Study for ball bearing outer race characteristic defect frequency based on nonlinear dynamics analysis

The characteristic defect frequencies are widely used for diagnosing the local defect of the ball bearing. The varying compliance (VC) frequency of a fault-free rotor–bearing system equals to the BPFO (ball bearing outer race defect frequency) due to the internal kinematic relationship of a bearing assembly. In order to indicate this issue, a semi-analytical method—the harmonic balance method with alternating frequency/time domain technique—is exploited to obtain the solutions of rotor–ball bearing systems with /without an outer race defect. The solutions and the features of a rotor–ball bearing system with essentially nonlinear parametric excitation are analyzed. We prove the VC frequency equals the BPFO and explain the reasons that the harmonics of the characteristic defect frequency generally appear in the frequency domain. The VC, BPFO as well as their harmonics affected by the primary and super-harmonic resonance of the system are found out. Finally, a test rig of a rigid rotor–bearing system is established to verify the theoretical analysis qualitatively by presenting the performance of VC, BPFO and their harmonics in the frequency domain. In addition, the tests are accomplished in a cycle of running up and down to reveal the primary and super-harmonic resonance characteristics. On the basis of the theoretical and experimental results, the basic BPFO is not enough to judge an outer race defect. The discussion on frequency spectrum, the primary and super-harmonic resonance provides a more reliable way to elucidate the characteristic defect frequencies.