Rotors damping

Improved rotor dynamic stability. The active magnetic bearing s ability to vary stiffness and damping permits rotation about the rotor s inertial axis, eliminating vibration and noise. 

The ability to center tliis damper in applications where relatively heavy rotors are used has proven to be very advantageous. Tlie limited axial space present with most machinery does not hinder its applicability. Furthermore, the accuracy in predicting the stiffness and damping is anotlier desuable feamre tliat is irtissing witli conventional damper designs. 

Figure 4-6 is an amplitude-speed eurve showing the loeation of the running speed to the eritieal speed, and the amplitude inerease near the eritieal speed. When the rotor amplifieation faetor, as measured at the vibration probe, is greater than or equal to 2.5, that frequeney is ealled eritieal and the eorresponding shaft rotational frequeney is ealled a eritieal speed. For the purposes of this standard, a eritieally damped system is one in whieh the amplifieation faetor is less than 2.5. 

Methods for calculating undamped and damped critical speeds that closely follow the works of Prohl and Lund, respectively, are listed herein. Computer programs can be developed that use the equations shown in this section to provide estimations of the critical speeds of a given rotor for a range of bearing stiffness and damping parameters. 

This speed becomes critical when the frequency of excitation is equal to one of the natural frequencies of the system. In forced vibration, the system is a function of the frequencies. These frequencies can also be multiples of rotor speed excited by frequencies other than the speed frequency such as blade passing frequencies, gear mesh frequencies, and other component frequencies. Figure 5-20 shows that for forced vibration, the critical frequency remains constant at any shaft speed. The critical speeds occur at one-half, one, and two times the rotor speed. The effect of damping in forced vibration reduces the amplitude, but it does not affect the frequency at which this phenomenon occurs. 

Lund, J.W., Stability and Damped Critical Speeds of a Flexible Rotor in Fluid-Film Bearings, ASME No. 73-DET-103. 

The replaeement of meehanieal seals by dry gas seals must be elosely examined. There have been many eases where the replaeement has eaused the eompressor to operate in an unstable manner. This is due to the faet that removal of the meehanieal seal eauses a ehange in the damping of the rotor and ean eause the rotor to operate eloser to its eritieal speed. 

Flexible rotor balancing must be performed with the rotor whirl configuration approximating the mode in question. The operating speed(s) is in the vicinity of a major flexible mode resonance (damped critical speed). As these two speeds approach one another, a tighter... 

Modal balaneing is one of the proven methods for flexible rotor balan-eing. Modal balaneing has also been applied to problems of dissimilar lateral stiffness, hysteretie whirl, and to eomplex shaft-bearing problems. In many diseussions on modal balaneing fluid-film damping is not ineluded. In other... 

The influenee eoeffieient method examines relative displaeements rather than absolute displaeements. No assumptions about perfeet balaneing eonditions are made. Its effeetiveness is not influeneed by damping, by motions of the loeations at whieh readings are taken, or by initially bent rotors. The least-square teehnique for data proeessing is applied to find an... 

The response of the entire rotor-bearing system to this unbalanee, eonsidering damping in bearings, joints, dampers, ete. 

In those application where the cross-coupling effects from the oil seal were detrimental to the rotor dynamics, the use of the gas seal is a dis tinct advantage. However, the down side is that should the oil seal ha c provided a good measure of damping, the impact on the rotor dynamics is reversed. None of this is irreversible, but certainly must be kept m mind at the time of design. 

Figure 9-13). A response, of course, is a sudden rise in amplitude at a speed. The analysis is performed using a mathematical model that includes the effects of damping in the equations, making the model much more complex than any previous analysis. The University of Virginia carries out continuous research in which a consortium of users, vendors, and researchers provide funds, and data and interchange ideas to advance the science of rotor dynamics. Other organizations, such as the Bently Rotor Dynamics Research Corporation and Texas A M University, are also carrying on similar work on a continuing basis.

The value of a damped response is that the areas under seals or other close clearance areas can be investigated on a dynamic basis. This can be done at any selected station on the rotor. If there is encroachment on clearance, the rotor can be tuned to avoid the problem areas. The reliability of the machine can be considered rather than arguing the need for large margins to avoid the unknown. 

If the load eonsists of a rotor of moment of inertia / and a damping deviee of damping eoeffieient C, then the load dynamies are... 

Stationary engines (historic), damp pulsations Spoked hub, steel rim Massive, low-speed rotors, belt or shaft mechanical connection to application... 

Automobile engine, damp out torque tor Solid metal rotor Mounted on engine shaft, very low cost... 

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