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

Abstract

One of the most important problems of rotor-bearing systems, the stability problem, especially in the case that the rotor is in misaligned position in respect with the bearing, is examined in this paper. Lyapunov's direct method was preferred in this analysis instead of a classical eigenvalue analysis in order to obtain the stability conditions in the form of analytical, expressions.

The eight dynamic coefficients (four stiffness and four damping) for the aligned, journal bearing or the 32 dynamic coefficients (16 stiffness and, 16 damping) for the misaligned case can be used here, in order to obtain, the analytical stability conditions and the stability charts. The results of the present investigation are compared with the results and. experiments in the literature and are found to be in good agreement.

The rigid, rotor model was chosen for work in order to concentrate on the misaligned bearing behavior, thus avoiding the flexible shaft influence on the system. The model used is comprised of a rigid rotor mounted on two linear isotropic misaligned bearings and is used to develop closed-form stability criteria.

Using the method presented, in this paper, the analytical expressions for the stability of misaligned journal bearings are obtained in the closed form of inequality constraints. The influence of the misalignment angles on the stability of the system is demonstrated as a function of the slenderness ratio and the dimensionless mass.

Finally, the comparison of the stability ranges, using first the eight and then the 32 dynamic coefficients, gives the degree of importance of all these terms, and from total point of view of the proposed method.

KEY WORDS:

• Journal Bearings
• Hydrodynamic Lubrication