Nonlinear lateral-torsional coupled motion of a rotor contacting a viscoelastically suspended stator

摘要

Interaction of a rotor with a stationary part is a kind of serious malfunction that could result in a catastrophic failure if remained undetected. Past analytical and numerical simulation work on rotor-stator interactions mainly focus on the vibrations along the lateral directions. The torsional degree of freedom (dof) is usually ignored. The present work is aimed to study the influence of a rotor to stator contact on the lateral-torsional coupled vibrations. A mathematical model consisting of interacting vibratory systems of rotor and stator is presented. The contact is modeled using contact stiffness, damping and Coulomb friction. Equations derived for kinetic, potential and dissipation energies and non-conservative external forces are used in the Langrange's equations for deriving the motion equations for the rotor-stator system. Equations revealed that the lateral-torsional motion coupling exists twofold for the rotor. The unbalance couples lateral-torsional motion of rotor through inertia and damping matrices. Coupling due to the rotor-stator friction occurs through a force vector. The nonlinear equations are solved using a Runge-Kutta fourth-order numerical integration scheme using relatively small time step. Results obtained through the proposed model are compared with the identical rotor-stator system without torsional dof and differences are identified. Effect of several parameters such as speed, relative inertia, coefficient of friction and contact damping on the bifurcation behavior of the rotor-stator motion has been investigated. Vibration motions presented in the forms of spectrum cascade of the coast-up response, and orbit and Poincaré plots of the steady-state response are exhibiting rich dynamic behavior of the system.