An improved model for investigating the vibration characteristics of ball bearing owing to outer race waviness under high speed.

In this study, an improved model for a ball bearing is established to investigate the vibration response characteristics owing to outer race waviness under an axial load and high speed. The mathematical ball bearing model involves the motions of the inner ring, outer ring, and rolling elements in the radial XY plane and axial z direction. The 2Nb + 5 nonlinear differential governing equations of the ball bearing are derived from Lagrange's equation. The influence of rotational speed and outer race waviness is considered. The outer race waviness is modeled as a superposition of sinusoidal function and affects both the contact deformation between the outer raceway and rolling elements and initial clearance. The MATLAB stiff solver ODE is utilized to solve the differential equations. The simulated results show that the axial vibration frequency occurred at l × fc and the radial vibration frequencies appeared at l × f_c ± f_c when the outer race waviness of the order (l) was the multiple of the number of rolling elements (k × Nb) and that the principal vibration frequencies were observed at l × f_c ± f_c in the radial x direction when the outer race waviness of the order (l) was one higher or one lower than the multiple of the number of rolling elements (k × N_b ± 1). At last, the validity of the proposed ball bearing model was verified by the high-speed vibration measurement tests of ball bearings. [ABSTRACT FROM AUTHOR]