A Modular Modeling Method of Mistuned Blisk Based on State-Space Theory with Fitting Aerodynamic Excitation

Abstract

In order to improve the solution efficiency of vibration characteristics for the mistuned blisk, a modular method combined with state-space method based on lumped-parametric model is developed for the first attempt, which provides a general modeling framework which can be employed to conveniently construct the lumped-parametric models of bladed disk systems with multiple mistuning and variable blade number. It is noteworthy that a pressure fit in the axial-span-pressure space is performed to obtain the continuous equations of aerodynamic forces according to the aerodynamic loads acting on the blade surface. The function of traveling wake excitation is established by considering the rotational velocity. Subsequently, 1N-degree-of-freedom (1N-DOF) and 2N-DOF lumped-parametirc models are respectively used to construct the mistuned blisk. A modular solution method of multiple mistuned lumped-parametirc model is derived from the controllable canonical form and minimum realisation, which reveals that the minimum dimension of the state space is two times of its DOF. The correctness of the present method is varified by several comparisions. Vibration localization is found in the transient response and steady-state response of the blisk. The effects of the mistuning on the blades and the disk are discussed, respectively.