Linear and Nonlinear Behavior Analysis of a Flexible Shaft Supported By Hydrostatic Squeeze Film Dampers

摘要

Linear and non linear models of a hydrostatic squeeze film damper are presented and numerically simulated by a step by step method on a modal basis, in order to stud y the non -linear dynamic behaviour of a flexible shaft. The Reynolds equatio n is solved at each step in order to evaluate the film forces. The eq uations of motion are then integrated by using the Newmark method with a variable step in order to obtain speeds and the position for the next step. The non-linear hydrostatic forces are determined by the application of the boundary conditions, and the integration of the pressure field is determined by resolution of Reynolds equatio n, by applying the central finite difference method. The aim o f this research is to study the effect of pressure ratio, viscosity, and rotational speeds on the vibratory responses and the transmitted bearing forces. The results are discussed, analysed and compared to a linear approach which is restricted to only small vibrations around the equilibrium position. The results show good agreements between linear and non -linear methods when the unbalance force is small, and then the linear model may be used for small vibrations in order to reduce compilation time during the iterative process