Stochastic finite element analysis using polynomial chaos on a flexible rotor with contact nonlinearity

The dynamic response of a rotor system can be significantly affected by uncertainties. It is essential to understand and quantify the influence of uncertain parameters on the rotor response. The purpose of this study is to evaluate the effect of perturbation in critical system parameters on the dynamic behaviour of a flexible rotor with localised contact. A test rig consisting of a localised contact element is developed. The critical rotor speeds are identified using the Campbell diagram, internal resonance diagram and experimental run-up analysis. Modal interactions influence the critical rotor speed. Modal interactions can be controlled using system parameters such as contact location, eccentric mass location and contact friction. Experimentally the sensitivity of the system parameters on the dynamic response is analysed. A stochastic finite element model is developed for the rotor–stator system using uncertain critical system parameters. The generalized Polynomial Chaos expansion (gPC) is used to evaluate the stochastic response of the finite element model with uncertainties. The approach uses a numerical collocation method for determining the coefficients of the gPC. The modal interaction is altered by varying the contact location, impulsive load location and the rotor–stator interface friction. The results from the experimental and numerical study indicate that the dynamic response at internal resonance rotor speed is more sensitive to the perturbation in system parameters compared to the critical speed corresponding to the first whirling mode.