Parametric instability of static shafts-disk system using finite element method

Abstract

Parametric instability condition is an important consideration in design process as it can cause failure in machine elements. In this study, parametric instability behaviour was studied for a simple shaft and disk system that was subjected to axial load under pinned-pinned boundary condition. The shaft was modelled based on the Nelson's beam model, which considered translational and rotary inertias, transverse shear deformation and torsional effect. The Floquet's method was used to estimate the solution for Mathieu equation. Finite element codes were developed using MATLAB to establish the instability chart. The effect of additional disk mass on the stability chart was investigated for pinned-pinned boundary conditions. Numerical results and illustrative examples are given. It is found that the additional disk mass decreases the instability region during static condition. The location of the disk as well has significant effect on the instability region of the shaft.