Machining parameters of spiral bevel gear by surface synthesis method

Spiral bevel gear is widely used in the field of mechanical power transmission. Its meshing theory and manufacturing technology have always been the research hotspot of experts and scholars all over the world. Since the 1990s, with the application of computer numerical calculation method, the meshing performance pre control theory and design technology of spiral bevel gears have developed rapidly. Litivin et al. Developed the “local synthesis” method and preset the second-order contact parameters at the reference point in order to control the gear transmission error and gear surface impression. Wu Xuncheng et al. [4-6] developed “active design” to pre control the meshing performance of the tooth surface by presetting the transmission law and modifying the contact line direction. Zhou kaihong and others developed a point meshing tooth surface design method based on predetermined meshing characteristics. Simon et al. Developed the optimization algorithm of machining parameters of spiral bevel gears. The above methods convert the surface meshing into point contact parameters, and realize the active control of the contact performance of spiral bevel gear through the synthesis of contact point parameters. However, the point contact parameter synthesis is complicated in the calculation of the vector and curvature parameters of the contact point. In most cases, it is not suitable for numerical calculation, and it is more inconvenient to apply the tooth surface reconstruction, reverse calculation and error correction technology.

(1) In view of the shortcomings of the existing calculation methods of machining parameters of spiral bevel gears, which are complex and unsuitable for numerical calculation, the ease off surface synthesis method is given. Based on differential geometry, the definition and topological method of second-order osculating surface are given; Within the range of second-order accuracy, the close surface has the same differential geometric properties as the original surface, so it can replace the original surface analysis.

(2) Through the generation model of spiral bevel gear machining, the ease off close surface and topological tooth surface contact area are constructed; The contact parameters of the tooth surface of the small wheel are determined through the surface synthesis, the machining parameters of the small wheel are solved by the numerical method, and the meshing simulation of the tooth surface of the spiral bevel gear is completed with the help of the ease off close surface. The surface synthesis method proposed in this paper is suitable for numerical calculation, can mainly control the tooth surface contact area, the preset parameters have good initiative, and the meshing simulation presents the complete information of tooth contact.

In view of the shortcomings of the above processing parameter calculation and meshing simulation methods, this paper intends to propose a surface synthesis method. Based on the integrity of the tooth surface contact process of spiral bevel gear, the tooth surface contact performance is pre controlled by ease off difference of the close surface topological contact area of the tooth surface. Based on differential geometry, the definition and topological method of second-order osculating surface and the numerical method of curvature parameters are given; Through the generation model of spiral bevel gear machining, the close surface of ease off difference tooth surface is constructed. The contact parameters of small wheel tooth surface are comprehensively determined through the close surface topology and contact parameters, and then the machining parameters of small wheel are solved by numerical method. Finally, the meshing simulation is completed with the help of close surface.

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