Stability analysis of horizontal symmetric flexible rotor mounted on hydrodynamic bearing and squeeze film damper using analytical approach

Abstract

The paper deals with the development of a close form solution to find the stability of flexible symmetric horizontal rigid and tuned flexible rotor mounted on hydrodynamic bearing with squeeze film damper system. The correlations are developed analytically to find the static equilibrium position of a rigid and flexible rotor-bearing-damper system and stability threshold of the system about its static equilibrium position under isoviscous conditions. Modified Reynolds equation with short damper approximation is used to derive the forces of hydrodynamic bearing and squeeze film damper using π-film approximation under both laminar and turbulent conditions. A simple iterative method is used to predict the stability threshold. Effects of shaft flexibility, damper support flexibility, damper mass and turbulence on stability are discussed. Deployment of squeeze film damper increases the stability limit of horizontal symmetric tuned flexible rotor-bearing system to nearly two times of its original limit and mass of damper play important role to increase the stability threshold of the system. Stability threshold of rigid system can be increased significantly by increasing the damper mass and stiffness. Insertion of turbulence reduces the limits of stability. Further work has been extended to find Thermo-hydrodynamic analysis of rotor -bearing -damper system by solving the Energy equation with adiabatic boundary conditions simultaneously with Reynolds equation with analytical approach. In case of rigid rotor bearing damper system, Thermo-hydrodynamic analysis overestimates the stability threshold as compared to isoviscous conditions, stability limit of horizontal symmetric tuned flexible rotor-bearing -damper system under estimates in comparison with isoviscous conditions till k⇀=1. Stability threshold of rigid system can be increased significantly by increasing the damper mass and stiffness.