In this paper, a theoretical model is proposed to analyze the friction effect on the rolling contact fatigue (RCF) life of the angular contact ball bearing (ACBB). Firstly, the quasi-static model without race control hypothesis is introduced to study the load characteristics of the ACBB under different loading conditions. Then, the friction coefficient is quantitatively calculated by analyzing the relation between the gyroscopic torque and the sphere-race contact load. The effects of the axial load, radial load, torque load and rotating speeds on the friction coefficient, the maximum value of the sub-surface von Mises stress (SSVS) and the maximum peak-peak value of the sub-surface shear stress (SSSS) are subsequently investigated. The results show that they can significantly affect the friction coefficient and further influence the stress field beneath the contact surface. Further studies illustrate that the friction coefficient cannot affect the maximum peak-peak value of the SSSS but can change the distribution of the SSVS field. The relative RCF life of the sphere-race contact is calculated and the published studies confirm the accuracy of the calculation.

In response to the fact that not all rolling balls are laden when the angular contact ball bearing working under the condition with certain combined loads especially when the axial preload is not large enough, an analytical method for the determination of the time-varying stiffness of angular contact ball bearing considering the effect of time-varying number of laden balls and load distribution is proposed in this paper. According to the definition of the stiffness, the time-varying stiffness under different sets of combined loads is obtained by the implicit function derivation method. Only the principal diagonal elements of the stiffness matrix are studied for the sake of simplicity. Several numerical examples are simulated and the simulation results indicate that the time-varying number of laden balls and load distribution have a significant effect on the stiffness. The period of the time-varying stiffness is consistent with the time required for the cage to rotate the angle between the adjacent rolling balls. The calculation of the ball bearing quasi-static model and the analytical method for the determination of the stiffness is verified by the existing references.

Due to the exist of the inevitable dimensional tolerance and assembling errors in the ball bearing, the interference amounts between the inner ring and the connected shaft are uncertain but bounded, which could directly affect the dynamics performance of the rotor-ball bearing system. Whereas, most of the works on the field of dynamics in a ball bearing have considered the varying compliance (VC) vibration as deterministic vibration and there are few quantitative studies considering the uncertain factors. Therefore, in this paper, an uncertain ball bearing-rotor dynamic model is presented based on the Chebyshev interval method. Firstly, the uncertain interference amounts between the bearing inner ring and the connected shaft are modeled by the Chebyshev interval method. Then the radial clearance and actual interference amounts of ball bearing are derived by the bearing-shaft interference fit model. The time-dependent ball-raceway contact probability is formulated and the influence of the average and deviation coefficient of the initial interference amounts on the vibration behaviors of the rotor under various rotational speeds are investigated based on the double degrees of freedom (2-DOF) ball bearing system. The numerical cases show that the amounts of the bearing-shaft interference fit are uncertain and could be affected by rotational speed, which have an obvious influence on the dynamic performance of the rotor-ball bearing system. Reasonable design of the interference amounts could reduce the dispersion of the displacement and time-varying stiffness. The numerical results obtained by the present study are compared to the Monte Carlo simulation (MCS), which show the validity of the study.

The rotating accuracy of the rolling bearing is closely related to its precision class and the actual fitting parameters. However, there are few quantitative evaluation models to describe their relationships. In this paper, considering the effect of the uncertain but bounded interference amounts between the bearing inner ring and the shaft, the Chebyshev interval analysis method is utilized and a rotating accuracy dynamic reliability model is presented based on the two degrees of freedom (2-DOF) rotor-ball bearing system. Firstly, the relationships between the bearing radial clearance and bearing-shaft interference amounts are investigated based on the shaft-bearing interference fit model. Thus, in terms of Chebyshev interval analysis method, the 2-DOF rotor-ball bearing system with uncertain bearing-shaft interference amounts is established. Then the rotating accuracy dynamic reliability model of the ball bearing is presented based on the Chebyshev interval theory. The effects of the average values and deviation coefficients of the initial interference amounts on the actual interference amounts, radial clearance and the resultant rotating accuracy dynamic reliability of the ball bearing are analyzed. The results show that the uncertain bearing-shaft interference amounts have a significant effect on the rotating accuracy dynamic reliability of the ball bearing and reasonable design could improve the rotating accuracy of the ball bearing. The results calculated by the present study are compared to the Monte Carlo simulation (MCS), which show the validity of the study.

When the ball bearing serving under the combined loading conditions, the ball will roll in and out of the loaded zone periodically. Therefore the bearing stiffness will vary with the position of the ball, which will cause vibration. In order to reveal the vibration mechanism, the quasi static model without raceway control hypothesis is modeled. A two-layer nested iterative algorithm based on Newton–Raphson (N-R) method with dynamic declined factors is presented. The effect of the dispersion of bearing parameters and the installation errors on the time-varying carrying characteristics of the ball-raceway contact and the bearing stiffness are investigated. Numerical simulation illustrates that besides the load and the rotating speed, the dispersion of bearing parameters and the installation errors have noticeable effect on the ball-raceway contact load, ball-inner raceway contact state and bearing stiffness, which should be given full consideration during the process of design and fault diagnosis for the rotor-bearing system.