Abhijeet Keer’s Post

Various International standards such as API 610, ISO 21940, etc. specify guidelines for the dynamic balancing of the Rotor. 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 the unbalance below these values of permissible unbalance masses at each correction plane. #pumps #mechanicalengineering #centrifugalpumps Fig. 1 Multistage Pump Rotor ( all dimensions are in mm)