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## Section 8, Complications Created by Unbalance in Overhung Rotors

Assume that a rotor, such as a fan, sheave, or coupling is within itself dynamically balanced on a balancing machine. Also assume that the residual dynamic unbalances recurring in the rotor in both correction planes are within tolerances designated by international standards, but only barely so. Also assume that the unbalances in each correction plane are not equal in magnitude nor are they either 0° or 180° out-of-phase with each other. However, this dynamic unbalance can be mentally separated into its components of static and couple unbalance as, as shown in Fig. 3. The problem lies with the static unbalance, especially when the static unbalance is relatively large compared to the couple unbalance, and when the static unbalance within a rotor (such as a pump impeller or turbo supercharger) is then mounted on the outboard portion of the total rotor assembly. For now, focus only on the static unbalance component.

Fig. 4 shows the main rotor with its couple unbalance components removed, revealing only its static unbalance components. Focus only on the static unbalance component. With the rotor's axial center of gravity equi-distant from each bearing, the reaction from the static unbalance will be at both bearings, equal in magnitude and in-phase with each other. The static unbalance will cause no couple.

Fig. 5 illustrates rotors mounted on their shafts whereby the total rotors' assemblies' CG is off to one side of the main rotor. The static force that is now officially called "quasi-static" (a term the writer has never fully accepted), means that the main rotors' static unbalance forces are no longer acting through their total assemblies, thereby creating new couple unbalance. However, these couple unbalances are not a real couple that actually exists in the main rotor. Instead, it is what Update calls a "false couple" -- a couple created by the static unbalance component in the main rotor.

As a reminder, the main rotor had dynamic unbalance expressed in two planes. The unbalances were then mentally separated into the main rotor's static and couple unbalance components. Therefore, for the total assembly there are two sets of couple forces. One set is the real residual couple in the main rotor, and the other set is the false couple that was crated by the rotor's static unbalance. Each couple can be expressed vectorially in each correction plane. For each correction plane there are, therefore, two separate couple forces. They combine vectorially into a resultant force for each plane. Now consider the difficulty this creates for the person attempting to balance the rotor.

If for example, the rotor is relatively narrow, such as a narrow fan or pump impeller, it usually has a relatively large amount of static unbalance within the outboard main rotor and relatively small magnitudes of real couple unbalance. The false couple forces in each plane combine vectorially with the real couple forces in the same planes. The vectorial combination of large false couple with small real couple can create very confusing problems during the balancing runs.

Each time the real static is reduced, the proportion of false couple it had created is also reduced. Therefore, the real couple with which it was vectorially combined is altered considerably. Some balancing machine programs are supposed to compensate for all this, and claims are made that it is no more difficult balancing overhung mounted rotors than inboard mounted rotors. However, most balancing machines in use today are not that new. Therefore, balancing overhung rotors is so difficult that the company doing the balancing often gives up, indicating that "outboard rotors can be balanced only in a single plane" (primarily removing only the static unbalance and leaving the remaining real couple). This may be appropriate for well-machined, uniform and relatively narrow rotors that don't have much remaining real couple in them. However, machinery users (as compared to many machinery builders) require considerably smoother running machines which have both their static and couple unbalances removed.

If the main rotor is far to one side along the length of the shaft or if it is mounted overhung, even a relatively small amount of static unbalance could create a false couple that is larger in its effect on vibration than the effect of the static unbalance alone. Depending on the balancing machine, its age and use of computer logic, this could create difficulties in balancing on a shop balancing machine or when performing in-place field balancing. For some of the latest balancing machines and field balancing computer programs, there seems to be no difficulty in balancing overhung rotors using the normal "left and right" plane separation method. But for rotors with larger static unbalance in the main rotor (such as is relatively common in overhung fanwheels), the static unbalance creates so much false couple that even the computer program doesn't adequately take care of it.

For those using balancing machines that do not readily handle this problem, they should set up their balancing machines for balancing the static and couple separately. Often they know that this should be done, but make the mistake of using the typical balancing machine operator's rule for two plane balancing of "removing the largest unbalance first and the least unbalance second." That rule works well with rotors mounted between support bearings. For example, if the left plane has the greatest unbalance, balance the left plane first, and then balance the right plane. However, with outboard rotors, most of the time this rule causes difficulty as the rotor's static unbalance acts in a plane so far away from the total rotor's center of gravity that the couple it creates is considerably larger than the static unbalance force from which it originated. Therefore, the static unbalance created couple could be much larger than the original static unbalance that created it. When balancing by separating static unbalance from couple unbalance, the static unbalance always has to be removed first. It not only has to be removed, but the further out it is cantilevered, the closer the static tolerance must be. Then when there is hardly any couple effect caused by the residual static unbalance, the remaining real couple can be corrected.

Another problem arises from the fact that most balancing machine operators have been taught to completely remove the unbalance from one plane before staring on the other (balancing in only one plane at a time). This works well when dynamically balancing a rotor that is mounted between its support bearings. However, for removing "pure" couple, it is not best to balance in one plane and then in the other. Instead, couple corrections should be performed in both planes at the same time, (in the same balancing run). Corrections in each plane have to be equal in magnitude and 180° apart. If the couple corrections are not "pure," then a residual static unbalance will result. As the static unbalance is acting outboard from the bearings (cantilevered), that new residual static unbalance creates yet another "false" couple -- and the whole mess starts all over again.

No wonder so many people either give up balancing outboard rotors in two planes, or they use wide tolerances that result in mediocre vibration levels, at best. It may also explain why so much field balancing is required on outboard rotors, such as cantilevered fans.

Reading all this may seem complicated for those who are not thoroughly familiar with the procedures of balancing overhung rotors and using the separation of static and couple unbalance. Once understood and routine, it is actually quite easy and allows balancing to as close tolerances as are used for balancing rotors mounted between support bearings. The same procedures are recommended for relatively narrow rotors whether mounted overhung or not. Here are the simple rules:

1. Separate static unbalance from couple.

2. Ignore the couple completely, no matter whether it is larger than the static unbalance or not, and remove only the static unbalance.

3. The larger the overhung rotor is cantilevered, the closer the static balancing tolerances must be (beyond the normal guidelines for non-outboard rotors).

4. After static balancing is completed, remove the remaining couple unbalance by working in both correction planes during the same balancing run.

5. Couple corrections have to be equal in magnitude and 180° out-of-phase.

6. Recheck the static unbalance. If there is more to correct, keep the first three steps in mind.

Theoretically, most balancing machine operators should have been taught all the right principles for balancing overhung rotors in two or more planes on the specific type balancing machine they are using; however, in reality this is sometimes not the case. Initial training may have been incomplete, hurried or perhaps overhung rotors were not even considered. If having difficulty, first check with the balancing machine manufacturer to determine if overhung rotors can be balanced without having to resort to the static and couple method. (Sometimes the problems of balancing outboard mounted rotors in two planes has been made relatively easy by the balancing machine's computer.) If not, and the static and couple method is required, the basic principles are as given.

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