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## Section 6, 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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