# Calculation of tooth surface adhesion wear of involute spur gear under low speed condition

Adhesive wear is the most common fault type on the working surface of mechanical system, which often occurs on the working surface with relative motion and contact. As the core component of vehicle transmission system, due to excessive load, poor lubrication and long-time operation, the meshing tooth surface will produce adhesive wear, which will change the original shape and load distribution of the tooth surface. Excessive wear will not only reduce the transmission accuracy and efficiency, but also make the system vibration intensified and produce noise. Therefore, it is necessary to deeply study the mechanism of tooth surface adhesion wear and the evolution law of tooth surface wear, so as to improve the reliability of gear system and prolong the working life of gear.

In view of the problem of gear adhesion wear, scholars at home and abroad have done a lot of research. Archard put forward a mathematical wear model earlier, that is, Archard wear formula. Subsequently, Archard wear formula is widely used in the wear prediction model of gear pair. Based on the generalized Archard wear formula and the simplified Winkler contact model, flodin and Anderson proposed an analytical model for predicting the wear of spur gears. Later, they extended their work to helical gears, where the teeth were equivalent to multiple slices of spur gears stacked along the axis and rotated at small angles in turn. Brauer et al combined the gear contact finite element model with Archard wear model to study the influence of gear wear on the tooth profile and interference of meshing gears. Based on the finite element contact mechanics model and Archard wear model, bajpai et al. Proposed a prediction method of gear surface wear considering machining error and tooth profile modification. Dhanasekaran et al. Neglected the influence of tooth surface wear on gear load distribution, and used Archard wear model to predict the influence of material characteristics on gear wear law in the case of no lubrication. Park et al. Proposed an approximate and fast wear calculation model for hypoid gears. The semi analytical contact model was combined with Archard wear model, and the surface interpolation method was used to improve the calculation efficiency of slip distance, contact pressure and tooth wear. Based on the Archard wear model, pan Dong et al. Simulated the wear of involute spur gear, and predicted the wear life of gear under different speed and torque, but ignored the influence of double tooth meshing area. Based on Hertz theory and Archard wear model, Zhang Jun et al. Established a quasi-static wear model of spur gear for real working conditions, studied the influence of meshing deviation and micro modification on tooth surface wear, but did not consider the influence of tooth surface wear on tooth deflection in load distribution model. The results show that when the modulus and transmission ratio change, the wear in the local contact area on the tooth surface changes significantly. Zhang Jiange et al. Put forward an analysis model which can accurately describe the wear process in the micro dimension, and studied the change law of tooth surface wear under the mixed lubrication state. Marco et al. Studied the influence of contact stress and oil film thickness on the tooth surface wear through experiments, and found that the tooth surface load distribution has a significant effect on the local wear. Flodin studied the effect of initial wear on the tooth surface morphology through experiments, and the results showed that the wear at the root of the pinion was the most serious. Brand ã O et al. Studied the influence of load and lubrication on wear coefficient. The experimental research can obtain more accurate results, but the test cost for gear wear is high, the cycle is long, and the wear characteristics of different parameters and different working conditions are different, so the results are lack of universality. In addition, the coupling relationship between tooth wear and load distribution is seldom considered in the above theoretical studies.

Therefore, considering the influence of wear on the load distribution coefficient of tooth surface, an effective load distribution calculation model is combined with Archard wear model, and a prediction model suitable for involute spur gear tooth surface wear is proposed. At the same time, the influence of load distribution and lubrication conditions on the tooth wear mechanism is considered, and the effectiveness of the proposed method is verified by comparing the maximum wear of the pinion with the experimental results. Then, the evolution and distribution of tooth surface wear under boundary lubrication are analyzed, which provides a theoretical basis for the prediction of gear meshing wear life under low speed condition.

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