A systematic study of ball passing frequencies based on dynamic modeling of rolling ball bearings with localized surface defects

Ball passing frequencies (BPFs) are very important features for condition monitoring and fault diagnosis of rolling ball bearings. The ball passing frequency on outer raceway (BPFO) and the ball passing frequency on inner raceway (BPFI) are usually calculated by two well-known kinematics equations. In this paper, a systematic study of BPFs of rolling ball bearings is carried out. A novel method for accurately calculating BPFs based on a complete dynamic model of rolling ball bearings with localized surface defects is proposed. In the used dynamic model, three-dimensional motions, relative slippage, cage effects and localized surface defects are all considered. Moreover, localized surface defects are modeled accurately with consideration of the finite size of the ball, the additional clearance due to material absence, and changes of contact force directions. The reasonability of the proposed method for the prediction of dynamic behaviors of actual ball bearings with localized surface defects and for the calculation of BPFs is discussed by investigating the motion characteristics of a ball when it rolls through a defect. Parametric investigation shows that the shaft speed, external loads, the friction coefficient, raceway groove curvature factors, the initial contact angle, and defect sizes have great effects on BPFs. For a loaded ball bearing, the combination of rolling and sliding in contact region occurs, and the BPFs calculated by simple kinematical relationships are inaccurate, especially for high speed, low external load, and large initial contact angle conditions where severe skidding occurs. The hypothesis that the percentage variation of the spacing between impulses in a defective ball bearing was about 1-2% reported in previous investigations can be satisfied only for the conditions where the skidding effect in a bearing is slight. Finally, the proposed method is verified with two experiments.