Nonlinear model updating of the rotor-bearing system by multi-harmonic balance method and analytical sensitivity derivation

Abstract

Responses of the bearing system are usually predicted or tested, to analyze its nonlinear dynamic characteristics. However, responses predicted from the bearing model constructed by Hertz contact theory usually show differences with their tested counterparts, denoting the improper setting of the nonlinear contact parameters. It is compulsory to reduce such differences and obtain a precise bearing model using nonlinear model updating techniques. In this paper, a novel nonlinear model updating framework is proposed following the Multi-Harmonic Balance Method (MHBM) and the analytical sensitivity analysis, for updating of the rotor-bearing system using the nonlinear responses in the frequency domain. With the derivation of bearing response sensitivities to the nonlinear contact parameters, increments of the nonlinear parameters can be ascertained by the sensitivity inverse and updating of the nonlinear bearing model can be implemented in an iterative way, until a precise bearing model with the response differences reduced to minima is obtained. Firstly, a novel MHBM model is derived for the bearing system, which is fully described by matrix operations and used to further deduce the analytical sensitivity formulations of the bearing responses to the design parameters. Afterwards, the bearing responses and sensitivities in the frequency domain are predicted by the continuation strategy. Finally, model updating is conducted for the bearing system using the traditional inverse-sensitivity framework. Two cases are used to demonstrate the feasibility of the method. The first case is to update bearing parameters of contact stiffness, clearance and eccentricity of a 2-DOF bearing system in order to match the predicted bearing responses with the measured ones in strong nonlinearity with the multivalued phenomenon. The next is to update the Hertz contact parameters of the left and right bearings, together with the disc eccentricity, of a Finite Element (FE) rotor-bearing system. These results show the validity and superiority of the proposed method.