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 Kalmegh1, Santosh Bhaskar2
1
Dept. of Mechanical Engineering, S.R.E.S. College of Engineering, Kopergaon, Pune University
Prof. Dept. of Mechanical Engineering, S.R.E.S. College of Engineering, Kopergaon, Pune University
2
1
amitkalmegh@gmail.com
santoshbhaskar12002@yahoo.co.in
2
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]
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.
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.
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.
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.
Fig.1 Centrifugal pump impeller [3]
409
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 6, June 2012)
Rotor balancing techniques can be mainly classified as:
 On-line balancing methods
 Off-line balancing methods
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.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.
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]
III. TYPES OF UNBALANCE
A. Static 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]
IV. UNBALANCE EFFECT
An unbalanced rotor generates an inertial force
(centrifugal) which increases with the square speed.
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]
Fig.6 Unbalance effect [2]
410
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 6, June 2012)
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
F = m.r.ω2 = U.ω2
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
Total residual accepted unbalance:
U[gr.mm] = Et.M
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]
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
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).
Sr.
No.
1
Regular
Italic
Impeller type
Single vane impeller
2
Balancing speed
1450 rpm
3
Length of the rotor
210 mm
4
Diameter of the
impeller
Suction diameter
Weight of the rotor
Balancing grade
310 mm
5
6
7
The calculated value is the same mass eccentricity:
160 mm
38.8 kg
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.
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.
Fig.7 Rotor placement on machine
411
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 6, June 2012)
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.
G1
G 0.4
Tape recorder and phonograph drives. Grinding
machine drives. Small electrical armatures with
special requirements
Spindles, disks and armatures of precision grinders.
Gyro
TABLE IIIII
BALANCING TOLERANCE [2]
TABLE III
BALANCING GRADES [5]
Balancing
Grades
G 4000
G 1600
G 630
G 250
G 100
G 40
G 16
G 6.3
G 2.5
Rotor Types
Crankshaft drives of rigidly mounted slow marine
diesel engines with uneven number of cylinders.
Crankshaft drives of rigidly mounted large twocycle engines.
Crankshaft drives of rigidly mounted large fourcycle engines.
Crankshaft drives of elastically mounted marine
diesel engines.
Crankshaft drives of rigidly mounted fast fourcylinder diesel engines.
Crankshaft drives of fast diesel engines with six or
more cylinders. Complete engines (gas or diesel) for
cars, trucks and locomotives.
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.
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.
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
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.
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
412
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 6, June 2012)
Where,
Et[μ] = total acceptable mass eccentricity
N [RPM] = maximum service rotor speed
G [mm/s] = balancing quality (grade)
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
Total residual accepted unbalance.
U[gr.mm]=Et.M
Where, M[kg] = Rotor mass
U[gr.mm] = 41.50×38.8
U[gr.mm] = 1610.2
Sr.
No.
1
Parameter
2
3
Angle [deg]
Radius [mm]
Plane 1
Amount of unbalance
[gr]
Plane 2
5.21
21.01
212.3
70
44.5
151
TABLE VI
BALANCING DATA - III
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
Parameter
Plane 1
Plane 2
Amount of unbalance
[gr]
5.15
2.11
2
3
Angle [deg]
Radius [mm]
213
70
45.5
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.
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.
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
TABLE IVV
BALANCING DATA - I
Plane 1
Sr.
No.
1
[1] Shiyu Zhou and Jianjun Shi, ―Active Balancing and Vibration
Sr.
No.
1
Parameter
Amount of unbalance
[gr]
6.25
30.62
2
3
Angle [deg]
Radius [mm]
210
70
45
153
Control of Rotating Machinery: A Survey‖, The Shock and
Vibration Digest, July 2001, Vol. 33, No. 4, 361-371.
Plane 2
[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.
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.
[5] Earl M. Halfen, ―Shop Balancing Tolerances A Practical Guide‖,
IRD Balancing.
Unbalance Correction Methods:
 Addition of mass
 Removal of mass
413