Dynamic Balancing of Centrifugal Pump Impeller - International ...

International Journal of Emerging Technology and Advanced Engineering 

Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 6, June 2012) 

Dynamic Balancing of Centrifugal Pump Impeller 

Amit Kalmegh 1 , Santosh Bhaskar 2 

1 Dept. of Mechanical Engineering, S.R.E.S. College of Engineering, Kopergaon, Pune University 

2 Prof. Dept. of Mechanical Engineering, S.R.E.S. College of Engineering, Kopergaon, Pune University 

Abstract— Vibration caused by mass imbalance in rotating 

machinery is an important engineering problem. The 

objective of balancing is to reduce rotor vibration to a 

practical minimum. Reducing rotor vibrations generally 

increases the service life of the rotating machinery. The 

fundamental difference between a centrifugal sewage pump 

impeller and those of its clear water cousins is its ability to 

pass solid materials that would normally clod later. Due to the 

unbalance in the impeller, vibration occurs and leads to 

decrease in fluid velocity and local pressure which may cause 

an undesirable turbulence and possible cavitation. Hence, to 

remove the unbalance in rotor is necessary. In this paper the 

focus is given on dynamic balancing of centrifugal pump 

impeller. 

Keywords—Impeller, dynamic balancing, vibration, 

unbalance, balancing tolerance, residual unbalance. 

I. INTRODUCTION 

A centrifugal pump is one of the simplest pieces of 

equipment in any process plant. Centrifugal pump comes 

under the category of rotating machinery. Its purpose is to 

convert energy of a prime mover first into velocity or 

kinetic energy and then into pressure energy of a fluid that 

is being pumped. The energy changes occur by virtue of 

two main parts of the pump, the impeller and the volute or 

diffuser. The impeller is the rotating part that converts 

driver energy into the kinetic energy. The volute or diffuser 

is the stationary part that converts the kinetic energy into 

pressure energy. 

Fig.1 Centrifugal pump impeller [3] 

1 amitkalmegh@gmail.com 

2 santoshbhaskar12002@yahoo.co.in 

409 

Rotating machinery is commonly used in mechanical 

systems, including industrial turbo-machinery, machining 

tools, and aircraft gas turbine engines. Vibration caused by 

mass imbalance is a common problem in rotating 

machinery. Imbalance occurs if the principal axis of inertia 

of the rotor is not coincident with its geometric axis. Higher 

speeds cause much greater centrifugal imbalance forces, 

and the current trend of rotating equipment toward higher 

power density clearly leads to higher operational speeds. 

Therefore, vibration control is essential in improving 

machining surface finish; achieving longer bearing, 

spindle, and tool life in high-speed machining; and 

reducing the number of unscheduled shutdowns. A great 

cost savings for high-speed pumps, turbines, compressors, 

and other turbo machinery used in industries can be 

realized by removing the unbalance. [1] 

Balancing is defined as ―the process of adding (or 

removing) mass in a plane or planes on a rotor in order to 

move the center of gravity towards the axis of rotation.‖ As 

the definition of balancing implies, material is either added 

to or removed from the rotating element to attain an 

acceptable balance level. 

To balance the rotor the amount of mass has to be 

removed or added in the rotor for which it is necessary to 

know the amount of unbalance along with the acceptable 

tolerance. This has to be done by the experimental method. 

The result shows whether the rotor is balanced or 

unbalanced. 

II. ROTOR BALANCING METHODS 

Rotor dynamics is the study of rotating machines and 

has a very important part to play throughout the modern 

industrial world. A great deal of resources put into the 

study of rotor dynamics to calculate safe operating ranges 

and unbalance before the machines goes into service and 

also methods of detecting imminent failure.



Rotor balancing techniques can be mainly classified as: 

On-line balancing methods 

Off-line balancing methods 

Fig.2 Rotor balancing methods [1] 

The off-line rigid rotor balancing method is mostly used 

in industrial applications. The rotor is modelled as a rigid 

shaft that cannot have elastic deformation during operation. 

