Vibration Analysis of Rotating Multi-packet Blade System Considering Mistuning Effect

Abstract

For the design of a rotating multi-packet blade system excited by multiple nozzle forces, transient and steady-state vibration characteristics of the system need to be identified accurately. The present study derives equations of motion of a rotating multi-packet blade system excited by multiple nozzle forces using the Rayleigh-Ritz assumed mode method. Using the equation model, resonance frequencies and their strengths are first identified. The study then investigates the effects of system parameters such as number of nozzles, number of packets, shroud coupling stiffness, disk coupling stiffness, damping constant and spin-up time constant on the transient response during a spin-up or spin-down motion which makes the nozzle passing excitation frequency pass through multiple resonance frequencies as well as the steady-state response around an operating angular speed. The relation between mode localization and transient response localization of a randomly mistuned multi-packet blade system is also investigated using the equation model. In a multi-packet blade system, random mistuning always exists among blades due to several reasons such as manufacturing tolerance, material irregularity and operation wear. It is well known that mistuning in a periodic structure often results in vibration localization phenomena such as mode and transient response localization. In this paper, a structural dynamic model of a randomly mistuned multi-packet blade system subjected to cyclic nozzle forces is proposed. The accuracy of the proposed model is first validated by comparing its numerical results to those obtained with a finite element model. Then, using the model, the correlation between mode and transient response localization is investigated and a design guideline for the multi-packet blade system subjected to cyclic nozzle forces is suggested.