Study of the Effect of Multi-Stage Cyclic Symmetric Modeling on the Natural Frequencies of Bladed Disks of an Aero Engine Rotor System

Abstract

Majority of the failures in Gas turbine Blades are caused by High Cycle Fatigue induced by the vibratory stresses in the rotor blades. The first step in blade design is the prevention of coincidence of natural frequencies of the blades with the frequencies of the fluctuating Gas loads. The forcing frequency is a function of number of upstream and downstream stator blades, and rotational speed. In gas turbines with multiple stages, modal analysis of bladed-disks is individually performed i.e. stage by stage. As the structure is rotationally periodic, cyclic symmetric boundary conditions can be utilized, over 360 degree modeling. The advantage of cyclic symmetry over full model lies in reduced degrees of freedom and hence reduced computational time. In most of the available tools, cyclic symmetry for modal analysis is limited to single stage. As such there is no provision to model and analyze multiple stages at the same time. This leads to inaccurate values of natural frequencies as the flexibility introduced by the adjacent stages is not being taken into consideration. An alternative to this is full 3D modeling and analysis of all the combined stages. Bladh et al. (2003) [1] have shown that interstage coupling can significantly affect the dynamics of the multi-stage assembly and in some cases lead to an underestimation of vibratory levels. Sokolowski et al [2] studied the influence of inclusion of shaft in the model on the natural frequencies and mode shapes of the shrouded bladed discs up to four nodal diameters for first two frequency series (mode shapes). Rzadkowski and Drewczynski (2006) [3] have used full 360 degrees models to study the free and forced dynamics of multi-stage systems. However this method is avoided as the computational cost is prohibitive. Multi stage cyclic symmetry overcomes this obstacle in which each stage is cyclically modeled and an inter-stage coupling is introduced between adjacent stages. The advantage of multi stage cyclic symmetry lies in the significant reduction in the number of elements and therefore computational time. Laxalde et al. (2007) [4] were the first to come up with the method of dynamic analysis of turbo machinery rotors with multi stage cyclic symmetry using interstage coupling. They considered an example of two-stage High Pressure compressor. The results were validated against a complete 360 degrees reference model. Forced response analysis of rotor stages to fluctuating gas loads with and without interstage coupling definition was also presented and compared. In the present work a complete Gas Turbine rotor system with multiple stages of Compressor, Shaft and Turbine were analyzed together.