Balancing the Centrifugal Pump Rotor: Types of Balancing Machine
Various International standards such as API 610, ISO 21940, etc. specify guidelines for the dynamic balancing of the Rotor. In my previous article, I spoke about the process of balancing and the guidelines given in ISO 21940, flexible and rigid Rotor, etc. Here in this article, I would like to give an example of calculation for dynamic balancing a multistage pump rotor and also the types of balancing machines.
Inputs:
( Rotor in the example is Rigid Rotor)
Pump Rotor weight, W=200 Kg
Required Balancing grade as per API 610( Table 19) =G2.5
Pump operating speed, N =2990 rpm
Speed at which Rotor will be balanced =1000 rpm
Calculation:
V =e . w
where, V = Vibration velocity, mm/s = 2.5 ( since balancing grade is G2.5)
e = mass eccentricity, mm
w = Angular velocity, rad/s = (2*pi*N)/60 = 313.112
Calculating mass eccentricity,
e = V/w = 7.984 x 10e-3 mm = 7.984 μm
Now, this eccentricity can be expressed as ( for 1 kg of total mass and 1 mm of radius),
e = 7.984 gm.mm/kg
Determining permissible residual unbalance, Uper
Uper = e x W = 1596.8 gm.mm
Being a rigid rotor, we are going for 2-plane balancing, hence calculating material to be removed from each plane.
Calculating permissible residual unbalance for each tolerance plane;
U per A = ( Uper x LB) / L = 781.6 gm.mm
U per B= ( Uper x LA) / L = 815.2 gm.mm
where,
U per A is the permissible residual unbalance in bearing plane A;
U per B is the permissible residual unbalance in bearing plane B;
Uper is the (total) permissible residual unbalance (in the mass centre plane);
LA is the distance from mass centre plane to bearing plane A ( Refer Fig.1);
LB is the distance from mass centre plane to bearing plane B ( Refer Fig.1);
L is the bearing span ( Refer Fig.1).
For the purpose of feasibility of material removal, the correction planes have to be chosen as shown in fig.1, near the bearing/tolerance planes. Here in this example, the corrections planes I and II are set at back shroud of 2nd Impeller and 7th Impeller respectively. ( counting from A)
The permissible residual unbalance tolerance value of the adjacent tolerance plane shall be allocated to the correction planes.
U per I = U per A = 781.6 gm.mm
U per II = U per B = 815.2 gm.mm
The radius at which, the material shall be removed, R = 105 mm ( Impeller diameter assumed is 225 mm; hence material is being removed from the back shroud at the farthest point from the center.)
Therefore, permissible residual imbalance mass = 7.44 gm at correction plane I and permissible residual imbalance mass = 7.76 gm at correction plane II
So, at the balancing machine, the operator has to have these values of permissible unbalance masses at each correction plane.
Now, one may wonder, what effect does the speed of balancing machine have while doing dynamic balancing operation. In the current example we are assuming the speed of balancing as 1000 rpm. As already stated, the Rotor we are talking about, in the given example, is the rigid one ( Read previous article for the difference between Rigid and flexible rotor and why is it not necessary to balance the rigid rotor at operating speed). Hence, it can be balanced at lower speed as well. Here comes into picture, the logic behind the types of Balancing machines.
There are two general types of Balancing machines: 1. Hard-bearing Balancing machine 2. Soft-bearing balancing machine.
Now, in our above example, we are balancing the Rotor at 1000 rpm. Hence the final vibration velocity, that will give indication, that the rotor is balanced at G2.5 will be,
V = e x W = 7.984 x 10e-3 x ((2 x Pi x 1000)/60) = 0.83 mm/s
So, in order to balance the Rotor at this speed, the machine shall be sensitive enough to detect the forces generated by the minimum vibration velocity of 0.83 mm/s.
Soft-bearing balancing machine has its supporting bearing structure such that, the support will move at least in one direction. The supports are flexible, so that the displacements of the rotor can be captured. The soft-bearing machine is, hence sensitive to lower balancing speed as well. However, the machine is pretty straight forward, as it measures directly the vibration values and mostly useful for On-field applications or for the applications where very accurate balancing is required. The reason for this is, because all the calculations done above are of no direct use for these type of machines, since it does not display any user friendly data on screen such as, how much is the unbalance in the correction planes and at what phase angle. Neither does it let one input the distances of correction planes. So, in order to balance the Rotor, it involves at least 3 trial runs and also manual calculations to establish the relation between the measured vibration velocities and actual unbalance mass and phase angle.
Hard-bearing balancing machine has stiff supports. This type of machines are mostly used by OEMs, since they allow easy, user friendly and quick balancing of the rotors. The main advantage is that, the calibration required only once and high volume production can be balanced. Only periodic balancing is necessary. The reason is that, hard-bearing balancing machines come with stiff supports and separate foundation, that need to be placed at fixed position into the facility. Since the supports are fixed, this type of machine measures the centrifugal force, unlike the vibration velocity in case of soft-bearing balancing machines. Since, directly force is being measured, it is easier to display the unbalance mass. With the help of proximity sensors, phase angles are also calculated. This saves lot of time and efforts and the rotors of various sizes, weights, etc. can be balanced without re-calibration. However, in the above example, the centrifugal force will be 9.2 N ( 0.9 kg)in each bearing plane at the balancing machine speed of 1000 rpm. Hence the Balancing machine shall be sensitive enough to measure these forces. Hence if the Balancing grades below G2.5 are necessary, it could be challenging to correctly balance the rotor.
Hence, depending upon the requirement ,the method of Balancing, whether with hard supports or soft supports, has to be decided.
An article by : Abhijeet Keer , Design Engineer R & D Centrifugal Pumps
For queries/feedback/suggestions; write to : keer.abhijeet98@gmail.com
