Practical Approach to Precision Balancing

4- Various Combinations of Dynamic Unbalance

There is a standard, official definition for dynamic unbalance. However, even balancing engineers sometimes have difficulty understanding it. Therefore, Update has developed its own easy to understand, practical definition that is just as accurate. Update's definition: "Dynamic unbalance is any combination of unbalances resolved to at least two correction planes." Review the diagram showing how all possible combinations of unbalance, whether they be static, couple or anything else, create "dynamic unbalance." (The vectors shown in the unbalance diagrams represent the unbalance units after they have been converted to centrifugal forces at operating speed.)

Confusion often results when "static unbalance" is also referred to as "dynamic unbalance." the confusion is very understandable as dictionary definitions suggest that the word "static" has an opposite meaning to the word "dynamic." True! But unfortunately, the phrase "static unbalance" was derived from an old method used for static balancing (on a static balancing machine, usually a set of rollers on a stand). The static unbalance was revealed as the rotor was rolled by gravity to the 6:00 o'clock position. For understanding unbalance itself and especially for vibration analysis, it's best not to visualize the method used for removing static unbalance, but to instead visualize the in-phase and equal forces.

Static Unbalance in a Uniform Rotor:

A single static unbalance force that is acting through the rotor's CG can be resolved to two separate forces, one in each chosen measurement plane. Each force would be half the magnitude of the original single force, equal to each other and at the same angle relative to each other (0° out-of-phase).

Static Unbalance in a Non-Uniform Rotor:

For a non-uniform rotor with unequal weight at each bearing, the plane for the lateral CG would no longer be equidistant from each bearing. Instead, it would be as shown in the plane of the imaginary fulcrum.

The static unbalance in the plane of the CG can be resolved to the two measuring planes, proportional to the rotor weight at each end. Therefore, the two static weights or forces will not be equal. For example, assume a rotor that has a total weight of four units, with its weight distributed so that the left bearing supported three units and the right bearing supported one unit.

In order to remain in "pure" static unbalance (no couple present) at each measuring plane adjacent to the bearings, the left plane SINGLE FORCE THROUGH PLANE static unbalance force will be 3/4 that of the original total static OF CREATING PURE STATIC unbalance. The right plane static unbalance force will be 1/4 UNBALANCE of the original static unbalance.

Couple Unbalance Forces:

For a dynamically out-of-balance rotor, assume that the static unbalance forces have been completely counter-balanced. With no static unbalance, the remaining forces in each plane are necessarily 180° opposite each other and equal in magnitude. This is called "couple unbalance." Looking at the same two couple unbalance forces from the end view, it is clearly seen that they counterbalance each other statically.

As couple unbalance always involves two equal forces, 180° opposite each other, the magnitude of this couple depends not only on the magnitude of each force in oz•in or g•mm, but also on the distance between the forces. Assuming the same oz•in or g•mm in each plane, the shorter the distance from each other, the smaller the couple unbalance. The longer the distance, the larger the couple. As indicated, couple unbalance units are measured in oz•in or g•mm for one of the two equal forces times the distance between the forces. The result is oz•in times in = oz•in2. For metric: g•mm times mm = g•mm2. Most often, couple units are not familiar to balancing or vibration specialists as most dynamic balancing procedures involve only one plane at a time. However, this writeup is provided for the basic understanding of unbalance forces, for the purpose of vibration analysis. It will also be used for minimizing the difficulties so often encountered in balancing cantilevered (overhung) rotors, or rotors where both correction planes are to one side of the total rotors' CG.

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