Tips and tricks

Shifting balancing planes

Question:
If you shift the balancing planes of a rotor with two balancing planes, will this affect the unbalance of the rotor?  If so, how?

Answer:
1. The state of unbalance of the rotor will not change, regardless of what balancing planes you choose - only the unbalance displayed will be different.

2. In general, you will measure different unbalances in both balancing planes, even if you only shift the position of one of them.

3. This is illustrated in Figs1-3:

Starting point (Fig. 1)
Let us assume that the length of a rotor is L, and that the balancing planes are the end faces of the rotor. The unbalance in the left-hand plane L is UL = 100 gmm, the unbalance in the right-hand plane R is UL = 0 gmm, i.e. there is no unbalance.
 


Problem
The left-hand plane is to be shifted to the right by an amount of x.


Theoretical experiment (Fig. 2)
Let's assume UL remains at the left-hand face end, and apply additional unbalances UL and - UL in the new balancing plane X (this will not change the overall state of unbalance). If we now consider UL in the balancing plane X as an individual unbalance, what remains is a couple unbalance UL _ x. If you relate this couple unbalance to the distance (L-x) between the planes X and R, you obtain an additional unbalance of UL x/ (L-x) in plane X, and of - UL _x/(L-x) in plane R.


Conclusion (Fig. 3)
The unbalance measured in balancing plane X is UX = UL + UL _x/(L-x) or: UX = UL [1+x/(L-x)], the unbalance in plane R is UR = - UL _x/(L-x).

4. Shifting the balancing plane L towards X (towards the plane R) will cause the unbalance to increase, whilst retaining its angular position. An unbalance acting in the opposite direction will appear in plane R.

Note: Shifting the balancing plane towards the outside (away from the plane R) will cause the unbalance UX to become smaller than UL. The angular position of UR will remain unchanged.

5. The new unbalance may appear rather large:
Assumption: x = L3/4.
UX = 4 UL = 400 gmm, UR = -3 UL = -300 gmm!

6. If an unbalance is also present in the right-hand plane R initially, will normally have a different angular position from that of UL. If the balancing plane L is shifted to X, this will change the magnitude and angular position of UR displayed. The same applies if the balancing plane R is moved. In this case, all changes are dependent on the angular position and magnitude of the unbalance UR and on the magnitude and direction of the shift.

If both planes are changed, generally the display of magnitude and angle will change. The unbalances UL and UR will be different both in magnitude and angular position.