Extended Finite Element Analysis of Journal Bearing Dynamic Forced Performance to Include Fluid Inertia Force Coefficients
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Reynolds equation governs the generation of hydrodynamic pressure in oil lubricated fluid film bearings. The static and dynamic forced response of a bearing is obtained from integration of the film pressure on the bearing surface. For small amplitude journal motions, a linear analysis represents the fluid film bearing reaction forces as proportional to the journal center displacements and velocity components through four stiffness and four damping coefficients. These force coefficients are integrated into rotor-bearing system structural analysis for prediction of the system stability and the synchronous response to imbalance. Fluid inertia force coefficients, those relating reaction forces to journal center accelerations, are routinely ignored because most oil lubricated bearings operate at relatively low Reynolds numbers, i.e., under slow flow conditions. Modern rotating machinery operates at ever increasing surface speeds to deliver more power in smaller size units. Under these operating conditions fluid inertia effects need to be accounted for in the forced response of oil lubricated bearings, as recent experimental test data also reveal. The paper presents a finite element formulation to predict added mass coefficients in oil lubricated bearings by extending a basic formulation that already calculates the bearing stiffness and damping force coefficients. That is, a small amplitude perturbation analysis of the lubrication flow equations keeps the temporal fluid inertia effects and develops a set of equations to obtain the bearing stiffness, damping and inertia force coefficients. The method does not impose on the cost of the original formulation which makes it very attractive for ready implementation in existing software. Predictions of the computational model are benchmarked against archival test data for an oil-lubricated pressure dam bearing supporting large compressors. The comparisons show fluid inertia effects cannot be ignored for operation at high rotor speeds and with small static loads. Copyright © 2012 by ASME.
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