Approximated Stiffness Coefficients in Rotor Systems Supported by Bearings with Clearance

Many kinds of rotating machinery are supported by bearings with clearance, which are further clamped in a supporting structure. When designing such machinery it is important to be able to predict dynamics and hence valid models are needed. Due to gravity, the shaft often vibrates close to a static equilibrium position leading to a possibility to linearise the equation of motion. Although several studies on bearings with clearance exist, there are still no reports on how such clearances affects the stiffness coefficients close to a static equilibrium position. Therefore, analytical expressions for such approximated pedestal stiffness coefficients have been derived in this paper. By using such approximated pedestals in simple rotordynamical models, it was found that the eigenfrequencies decrease significantly with clearance. It is further shown that the approximated pedestal stiffness coefficients only will be valid for vibrations close to the static equilibrium position