Modelling of a Porous Functionally Graded Rotor-Bearing System Using Finite Element Method

In the present work, a functionally graded (FG) Jeffcott rotor system, consisting of a uniform steel disc, an FG shaft and linear isotropic bearings, is considered. While fabricating an FGM, the formation of porosities is inevitable; hence it is one of the foremost imperfections to consider while assigning material properties, as well as, modelling the FG rotor-bearing system. Dynamic modelling of a porous functionally graded rotor-bearing system has been carried out using the finite element method (FEM) to compute natural frequencies. A two-noded porous FG shaft element with four degrees of freedom (two translational and two rotational) on each node has been developed using Timoshenko beam theory (TBT) by including the effects of translational inertia, rotatory inertia, gyroscopic moments, transverse shear deformation and volume fraction of porosity. An FG shaft, whose inner core is composed of metal, which is stainless steel (SS), and outer layer made of zirconia (ZrO₂) is considered to investigate the effect of porosity and the power-law index on natural frequencies. A finite element code is developed using Python to calculate the radial variation of material properties, as well as, to solve the eigenvalue problem of a porous FG rotor system. The natural frequencies of the FG rotor-bearing system have been calculated for different power law indices and volume fractions of porosity. It is deduced that the natural frequencies are affected due to the influence of the power-law index and volume fraction of porosity.