Uncertainty Quantification for Nonlinear Vibration of Supercritical Drive Shaft With a Dry Friction Damper

The supercritical drive shaft is becoming increasingly popular in helicopter transmission system. Dry friction dampers are specially employed to ensure the supercritical shafts crossing the critical speed safely. Due to design tolerances, manufacturing errors and time-varying factors, the parameters of the damper are inherently uncertain, affecting the safety performance of the rotor system. This paper incorporates these parameter uncertainties to investigate the dynamic response uncertainties of a supercritical shaft and dry friction damper system, which is characterized by its high dimensionality and nonlinear behaviors of rub-impact and dry friction. The nonintrusive Polynomial Chaos Expansion (PCE) is adopted to achieve the propagation of uncertainties in the rotorsystem. To achieve efficient uncertainty quantification for this high-dimensional nonlinear system, a double-layer dimensionality reduction algorithm combining modal superposition with sparse grid technique has been applied. In the computational workflow, the inner layer uses modal superposition and the outer layer uses sparse grid techniques. The stochastic dynamic response of the rotorsystem is analyzed considering the uncertainty of five design parameters of the damper. Furthermore, as a post-processing of the PCE coefficients, the Sobol global sensitivity analysis is conveniently conducted. The influence of individual parameters or groups of parameters on the dynamic response is studied. A multi-objective optimization design for the key parameters is then carried out based on the established PCE model. The dynamic model and optimization design method are verified by experiments. The results will benefit uncertainty quantification analysis of high-dimensional nonlinear rotorsystem.