# Research status of involute gear geometry theory

Chinese scholars have also made many useful contributions to point meshing involute gear pairs. Tao Shengyuan and others discussed in detail the meshing principle and design calculation of Novikov involute gear. Based on the spatial meshing theory, he Jingliang and others analyzed and studied the meshing relationship between conjugate gear pair and common rack, studied the meshing principle of staggered shaft involute bevel gear pair, which laid a theoretical foundation for the geometric design of staggered shaft involute bevel gear pair. Starting from the meshing principle, Mao Shimin et al. Expounded the full forming processing principle of point contact internal meshing spur bevel gear, gave a calculation example and carried out the tooth cutting test. The rolling inspection results of the processed involute gear on the gear rolling inspection machine meet the theoretical expectation. Wu Rongliang studied the formation principle and meshing characteristics of double circular arc gear teeth with circular arc tooth line, and deduced its conjugate tooth surface equation by using the conjugate meshing principle and the method of differential geometry. It is considered that the meshing principle of double circular arc tooth profile is consistent with that of single circular arc tooth profile, and one side of circular arc convex tooth of single circular arc gear is also the tooth surface outside the pitch circle of double circular arc gear; One side of circular arc curve concave tooth of single circular arc gear is also the tooth surface of one side within the pitch circle of double circular arc gear. Duan Derong pointed out that there are misunderstandings in the traditional point meshing principle of circular arc gear based on contact line, and proposed to apply the forming principle of point contact conjugate tooth surface of new circular arc gear based on envelope method to replace the forming principle of point contact conjugate tooth surface of circular arc gear based on line contact method. On the basis of involute gear, circular arc gear and graded double circular arc gear, Zhang Guanghui proposed graded double involute gear. The tooth profile of the involute gear is formed by connecting two segments of staggered involutes with a segment of arc envelope transition curve in the middle, and the two involute tooth profiles of the tooth top and tooth root form a stepped distribution, which integrates the advantages of ordinary involute gear and stepped double arc gear, and inherits the good process and kinematic characteristics of general involute gear.

Chen Bingkui and others put forward the new concept of point line meshing gear pair, and put forward the configuration method of point line meshing cycloidal gear on the basis of traditional line line meshing involute gear pair. According to different linear meshing transmission mechanisms such as cycloidal pin gear planetary transmission, involute planetary transmission with small tooth difference and involute external meshing transmission, the point line meshing gear pair model is constructed and studied theoretically and experimentally. It is found that after the linear meshing gear pair is changed into point line meshing gear pair, the sliding rate between tooth surfaces of involute gear pair is greatly reduced and the transmission efficiency is improved. Hu Wen et al. Put forward the arch arc tooth cylindrical gear transmission. The teeth on the cylinder are arch arc arranged, not linear; The tooth profile surface of arch arc cylindrical gear is the same as that of ordinary cylindrical gear, which can be either involute surface or Novikov arc curve surface. Arch spiral cylindrical gear has the advantages of good meshing performance, overlapping coefficient, axial force can offset each other, high transmission efficiency, high bending strength, and can be processed by continuous generation method. Li Haixiang and others put forward some suggestions

The pinion of the transmission is a modified involute short tooth helical gear, the upper tooth part of the big gear is a helical gear with involute convex tooth profile, and the lower tooth part is a helical gear with concave tooth profile of transition curve; In meshing transmission, there are not only linear meshing with straight contact line, but also point meshing with concave convex tooth profile contact, which forms a surface contact after load deformation. At present, the involute gear pair has been applied in metallurgy, mining, hoisting, transportation, chemical industry and other industries.

It can be seen that the traditional conjugate surface meshing theory still plays a major role in the research of involute gear meshing theory. However, with the progress of science and technology, in order to meet the various requirements of involute gear transmission mechanism put forward by industrial practice, the new meshing theory is also developing.

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