Balancing flexible rotors.

A rotor is considered to be flexible if it runs higher than 80% of its first critical speed. To see the affect of the rotor running close to the first critical let us consider a rotor which has been low speed balanced in a balancing rig. As can be seen the rotor has been balanced using the end balance planes. This rotor is statically balanced and has no couple imbalance. However when the rotor is run to operating speeds above 80% of the 1st critical the rotor begins to bend into the skipping rope shape characteristic of 1st mode. When this happens the unbalance mass is at a greater radius than the balance weights and so the rotor is now unbalanced at the 1st critical.

Note also that the mode shape emphasises the static imbalance and 1st mode vibration will be predominantly in phase.

Unbalance

Balance wts

In a similar manner if the rotor runs close to the 2nd critical then the couple imbalance masses will be at a greater distance from the rotation centre than the balance weights added at the end planes. The rotor will therefore be unbalanced at 2nd critical. \ Note also that the centre of the rotor in this mode has no displacement and therefore will not be affected by the static imbalance. This mode is dominated by the couple imbalance and will have little static imbalance indication. I.e. the vibration vectors will be 180° out of phase. Because the 2nd critical is at a much higher speed, the force and therefore the vibration will be much higher for the same degree of residual imbalance. The mode shape for each critical speed has a significant influence on the effect of balance weights. It is possible for a rotor which is balanced in a rig to require balancing to enable it to run through the critical speeds. This happens if the degree of residual imbalance and/or the damping factor is such that the vibration is too high to safely run through a critical speed. In many cases on larger machines the rotor may be too large to be low speed balanced and therefore must be balanced entirely insitu. Whatever the case, the rotor will have to be balanced at a speed below the critical to enable it to run through the critical safely. As the phase changes rapidly with only small variations in speed near the critical it is important that the balance speed selected must be:-

• Repeatable • At a speed where the phase is stable. • The vibration is low enough that the machine is safe to run at that

speed for several minutes. The balance speed is best selected using a Bodé plot (phase and amplitude verses speed.)

Figure 1. Bode Plot of a run up.

The above Bode plot is of a rotor with a 1st critical at 850 RPM. Note the rapid phase change above 700 RPM. If it was required to balance this rotor to enable it to run through the critical a speed of 600 RPM would give a stable repeatable phase. The procedure to balance a flexible rotor to allow it to run to full operating speed is called modal balancing. Each mode of the rotor is balanced separately.

To balance to allow the rotor to safely run through 1st critical the static component is separated from the vibration data and balanced by adding in phase weight to each end of the rotor. To balance close to or above 2nd critical the couple component is extracted and the rotor balanced by adding weights 180° out of phase. Let’s look at an example. A rotor running just above the 2nd critical has the following vibration at 1X

BRG 1x Phase

Brg7 21.65 175

Brg8 29.3 345

If we split the static and couple components out, we get:-

4.4 320. Static

25.4 169. Couple on Brg 7

25.4 349. Couple on Brg 8

While there is some static imbalance present the vibration is dominated by the couple. If we attempted to do a standard 2 plane balance on this rotor the lack of response to the static component would result in a nonsensical weight change. Because the rotor is running close to the 2nd critical this mode should be balanced out separately. The procedure is to carry out a single plane balance using the couple data from brg 7 and for each weight change add equal weights to each end 180° out of phase.

In this case the maximum weight which could be added to each end was 1300 grams and this weight resulted in the following final balance.

1x Phase

Brg7 3.07 29.9

Brg8 1.06 300

Which is equivalent to

1x Phase

1.6 11. Static

1.6 49. Couple brg 7

1.6 229. Couple brg 8

For this particular rotor this balance was carried out at full speed. If the balance was required to get through the critical speed the balance may still have to be adjusted at operational speed condition.

Exercise 9.

The rotor above runs just above its 2nd critical has the following reference and trial weight data. Reference Data. March 1998

BRG 1x Phase

Brg7 10.4 3

Brg8 12.5 160

Trial weights fitted. Brg7 725 Grams 088°.

at

Brg8 725 Grams

at 268°

Final balance state.

BRG 1x Phase

Brg7 1.5 135

Brg8 3.1 314

In June 2000 after maintenance, the balance state has changed to give

BRG 1x Phase

Brg7 21.65 175

Brg8 29.3 345

The balance planes have eight weight positions (see photo above) and there is a maximum weight of 500 grams in any one position, calculate the correction weight. With this weight fitted the vibration drops to

BRG 1x Phase

Brg7 3.07 29.9

Brg8 1.06 300

Balance positions accessible while rotor is in the stator.

During service a year later (May 2001) the balance condition changes due to mass movement and results in the following vibration.

BRG 1x Phase

Brg7 7.4 354

Brg8 7.1 150

Based on all the balance data above calculate the optimum balance weight change to correct this rotor.

Exercise 9.

A rotor which runs just above its 2nd critical has the following reference and trial weight data. Reference Data. March 1998

BRG 1x Phase

Brg7 10.4 3

Brg8 12.5 160

Weights fitted.

Brg7 725 Grams

at 088°.

Brg8 725 Grams

at 268°

Final balance state.

BRG 1x Phase

Brg7 1.5 135

Brg8 3.1 314

In June 2000 after maintenance, the balance state has changed to give

BRG 1x Phase

Brg7 21.65 175

Brg8 29.3 345

The balance planes have eight weight positions and there is a maximum weight of 500 grams in any one position, calculate the correction weights to be fitted.

With these weights fitted the vibration drops to

BRG 1x Phase

Brg7 3.07 29.9

Brg8 1.06 300

During service a year later (May 2001) the balance condition changes due to mass movement and results in the following vibration.

BRG 1x Phase

Brg7 7.4 354

Brg8 7.1 150

Based on all the balance data above calculate the optimum balance weight change to correct this rotor. Note that it requires 24 hours to do a weight change with a production loss of $240000 per change. Available balance weights are 500 grams, 240 grams, and 140 grams. Only one weight can be fitted to any one position. You have as many weights as required of each size to choose from. The solution to this balance problem is to only balance the couple components out at each stage (Notice the original weight fitted is an out of phase pair)