A new solving method for ball bearing dynamics model based on optimization with nonlinear constraints: Contact angles as iterative variables

Bearing dynamics model is the premise for bearing vibration analysis and fault diagnostics. This paper proposed a novel modeling and solving method for angular contact ball bearing dynamics. It transformed the problem of solving nonlinear model equations into an optimization issue with equality constraints by choosing contact angles rather than deformations as the iteration variables. Additionally, to accelerate the solving convergence and reduce dependence on the initial values, a polynomial model was adopted to approximate and define the contact angle initials by analyzing their value distribution characteristics at different ball positions. Furthermore, a genetic algorithm was applied to reset the initial values at every iteration to speed up the solving process and improve the global search capability. Simulations under various conditions were used to validate the proposed method and compared with the traditional Newton–Raphson solving method. The influence of contact angles on bearing fatigue life was also analyzed. Results showed that the accuracy, efficiency, and dependence on the initial values were thoroughly improved.