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# Dynamics of Machinery 2D Elastic Casing, with Central Hole, Subject to an In-Plane Deflection-Dependent Rotating Load

F. M. A. El-Saeidy1

1 Damro-Salman,Desouk,Kafr-El-Sheikh, Egypt

Computer Modeling in Engineering & Sciences 2000, 1(3), 33-42. https://doi.org/10.3970/cmes.2000.001.335

## Abstract

In rotating radial ball bearings supported on elastic casings with the bearing outer ring lightly fitted into the housing, the force due to the ball elastic contact is indeed a rotating load rolling over the housing. For accurate estimation of the dynamic deformations of the casing annulus (hole), which in turn affect the bearing tolerances and hence the magnitudes of the generated forces, effect of the load rotation (motion) should be considered. Considering the integral casing and the outer ring to be a plate, an isoparametric plane stress finite-element (FE) based analytical procedure is presented for the dynamic analysis of the housing as affected by the load vector rotation. The Hertz equation for elastic contact is used to model the nonlinear elastic coupling between the external moving load and the vibrations of the housing. The equations of motion are obtained using Lagrange's equations and decoupled using the normal coordinates representation and solved using a special numerical integration scheme. The computations are carried out using the FE program 'DAMRO 1' and the results are discussed using time domain, motions in the state plane, Poincare' return map, and FFT. The results show that the overall amplitudes of the deformation vector around the annulus circumference and hence amplitudes of the dynamic load vary between maximum in the direction of the casing rigid support and minimum in the orthogonal direction. These regular variations can initiate/accelerate fatigue in the elastic components of the system. The vibrations measured at the casing outer surface show that the dominant peak in the horizontal direction and the one in the vertical direction do not coincide. And this recommends using one vibration measuring probe in the horizontal direction and another probe in the vertical direction, to capture all the important vibrations.

## Keywords

M., F. (2000). Dynamics of Machinery 2D Elastic Casing, with Central Hole, Subject to an In-Plane Deflection-Dependent Rotating Load. CMES-Computer Modeling in Engineering & Sciences, 1(3), 33–42.

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