A new modeling approach for an eigenvalue analysis of a shrink-fitted shaft-disc assembly

Abstract

An assembly of a disc shrink-fitted on a shaft are widely used in industry to provide a tight mounting enabling a positive drive. Although this kind of mounting alleviates the need for keyways and keys, the contact pressure from the interference fit generates localized stress and deformation in the shaft and the mounted disc. The increased stress may influence the natural frequencies and the dynamics of the shaft depending on the disc/hub dimensions. Earlier, the effect of such a disc mounting was accounted for in the model by raising the diameter of the shaft at the mounting location, without systematically studying the effect of the varying degree of the interference fit. The present work introduces a novel analytical approach to account for the shrink-fit of the mounted disc on the shaft for different interference fit levels and shaft-disc configurations (disc diameter and thickness). The contact pressure due to shrink fit is modelled as a uniform axisymmetric pressure band in the shrink fit region. The stress and deformation in the shaft and disc are evaluated using the Fourier-Bessel formulation. The proposed method utilizes mathematical formulation to evaluate the fit-induced axial stress and the corresponding increase in the stiffness. The method then estimates the required diameter of the step at the shrink-fit region more precisely than predicted by a previous approach. The objective is also to investigate the extent of the influence of the induced local stress due to the shrink fit on the bending natural frequency of the shaft-disc assembly. To validate the proposed approach, an experimental modal analysis is performed on the test specimen with shrink fit and the measured natural frequencies are compared with the calculated ones. The experimental natural frequencies for off-center shaft-disc configurations and overhung shaft-hub configurations are within 5 % of those obtained theoretically, signifying the capability of the proposed mathematical approach to model the shrink-fit assembly accurately. In contrast to the empirical approach of modeling the shrink fit, the novel modelling approach presented in the paper offers a systematic and better way of modeling and of accurately predicting the associated bending natural frequencies.