An Energy Approach to Linearizing Squeeze-Film Damper Forces

Analyses of multi-degree of freedom rotor-bearing systems incorporating non-linear elements, such as squeeze-film dampers, generally necessitate time consuming transient solution. Consequently, it is often too expensive to carry out parametric design studies on such systems. This paper presents a general technique for linearizing the non-linear element forces using equivalent stiffness and damping coefficients with energy dissipation and energy storage-release concepts. The approach is illustrated and tested for both centrally preloaded squeeze-film dampers and for squeeze-film dampers without centralizing springs under a combination of unidirectional and unbalance loading. The results predicted by using such equivalent stiffness and damping coefficients agree quite well with those obtained from the full transient solution, even where the unidirectional load exceeds the dynamic load and the damper is operating at high eccentricity. An iterative procedure is proposed which, with the aid of such stiffness and damping coefficients, should significantly reduce the computation time presently needed to carry out parametric design studies on general multi-degree of freedom systems incorporating non-linear elements such as squeeze-film dampers.