An integrated approach for response prediction in large-scale rotor-bearing system with local nonlinear joints based on FRF-based harmonic balance method

Abstract

In the development and maintenance of gas turbines, the efficient computation to predict the responses of large-scale and complex rotating structures with local nonlinear joints is crucial. In this paper, a novel integrated strategy as a trade-off between time expense and accuracy for response prediction in large scale rotor-bearing system with local nonlinear joints is developed using the frequency response function based harmonic balance method (FRF-based HBM). To tackle the numerical challenges arising from asymmetrical matrices in rotating systems, a new approach is presented to compute the FRF using a spectral decomposition in second-order state space. Furthermore, the analytical mapping of eigen-solution against rotational speed based on Taylor series expansion is developed to address the computational expenses associated with speed-dependent FRF matrices. Then, a model reduction is adopted to mitigate the additional computational costs arising from the high-order unsymmetric matrices. The superior qualities and practical value in engineering of the new strategy are demonstrated on two numerical cases. The first is a one-dimensional rotor-bearing model subjected to the cubic nonlinear force under investigation, this approach shows an exceptionally high level of accuracy in response prediction, when compared to both the Runge-Kutta method and the harmonic balance method (HBM) without any form of model reduction. Another is a large-scale rotor-bearing model with two squeeze film dampers, the computational speed, being thousands of times faster than the HBM method and several times faster than the HBM considering the CMS model reduction, underscores the efficiency of this approach.