Parametric modelling of vibration response for high-speed gear transmission system

In the process of dynamic modelling and vibration response simulation for the high-speed gear transmission system, complex structures with a high degree of freedom (DOF) often lead to very large calculation errors, especially under conditions with unpredictable internal and external excitations. In this paper, a novel parametric probabilistic regression (p-PR) model based on data-driven and parametric modelling theories are proposed for the vibration signals of the high-speed gear transmission system. Based on the proper orthogonal decomposition (POD) method, the dataset of vibration signals is constructed, and a new truncated parametric reduced-order model (PROM) of the dataset is given for the gear vibration, with the truncated modes and corresponding coefficient vectors obtained. Through training the PROM and operating parameters using probabilistic regression, maximum likelihood estimation, and the parametric mode reconstruction, the p-PR model of vibration data for the gear transmission system is established. To validate the parametric modelling theories and the p-PR model, a bevel gear transmission experimental rig and a vibration signal test system are built, and the constant-speed test (CST) experiment and speed-up frequency sweep (SUFS) experiment are conducted. Based on the results of the CST experiment, the p-PR model for the experimental system is established and compared with the SUFS results. Results show that the p-PR model can accurately predict the vibration signals in both the time-domain and the frequency-domain, and the maximum predictive error for the experiment is 7.8%, which validates the accuracy and feasibility of the proposed theories and methods.