Dynamic Instability of a High-Speed Rotor Containing a Partitioned Cavity Filled With Two Kinds of Liquids

Abstract

This paper is concerned with the dynamic instability of a high-speed rotor containing a partitioned cavity filled with two kinds of liquids of different density. The system considered simulates a centrifuge of two liquids type, in which the cylindrical cavity is divided into fan-shaped compartments in order to suppress asynchronous whirling motions induced by waves in the liquids traveling around the cavity. Assuming rotor vibrations to be small, liquids inviscid, and external damping negligible, perturbed motions of the liquid-rotor system are analyzed. The theory shows that the rotor containing a partitioned cavity can still exhibit unstable behavior, similar to that observed for a rotor system equipped with centrifugal pendula, in the region where the rotor speed is nearly equal to the sum of the critical speed of the system and the natural frequency of the liquids. The theory has been verified by the experiments. The dependence of the unstable region on the main system parameters is also discussed.