STABILITY INVESTIGATION OF ROTORS EXCITED BY UNBALANCE OF THE ROTATING PARTS AND SUPPORTED BY SHORT NON-CIRCULAR FLUID FILM BEARINGS

Abstract cze:
Abstrakt: Properties of fluid film bearings are significantly influenced by the shape of the cross section of the holes in the bearing shells. In computational models they are usually incorporated by means of nonlinear force couplings. To determine components of the hydraulical forces it is necessary to solve a Reynolds' equation to obtain a pressure function that describes a pressure distribution in the oil layer. In the case of short bearings the pressure function can be expressed in a closed form. If at some location in the bearing gap the pressure drops below a certain limit, a cavitation takes place. Accommodation of this phenomenon in the computational procedure assumes that pressure of the medium in cavitated areas remains approximately constant. Components of the bearing forces are then calculated by means of integration of the pressure distribution around the circumference of the bearings. The considered model rotor systems are able to cover all significant properties of the real ones. Their steady state response on excitation produced by centrifugal forces due to unbalance of the rotating parts can be determined for a certain class of problems by application of a trigonometric collocation method. To perform stability and bifurcation analysis a perturbation technique based on utilization of a Floquet theory has been used. Principal steps of this procedure consist in setting up a transition matrix over the span of time of one period and in calculation of its eigenvalues.

Abstract eng:
Abstract: Properties of fluid film bearings are significantly influenced by the shape of the cross section of the holes in the bearing shells. In computational models they are usually incorporated by means of nonlinear force couplings. To determine components of the hydraulical forces it is necessary to solve a Reynolds' equation to obtain a pressure function that describes a pressure distribution in the oil layer. In the case of short bearings the pressure function can be expressed in a closed form. If at some location in the bearing gap the pressure drops below a certain limit, a cavitation takes place. Accommodation of this phenomenon in the computational procedure assumes that pressure of the medium in cavitated areas remains approximately constant. Components of the bearing forces are then calculated by means of integration of the pressure distribution around the circumference of the bearings. The considered model rotor systems are able to cover all significant properties of the real ones. Their steady state response on excitation produced by centrifugal forces due to unbalance of the rotating parts can be determined for a certain class of problems by application of a trigonometric collocation method. To perform stability and bifurcation analysis a perturbation technique based on utilization of a Floquet theory has been used. Principal steps of this procedure consist in setting up a transition matrix over the span of time of one period and in calculation of its eigenvalues.

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