Nonlinear Response of Short Squeeze Film Dampers

This paper considers the methodology of numerical integration for prediction of dynamic response of squeeze film damper systems. A planar rotor carried in a squeeze film damper with linear centering spring is considered. Governing differential equations are expressed in polar coordinates, and fluid forces are obtained from the Ocvirk short bearing integrals. The rotating unbalance response is presented as a function of speed, unbalance, and a bearing parameter. Runge Kutta integration techniques are used to obtain numerical solutions for transient response and frequency response. The 2π film approximation results in almost linear frequency response curves. However, the π film response is very nonlinear, demonstrating the well known multiple valued response and associated hardening jump/drop phenomenon. The π film transient response is analyzed within the speed range of bistable operation to determine the effects of initial conditions, the domains of convergence, and the relative strengths of stability of each solution. The transient response is found to be most sensitive to initial values of phase angle and phase angle velocity. Initial eccentricity and eccentric velocity are much less important. In general, of the two steady state solutions, the one with lower eccentricity appears to be more stable, with a larger domain of convergence. Examples show how premature termination of the integration can lead to erroneous conclusions.