Derivation of Hydrodynamic Bearing Coefficients Using the Minimum Square Method

Abstract

A linear analysis of the parameters for the orbital transient response of journal-bearing systems is made with the purpose of computing the bearing dynamic coefficients using the minimum square method. The journal-bearing response is obtained from a nonlinear simulation that includes a transient solution of the Reynolds equation. The minimum square method permits the adjustment of coefficients with only one orbit and does not need prior linearization of the response. Therefore it was found to be advantageous compared with the more traditional experimental method of using a frequency domain method with two orbital responses. Three different Sommerfeld numbers were analyzed. Comparisons between the eight adjusted coefficients and the linear coefficients obtained from perturbations of the Reynolds equation about the equilibrium position permit the establishment of the ranges where the bearings behave linearly.

Nonlinear Prediction of Rotordynamic Coefficients For a Hydrodynamic Journal Bearing

“…The relative percentage deviations of dynamic coefficients with force magnitude are predominantly higher for external load orientation of a=O" than for a=90°. Muller-Karger and Granados (11) obsewed that when the application of dynamic load is in horizontal direction, then the orbits are slender and nonlinearities are predominant compared to case when the dynamic load is in the direction of rotor weight (i.e., in a vertical direction).…”

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

“…It is shown that all the higher order coefficients K xyy , K yyy , C xyx , C yyx , C xyy , C yyy decrease in the range of their values with increase in L/D ratios from 0.5 to 1.5, which is similar to the variation of higher order coefficients contained in the expressions for coefficients K xx and K yx . The variation of the stiffness and damping coefficients along the journal orbit is considered for various journal operating conditions, similar to those studied by Muller-Karger and Granados (1997). The bearing parameters, operating conditions and the type of external dynamic load are given in Table 2.…”

“…Results using the above nonlinear model indicate that the linearized bearing coefficients are valid for 0.06 of displacement perturbations. Muller-Karger and Granados (1997) presented a methodology wherein the dynamic coefficients are adjusted using minimum square method for one orbit. Their studies indicated that nonlinearity depends on the size and shape of the orbital motion.…”

Evaluation of the determinant of identification equations for a linear model of a mechanical vibratory system

“…Recent publications, however, have shown that time-domain methods are simpler and more effective. Most interesting in this regard are papers [12,13] in which the time-domain approach is combined with the method of least squares and it is shown that the necessary number of tests is less than in frequency-domain methods.…”

“…Recent publications, however, have shown that time-domain methods are simpler and more effective. Most interesting in this regard are papers [12,13] in which the time-domain approach is combined with the method of least squares and it is shown that the necessary number of tests is less than in frequency-domain methods. where P is an n x n matrix of unknown coefficients, z is an n-dimensional phase column-vector (the vector of deviations of the generalized coordinates and velocities from the values in steady motion) and t is the time; a dot denotes differentiation with respect to t. Present-day measuring equipment yields numerical values of the generalized coordinates and applied forces as continuous functions of time.…”