Abstract

Bearing preload significantly affects the running performance of a shaft-bearing system including the fatigue life, wear, and stiffness. Due to the mounting error, the bearing rings are often angularly misaligned. The effects of the combined bearing preload and angular misalignment on the fatigue life of ball bearings and a shaft-bearing system are analyzed in this paper. The contact force distribution of angular contact ball bearings in the shaft-bearing system is investigated based on the system model. The system model includes the bearing model, and the shaft model is verified by comparing with the manufacturer’s manual and the results from other theoretical models, with the difference between the results from the present bearing model and manufacturer manual within 3%. The global optimization method is used to replace the Newton–Raphson algorithm to solve the ball elements’ displacements and friction coefficients, which improves the computation efficiency of the system model. The fatigue life of each bearing is evaluated with the consideration of the two preload methods and two angular misalignment cases. The fatigue life results show that the system life at the optimal angular misalignment is more than 1.5 times that without angular misalignment at the low preload value, and this ratio decreases as the preload value increases. The optimal angular misalignment of both the shaft-bearing system and the misaligned bearing is not always consistent, which depends on the preload value and bearing life. Both the constant-displacement preload and constant-force preload do not cause a significant difference in the highest system life. The different misaligned bearings can lead to different highest system lives as the preload value is low.

Highlights

  • The shaft-bearing system is a key part in mechanical transmissions, in which the rolling element bearing is commonly applied due to its low friction, low wear, and low energy consumption

  • Yang et al [9] analyzed the effects of the combined external loads and angular misalignment on the double-row tapered roller bearing, and the results demonstrated that the external load, rotation speed, and angular misalignment had a significant influence on the fatigue life of a double-row tapered roller bearing

  • As the preload displacement increased to 0.050 mm, the system life depended on the fatigue life of both Rear Bearing 1 and the preloaded front bearing, and the optimal angular misalignment turned to −0.21 mrad

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Summary

Introduction

The shaft-bearing system is a key part in mechanical transmissions, in which the rolling element bearing is commonly applied due to its low friction, low wear, and low energy consumption. Many researchers have conducted numerous studies on the fatigue life of the rolling element bearings considering the preload and angular misalignment. Considering the significance of the pressure distribution of roller elements on the fatigue life estimation, Tong et al [8] extended the 3D elastic contact method to simulate the contact pressure and analyzed the fatigue life of a tapered roller bearing with the consideration of the angular misalignment effect. Zhang et al [15] investigated the effect of external load and preload on the number of rolling elements in the contact zone based on the a quasi-dynamic model and determined an optimum preload for a simplified bearing-rotor system by taking the bearing fatigue life as the optimization target. Very few studies have investigated the effects of the combined preload and angular misalignment on the fatigue life of rolling element bearings and the shaft-bearing system at high speed.

Quasi-Static Model of Angular Contact Ball Bearing
Forces
Shaft Model
Preload and Angular Misalignment Factors
Numerical Solution of the System Model
Model Validity
Flowchart
10 The contact force distribution in each bearing is LL
Results and Discussion
The Constant-Displacement Preload Condition
The Constant-Force Preload Condition
Conclusions

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