In this method, any imbalance distribution in a rigid rotor 

can be balanced in two different planes. Rigid rotor 

balancing is again categories as single plane and two plane 

balancing. Here, we are performing two plane balancing on 

the pump impeller. 

A. Static Unbalance 

III. TYPES OF UNBALANCE 

A condition of static unbalance exists when the mass 

center does not lie on the axis of rotation. Static unbalance 

is also known as Force Unbalance. As defined, static 

unbalance is an ideal condition, it has the additional 

condition that the axis of rotation be parallel to the central 

principal axis - no couple unbalance. [4] 

Fig.3 Static unbalance [4] 

B. Couple Unbalance 

A specific condition that exists when the central 

principal axis of inertia is not parallel with the axis of 

rotation. As defined, couple unbalance is an ideal 

condition. It carries the additional condition that the mass 

center lies on the axis of rotation – no static unbalance. [4] 

410 

Fig.4 Couple unbalance [4] 

C. Dynamic Unbalance 

The most general case of unbalance in which the central 

principal axis is not parallel to and does not intersect the 

axis of rotation. Dynamic unbalance is also referred to as 

two plane unbalance, indicating that correction is required 

in two planes to fully eliminate dynamic unbalance. 

Dynamic unbalance captures all the unbalance which exists 

in a rotor. This type of unbalance can only be measured on 

a rotating balancer since it includes couple unbalance. 

Since dynamic unbalance is a combination of static and 

couple unbalance and since static and couple unbalance 

have different units, there are no unique units for dynamic 

unbalance. It can be expressed as static and couple or in 

terms of the balance corrections required. [4] 

Fig.5 Dynamic unbalance [4] 

D. Quasi-Static Unbalance 

A special form of dynamic unbalance in which the static 

and couple unbalance vectors lie in the same plane. The 

central principal axis intersects the axis of rotation, but the 

mass center does not lie on the axis of rotation. This is the 

case where an otherwise balanced rotor is altered (weight 

added or removed) in a plane some distance from the mass 

center. The alteration creates a static unbalance as well as a 

couple unbalance. Conversely, a rotor with quasi-static 

unbalance can be balanced with a single correction of the 

right magnitude in the appropriate plane. [4] 

IV. UNBALANCE EFFECT 

An unbalanced rotor generates an inertial force 

(centrifugal) which increases with the square speed. 

Fig.6 Unbalance effect [2]



F = m.r.ω 2 = U.ω 2 

Where, 

U = m.r = unbalance [kg.m] 

ω = angular speed [rad/s] 

ω = 2π.N / 60 

Where, 

N = revolutions/minute 

F = Centrifugal force in Newton 

The vector unbalance U (multiplied by the factor ω 2 , 

square of the angular speed) originates the centrifugal force 

F; this means that the load caused by the unbalance 

increases with the square of the speed (doubling the 

running speed the centrifugal force (inertia force) becomes 

four times greater). [2] 

V. BALANCING TOLERANCES 

International standard ISO 1940 gives a rule in order to 

calculate an acceptable residual unbalance, having 

following features: 

Gross unbalance deficiencies are avoided 

Useless and expensive balancing works are 

avoided 

For each rotor type, depending on its maximum service 

speed the acceptable total residual unbalance per unit of 

mass is calculated [(gr.mm)/kg] (specified residual 

unbalance). 

The calculated value is the same mass eccentricity: 

Where, 

E = Mass eccentricity [microns] 

U = Unbalance [gr.mm] 

M = Rotor mass [kg] 

According to ISO 1940 standard, all rotors are classified, 

depending on their balancing requirement. Balancing 

quality G is a number which defines the balancing accuracy 

required; for instance G = 6.3 means that a normal 

balancing is accepted. The maximum service speed is 

reported on the horizontal x axis, while the acceptable 

specific unbalance (acceptable unbalance per unit of mass 

or acceptable residual mass eccentricity) is reported on the 

vertical y axis. 

