Tips and tricks

Relationship between unbalance, speed, centrifugal force and rotor weight

In balancing practice, the relationship between unbalance and centrifugal force at a given speed often takes on a special importance, for example, when you have to calculate a rough estimate of the centrifugal forces generated at operating speed at the maximum permitted unbalance.

What unbalance can you still tolerate?

The question also arises, if you need to get a rough idea of what unbalance you can tolerate at balancing speed, so that the rotor will not bounce about on the supporting rollers: If a specific centrifugal force is exceeded, the rotor will bounce from one supporting roller to the other during balancing. This will cause a rattling noise and in the long run, significant damage to the surfaces of the roller carriage and the rotor journal.

Rule of thumb answer to the problem

Table 1 illustrates a "Rule of Thumb", which has been found useful in practice: At a speed of 1000 rpm an unbalance of, i.e., 1 gmm will generate a centrifugal force of 1g.

 u F1000
1 gmm
1 g
1 gcm
10 g
1 kgmm
1 kg
1 kgm
1.000 kg

Table 1: Relationship between unbalance and centrifugal force at 1000 rpm (..with an accuracy of 10 %)

Limitations of the rule of thumb

Centrifugal forces caused by unbalance increase with the square of the speed. If you consider the centrifugal forces at an arbitrary speed and at 1000 min-1

.. and relate them to each other ...

.... you will see that the centrifugal forces can be calculated easily by multiplying the centrifugal force at 1000 min-1 established with the help of the rule of thumb with the square of the speed ratio.

This state of affairs is illustrated in Table 2. As you will see, if speed is increased to 10,000 min-1, the centrifugal force increases by a factor of 100 from the „reference centrifugal force“ at 1000 min-1. When speed is reduced to 700 min-1, centrifugal force goes down to about half.

0,1 0,01
500 0,5 0,25
0,7 0,49
2 4
5 25
10 100

Table 2: Relationship between the centrifugal force at an arbitrary speed and the "reference centrfugal force" at 1000 min-1

Fig. 1

Sketch of an electric armature, with unbalance tolerance and centrifugal force at operating speed

Rule of thumb:

Fpermissible/LS = 2.0 % . m = 2000 kg
(provided that Ø rotor journal < Ø supporting roller)

Fig. 2
Sketch showing a cylinder in the balancing machine, the permissible force or unbalance per bearing pedestal

Learn by doing
Start making your own rough calculations? When you next balance a new rotor, just calculate the centrifugal forces generated by the specified residual unbalance. Then relate these centrifugal forces to the weight of the rotor. Learn to distinguish reasonable and excessive balancing tolerances or use the rule of thumb to work out the unbalance per bearing pedestal at which the cylinder will not become unstable on the roller carriage.

Good luck!