Balancing of Rotors : Centrifugal Pumps
The title may seem familiar to those who are working with Rotating equipments or in all in mechanical engineering. Any mass that is rotating about certain axis of rotation will experience the forces, which are proportional to the square of rotating speed and the distance between the axis of rotation and the axis which passes through centre of gravity of that mass. The force, we know it as Centrifugal force.
In case of rotating equipments such as, centrifugal pumps or compressors, turbines, whatsoever, these centrifugal forces would directly reflect as vibrations. It is simple to understand that; the rotating body of the equipment is housed inside a stationary body. Certainly, the Bearings are the points, where the rotating body contacts the stationary body and through these bearings, all the forces that are being experienced by the body are grounded. Now, if the forces are unusually high, then these will be evident through the increased vibrations at the bearings.
Initially, the act of balancing began with merely making the components symmetric. The procedure was acceptable till the running speed of the machinery was very low. Later, as the advancements took place, the speed of rotating machineries is now incredibly high, which now calls for precise act of balancing. Initially through VDI 2056 “Evaluation of Mechanical Vibrations of Rotating Machinery” guidelines were introduced; which are now ISO 10816 having divided in 6 different parts. Today, there are various standards available for Balancing.
ISO 21940 is one of popularly used standard for Balancing of rotating body for centrifugal pumps.
As defined by ISO 21940, the Rotor is divided into 2 categories; 1. Flexible Rotors 2. Rigid Rotors .
The important definitions from the user point of view are; the flexible Rotors are the ones which run above 70% of their 1st critical speed. And the rigid Rotors are the ones, which run below 70% of their 1st critical speed.
Most of the Rotors pertaining especially to Centrifugal pumps today are designed in such a way that they will fall in the second category i.e. Rigid Rotors. Advantage of Rotors with rigid behaviour is that, once balanced at certain speed, they can be operated at any speed in that operating range without the need of balancing them at that particular operating speeds, since the 1st critical speed occurs at beyond the operating range.
On the other hand, flexible Rotors can be operated at the speed at which it is balanced. If the operating speed is to be changed then the Rotor has to be balanced for that speed.
The reason being, the resonance, as the natural frequency (Critical speed) of the rotor coincides with the operating speed; the rotor will vibrate with highest amplitude.
Particularly, the Rotors with rigid behaviour are balanced as per guidelines mentioned in ISO 21940–11. There are two types: Static (Single Plane)balancing and Dynamic (Two Plane) balancing. The explanation for it, is that, consider a disc having a large diameter but with relatively less thickness. The components with relatively shorter axial length. Here the axis of rotation and axis passing through centre of gravity can be approximated by just a linear distance i.e. here the centre of gravity is a single point on the disc and the axis can pass through any direction and one can assume it to be parallel to the axis of rotation. This simplifies our task and we can bring this centre of gravity as close to the centre of rotation as possible.
Now when we consider, two plane balancing, we are having rotor which is having significant length. Imagine there are two discs placed on a shaft, say 300 mm apart. Now both discs are having their individual centre of gravity. If you draw an axis, which has to pass through the centres of gravity of both the discs, you will quickly realize that the axis may not be parallel to the axis of rotation. Rather it may intersect the axis of rotation as well. This is why, it is necessary to balance the force, as well as the couple which will be introduced by two centrifugal forces of these two discs. This is achieved through two plane balancing.
Further, the process and what should be the diameter to length ratio, in order to go for either single plane or two plane balancing can be easily understood through the guidelines from various standards available.
As per ISO 21940, it can be seen that the rotor can be balanced with different grades available. These are G0.4, G1, G2.5, G6.3 up to G4000; all are multiples of 2.5. One thing to note is that, theoretically, these values are nothing but the allowable vibrations in mm/s for an equipment.
When we are balancing the rotor at G2.5, theoretically the vibration velocity for the equipment is 2.5 mm/s.
Now, to achieve this balance, the theory is simple i.e.
V = r x w; where V = vibration velocity, mm/s
r = eccentricity, mm
w = angular velocity = (2*pi*(RPM))/60 rad/s
Now, from balancing grade, the allowable eccentricity for given operating speed can be easily calculated. Now this eccentricity multiplied by total rotating mass will give allowable unbalance in gm-mm; which is desired to balance the rotor on modern balancing machines at shop. This unbalance can be further allocated to two planes by simple ratio multiplications. One thing to note is that, since the unbalance is in gm-mm; as we go farther from the centre of rotation, the material to be removed from the body (an impeller in case of Centrifugal pumps) is less. The balancing machine displays the value of unbalance and the phase angle from the previously determined reference point. With several runs, one can achieve allowable level of unbalance for particular balancing grade.
The balancing machine can typically show graphical representation; a polar graph with the mass (to be removed) from each plane at given phase angle. The method is based on a traditional graphical approach. Once the input values such as, the distances of the correction planes from the bearing locations, the radii at the two correction planes and the required balance grade are available, the balancing activity can be started. One thing to typically note is that, the process employed above is used for Rotors with rigid behaviour and balances statically and additionally only one couple. Hence most of the shop balancing machines are limited to single or two plane balancing for Rotors with rigid behaviour.
With all this explanation, a question may come arise, why only single or two plane balancing? Why is it not necessary to balance the rotor at Multiplane or more than two planes?
The answer lies in the definition of Rigid and flexible Rotors . As we pointed out that, the Rotors showing rigid behaviour are operated below 70% of their 1st critical speed and however, those the flexible Rotors , since being operated above their critical speed, can show different mode shapes at 2nd, 3rd critical speeds respectively. Below are some sketches showing how the Rotor bends at different critical speeds.
This is important to know, since the Rotor which is 1st balanced as a rigid rotor as described above, is balanced through nullifying the effect of couple. This means that, whatever the residual unbalance is there, is corrected at 2 correction planes which were initially chosen and are away from the middle of the rotor or in most of the cases, are in the middle of the middle point of rotor and the bearing location. This is done because, during rigid rotor balancing, the rotor is most sensitive to the unbalance which is close to the middle of the rotor, as the sag between the rotor can be clearly seen. So when the rotor might approach to 2nd critical speed, the rotor will have node point at the middle of the rotor and residual unbalance, if near this node point, will not impact the vibration response. However, if it is in the middle of centre and the bearing location, (where we have initially balanced it during Rigid balancing) then it may impact the vibration response considerably. Hence, in case of flexible Rotors , ISO 11342 gives guidelines to balance the rotor with (N+2) correction planes along the length of the rotor, if the speed of the Rotor approaches or exceeds Nth critical speed.
In case of Pumps, this will be unusual to have operating speeds which will be above 2nd critical speed. So where the operating speed is going beyond 2nd critical speed then, in that case, multiplane balancing with at-speed modal balancing may be required. Hence, the standards like API 610 also recommends to have two plane balancing and considers the condition, where it shall be evaluated, if the rotor will approach 1st or 2nd wet critical speed with worn out condition of wear rings and increased internal clearance.
An article by : Abhijeet Keer , Design Engineer R & D Centrifugal Pumps
For queries/feedback/suggestions; write to : keer.abhijeet98@gmail.com
