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 para-metric probabilistic regression (p-PR) model based on data-driven and parametric modelling theories are pro-posed 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 cor-responding coefficient vectors obtained. Through training the PROM and operating parameters using probabi-listic 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 vali-dates the accuracy and feasibility of the proposed theories and methods.