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Unbalance is an important source of vibration and the focus of attention for the operation, reliability and maintenance of turbomachinery. Balancing, then, is a process of attaching masses to or removing masses from the rotor assembly so that the centrifugal forces on the rotor are balanced.
The art of balancing depends on logical methods for the selection of these masses. Instead of attaching a correction mass to the rotor at an appropriate location, the same balancing effect can be achieved by removing the same size mass from the diametrically opposite side of the rotor at the same axial location.
The inherent unbalance forces should be in equilibrium after the balancing. Balancing procedures have been well established for many years for rigid rotors, although modern developments in automation, instrumentation and computation have produced marked improvements in practice. However, the balancing of flexible rotors has been less clearly understood and is a matter for debate. Fortunately, routine procedures have been established for flexible rotors.
The balancing procedure is a step-by-step approach in which the unbalance in each mode is corrected in turn, starting with the first mode. At each stage, the residual modal unbalance (the initial unbalance in the mode plus the modal effect of any corrections made to the lower modes) is determined by a modal interpretation of the rotor vibration for a speed close to the corresponding critical speed.
The first step is to choose a balancing speed, close to the selected critical speed. Then, measure shaft vibration at convenient locations. The correction step is to attach a series of trial masses (number of masses is equivalent to mode number) to the shaft at properly selected axial locations. These are selected to lie on either side of the node point in the selected mode (opposite sides). In addition, trial masses should be proportioned so that these masses will not upset the previous mode correction.
For example, three correctly proportioned masses are needed to balance the resultant defect in the third mode without upsetting the balance attained previously in the first and second modes. The procedure depends upon the orthogonality, or independence, of the modes of vibration. The process can be theoretically extended to any number of modes.
How Many Modes?
For flexible rotors, the important point is that the first and second modes have been balanced successively: and that in correcting the second mode defect, no new unbalance has been introduced into the first mode. Further modification of the components of unbalance in the third, fourth and higher modes can be done. But this is of less importance if these modes are far above the operating speed. It is not easily known whether the modification increases or decreases the various components of unbalance.
Sometimes it is necessary to balance modes whose critical speeds are above the maximum operating speed (or test speed) due to different reasons. For a large, critical piece of turbomachinery which needs a fine level of balancing, the equipment may be balanced in its first three modes for which the critical speeds are below its operating speed. However, it may have a relatively significant vibration at the operating speed due to unbalance in the fourth and fifth modes.
A complication can arise in the above process in relation to closely located critical speeds. The modal balancing technique deals with the unbalance in each mode, in turn, by identifying the corresponding component of vibration. If two critical speeds are close together, so that the modal components of unbalance cannot be separated in this way, an advanced method (such as a polar plotting technique) should be used for the isolation of the modes. In these circumstances, vibration measurements are made at shaft speeds throughout a range of speeds around the corresponding critical speed.
The combination of modal balancing is normally enough to ensure that the vibration of the shaft is reduced to tolerable levels throughout the operating speed range. This procedure does not ensure that there is no residual unbalance in the rotor assembly. Within the accuracy of practical procedure, the residual unbalance in the lower modes will have been reduced to near zero and the vibration at the operating speed kept within specified tolerances. Almost certainly, though, after balancing, the residual unbalance will have non-zero components in modes higher than those for which corrections were made. In principle, this residual unbalance will not lead to significant vibration within the operating speed range of the machinery.
Vibration caused by unbalance can result from an initial bend in the shaft. This is manifested by the run-out at a low speed, although the characteristics are different. If a shaft has an initial bend instead of, or in addition to, unbalance, it experiences a forced whirl with shaft speed frequency, similar to that encountered due to unbalance. But there are subtle differences that can be important in practice in applying the balancing procedure.