Unbalance Response of a Jeffcott Rotor Incorporating Long Squeeze Film Dampers

Abstract

The steady state unbalance response of a Jeffcott rotor incorporating long squeeze film dampers executing circular centered precession is obtained. Fluid inertia forces are included in the model of the squeeze film dampers, using an energy approximation. The fluid velocity profiles are assumed not to change much due to fluid inertia, and the kinetic coenergy of the fluid is calculated. The fluid inertia forces are then obtained by Lagrange’s equations in conjunction with Reynolds transport theorem. The unbalance response of the rotor is obtained by assuming circular centered precession, and it is shown that fluid inertia results in the excitation of a second mode for the Jeffcott rotor and decreases the useful range of vibration isolation of the dampers. It is also shown that the second mode can exhibit the jump resonance phenomenon.