Shape of a Wire in a Centrifugal Field—Application to Quasi-Circular Bare Filament Flywheels

Abstract

In order to calculate the stress distribution in bare filament rotors it is necessary to evaluate with good approximation the shape taken by the wires in the centrifugal field (sometimes referred to as “polar catenary”). This problem is usually solved via a numerical integration of the equilibrium equation of the wire. In this paper a series solution of the same equilibrium equation is obtained. The calculation of the stress distribution in the rotor, which is an interative one and requires the evaluation of the shape of each wire several times, becomes faster and can be performed also in those conditions in which the numerical calculation failed (i.e., at low speed, when the “subcircularity” of the wires is too great to be taken into account in that way). Photographic and photoelastic tests are in good agreement with theoretical results.