An Efficient Approach for the Frequency Analysis of Nonaxisymmetric Rotating Structures: Application to a Coupled Bladed Birotor System

The improvement of efficiency in the design of turbomachines requires a reliable prediction of the vibrating behavior of the whole structure. The simulation of blades vibrations is decisive and this is usually based on elaborated finite element model restricted to the bladed-disk. However, the blades dynamic behavior can be strongly affected by interactions with other parts of the engine. Global dynamic studies that consider these other parts are required but usually come with a high numerical cost. In the case of a birotor architecture, two coaxial rotors with different rotating speeds can be coupled with a bearing system. The mechanical coupling between the shafts generates energy exchange that alters the dynamic behavior of the blades. The equations of motion of the whole structure that take into account the coupling contain periodic time-dependent coefficients due to the difference of rotational speed between both rotors. Equations of this kind, with variable coefficients, are typically difficult to solve. This study presents a preprocessing method to guarantee the elimination of time-dependent coefficients in the birotor equations of motion. This method is tested with a simplified finite element model of two bladed-disks coupled with linear stiffnesses. We obtain accurate results when comparing frequency analysis of preprocessed equations with time-integration resolution of the initial set of equations. The developed methodology also offers a substantial time saving.