Dynamic Analysis of Gear–Shaft–Bearing Coupled System Considering Bearing Waviness Defect

Using finite element and lumped parameter methods, a gear–shaft–bearing coupled vibration model was developed for a single-stage gear transmission system considering bearing waviness, bearing clearance, time-varying transmission error excitation, and shaft flexibility. Runge–Kutta algorithm was applied for solving the dynamic response of the coupled model. The influences of rotational speed, the number, and amplitude of bearing waviness on the dynamics were studied. Results show that any change in the number of bearing waviness has an obvious impact on the dominant frequency component of the dynamic transmission error. When the number of bearing waviness is equal to the number or multiples of the rolling element, the dynamic mesh force occurs peak response and the system vibrates violently. At low and medium speeds range, the gear transmission system with bearing waviness has larger vibrational energy than the gear transmission system without bearing waviness, leading to unstable dynamic response, which would potentially cause a significant chaotic response. The dominant frequencies of the dynamic transmission error for the gear transmission system with bearing waviness are the ball passage frequency (BPF) and its harmonic frequency. At high speeds range, the main excitation is the transmission error both for the gear transmission systems with and without bearing waviness. In addition, the increasing amplitude of bearing waviness would enlarge the dynamic mesh force and decrease the number of loaded rolling elements.