“Snapping” Torsional Response of an Anisotropic Radially Loaded Rotor

Abstract

A rotor system with two orthogonal lateral and two angular (torsional) degrees of freedom is considered. The rotor has asymmetry of the lateral stiffness and is laterally loaded with a constant radial force and a rotating unbalance. Constant driving and load torques are applied to the rotor. The important part of the research includes an analysis of “snapping” action, when, during rotation, the rotor experiences a peak of torsional acceleration. This occurs when the “strong stiffness” axis of the anisotropic rotor passes under the axis of the sideload. The numerical simulation of the analytical model exhibits a snapping (accelerated) torsional response of the rotor at twice synchronous frequency (2×), and it is especially pronounced at 1× and 2× torsional resonances. The snapping response can initiate a rotor crack in the area of stress concentration, can stimulate existing crack propagation, and can be a cause of the coupling failure. The analytical results are obtained by the Averaging Method application. They confirm the numerical results and show the possibility of combination resonance occurrences. The synchronous dynamic stiffness for the frequency range around 1× lateral resonance is analytically obtained. The specific shape of the quadrature dynamic stiffness component can serve as a shaft crack indicator and can be used for early detection of a lateral crack on the rotor.