Critical Speed of Rotor in a Liquid

概要

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Analytical results on the fundamental critical speed of a shaft in a viscous fluid are presented. When the fluid is set in motion by the shaft whirling, dynamic forces imposed by the fluid on the shaft are obtained by solving the two-dimensional Navier -Stokes equations under appropriate boundary conditions and on the assumption of small amplitude of the whirling motion. Added mass coefficients of the fluid and viscous damping coefficients are determined using these dynamic forces, and accordingly the equations of whirling motion of the shaft are derived. The critical speed of the shaft are found by solving these equations of whirl motion. In this analysis, configurations of the shaft are assumed to be a uniform elastic beam or a diskattached elastic beam, whose both ends are simply supported by bearings. For the latter case, an experimental study was made in order to confirm the analytical results. From this study, it was revealed that the critical speed decreases for large viscosity of the fluid, and when the fluid fills an annulus between the shaft and a cylindrical wall, the critical speed decreases for small annular gap width.
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