# Friction coefficient and meshing efficiency of spiral bevel gears

Spiral bevel gears are widely used in heavy load conditions such as helicopters, ships and automobiles. Their friction characteristics are the main factors affecting efficiency loss, vibration and noise. Therefore, in-depth study on the friction characteristics of spiral bevel gear is of great engineering significance to improve the service life and transmission efficiency of spiral bevel gear.

Friction characteristics play an important role in contact interface wear and energy loss. Therefore, scholars have done a lot of research on the friction characteristics of point contact and line contact. Due to the complexity of the contact geometry and conjugate principle of spiral bevel gears, and the entrainment speed has any entrainment angle (the included angle between the entrainment speed vector and the main direction of the contact ellipse), the lubrication analysis of spiral bevel gears is complex. Therefore, the simplified analysis model is mostly used to study the friction characteristics of spiral bevel gears under lubrication Based on the point contact elastohydrodynamic lubrication model, Wang Yanzhong and others analyzed the variation of the minimum oil film thickness of high-speed spiral bevel gears, and studied the thermal friction behavior of spiral bevel gears combined with the finite element model, but the included angle in the direction of coiling speed was not considered in the lubrication analysis model Based on the solution of a large number of Line Contact Elastohydrodynamic Lubrication, Xu and Kahraman gave the fitting formula of friction coefficient with multi parameters, and studied the transmission efficiency of spiral bevel gear Kolivand and kahrama analyzed the friction loss of spiral bevel gear based on the mixed lubrication analysis model, in which the non-Newtonian characteristics of fluid were considered However, in order to simplify the calculation, the point contact of spiral bevel gear is simplified to line contact Similar simplifications are also used to study the friction characteristics of spiral bevel gears. Zhang studied the friction coefficient and wear behavior of spiral bevel gears based on the mixed thermoelastohydrodynamic lubrication theory, but it was assumed that the direction of coiling speed coincided with the direction of the short half axis of the contact ellipse Mohammadpour et al. Established a hybrid lubrication model which is more in line with the real contact situation of spiral bevel gears. The characteristics of non-Newtonian fluid and the included angle of entrainment speed are considered in the model, but the change of the included angle of entrainment speed is ignored Gu Jiangong et al studied the average meshing efficiency of spiral bevel gears by using the empirical formula of mixed elastohydrodynamic lubrication In the above research, a large number of assumptions are used in the lubrication model to solve the friction coefficient, and the surface roughness of spiral bevel gear is not considered or the statistical roughness model is used Pu Wei et al. Established the lubrication analysis model of spiral bevel gear under heavy load, which comprehensively considered the parameters such as contact geometry, arbitrary entrainment speed angle and so on.

When the spiral bevel gear is loaded, the friction loss caused by rolling and sliding between the tooth surfaces leads to the reduction of the transmission efficiency of the spiral bevel gear The friction loss is directly related to the friction coefficient between tooth surfaces, and most studies use simplified models In view of this, in this paper, the load contact analysis model of spiral bevel gear is coupled with the hybrid lubrication model to solve the instantaneous friction characteristics of spiral bevel gear, and the meshing efficiency of spiral bevel gear is further studied The coupling model comprehensively considers the parameters such as real surface roughness, contact load, contact geometry, velocity vector and arbitrary entrainment angle, which can realize the numerical analysis of spiral bevel gear under actual contact At the same time, the friction coefficient and meshing efficiency of spiral bevel gear are studied by using the friction coefficient simplification algorithm (line contact simplification) and the empirical formula of friction coefficient, and compared with the calculation results to analyze the solution error of the simplified algorithm and empirical formula.

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