Unbalance Response of a Multi-Mode Rotor Supported on Short Squeeze Film Dampers

Abstract

This paper describes a fast algorithm to obtain the steady state unbalance response of a multi-mode rotor supported on short squeeze film dampers (SFDs). The presented algorithm is developed based on planar modal theory. Undamped critical speed analysis is first performed to obtain the rotor critical speeds and their associated mode shapes. The modal analysis technique is then applied to the linear part of the rotor-SFD assembly to obtain the system differential equations. The rotor is assumed to execute circular centered orbits, hence all differential equations are reduced to algebraic ones. The resulting equations are manipulated algebraically to form a polynomial in rotor rotational speed. The roots of the polynomial are found and the full unbalance response is obtained. A conventional rotor is used to describe the developed algorithm numerically. Results show that the proposed algorithm gives accurate response in comparison to that obtained by integrating the system differential equations numerically. The great advantage of the proposed algorithm is the saving in the execution time which is extremely dramatic with respect to numerical integration, in addition to other advantages such as the possibility of obtaining all solutions occurring in regions of multiple steady state. Accuracy and speed of execution are quite advantageous regarding parametric studies on multi-mode rotors. These parametric studies can help in the optimization of SFDs design.