Some Observations on the Vibration and Whirling of Continuously Loaded Spindles

Abstract

Formulas are derived for the frequency of flexural vibration of a vertical uniformly tapered circular shaft mounted at one end. The Rayleigh and Dunkerley methods are used and the results compared both with known results of exact analysis and with experi ment.On the basis of an extension of Dunkerley's principle, a simple formula is derived for the effect of the mass of a textile package on the critical speed of a vertical shaft held at its base.