NONLINEAR VIBRATIONS OF FLEXIBLE HIGH-SPEED ROTORS SUPPORTED BY VISCO-ELASTIC BEARINGS

In the present paper, the dynamics of the rotor of an exhaust gas turbocharger for passenger cars is studied. The non-linear equations of motion of the flexible rotor are derived by means of the Lagrange equations in combination with a Ritz method directly resulting in a set of nonlinear ordinary differential equations of motion. The floating frame of reference formulation (FFRF) is used, where the orientation of the rigid rotor is defined by three suitable Bryant angles. The elastic deformation is described by Ritz approximations using linear elastic modes of the non-rotating rotor. The corresponding modes are obtained from a detailed 3D model of the elastic rotor in ANSYS. The kinetic energy of the system as well as the potential energy and generalized forces are needed to set up the Lagrange equations, which are derived by means of the symbolic code MATHEMATICA. In order to study run-up simulations and resonance phenomena, no linearization of the resulting equations of motion are performed. The resulting spatial integrals over the rotor domain are evaluated a-priori to the time-integration leading to a significant improvement of computation time. Time-integration of the equations of motion is performed with the implicit time integration code HOTINT. CPU time for a run up simulation of the rotor system using the presented approach is very short in comparison to conventional multi-ody dynamics software. The results obtained from the full nonlinear set of equations are compared to different sets of linearized ones.