411 

The following formula can be used instead of previous 

diagram: 

Et = (9550 / M).G 

Where, 

Et [μ] = Total acceptable mass eccentricity 

N [RPM] = Maximum service rotor speed 

G [mm/s] = Balancing quality grade 

Total residual accepted unbalance: 

U[gr.mm] = Et.M 

Where: M [kg] = Rotor mass 

Total residual admitted unbalance in grams is m= U/R 

Where, R [mm] is the compensation radius. [2] 

VI. EXPERIMENTAL METHOD 

TABLE I 

IMPELLER SPECIFICATIONS 

Sr. 

No. 

Regular Italic 

1 Impeller type Single vane impeller 

2 Balancing speed 1450 rpm 

3 Length of the rotor 210 mm 

4 Diameter 

impeller 

of the 310 mm 

5 Suction diameter 160 mm 

6 Weight of the rotor 38.8 kg 

7 Balancing grade G6.3 (As per Internal 

Standard ISO 1940) 

Set up the rotor in the balancer (balancing machine) and 

secure it. Mount the rotor vertically on the shaft of the 

balancer. Make sure that the rotor is place in proper vertical 

position. There is no misalignment in the rotor and the shaft 

of the balancer. Feed the balancing grade in the machine. 

Make sure that the rotor is freely rotating. This machine is 

the vertical axis semiautomatic machine and has the 

capability of performing two-plane balancing with required 

balancing speed and provides us the exact information of 

unbalance amount and location on the rotor. 

Fig.7 Rotor placement on machine



Balancing machine screen provides various details of the 

plane radius , rotor radius, acceptable unbalance for the 

rotor. We can feed the balancing grade (G6.3 for pump 

impeller) and machine automatically calculates the 

tolerance per plane data and displays on the screen of the 

balancing machine. 

Start the balancer with the balancing speed of 1450 rpm 

and read out the details on the screen. This specifies the 

details about the rotor and the acceptable unbalance. Before 

starting mark the location of zero on the rotor which should 

matches the arrow mark on the balancing machine table. 

TABLE III 

BALANCING GRADES [5] 

Balancing Rotor Types 

Grades 

G 4000 Crankshaft drives of rigidly mounted slow marine 

diesel engines with uneven number of cylinders. 

G 1600 Crankshaft drives of rigidly mounted large twocycle 

engines. 

G 630 Crankshaft drives of rigidly mounted large fourcycle 

engines. 

Crankshaft drives of elastically mounted marine 

diesel engines. 

G 250 Crankshaft drives of rigidly mounted fast fourcylinder 

diesel engines. 

G 100 Crankshaft drives of fast diesel engines with six or 

more cylinders. Complete engines (gas or diesel) for 

cars, trucks and locomotives. 

G 40 Car wheels, wheel rims, wheel sets, drive shafts. 

Crankshaft drives or elastically mounted fast fourcycle 

engines (gas or diesel) with six or more 

cylinders. Crankshaft drives for engines of cars, 

trucks or locomotives. 

G 16 Drive shafts (propeller shafts, cardan shafts) with 

special requirements. Parts of crushing machinery. 

Parts of agricultural machinery. Individual 

components of engines (gas or diesel) for cars, 

trucks and locomotives. Crankshaft drives of 

engines with six or more cylinders under special 

requirements. Slurry or dredge pump impeller. 

G 6.3 Parts or process plant machines. Marine main 

turbine gears (merchant service). Centrifuge drums. 

Fans. Assembled aircraft gas turbine rotors. Fly 

wheels. Pump impellers. Machine tool and general 

machinery parts. Normal electrical armatures. 

Individual components of engines under special 

requirements 

G 2.5 Gas & steam turbines, including marine main 

turbines (merchant service). Rigid turbo-generator 

rotors. Rotors. Turbo-compressors. Machine tool 

drives. Medium and large electrical armatures with 

special requirements. Small electrical armatures. 

