Practical Solutions to Machinery and Maintenance Vibration Problems
Chapter 5, Unbalance
Section 7, How a Single Unbalance Force Can Cause Some Couple Unbalance
However, for pure couple unbalance two equal forces 180° opposite each other), it makes no difference to the net effect on the rotor's unbalance if the two forces are moved to different planes, but at the same distance from each other. For example, the previously shown couple unbalance forces are acting in the planes at the ends of the rotor. The rotor can have the same resulting couple even if the planes in which the two equal forces are acting are changed to different axial locations. However, for the couple to remain the same magnitude, they have to have the same oz•in2 or g•mm2. If this distance between the two forces is decreased for example, by 20 percent, then to maintain the same magnitude, both unbalance forces will have to be increased by 20 percent.
The primary focus of this section is to show that couple unbalance forces can be applied anywhere along a rotor's axial length and as long as they have the same in magnitude in oz•in or g•mm, the rotor reacts the same (same effect at the bearings). Static unbalance force, or any single plane unbalance force that is placed in another axial plane, changes the net effect on the rotor. It has already been shown that for static unbalance to remain pure, its net effect must act through the rotor's CG.
Again assume a single plane unbalance force that is applied to one side of the rotor's CG. Based on the position of the imaginary fulcrum (in the plane of the CG), the rotor will tilt. For a rotating rotor, the single plane unbalance will create its own couple unbalance. The further the force is from the CG, the larger is its created couple. The couple magnitude is oz•in times the distance to the CG.
The same quasi-static unbalance on the rotor can be represented as a combination of static and couple. Notice that the same single plane unbalance is transferred back to the plane of the CG. The couple represents the tilting force that results when the single plane unbalance is to the left side of the plane of the CG.
To summarize: A single plane unbalance, acting through a rotor's lateral CG, is called "static unbalance" ("in-phase unbalance" or 0° out-of-phase unbalance"). Two forces that are in-phase and have their resultant effect acting through the rotor's CG are also called static unbalance. Pure static unbalance creates no couple of its own. However, moving the resultant force to one side of the CG creates its own couple.
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