The case of a symmetric rotor supported on two identical, rigidly mounted, self-aligning, finite-length (L/D = 1) fluid-film journal bearings is considered. Rotor position is described by two translation coordinates in a plane perpendicular to the bearing line of centers, and by three Euler angles. Introduction of various amounts of dynamic unbalance via the inertia tensor off-diagonal terms (products of inertia) allows determination of angular velocity and static eccentricity ratio combinations leading to bearing “failure” defined for arbitrary maximum allowable eccentricity ratios. Instability hysteresis, defined here as the persistence, during rotor deceleration, of instability to speeds below which it first appeared, is considered by means of the above model. Equations and methods developed for the unbalance investigation are adapted to a variable-speed analysis. With both constant and variable mean bearing temperatures, variable-speed simulations terminating at constant speed are observed to be stable when the terminating point is below the instability threshold curve on the angular velocity-static eccentricity ratio parameter plane and unstable when above. The slope of the threshold curve and the shape of the equilibrium-condition path on the parameter plane (single-line path for constant temperature, closed curve for variable temperature) apparently combine to produce hysteresis in the variable temperature case and none at constant temperature.
Rigid-Body Rotor Dynamics: Dynamic Unbalance and Lubricant Temperature Changes
R. H. Badgley,
R. H. Badgley
Rotating Systems Dynamics, Mechanical Technology Inc., Latham, N. Y.
J. F. Booker
School of Mechanical Engineering, Cornell University, Ithaca, N. Y.
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Badgley, R. H., and Booker, J. F. (July 1, 1970). "Rigid-Body Rotor Dynamics: Dynamic Unbalance and Lubricant Temperature Changes." ASME. J. of Lubrication Tech. July 1970; 92(3): 415–421. https://doi.org/10.1115/1.3451431
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