Finite element based stability analysis of a rotor-bearing system having a functionally graded shaft with transverse breathing cracks

Abstract

In spite of gaining practical importance of functionally graded (FG) shafts, stability analysis of such FG rotor-bearing system has not been reported yet. This paper presents the development of a finite element (FE) procedure and code for stability analysis of cracked FG rotor-bearing system under thermal environment. Two-noded Timoshenko beam elements are used to model the FG shaft considering the effects of gyroscopic moments, translational and rotary inertia, bending and shear deformation and material damping. Zirconia (ZrO2) and stainless steel (SS) are considered as constituents of the radially graded FG shaft with temperature dependent material properties. Considering breathing crack behaviour, local flexibility coefficients (LFCs) are derived using the Paris's equation and the Castigliano's theorem. Results show that while the depth, orientation and locations of cracks, thermal gradient and material damping affect the stability threshold speed, it is important to choose the material gradient index judiciously. Thus, even when surface cracks appear on the FG shaft, threshold speed could still be in the desired range, which is important for damage tolerant design in high temperature applications.