# Analysis of sliding rate of involute gear transmission

In the meshing process of involute gear teeth, the linear speed at a certain meshing point is different, except for nodes, there is relative sliding between teeth. In engineering, the sliding rate is usually used to express the relative sliding degree of teeth. The absolute value of sliding rate has a direct effect on the wear degree of tooth profile. Wang Zhen analyzed and calculated the sliding rate of involute gear teeth, but the calculation of the sliding rate was based on the pressure angle of the meshing point, which could not well reflect the sliding rate of relative sliding rate at different meshing points on the meshing line. Mo Jiangtao and others analyzed the calculation formula of sliding rate of involute cylindrical gear pair, but did not analyze the influence of parameters on sliding rate. Xu Rong et al. Analyzed the influence of parameters on the maximum sliding rate of gear on the actual meshing line, but did not analyze the change rule of sliding rate on the meshing line. Zhang Yicheng et al. Analyzed the relative sliding rate of involute external gear pair, but did not involve the influence of pressure angle, tooth top height coefficient and other parameters on the sliding rate.

According to the calculation formula of relative sliding rate of involute cylindrical gear, this paper deduces the calculation formula of sliding rate of gear pair under the coordinate of meshing line, and analyzes the influence law of parameters such as gear number (transmission ratio), module, pressure angle, modification coefficient, tooth top height coefficient, center distance variation coefficient on sliding rate, so as to further analyze the influence degree of each parameter on gear wear.

(1) According to the established calculation model, it can be seen that the sliding rate is the position function of each meshing point on the gear meshing profile. The maximum sliding rate of the driving gear root is higher than that of the driven gear root, and the sliding rate of the same gear root is higher than that of the top. The sliding rate affects the wear and gluing of gear tooth surface, so the value of sliding rate should be minimized.

(2) The change of the sliding rate is related to the number of teeth (transmission ratio), pressure angle, modulus, modification coefficient, tooth top height coefficient, center distance variation coefficient and other parameters. The influence of each parameter on the sliding rate is analyzed. Among them, the changes of the number of teeth, pressure angle, modulus and center distance of the gear all affect the bending degree of the sliding rate curve. With the increase of the parameters, the bending degree of the sliding rate becomes smaller. Except for the nodes, the sliding rate of the gear decreases, which is conducive to improving its anti-wear, gluing and pitting ability. The change of the modification coefficient and the tooth top height coefficient can only cause the change of the starting and ending position of the meshing point, and does not affect the bending degree of the sliding rate curve.

(3) With the increase of the gear module, the theoretical meshing line and the actual length of the meshing line of the gear pair increase, and the bending degree of the sliding rate curve changes, but the change of the module does not affect the sliding rate of the starting and ending positions of the meshing.

(4) When positive displacement occurs, the relative sliding at the top of the gear increases, but at the root of the gear decreases. When the coefficient of variation of center distance remains unchanged, with the increase of the coefficient of variation of the gear, the sliding rate at the top of the gear increases, and the sliding rate at the root decreases; the change of the sliding rate of another meshing gear is the opposite. 