Micro-Slip Friction Characteristics Of Grooves Of High-Speed And Light-Loaded Spindle Ball Bearings

For the micro-slip and rolling friction problems of the main shaft ball bearings of aircraft engines under high-speed and light-load conditions, it is assumed that the rolling friction of the contact surface is negatively correlated with the area of ​​the adhesion zone. A micro-slip model is established based on the elastic deformation principle of the contact surface material to study the sliding displacement lines, sliding velocity lines, Hertz contact stress, sliding-rolling ratio and rolling friction of the load-bearing steel ball in the inner and outer grooves. The results show that increasing the bearing speed makes the sliding displacement line and sliding speed line of the steel ball in the inner and outer grooves tend to the contact stress peak area, the rolling friction increases, and the sliding tendency is enhanced; reducing the radial load of the bearing leads to an increase in the micro-slip tendency of the steel ball in the inner groove, and has a smaller effect on the outer groove; when the speed is 22 000 r/min, the sliding-rolling ratio of the steel ball to the outer groove is 4.4 times that of the inner groove; under the same speed conditions, the rolling friction between the steel ball and the outer groove is 7 to 13 times that of the inner groove; when the radial load is 50 N, the rolling friction between the steel ball and the outer groove is 7.6 times that of the inner groove, and the steel ball is more prone to overall sliding and micro-slip wear in the outer groove.

Keywords rolling bearing; spindle bearing; aircraft engine; groove; rolling friction; micro-slip
The rotor of modern aircraft engines is light in weight and high in speed, and the resulting high-speed and light-load conditions affect the contact friction characteristics of the spindle ball bearing groove. During normal operation, the bearing steel ball is not allowed to slide macroscopically on the groove. However, due to the tightness between the inner and outer rings and the steel ball (the ratio of the steel ball radius to the ring groove curvature radius) and the elastic deformation of the contact material, the steel ball always has tiny local sliding in the contact area. High speed causes the local sliding of the steel ball to tend to the peak area of ​​contact stress. The micro-slip speed is too high, resulting in serious groove wear and shortening the bearing life. High speed reduces the adhesion area of ​​the steel ball in the contact area, increases the rolling friction, and makes the steel ball tend to slide macroscopically. Light load on the bearing also increases the rolling friction of the steel ball, making it easy for the steel ball to slide as a whole. Therefore, the micro-slip and rolling friction characteristics of the bearing steel ball in the groove limit the maximum speed and load conditions of the bearing. Once the micro-slip extends to the entire contact area, it will cause serious engine failure. Distinguishing the adhesion area and slip area of ​​the contact ellipse and predicting the local micro-slip and rolling friction characteristics of the steel ball are beneficial to bearing design, safe application and performance analysis.
Domestic and foreign scholars have conducted a large number of studies on the contact friction characteristics of ball bearing grooves [1-3]. The focus is on the friction shear stress, friction traction and drag torque of the steel ball in the groove. The total friction traction is obtained by integrating the friction shear stress in the entire contact area. However, the local micro-slip and stick-slip characteristics are usually not considered for the contact area, and the integral boundary of the shear stress is not distinguished. In fact, the steel ball rolls incompletely in the contact area. As the slide-roll ratio increases, the elastic deformation of the contact surface material increases. When it accumulates to a certain extent, the groove will have local micro-slip, and then the elliptical adhesion area will continue to decrease, and the rolling friction will continue to increase. Finally, the entire contact area evolves into a slip zone. The rolling friction of the steel ball is closely related to the friction coefficient, contact stress, geometric dimensions and adhesion area of ​​the contact area. REUSS et al. [4] established a rolling friction model for linear ball bearings, assuming that the rolling friction in the contact adhesion area changes linearly with the rolling displacement. The stick-slip transition line and the pure rolling line are determined using the maximum relative displacement and the minimum friction torque as conditions, respectively, and the stick-slip properties of the contact elliptical surface are analyzed to obtain the friction of each stick-slip zone. KIMURA et al. [5] studied the micro-slip wear problem between steel balls and grooves. The adhesion zone of the contact ellipse was determined based on the relative sliding displacement caused by the elastic deformation of the contact surface material to adapt to the rolling speed difference, and the slip zone was divided according to the traction force at the contact point exceeding the maximum static friction force. Ning Fengping et al. [6] proposed a micro-slip model for the contact between steel balls and grooves, but did not conduct in-depth research on the modeling process, micro-slip behavior and friction influencing factors.
Some scholars have conducted research on the groove contact characteristics of ball bearings for helicopter reducers and wind turbines [7-8], focusing on the groove micro-motion wear: KWAK et al. [9] established a local elastic contact model of wheel hub angular contact ball bearings based on the semi-infinite body assumption, and used influence functions to perform three-dimensional contact analysis to obtain the position and size of the groove contact ellipse under the limit axial load; PATHUVOTH et al. [10] used the maximum contact stress of the ellipse truncation to evaluate the static load-bearing capacity of the turntable bearing; Ma Zikui et al. [11] calculated the friction torque of the ball bearing based on the rolling contact creep theory, revealing the adhesion and rolling characteristics of the steel ball in the groove. The above studies mainly analyze the micro-slip characteristics of ball bearing grooves under low-speed and heavy-load conditions, and the research on the groove slip-roll ratio is insufficient. Usually, the slip-roll ratio between the steel ball and the groove is small, but it is the main factor affecting the groove friction [12]: Zhao Erhui et al. [13] established a point contact elastohydrodynamic lubrication model to study the effect of the slip-roll ratio on the oil film interface in elastohydrodynamic lubrication, pointing out that the increase in the slip-roll ratio leads to a significant increase in the interface slip amplitude and slip range, and the bearing capacity of the slip zone decreases by 6.4%; Zhang Binbin et al. [14] studied the effect of the slip-roll ratio on the thermal elastohydrodynamic lubrication of angular contact ball bearings. The results show that increasing the slip-roll ratio causes the oil film pressure peak and oil film depression to tend to the pressure center, and the amplitude continues to increase; Zhang Yu et al. [15] studied the friction characteristics of rolling bearings in elastohydrodynamic lubrication state and pointed out that increasing the slip-roll ratio can increase the rolling friction coefficient. Therefore, the slip-roll ratio of the contact surface directly affects the contact load distribution and the size of the slip zone.
In summary, in the past, when studying the friction drag torque of the steel ball in the groove, the entire contact ellipse was used as the integral boundary of the shear stress, without distinguishing between the adhesion zone and the slip zone, and it was impossible to predict the local sliding and friction characteristics. There was also a lack of research on the micro-slip friction characteristics of the groove under high-speed and light-load conditions. Therefore, this paper aims at the high-speed and light-load conditions of aircraft engines, assumes that the rolling friction force of the contact ellipse is negatively correlated with the area of ​​the adhesion zone, and establishes a micro-slip model of the spindle ball bearing based on the elastic deformation principle of the contact surface material. The sliding displacement lines, sliding velocity lines, Hertzian contact stress distribution, sliding-rolling ratio, and rolling friction of the steel ball in the inner and outer grooves are studied to reveal the local micro-slip and rolling friction characteristics of the groove under high-speed and light-load conditions.