Nonlinear forced vibrations analysis of overhung rotors with unbalanced disk

Abstract

In this paper, primary resonances of a cantilever flexible shaft carrying a rigid disk at its free end (overhung rotor) are investigated. Unbalance forces due to eccentricity and disk skew are simultaneously considered, and the shaft has initially static deflection due to the rotor’s weight which causes asymmetry in the equations of motion. The rotor has large amplitude vibrations, which lead to nonlinearities in curvature and inertia. In the model, rotary inertia and gyroscopic effects are included, but shear deformation is neglected. The method of multiple scales is applied to the discretize differential equations of motion. It is shown that the static deflection creates second-order nonlinear terms and near the primary resonances only the forward modes are excited. With considering the gravity, the inertial nonlinearities become stronger near the primary resonances. So, gravity decreases the hardening effect, and the nonlinear system tends to a linear system. It is concluded that the gravity effect has a softening effect. By using this property of gravity, a relation between weight and external forces is derived, in which by applying this relation the jumping phenomenon is eliminated. Numerical examples are presented, and the result is verified by numerical simulations.