Critical-Speed Behavior of Unsymmetrical Shafts

Abstract

Abstract The development of large two-pole turbine generators with rotors running above the critical speed, and having long core bodies slotted for field coils, makes desirable a working familiarity with the vibrational characteristics of unsymmetrical shafts. It is the purpose of this paper to describe these characteristics which are distinctly peculiar. This problem has received some attention from previous writers (6-9), who have pointed out an unstable range of operation due to dissymmetry of the shaft, and some of whom made small-scale tests for demonstration. In the present investigation, experimental work on a special rotor of 10 1/2 ft span and weighing over 5000 lb was carried out, to test in some detail the indications of a thorough analysis of the problem by the late V. Petrovsky of the Lynn Works of the General Electric Co. This analysis is given in outline in an Appendix. The first part of the paper deals briefly with the static characteristics of unsymmetrical shafts, as a basis for defining the “degree of dissymmetry.” The critical-speed behavior of ordinary round shafts is then reviewed and the theoretical differences due to dissymmetry are described. These are: (a) With moderate dissymmetry compared with the degree of damping, a marked increase in the critical-speed amplitude, and a pronounced variation in the amplitude with the angular position of the unbalance of the rotor; (b) with greater dissymmetry, beyond a limiting value, an infinite critical-speed amplitude, or rather, two infinite peaks, with unstable operation between them; (c) considerable distortion of the phase-angle curves, such that in general the phase angle may be much larger or smaller than 90 deg at the critical speed; (d) double-frequency vibration, if the shaft is horizontal, with an auxiliary peak, or “subcritical” at half the main critical speed. Tests on the 5000-lb rotor are described which give general confirmation of these characteristics.