The Mechanism on Prediction of Transient Maximum Amplitude for Tuned and Mistuned Blisks

Abstract

Blisks are subjected to frequent acceleration and deceleration, which leads to a transient forced response; however, there is limited understanding of this response. In this work, the mechanism on prediction of transient maximum amplitude is found. An analytical link is proposed between the transient maximum amplitude and a fundamental dimensionless parameter which combines the damping ratio, natural frequency, acceleration, and engine order of the system to reveal the mechanism of the transient maximum amplitude. Therefore, the transient maximum amplitudes of tuned and mistuned blisks are predicted analytically. First, a lumped parameter model is used to study the mechanism of the transient maximum amplitude for a tuned blisk, and an approximated analytical expression is derived between the fundamental parameter and the transient amplification factor of a 1DOF (degree-of-freedom) model. The relationship is also applicable to a reduced order, tuned finite element model (FEM). Second, the mechanism of the transient response for a mistuned blisk is studied in the decoupled modal space of the blisk, based on the 1DOF transient relationship. The transient maximum amplitude in a reduced order, mistuned FEM is predicted. Two lumped parameter models and a FEM are employed to validate the prediction.