Abstract
Abstract : The motion of an unbalanced rotor during acceleration through its critical speed is studied by numerical solutions obtained with a digital computer. The rotor is laterally restrained in two orthogonal directions by linear springs and is accelerated by a constant applied torque. It is found that, for a fixed combination of rotor unbalance and lateral stiffnesses, the applied torque must exceed a limiting value in order to accelerate successfully through the critical speed region. With smaller applied torques, after initial acceleration from rest the speed oscillates continually about the critical speed and the lateral excursions grow steadily. The conditions necessary for a successful acceleration are established and the maximum lateral excursions during successful accelerations are determined. The effects of small amounts of viscous damping in the lateral directions are also obtained. Finally, an example problem is solved to illustrate the extension of the solution to those problems where applied torque is a function of speed.
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