Turbine driven pumps. 

412 

G 1 Tape recorder and phonograph drives. Grinding 

machine drives. Small electrical armatures with 

special requirements 

G 0.4 Spindles, disks and armatures of precision grinders. 

Gyro 

TABLE IIIII 

BALANCING TOLERANCE [2] 

The maximum service speed is reported on the 

horizontal x axis, while the acceptable specific unbalance is 

reported on the vertical y axis. The formula can be used 

instead of previous figure. 

Et (μ) = (9550/N).G 

Et (μ) = 9550/1450×6.3 = 41.50



Where, 

Et[μ] = total acceptable mass eccentricity 

N [RPM] = maximum service rotor speed 

G [mm/s] = balancing quality (grade) 

Total residual accepted unbalance. 

Where, M[kg] = Rotor mass 

U[gr.mm] = 41.50×38.8 

U[gr.mm] = 1610.2 

U[gr.mm]=Et.M 

Acceptable unbalance per plane 

= 1610.2/2=805 gr.mm 

Plane 1 acceptable unbalance 

= 805/80=10.1 gr 

Plane 2 acceptable unbalance 

= 805/154=5.2 gr 

Wait for some time to stabilize the data on the balancing 

machine screen. This data gives us the amount of 

unbalance and the angle of the same on the rotor. Once the 

data is stabilized, stop the balancer and read the data on the 

screen. The screen is mainly divided into two parts, on the 

left hand side the data is for plane 1 and on right hand 

screen the data is for plane 2. The data is represented in two 

colours – red and green. Green colour shows that the 

unbalance amount is under acceptable limit whereas the red 

colour data shows the unbalance has to be removed as this 

exceeds the tolerance limit. 

TABLE IVV 

BALANCING DATA - I 

Sr. 

No. 

Parameter Plane 1 Plane 2 

1 Amount of unbalance 

[gr] 

6.25 30.62 

2 Angle [deg] 210 45 

3 Radius [mm] 70 153 

If the data shows in green, then the rotor if said to be 

balanced. Otherwise we need to remove the unbalance 

amount from the rotor. 

Unbalance Correction Methods: 

Addition of mass 

Removal of mass 

413 

Repeat the same balancing process until the data comes 

under the acceptable limit of the rotor as per ISO 1940/1 

grade G 6.3. 

TABLE V 

BALANCING DATA - II 

Sr. 

No. 



[gr] 

5.21 21.01 

2 Angle [deg] 212.3 44.5 

3 Radius [mm] 70 151 

TABLE VI 

BALANCING DATA - III 

Sr. 

No. 



[gr] 

5.15 2.11 

2 Angle [deg] 213 45.5 

3 Radius [mm] 70 153 

TABLE VI shows that the unbalance amount is within 

the balancing grade limit. Hence, we can say that the 

impeller is balanced as per G6.3 grade. 

VII. RESULTS 

Rotor dynamics is the study of rotating machines and 

has a very important part to play throughout the modern 

industrial world. The experimental results of rotor dynamic 

balancing shows the data within acceptable limit as per ISO 

1940/1, grade G6.3 for pump impeller. 

References 

[1] Shiyu Zhou and Jianjun Shi, ―Active Balancing and Vibration 

Control of Rotating Machinery: A Survey‖, The Shock and 

Vibration Digest, July 2001, Vol. 33, No. 4, 361-371. 

[2] Ing. G. Manni, ―Balancing Theory and Applications‖, CEMB S.p.A. 

– Via Risogimento, August 1999, Rev. 2.1. 

[3] Joe Evans, ―Sewage Pump Impeller Selection‖, Pacific Liquid & Air 

Systems. 

[4] Gary K. Grim, John W. Haidler, Bruce J. Mitchell, Jr., ―The Basics 

of Balancing‖, Balance Technology Inc. 

[5] Earl M. Halfen, ―Shop Balancing Tolerances A Practical Guide‖, 

IRD Balancing.

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