The manufacturing accuracy of spiral bevel gear directly affects the transmission efficiency, noise, motion accuracy and service life of machinery and equipment. Therefore, the processing and manufacturing of spiral bevel gear has also been widely concerned and studied by experts at home and abroad. The traditional spiral bevel gear processing must be completed on a special mechanical spiral bevel gear processing machine with a special disc milling cutter. With the development of numerical control technology, major gear manufacturers all over the world have launched special numerical control spiral bevel gear processing machine tools. In the field of spiral bevel gear processing, special numerical control machine tools are gradually replacing mechanical machine tools.
The traditional manufacturing of spiral bevel gear is mainly through manual computer machine adjustment card and mechanical machine tool processing. It often needs multiple trial cutting to complete the processing of spiral bevel gear. This process is time-consuming and laborious, especially when processing small batch of gears. With the development of computer technology and numerical control technology and the development of related algorithms of spiral bevel gear theory, the manufacturing of spiral bevel gear is developing in the direction of digitization. In the advanced digital manufacturing process, due to the adoption of spiral bevel gear numerical control machine tool and its supporting spiral bevel gear digital manufacturing technology, the machining accuracy and efficiency of spiral bevel gear are greatly improved, and the human factors in the process of adjusting the contact area are greatly reduced.
The disadvantages of traditional spiral bevel gear machining are as follows: the theoretical basis of data calculation of adjustment card is the second-order tooth surface contact analysis, and there is a certain error between the calculated machine tool adjustment parameters and tool parameters; In the process of machining, the accuracy of gear milling machine is reduced due to the error of machine tool adjustment parameters and the error of tool manufacturing and installation accuracy; In the process of machining, the tooth surface is deformed due to the influence of cutting force, cutting heat and tool wear; The internal stress caused by heat treatment causes tooth surface deformation. In order to introduce numerical control technology into the manufacturing field of spiral bevel gear milling machine, scholars at home and abroad have conducted in-depth research on the production of high-quality gear pairs using free form machine tools. Litvin et al. Put forward the transformation principle and method based on spatial coordinate transformation, which reproduces the relative position and motion relationship between the cutter head and the machined gear in the traditional mechanical shaking table machine tool on the free form machine tool. Zhang Yanhong and others studied the principle of transforming the adjustment parameters of the cutter tilt method gear milling machine into the adjustment parameters of the free form gear milling machine. Wang Xiaochun and others analyzed the principle of transforming the adjustment parameters of tool tilt machine tool into the adjustment parameters of free form machine tool from the perspective of spatial kinematics, and gave the explicit conversion formula. Based on the transformation of spatial coordinate system, Wei Bingyang and others studied the equivalent principle of machining spiral bevel gear by denaturing method. Zhang Hua et al. Proposed the method of machining hypoid gear by using 4-axis linkage NC gear milling machine to realize the denaturing method. On the basis of Wang Xiaochun’s research, Zhang Wei and others use McLaughlin formula to approximate the motion of each axis during tool inclination processing, which improves the calculation efficiency, but it can only be applied to five axis linkage and single tooth indexing. Shin et al. Studied the conversion relationship between mechanical shaking table machine tool and free form gear milling machine by coordinate transformation method, and used it for high-order correction of tooth surface error. Su Chengli et al. Established the mathematical model of tool inclination machining based on spatial coordinate transformation, which can realize single tooth indexing and continuous indexing.