A New Multi-Harmonic Method for Predicting the Forced Response of Mistuned Bladed Disks with Dry Friction Damping

Abstract

Misturiing refers to the variations of blades properties due to procession and wear etc. Though these variations is small, they can confine the vibration energy in a few blades, and increase the resonant response of those blades. Therefore, dry friction dampers are often used to reduce the vibration of blades. In order to investigate the effects of mistuning and the performance of dry friction dampers, it is necessary to develop an efficient numerical method to predict the resonant features of the bladed disks with dry friction dampers. We propose an efficient multi-harmonic (MH) method which is based on the harmonic balance method. The formulation of the method can take the advantage of fast Fourier transformation (FFT) which can facilitate the analysis efficiency significantly. The iterative Newton-Raphson procedure are used to solve the nonlinear vibration equation. The MH method has been used in a mass-string model of bladed disk, and validated by numerical integration method. The analysis of forced response features is performed by the MH method for both tuned and mistuned systems with various coupling strength, viscous damping, dry friction damping and blade stiffness mistuning etc. The results indicate that the MH method can efficiently predict the resonant response of the bladed disks with nonlinear dry friction damping. It is found that, for the weakly coupled bladed disk with nonlinear blade-to-blade dry friction damping, mistuning can reduce resonant amplitudes of the system significantly when dry friction and viscous damping are all smaller. This is not common for mistuning effects. In other situation, Mistuning can increase the resonant amplitudes, broaden the resonant frequency region, and produce multiple resonant peaks.