Analysis of Rotor Supported in Double-Layer Porous Journal Bearing with Gyroscopic Effects

In this paper, a numerical analysis on the dynamics of a multi-degree of freedom shaft–rotor, supported on bearings, is presented. The system is a shaft with multiple rotor discs attached to it and supported on double-layer porous journal bearings. The system is modelled using finite element methods. Euler-Bernoulli beam element theory is used for modelling the shaft. The discs are considered as rigid. The support bearings are modelled based on linear spring elements for stiffness and linear damping elements for viscous damping coefficients. The rotor dynamic model of the system is analysed by incorporating the gyroscopic effects due to the precession of the offset discs and the bearing stiffness and damping anisotropy. The fluid flow in double-layer porous film is analysed using Brinkman equations to consider lubricant additives influences. The pressure gradients with respect to linearized perturbation of displacements and velocities under dynamic conditions are derived using Reynolds modified equation for Ocvirk (short) bearing. The dynamic linear and cross-coupled coefficients (stiffness and damping) dependent on speed are calculated using dynamic pressure gradients for the double-layer porous journal bearings. The system is represented in reduced order state-space form, and eigen value problem is solved to calculate its whirl frequencies. The rotor system critical speeds are obtained by plotting the Campbell diagram. This paper provides the basis for rotor system design with support bearings, representative of a multi-stage centrifugal pump. The design helps to identify and prevent rotor vibrations.