The calculation of whirling speeds of a system of rotors keyed to co-axial shafts

Abstract

The whirling of shafts carrying rotors is a subject which has attracted the attention of many engineers and mathematicians notably Dunkerley, Chree, Stodola, Jeffcott and Morris during the past fifty years. The last mentioned writer has given some valuable historical surveys and criticisms in addition to his own elucidation of several aspects of the general problem. The main purpose of this paper is to bring the calculation of whiffing speeds of an important class of systems within the scope of the iterative technique of Duncan and Collar, and to demonstrate by theory and example that problems involving large numbers of degrees of freedom may thereby be efficiently dealt with. It would appear that the power of this iterative method is not so widely appreciated as it might be. One erroneous belief is that the utility of the method ceases whenever slow convergence of the iteration ensues. An additional refinement of procedure, which the writer has exploited, allows two or more modes to be extracted more or less simultaneously from an iteration which is converging slowly.