The Eigenvalue Dependence of Reduced Tilting Pad Bearing Stiffness and Damping Coefficients

A method is presented for calculating reduced tilting pad bearing stiffness and damping coefficients eliminating the explicit dependence of the pad degrees of freedom. Previous analyses are extended to include the real part of the system eigenvalues, so the present analysis is applicable to general free damped vibratory motion as well as synchronous and nonsynchronous steady state response previously considered. The number of coefficients is reduced from a total of 2(5n + 4), when the pad rotational degrees of freedom are retained, to eight, the number required to describe the translational dynamics of a rotor in fixed pad hydrodynamic bearings. The eight coefficients are especially suited for we in bearing optimization schemes for optimizing the stability of rotor-bearing system. Calculations are presented for five pad bearings with the static load directed between pads and with negligible pad inertia for a range of bearing preload and operating Sommerfeld number.