A Nonlinear Model for Prediction of Dynamic Coefficients in a Hydrodynamic Journal Bearing

Abstract

This paper investigates the variation of nonlinear stiffness and damping coefficients in a journal orbit with respect to equilibrium position. The journal orbit is obtained by the combined solution of equations of motion and Reynolds equation.In the linearized dynamic analysis, dynamic pressure is written as a perturbation of static pressure and pressure gradients at equilibrium position. However, in order to obtain nonlinear dynamic coefficients about equilibrium position, the dynamic pressure gradients in the orbit are also written as the first order perturbation of static pressure gradients and higher order pressure gradients for displacement and velocity perturbations. The dynamic coefficients are functions of bearing displacement and velocity perturbations. The higher order pressure gradients at equilibrium position are evaluated at various eccentricity ratios and L/D ratios of 0.5 and 1.0. The variation of nonlinear dynamic coefficients is analyzed for three Sommerfeld numbers of a two-axial groove journal bearing under the action of an external synchronous load along and perpendicular to the radial journal load. Results indicate that the oil film nonlinearities affect the journal motion at lower eccentricity ratios (higher Sommerfeld numbers) with wide variation in stiffness and damping coefficients.Linearized stiffness and damping coefficients are widely used for the stability and journal response of rotor bearing systems.In the linearized analysis, bearing stiffness and damping coefficients can be evaluated at the journal equilibrium position. However, the linearized dynamic coefficients do not provide insight into the variation of dynamic coefficients for large amplitude journal motion about equilibrium position. Fluid film forces in a journal bearing are nonlinear functions of journal center positions and velocities. The large amplitude journal (transient motion is generally obtained by nonlinear analysis which is based on the combined solution of governing Reynolds equation and journal equations of motion at each time step. However, it is important to estimate the variation of dynamic coefficients along the journal orbit in order to determine the degree of nonlinearity of the orbital response. Lund's (1978Lund's ( , 1987 infinitesimal perturbation method or finite perturbation approach (Qiu and Tieu, 1996) are used for evaluation of linearized stiffness and damping coefficients about journal equilibrium position. Lund (1987) reported that although the dynamic coefficients are evaluated by infinitesimal approach, they are valid up to a 0.4 of the bearing clearance. Qiu and Tieu (1996) calculated the dynamic coefficients at different perturbation amplitudes. They concluded that perturbation displacements and velocities should be within 5% and 4%, respectively, to keep the difference between the coefficients obtained from finite and infinitesimal perturbations under 2.5%. Hattori (1993) analyzed the variation of stiffness and damping coefficients with large dynamic loads over one rotor revolution of a jo...

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Nonlinear model identification of oil-lubricated tilting pad bearings

“…They concluded that the proposed nonlinear modeling of oil film forces can be employed in the nonlinear dynamic analysis of other types of oil-film bearings. The aforementioned research [9][10][11][12][13][14][15][16][17][18] have indicated the ability of the nonlinear models based on higher order Taylor series expansion of oil film forces to identify the nonlinear effects within the associated journal bearings.…”

“…Variations of nonlinear dynamic coefficients with reference to the linear ones were presented to establish a criterion for using the linear coefficients in different operating conditions. In a similar study [14], the variation of nonlinear stiffness and damping coefficients along the journal orbit with respect to equilibrium position was investigated. It was shown that the degree of nonlinearity introduced into the nonlinear dynamic coefficients in the nonlinear analysis might be larger at low eccentricity ratios than at high eccentricity ratios.…”

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