| description abstract | Fluids are often introduced accidentally and trapped inside of high speed rotors. This has given concern as to the possible deleterious effects of such trapped fluids on the system’s vibration characteristics. Trapped fluids will induce asynchronous vibratory motion of high speed rotors at supercritical rotational speeds. This tendency is examined in analytic detail. Assuming that the circumferential velocity of the trapped fluid varies linearly with radius, the generalized shape of the fluid film is derived. Integrating the fluid pressure on the cavity walls gives the net fluid forces and permits computation of whirl frequency and whirl amplitude as functions of rotative speed. Generalized plots are given of the film geometry, of the rotative speed at which asynchronous whirl starts, and of the induced whirl speed. General response curves are also given, showing whirl amplitude as a function of rotative speed. The detailed results indicate that whirl occurs at a rotative speed approximately double the induced whirl frequency (as happens with many rotor whirl mechanisms). Higher values of the system parameter g result in somewhat lower whirl onset speeds. The whirl velocity is approximately equal to the rotor critical speed, or slightly lower for large masses of trapped fluid. Rotor whirl amplitude increases sharply with rotative speed above onset speed until a limiting condition where the fluid film (and analytic solution) break down, at a rotative speed about 6 percent above onset speed. Trapped fluids will also influence the normal synchronous vibrations induced by rotor unbalance. Analyses of a simple model of synchronous, solid body rotation are made which give exact solutions for the condition of a fully welted cavity periphery, and give approximate solutions for a partially welted periphery. It is concluded that the trapped fluid generally reduces the critical frequency, reduces critical amplitude, and reduces high speed (supercritical) amplitude. The effect is quite small with a partially welted circumference, but is surprisingly large in the case where the periphery of the cavity stays fully welted at maximum vibration amplitude. In this case, the rotor acts as if the cavity were entirely full of fluid, even though actual trapped fluid may fill only a small fraction of the cavity volume! Significant reductions in critical frequencies and amplitude are thereby observed. In the case of systems that are partially welted in going through their resonance peak, a “rightward leaning” resonance peak is observed which results in jump phenomena and hysteresis in amplitude on accelerating and decelerating through the peak. | |
