Whirling Analysis of Stepped Timoshenko Shaft Carrying Several Rigid Disks

Abstract

Rotor system is the main part of turbomachines. Critical speeds occur when the rotor spin-speed matches with its natural frequencies, and result in great vibration amplitudes often leading to catastrophic failure. Design specifications based on these critical speeds become essential for the engineer. In this paper, whirling vibrations of a spinning, stepped Timoshenko shaft carrying three identical rigid disks are solved using a developed program in Fortran 90 language, based on relationships between the solution coefficient vectors of differential equations of motion. The flexural vibrations are considered in two orthogonal planes. Shear deformation, rotary inertia, and gyroscopic moments are taken into account. This study shows that in the case of the Timoshenko model, the relationship matrix form between the aforementioned vectors presents an advantage, that reduces the number of multiplied matrices when adjacent shaft segments have the same mechanical and geometric properties. The presented approach and Natanson's technique are combined to determine the whirling mode shapes. The accuracy of the presented technique is confirmed by comparing the obtained results with those available in the literature.