TCA is to use computer simulation to analyze the contact marks and transmission error curves of gear teeth under no load or light load state, so as to avoid large design errors before putting them into practical use. In the 1940s, e. wildhaber of Gleason company put forward a series of theories about hypoid gear design. Then Ernst. Wildhaber and Meriwether L. Baxter studied the theory of hypoid gear with the help of computer technology, and designed TCA By using computer simulation technology, they obtained the contact marks of hypoid gear in the meshing area and the transmission error curve of the gear, and analyzed the relationship between the meshing area of the tooth surface and the quality of the gear transmission, which provided a theoretical basis for the later hypoid gears to design and process the tooth surface by adjusting the cutting tool parameters and machine processing parameters. Then Vilmos proposed an optimization method to define the gear processing parameters of FH hypoid gears, which largely depended on TCA analysis.
In the 1970s, a large number of experts and scholars emerged in the design and research of hypoid gears in China, and achieved remarkable results. Zhang Hongbiao adjusted the installation position and angle of rough cutting machine tool based on the position of the machine tool installed during precision cutting, which ensured that the allowance on both sides of the hypoid gear was uniform when the shaping method was used for rough cutting. Zheng Changqi advanced through the processing principle of quasi hyperbolic gear In this paper, the calculation formula of hypoid gear processing by adjusting machining parameters is derived, and the formula adjustment cards for computer program and manual calculation are listed respectively. In recent years, the tooth surface design method based on contact impression has also made great progress. Fang Zongde deduced the tooth surface equation of hypoid gear and other related gears, established a complete mathematical model of gear cutting, and carried out TCA Analysis, including tooth surface edge contact analysis; Zhuo Yaobin and others use the average contact ellipse long half axis to evaluate the tooth surface contact impression; Liu Xiangyang carries out virtual assembly of the established tooth surface equation, and obtains the basic meshing equation group of TCA, and obtains the tooth surface contact mark according to the meshing characteristics.
Because of the direct control of tooth surface contact marks, it has become the main method of hypoid gear design, manufacturing and inspection. However, the design of tooth surface and detection of gear machining quality according to the contact mark of tooth surface have certain uncertainty, and rely on the experience of technical personnel excessively. The goal of this method is to get approximate design results and determine the machining parameters. After the tooth surface is machined, verify whether the design requirements are met. If not, continue to adjust the design parameters until the design requirements are met. This process is called “passive design”, which is not suitable for modern high-performance.