Because circular arc bevel gear is most widely used in China, domestic scholars have done a lot of research work on the tooth profile geometry, machining principle and error analysis of circular arc bevel gear. Professor Wang Xiaochun, a Chinese scholar, established a complete third-order contact analysis system with mathematical tools such as curvature tensor and movable frame. This method can not only calculate the instantaneous transmission ratio, acceleration, the direction of contact trace and the shape of instantaneous contact area, but also calculate the high-order acceleration, geodesic curvature of contact trace and the change of instantaneous contact area.
By introducing the concepts of load equivalent installation adjustment value and transmission angle displacement coordination principle, Zheng Changqi established a set of analysis and calculation methods of local conjugate gear pairs. Wu Xutang and others use the redundant optional parameters of the machining machine tool to optimize the third-order contact parameters of the spiral bevel gear, so as to achieve good contact performance in the whole transmission process. Cao Xuemei and others put forward the active design method of point meshing tooth surface of spiral bevel gear for tooth surface impression and transmission error. This method can ensure that the tooth surface can meet the requirements of pre-designed transmission error and tooth surface contact path in the whole meshing process, so as to achieve the whole process control of tooth surface meshing quality. Liu Guanglei and others analyzed the sensitivity of the transmission error curve to the changes of various types of installation errors and included the system installation errors. Through the contact analysis of gear teeth, the contact marks between the transmission error curve and the tooth surface were obtained, and the changes of the transmission error curve under different installation errors were quantitatively analyzed. Wang Zhiyong and Zeng Tao studied the tooth profile error correction method of spiral bevel gear. On the basis of establishing the relationship between the characteristic parameters of difference surface and proportional correction parameters, according to the proportional correction parameters calculated by spiral bevel gear cutting and the tooth profile error value of the actual tooth surface at each discrete point, a tooth profile error correction method based on proportional correction parameters is established. Zhou Chao et al. Put forward the concept of error sensitive direction of spindle eccentricity error and verticality error and the calculation method of determining the error sensitive direction, and obtained the correlation law between grinding wheel position error and tooth surface error in the error sensitive direction, as well as the distribution law of tooth surface error when grinding wheel position error occurs. Wang Yuqing et al. Proposed an algorithm to determine the tooth surface boundary, tooth surface information points, and points on the root cone and face cone of spiral bevel gear, and constructed a three-dimensional tooth surface model according to the four boundary information points of tooth surface.
At present, Professor Dong Xuezhu has mainly studied the continuous indexing cutting principle of Cycloid Bevel gear, focusing on the modification of the tooth surface geometric design and milling adjustment calculation method of Klinger cycloid gear and hypoid gear. Nie Shaowu et al. Took the cycloidal bevel gear machined by the full generation method as the research object, proposed a tooth profile modification method that can be realized on the traditional mechanical rocking machine tool by designing the cutter profile curve as a fourth-order curve without changing the shape motion relationship in the tooth cutting process. At the same time, they used the optimization algorithm to calculate the modified tooth surface and carried out the numerical simulation of tooth surface modification, The tooth surface contact analysis of the modified tooth surface is carried out. According to the relative position and motion relationship between the cutter head, the shaping wheel and the processed wheel blank in the process of tooth milling, Li Wei et al established the tooth cutting meshing coordinate system and deduced the tooth surface equation of the shaping wheel; The tooth surface equation of Cycloid Bevel gear is deduced by using the tooth cutting meshing relationship and spatial meshing principle, and the three-dimensional graphics of the tooth surface of generating gear and bevel gear are drawn by computer. Wang Zhiyong et al. Established the tooth surface equation of cycloidal bevel gear by using the method of vector operation based on the gear meshing principle and the gear cutting principle of cycloidal bevel gear, and the relative position relationship and relative motion relationship among gear, gear blank and tool in the gear cutting process. Tang Zhaoping and Sun Jianping analyzed the machining characteristics and tooth form forming principle of Klinger Cycloid Bevel gear. Combined with the characteristics that the tooth length direction is the conical generating line of the long amplitude epicycloid of the generating gear and the spherical involute of the tooth profile, the corresponding curve equation is deduced. Using the Object-Oriented Visual Basic 6.0 programming language as the development tool, Wang Qingyun compiled the computer-aided design and calculation program module of Klinger Cycloid Bevel gear. Then, taking AutoCAD2004 as the software graphics system development platform and based on ActiveX Automation Technology, Wang Qingyun compiled the parametric drawing and simulation program module of Cycloid Bevel gear.