The Dynamics of Rotor-Bearing Systems Using Finite Elements

A procedure is presented for dynamic modeling of rotor-bearing systems which consist of rigid disks, distributed parameter finite rotor elements, and discrete bearings. The formulation is presented in both a fixed and rotating frame of reference. A finite element model including the effects of rotatory inertia, gyroscopic moments, and axial load is developed using the consistent matrix approach. A reduction of coordinates procedure is utilized to model elements with variable cross-section properties. The bearings may be nonlinear, however, only the linear stiffness and viscous damping case is considered. The natural whirl speeds and unbalance response of a typical overhung system is presented for two sets of bearing parameters: (i) undamped isotropic, (ii) undamped orthotropic. A comparison of results is made with an independent lumped mass analysis.