Plastic Design of Rotating Discs

Abstract

The labour involved in calculating stresses in turbine or compressor discs is usually considerable. The equations cannot in general be solved explicitly, and tables and charts must be used. The basic difficulty arises from the fact that a second-order non-linear differential equation governs the problem. If, however, attention is confined to the condition at which the disc is on the point of collapse, that is, at which the whole of the disc has just become plastic, the problem is simplified considerably. Instead of using an elastic ‘safety factor’ on stress, an overspeed factor is used; further, one of the stress components is known at collapse, and only a first-order differential equation has to be investigated. This plastic design method will lead to profiles similar to those given by elastic design, but the calculations are much more rapid. At the end of the paper is given a fully worked design example; before reading the bulk of the paper, the designer may wish to compare this plastic design with the results given by one of the more usual methods.