8 .3 ASYNCHRONOUS VIBRATIONS

In the asynchronous vibration field it is necessary to make a further distinction between vibration frequencies that are multiples of the rotating speed and vibration frequencies lower or higher than rotating speed but not multiples.

To the first type belong Vibrations usually caused by lg cal factors such as: misalignment, rubbing between rotg ting and static parts, excessive stresses in the piping, foundations, etc.

To the second type belong vibrations that have been the cause of more serious problems especially in the field of high pressure compressors. They may be caused by external phenomena (forced vibrations: for example, the effect of aerodynamic forces) or by phenomena intrinsic tth ' 0 e movement of the rotor itself (self-exciting vibrations), which impair stability at its base.

Stability is a function of a balance of several factors The main ones are: 

1. Rotor-support system with its elastic characteristics
2. aerodynamic effects
3. oil seals;
4. labyrinth seals

Each factor plays its part in the balance of stability and may be either positive or negative. The system is more or less stable or instable according to the result of this balance.

A theoretical approach for predicting the stability of a rotating system is the log decrement calculation (figure 8.4).

The programme calculates the natural damped frequencies of the rotor—support system at selected speeds and supplies, for each frequency, the value of the log decre- ment that is a sound indication of the stability of the system itself.

1.  As far as the rotor is concerned,we have already seen how the natural frequencies aredeterminedandhowthe bearing effectiveness can be evaluated on the basis of the bending shapes. To avoid or minimize internal hysteresis, shrunk assembled elements (such as sleeves, spacers, impeller, etc.) must be as axially limited as possible.The keyways may cause differentiated elastic response in the various planes. For this reason they are reduced to the minimum size, staggered at 90 degrees between one impeller and the next, and in some cases they are eliminated. As regards bearings in order to avoid oil whip problems the tilting gad type is generally used. In some cases damper type bearings are also used (fig.8.5).These offer the advantage of allowingindependent adjustment of damping and stiffness coefficients.
2. The occurrence of rotating stall in one or more impellers may explain the presence of pulsations indicating vibrations at the same frequency (forced vibrations). All centrifugal compressors, whatever the pressure, are affected.by aerodynamic excitation. Other conditions being equal, these effects increase in intensity in proportion to the actual density of the gas. The determinant parameter is not only pressure, but also temperature, molecular weight and compressibility together. This is the reason why the problems of vibrations excited by aerodynamic effects occur more frequently in reinjeotion or urea synthesis plants than in ammonia synthesis or refinery compressors, even when running at the same pressure levels. N.P. has deeply studied and experimentally checked the "unsteady flow phenomena" in its standard stage configuration. The conclusions were that the aereo-dynamic disturbance and the consequent pressure pulsations were coming from stator blades of the return channel well before coming from the impeller itself. In this case the relevant shaft vibration had the following characteristics:
   • stability in amplitude
   • very low frequency (order of magnitude about 10% of the running speed)
   • amplitude function of the tip speed and the density of the gas. 
   
   
3.  The shaft end oil seals are still one the most critical parts in the manufacture of high pressure centrifugal compressors. An important requirement that the oil seals must satisfy is to contribute to the stability of the system or at least not to disturb it too much. It is easy to understand that seals, owing to their nature, would be very negative components in the stability balanceof the system if they were "locked", because they would act as lightly loaded, perfectly circular bearings. This negative tendency is generally countered by making the rings floating asnmch as possiblejJ1operating conditions. This can be obtained by distributing the oil pressure drop on the atmospheric side amongst several rings, and reducing the surface of each ring where the pressure acts by lapping the surfaces. When these techniques are insufficient to avoid "locking" (i.e., a high detachment limit force value), circumferential or axial grooves on floating rings may make a positive contribution to the stability influencing damping and stiffness characteristics of the system.
4. Another important possible cause of instability and sub-synchronous vibration can arise from the labyrinth seals.In the annular surfaces the gas circumferential motions, because of the rotor displacement, can become uneven; therefore they can cause a non-symmetrical distribution of the pressure, with a resultant force perpendicular to the displacement itself (so called cross-coupling effect). This is a typical self-exciting phenomenon causing instability. The importance of the phenomenon grows with gas density (therefore with the pressure) and with the location of the seal. In fact the vibration which always initiates above the first critical speed, has a characteristic frequency just equal to the first critical speed with the same mode shape. Therefore particularly delicate from this point of view are the back-to-back compressors in which the biggest labyrinth is in the middle (as is the highest pressure) where the shaft motions are greater. The labyrinth in figure.8.6 represents a first attempt to decrease or try to interrupt the circumeferential motions by means of many septums placed axially on the labyrinth. The labyrinth in figure.8.7 is derived from the previous one by putting the annular surface between two consecutive teeth in communication with an inner toroidal chamber in order to equalize pressure inside as much as possible.

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