Unstable Vibrations in a Rotating Shaft System with Nonlinearity of Unsymmetry subjected to Base Excitation

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This research is presented theoretically and experimentally on unstable vibrations in a rotating shaft system with nonlinearity or unsymmetry of the shaft, where base excitation is added. Two main themes are summarized as follows :1. Forced oscillations in a nonlinear rotating shaft system subjected to base excitationThe response of a rotating shaft, whose base is excited by a sinusoidal force, is studied. The shaft has nonlinear spring characteristics due to the clearance in the ball bearings. By using the nonlinear components represented by the polar coordinates, we analyze the response of the rotating shaft. As a result, it becomes clear that the orbit of the shaft is elliptic, and that the response curve of the shaft varies intricately depending on the shaft speed. It is also found that the non-synchronous oscillation, whose amplitude varies slowly with time, occurs within the region of the excitation frequency, where the steady state solution is unstable. This oscillation contains … More many components whosc frequencies align in equal spans on both sides of the excitation frequency. In experiments, we obtained qualitatively the same results as the theoretical values.2. Unstable Vibrations of an Unsymmetrical Shaft Supported by a Flexible Base Near the Major Critical SpeedWe deal with an unsymmetrical shaft supported by a flexible base. In this system, a rotor is mounted in the middle of the shaft, and the base is movable in a transversal direction to the shaft. We analyze the unstable vibration near the major critical speed by taking into account the effects of damping. From a theoretical analysis, it is found that the unstable region near the major critical speed is divided at most into six zones which depend on the mass of the base, the stiffness of the base, and the unsymmetry of the shaft. There exist two types of vibration modes in these divided, unstable zones. In experiments, we obtained five types of response curves which contained n unstable zones(n=1, 2. . . ., S)near the major critical speed, by changing the mass of the base. and got good agreement between the theoretical values and experimental results. Less