Rubbing Of a Bladed Disk Considering Coriolis Effect: A Reduced Model Based on Complex Modal Analysis

Due to the high demands of aerodynamic efficiency in modern aero-engines, tip clearances between blades and casings are becoming smaller. This increases the possibility of rubbing between rotating bladed disks and their surrounding casings. Rotational effects exhibit increased significance in the latest generation of fans, which currently have relatively long blade and elongated cantilevered shaft. Previous studies on the rotor dynamics during rub impact have mainly focused on simplified models. However, it is necessary to take both realistic blades and Coriolis effect into account. Based on an open-source bladed disk model, the impact of the Coriolis effect on rub-induced responses is investigated. A two-step model reduction method is adopted by combining the fixed interface reduction and cyclic symmetry reduction. Both centrifugal and gyroscopic effects are incorporated in the numerical model. Complex modal analysis, based on classical Craig-Bampton method, is used to improve the model reduction of the gyroscopic system. The response of a flexible bladed disk to a simplified pulse rubbing force is investigated. With the time and space Fourier transform, a Coriolis-induced frequency split is observed on some nodal diameter lines, which indicates the significance of the Coriolis effect in rub-induced responses. A complex model reduction has been successfully applied to the rub-impact problem of cyclic symmetric bladed disks. Compared with the classical model reduction, the numerical results obtained by complex modal analysis are more reasonable. This lays a solid foundation for further rub-impact research considering rotor dynamics.

Space, Time, and Location

This chapter is an account of the particularity of spatial and temporal regions as they appear within our experience. It argues that the spatial and temporal relations of these regions are sufficient to individuate them, despite standard objections. This involves a kind of moderate substantivalism about space. The chapter also explores some of the complex modal structure of the spatial relations in question, relevant for instance to geometric truth and the way in which things seem to reverse in mirrors. The eternalist view of time presumed by this account is defended against alternative conceptions of time such as presentism and the moving spotlight theory.