Ring model of railroad wheel vibrations

A ring model for prediction of the vibration characteristics of railroad wheels is presented. Earlier workers showed that ring theory gave a good explanation of the ratio of resonant frequencies in the railroad wheel, assuming flexural modes are excited in the rim. It was assumed that the massive rim drove the plate of the wheel in forced vibration. In this paper the wheel is modeled by taking the flange, the rim, and the plate as a series of elastically connected concentric rings. The differential equations governing normal mode flexural vibrations are developed for such a system of n elastically connected rings, based on the general equations developed by Love. The free vibration of the system, with displacements both in the plane and out of the plane of the wheel was studied. Modifications were made to include wear on the flange and tread. The effect of hoop stresses in the rim was also modeled. The results agree well with those from other theoretical models and also with experimental values. [Work supported by Association of American Railroads.]