###### Abstract  
The traditional slewing bearing with circular raceway has the problem of stress concentration under the large overturning moment. In this paper, a new non-circular raceway of a slewing ball bearing was presented to conquer this problem. To obtain the new non-circular raceway, first, the static equilibrium equations of the slewing ball bearing was established by the vector method, which is a constraint condition for life optimization; secondly, the life optimization function was established to calculate the contact load distribution in the bearing when the bearing life is at its maximum; finally, through the contact deformation with the contact load, the non-circular inner raceway corresponding to the maximum bearing life was obtained, and the non-circular shape corresponding to the raceway under axial load and overturning moment was studied. The results show that the non-circular raceway devised by this method can evenly reduce the contact force of the raceway and effectively improve the bearing capacity. Moreover, the position where the non-circular raceway deformation occurs is the position where the contact force is different before and after optimization. Therefore, the overturning moment has an effect on the shape of the raceway, whereas the axial load only affects the amplitude of the deformation, and has no obvious effect on the shape of the raceway. slewing-row four-point contact ball bearing; non-circular raceway; vector method; life optimization +
Footnote †: journal: Applied  
15 December 2022  
inner ring gravity, along the axial direction), and studied the relationship between the internal contact force of the bearing and the negative clearance. [PERSON] et al. [13] studied the influence of clearance on the load distribution of a single-row four-point contact slewing ball bearing by static method. The research shows that the smaller clearance value is beneficial to improve the bearing capacity. Researchers [14; 15; 16] have studied the existence of radial clearance and the influence of the shape of rolling elements on the contact stress, and suggest that having radial negative clearance minimizes the mutation of maximum contact stress. [PERSON] [17] established a nonlinear mechanical solution model to study the influence of different geometric parameters of the bearing on the bearing capacity. It was concluded that the axial clearance has an effect on the contact force, whereby it decreases with the decrease in axial clearance; when the clearance is close to 0, the contact force can be minimized and the bearing capacity can be effectively improved. The above scholars employed the method of uniformly reducing the contact load of the bearing. Compared with other traditional methods, the negative clearance can directly change the contact deformation of the rolling element and the raceway, which is better for uniformity and for reducing the contact load of the raceway. However, when the negative clearance is not selected properly, it increases the contact load of the raceway and the friction torque of the bearing. Moreover, the existing negative clearance method uses the same clearance in the circumferential direction of the slewing bearing, and does not give full play to the deformation control of the rolling element and the raceway. In order to solve this problem, a new idea of designing a non-circular raceway for a slewing bearing is proposed in this paper, which is to uniformly reduce the contact load of the rolling element and improve the bearing capacity by precisely controlling the deformation of the raceway locally. Scholars at home and abroad have done relevant research on non-circular deformation of bearing raceways. [PERSON] et al. [18; 19] proposed a method based on vector representation to establish a static model of an arbitrary shape raceway of a four-point contact slewing ball bearing.