A Nonlinear Dynamic Model With Confidence Bounds for Hydrodynamic Bearings

In conventional rotordynamic modeling, hydrodynamic bearings are often characterized by a set of linear stiffness and damping coefficients obtained from a first-order Taylor series expansion of bearing reactions. Theoretically, these coefficients are only valid for small amplitude motion about an equilibrium position. In this paper, a nonlinear dynamic model that overcomes the small amplitude assumption in the conventional linear analysis is described. By including higher-order terms in the bearing reaction expansion, nonlinearity in the oil film forces for large amplitude motion can be captured and represented by a set of nonlinear stiffness and damping coefficients. These coefficients are functions of static bearing displacement. A finite difference approach is described and is used to solve for these coefficients. The stated model is applied to a conventional slider bearing and a mechanical smart slider bearing that experiences large variations in load. Error assessment is performed numerically on the higher-order solutions to determine an acceptable displacement bound for the higher order coefficients.