.ysteretic .hirl. This type of whirl occurs in flexible rotors and resultsfrom shrink fits. When a radial deflection is imposed on a shaft， a neutralstrain axis is induced normal to the direction of flexure. From first-order consid-erations， the neutral-stress axis is coincident with the neutral-strainaxis， and a restoring force is developed perpendicular to the neutral-stress axis. The restoring force is then parallel to and opposing the induced force. In actu-ality， internal friction exists in the shaft， which causes a phase shift in the stress. The result is that the neutral-strain axis and neutral-stress axis are displaced so that the resultant force is not parallel to the deflection. The tangential force normal to the deflection causes whirl instability. As whirlbegins， the centrifugal force increases， causing greater deflections-which result in greater stresses and still greater whirl forces. This type of increasing whirl motion may eventually be destructive as seen in Figure 5-22a.
Some initial impulse unbalance is often required to start the whirl motion. Newkirk has suggested that the effect is caused by interfaces of joints in a rotor (shrink fits) rather than defects in rotor material. This type of whirl phenomenon occurs only at rotational speeds above the first critical. The phenomenon may disappear and then reappear at a higher speed. Some success has been achieved in reducing this type of whirl by reducing thenumber of separate parts， restricting the shrinkfits， and providing some lockup of assembled elements.
Dry-friction .hirl. This type of whip is experienced when the surface of a rotating shaft comes into contact with an unlubricated stationary guide.The effect takes place because of an unlubricated journal， contact in radialclearance of labyrinth seals， and loss of clearance in hydrodynamic bearings.
Figure 5-22b shows this phenomenon. When contact is made between thesurface and the rotatingshaft， the coulomb friction will induce a tangential force on the rotor. This friction force is approximately proportional to the
Figure 5-22a. Hysteretic whirl (Ehrich，F F ， ""Identification and Avoidance ofInstabilities and Self-Excited .ibrations in RotatingMachinery，"" Adopted fromASME Paper72-DE-21， General ElectricCo ， Aircraft EngineGroup， Group Engin-eeringDivision， May11， 1972 )
Figure 5-22b. Dry friction whirl (Ehrich，F F ， ""Identification and Avoidance ofInstabilities and Self-Excited .ibrations in RotatingMachinery，"" Adopted fromASME Paper72-DE-21， General ElectricCo ， Aircraft EngineGroup， Group Engin-eeringDivision， May11， 1972 )
radial component of the contactforce， creating a condition for instability. The whirl direction is counter to the shaft direction.
Oil .hirl. This instability begins when fluid entrained in the space between the shaft and bearing surfaces begins to circulate with an average velocity of one-half of the shaft surface speed. Figure 5-23a shows the mechanism of oil whirl. The pressures developed in the oil are not symmetric about the rotor. Because of viscous losses of the fluid circulating through thesmall clearance， higher pressure exists on the upstream side of the flow thanon the downstream side.Again， a tangential force results. A whirl motion exists when the tangential force exceeds any inherent damping. It has been shown that the shafting must rotate at approximately twice the critical speedfor whirl motion to occur. Thus， the ratio of frequency to rpm is close to 0.5for oil whirl. This phenomenon is not restricted to the bearing， but it also can occur in the seals.
The most obvious way to prevent oil whirl is to restrict the maximum rotor speed to less than twice its critical. Sometimes oil whip can be reduced or eliminated by changing the viscosity of the oil or by controlling the oil
Figure 5-2.a. Oil whirl (Ehrich，F F ， ""Identification and Avoidance of Instabilitiesand Self-Excited .ibrations in RotatingMachinery，"" Adopted from ASME Paper72-DE-21， General ElectricCo ， Aircraft EngineGroup， Group EngineeringDivision， May11， 1972 ) 中国航空网 www.aero.cn 航空翻译 www.aviation.cn 本文链接地址：燃气涡轮工程手册 Gas Turbine Engineering Handbook 1(78)
