13.2.5 Various expressions of unbalance

In this section various terminologies used in industry related to unbalance is described. When a static unbalance exists, a centrifugal force exists.This unbalance force is eliminated if mass , which satisfied the relationship , is added at radius a in the same plane as the center of gravity G . From this condition it is clear that the product is more important than the eccentricity itself. Therefore, the quantity

(13.9)

is called an unbalance vector and its magnitude is called a magnitude of unbalance . These quantities are sometimes called simply unbalance . Different types of expressions are described in the general case where an eccentricity e and an inclination φ of the principal axis of moment of area coexist.

(a) Resultant Unbalance”  and “Resultant Unbalance moment :

(13.10)

(13.11)

The quantity

(13.12)

is called a “resultant unbalance moment” concerning point o, where  is a unit vector in the direction of the bearing centerline and × is the cross product of vectors. Multiplying this by , we get the moment  produced by the centrifugal forces of all elements.

(13.13)

This moment is called a “resultant moment” of the unbalance force. We can represent the unbalance of a rigid rotor by using the “resultant unbalance ” and the “resultant unbalance moment ”.