Dynamic Instability of High-Speed Rotating Shaft with Torsional Effect

Abstract

Today’s design of machine rotor requires the rotor to operate at a high rotational speed to improve the efficiency of the machine. However, the existence of disturbances such as periodic axial load may cause parametric resonance to the rotor system in addition to the common force resonance. Previous studies on this parametric resonance of shaft typically included the element of translational and rotary inertia, gyroscopic moments and bending and shear deformation but surprisingly neglected the effect of the axial torque. This paper investigated the parametric instability behaviour of the shaft rotating at high speed while considering the torsional effect of the shaft. Based on the finite element method, a shaft model that includes torsional deformation as one of its degree of freedom was established. The Mathieu-Hill equation was derived, and then the Bolotin’s method was used to solve the equation by establishing the parametric instability chart. Two types of the rotary system were studied: a shaft with different boundary conditions and shaft with different bearing types. The results were initially validated with past findings. Following that the results were compared to the results correspond to the Timoshenko’s beam formulation that omits the torsional degree of freedom. The effect of axial torsional deformation was found to be very significant especially at high speed. The developed model in this study shows that at the shaft speed of 40000 rpm, the effect of torsional deformation has given the difference of more than 100% in the frequency ratios correspond to the 4DOF and 5DOF models for the case of fix-free boundary condition.