CNC gear milling machine tool costs 1.2 million US dollars. Therefore, the use of end face milling method to process arc bevel gears requires large equipment investment.
The Cycloid Bevel gear adopts the equal height tooth system. In theory, the cutting surface of the large and small wheel cutter head can be made the same. The indirect generation method is used to continuously divide the teeth to process the fully conjugate gear. In practical application, the curvature correction method is also used to process the tooth surface with local contact characteristics. During continuous tooth division, the relative movement between each group of cutter teeth of the cutter head and the workpiece gear distributes the tooth lines on both sides of the tooth surface of the plane crown wheel on the pitch plane in the way of equal angular displacement. Therefore, the rough and finish machining of both sides of the gear can be completed in one installation, the machining efficiency is greatly improved, and the investment in the machine tool is greatly reduced compared with the method of machining arc bevel gear by end face milling. After decades of development and improvement, the world’s two major manufacturing giants of bevel gear processing machine tools, Klingenberg orikon company of Germany and Gleason company of the United States, have formed the system theory of Cycloid Bevel Gear Design and gear cutting adjustment calculation, and developed a fully CNC free gear milling machine (Fig. 3 and FIG. 4) and a fully CNC cycloid cutter head gear grinding machine, The machining quality of this kind of gear is improved. At present, spiral bevel gear manufacturing enterprises in the United States, Germany, Japan and other countries have widely used the end face hobbing method to process cycloidal bevel gears instead of the end face milling method to process arc bevel gears. As a result, the replaced second-hand arc bevel gear processing equipment has been sold to China, which is very unfavorable to the development of the overall technical level of the domestic bevel gear industry.
Compared with arc bevel gear, Cycloid Bevel gear is less used in China. In the 1960s, China introduced some SKM2 gear milling machines from Oerlikon company in Switzerland to process cycloidal bevel gears by end face hobbing method. Due to the need to take into account the contact performance of both sides of the gear, and limited by the cutting adjustment calculation method and machine tool structure at that time, it is difficult to adjust the contact area during machining. After being introduced into China, its application effect is not ideal. Since then, the introduction and Research of this machining method in China has been relatively stagnant. With the deepening of people’s understanding of Cycloid Bevel gear, its high efficiency of continuous tooth division processing and good stability of meshing process are gradually valued by the industry. In recent years, China’s automobile output has increased rapidly, and the annual demand for Cycloid Bevel gear is increasing year by year, which makes its application range more and more extensive. Especially, it is gradually used in some cars, commercial vehicles and buses with high noise requirements, and there is a trend to gradually replace the arc bevel gear processed by intermittent gear splitting. Domestic bevel gear manufacturing enterprises, such as Zhuzhou Gear Co., Ltd. and Hubei axle Co., Ltd., have introduced fully CNC gear milling machines manufactured by German Klingenberg orikon company and American Gleason company respectively, which are applied to the processing of cycloidal bevel gears. However, due to the insufficient attention paid to the machining method of end face hobbing in China for a long time, coupled with the strict confidentiality of relevant technical data by Klingenberg orikon company in Germany and Gleason company in the United States, there are few published documents, and most of them only introduce the tooth surface model and contact analysis calculation method of cycloidal bevel gear for end face hobbing, The calculation method of cutting adjustment parameters of its core part is rarely mentioned, which makes the research on the basic theory of this processing method seriously insufficient in China. To a certain extent, China has not developed a complete set of cycloidal bevel gear processing technology and equipment applied to production practice [8,9]. Although domestic bevel gear manufacturers can process qualified Cycloid Bevel Gear Products by introducing foreign Cycloid Bevel Gear calculation software and processing complete sets of equipment, it has limited effect on the improvement of China’s technical level in this field. On the other hand, due to the monopoly position of foreign countries in this technology, imported machine tools are very expensive. Take the C series full CNC bevel gear milling machine of Klingenberg Oricon company and its supporting auxiliary equipment and software system as an example, its price is US $3-4 million. In addition to the high price, the maintenance of these machine tools is also very inconvenient. After failure, it is often necessary to hire special engineers from abroad for maintenance. The long cycle also limits its general promotion in China.
In view of the urgent needs of China’s automobile and other industrial fields for the design and manufacturing technology of end face hobbing spiral bevel gear, this project solves the complete set of basic theoretical problems of end face hobbing of spiral bevel gear and bevel gear, which can provide a solid foundation for the development of complete sets of equipment for end face hobbing in China; The follow-up results are of great significance to improve the manufacturing level of bevel gear manufacturing enterprises in China, improve the processing efficiency of spiral bevel gears, save manufacturing costs, and improve China’s independent innovation ability in the technical field related to spiral bevel gear end hobbing.