Finite-element vibration analysis of a cantilever plate with a central circular hole subject to an in-plane moving (rotating) load

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 vector rolling over the housing. For accurate estimation of the casing annulus ͑circular hole͒ dynamic deformations, which in turn affect bearing tolerances and the magnitude of the generated forces, the effect of the load rotation ͑motion͒ on the housing vibration should be considered. Considering the integral casing and outer ring to be a plate, an isoparametric plane stress finite-element ͑FE͒ based analytical procedure is presented for dynamic analysis of housing as affected by load vector rotation. 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. Results in both time and frequency domains are discussed and it is found that higher load rotational speeds decrease deformations and increase the smoothness of the annulus surface. With lower speeds, the deformations are always positive ͑contraction͒, and at higher speeds they exhibit both contraction and expansion around the annulus circumference. The vibrations measured at the casing outer surface show that the spectrum in the direction of casing rigid support attracts more system natural frequencies compared to the orthogonal direction spectrum. This underlines the importance of the vibration measuring probe͑s͒ orientation with respect to the casing rigid support direction to capture all the important vibrations.