Free and Forced Whirling Analyses of Rotors with Multiple Unbalanced Discs Under Axial Force

In this paper the set of equation for free and forced whirling analyses of rotors with any number of discs is derived. By considering gyroscopic effects, the rotor is modeled based on the Timoshenko beam theory and discs are considered as concentrated elements having both translational and rotational inertias. At the position of each disc, the rotor is imposed to distributed and concentrated axial forces which vary versus time. Also, transverse load composed of unbalanced masses and total weight of the system is considered. For forced whirling analysis, static deflection of the rotor is considered as the initial conditions and rotational speed of the rotor is considered as a time variable parameter which increases from zero to its nominal value in a limited period of time. For a simply supported rotor, the free whirling analysis is investigated using Galerkin method and using Galerkin and Newmark-beta methods, the forced whirling analysis is studied numerically. Forward and backward frequencies and Campbell diagrams are presented in free whirling analysis and variation of deflection, bending moment and shear force in any point of the rotor are depicted versus time in forced whirling analysis. The most advantages of the presented paper are consideration of time-dependency of rotating speed in forced whirling analysis and its applicability for rotors with any number of mounted discs.