Lyapunov’s Stability of Non-Linear Misaligned Journal Bearings

Abstract

In this paper the stability of non-linear misaligned rotor-bearing systems is investigated, using the Lyapunov direct method. A finite element formulation is used to determine the journal bearing pressure distribution. Then the linear and nonlinear stiffness, damping and hybrid (depended on both displacements and velocity) coefficients are calculated A general method of analysis based on Lyapunov’s stability criteria is used to investigate the stability of non-linear misaligned rotor bearing systems. The equations of motion of the rigid rotor on the non-linear bearings are used to find a Lyapunov function using some of the above coefficients, which are depending on L/D ratio and the misalignment angles ψa, ψr. The analytical conditions for the stability or instability of some examined cases are given and some examples for the orbital stability are also demonstrated.

Dynamic Stability of Linear Misaligned Journal Bearings Via Lyapunov's Direct Method©

“…From Eqs. [I81 and[19], the followi~lg additional conditions for the stability are obtained:where A K, BK, A I B1 and C I , , 13, K, P are defined in Ref.(23). Similar expressions are obtained for the minors of the damping determinant.…”