Application of Transfer Matrices to Non-Linear Rotor Bearing Systems

Abstract

Abstract To obtain the steady state unbalance response of rotor bearing systems, it is common to linearise the hydrodynamic bearing forces about their static equilibrium position. Such linearisation is increasingly approximate with increasing unbalance as it ignores the possibility of typical non-linear phenomena such as sub- and super-harmonic response and multi-stable response. Even in the case of mono-stable synchronous response, the amplitudes are differently attenuated as a result of non-linear effects. This paper shows how the transfer matrix approach, traditionally applied to linear systems, can be extended to evaluate the steady state response of non-linear systems, using harmonic balance to accommodate the various response harmonics. The technique is illustrated using a hydrodynamic journal bearing and a squeeze film damper as the non linear elements.