In the analysis of HD journal bearings the effect of fluid inertia is generally neglected in view of its negligible contribution compared with viscous forces. However, there is a necessity to evaluate its influence at moderate values of the modified Reynolds number. An attempt is made to study the effect of inertia forces of the lubricant on the stability of finite journal bearing for a flow in a laminar regime. Furthermore, the stability analysis is extended to bearing with elastic layer on the shaft. In this way a complex solution of the problem is achieved with consideration of the shaft motion, instigated from the unbalanced HD forces of lubricant. The generalized Reynolds equation is obtained by averaged acceleration method. To solve the elastic part of the problem without linear approximations, a new, more precise method of displacements determination is used. In present study modified stability criteria by Hurwitz and Ljapunov are introduced. An adaptive procedure for determination of critical stability of the considered dynamic system is used.

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