Finite element analysis of a functionally graded shaft with transverse cracks in a rotor-bearing system
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During last few decades, functionally graded materials (FGMs) have been recognized as future advanced composite material, featuring thermo-mechanical loading, multi functionality and gradation at micro and nano scales. In many rotating machineries, like gas turbine, steam turbine, shafts, blades etc. are exposed to very high temperature environment. Due to their superior performances in high temperature applications, these FGMs are also recognized as potential materials for rotating machinery components like shafts, blades etc. Similar to homogeneous structures, presence of cracks in functionally graded (FG) shafts also make a serious threat to their safe performances. It is therefore important to understand the dynamic behavior of such FG shafts under loading. Therefore, the present dissertation deals with finite element (FE) formulation and analysis of a FG shaft with transverse breathing crack/cracks in a rotor-bearing system. The FG rotor system is considered to comprise a set of interconnecting components consisting of shaft elements with internal viscous and hysteretic damping, rigid discs and bearings. Hamilton’s principle and Lagrangian equation have been used to derive the equations of motion for FG shaft element and rigid disc element respectively. Two noded Timoshenko beam element with four degrees of freedom (DOF) per node is used considering the effects of translational and rotary inertia, transverse shear deformations, and gyroscopic moments. The FG material is considered to be composed of aluminum oxide (Al2O3) and zirconia (ZrO2) as ceramics and stainless steel (SS) as metal. Temperature dependent thermo-elastic material properties of the FG shaft are considered graded in the radial direction following power law of material gradation. Fracture mechanics concepts have been combined with rotor dynamical system to obtained stress intensity factors (SIFs) as well as local flexibility coefficients (LFCs) of cracked FG shafts, which change the system dynamic behavior globally.
Supervisors: Debabrata Chakraborty and Rajiv Tiwari