In terms of the theory of face hobbing of spiral bevel gears, F.L. Litvin and Qi fan analyzed the machine tool adjustment and movement of face hobbing, studied the tooth surface forming principle based on the basic machine tool model, and deduced the tooth surface equation. Shih and Fong established the unified tooth surface equation for the machining method of Austrian and restrained end face hobbing, studied the tooth shape correction and tooth surface contact analysis method, and analyzed the influence of the movement change of each NC axis on the tooth surface shape.
Zhang Yi, Wu Zhi studied the tooth surface geometry of spiral bevel gear machined by end face hobbing method, deduced the tooth root fillet equation, and accurately modeled the large and small tooth surfaces. M. Vimercati et al. Studied the mathematical model of face hobbing, the accurate model construction of face hobbing bevel gear and the strength finite element calculation method. Takayuki Nishino established the mathematical model of tooth surface equation processed by end face hobbing method, constructed the solid model of gear pair, and then studied the loading contact characteristics of gear pair. Ma ´ rk lelkes studied the theoretical tooth surface contact analysis method of Klingelnberg face hobbing spiral bevel gear, developed the corresponding program, and analyzed the influence of each cutting adjustment parameter on the contact characteristics.
Masaki Kano puts forward a calculation method for gear cutting adjustment of spiral bevel gear end face Hobbing with the blade trajectory surface as the profile tooth surface of small wheel, and obtains the same control results of contact characteristics as Gleason calculation system. Wu Lianyin studied the forming principle and geometric structure of Cycloid Bevel gear. Wu Lianyin, Li Haitao and Nie Shaowu established the tooth surface equation and tooth surface contact analysis algorithm of spiral bevel gear machined by orikon end face hobbing, and developed the simulation analysis software of contact area.
Zhang Wenxiang deduced the undercutting limit curve of Cycloid Bevel gear, determined the minimum number of teeth without undercutting, and deduced the correction coefficient of Cycloid Bevel gear transmission ratio and the formula of limit pressure angle. Liu Zhifeng studied the tooth surface contact analysis, edge contact analysis and dynamic loading tooth surface contact analysis method based on error. Yu Wentao studied the tooth cutting calculation of Cycloid Bevel Gear by full generation method and half generation method, and compiled the calculation software of tooth surface geometric design and tooth cutting adjustment. Other scholars have also carried out a series of research on the principle of continuous indexing milling of spiral bevel gear for face hobbing, the structure of gear cutting cutter head and cutter bar, gear modeling and parametric design, gear cutting simulation and so on.