Equivalent Linearization of a Squeeze Film Damper

Abstract

In this paper, the equivalent linearization of an intershaft squeeze film damper in a two shaft engine system is investigated. The two shaft centers at the damper position are assumed to move in different elliptical offset orbits and at synchronous frequency with the unbalanced rotor (e.g., the high pressure rotor). The nonlinear damper force is resolved into two orthogonal components along the absolute coordinate directions and, in turn, each of these force components is supposed to be equivalent to the sum of an average force, a linear spring force, and a linear damping force in the corresponding direction. By using the method of equivalent linearization by harmonic balance, the six parameters of the equivalent forces, including two average forces, two equivalent spring coefficients, and two equivalent damping coefficients, are expressed analytically by the squeeze film forces and the assumed orbital motion of the two shaft centers at the damper position. The analytical expressions of the squeeze film forces are derived from an approximate solution of the basic Reynolds equation. The results obtained are verified by the method of equivalent linearization by minimum mean square errors. It shows that the six obtained parameters make the mean square errors minimum over a cycle period of motion, the errors being the difference between the equivalent forces and the actual nonlinear forces.