Balancing Technique for Turbo Machinery Rotor
PRAMOD BELKHODE
General Engineering Department, Laxminarayan Institute of Technology
Rashtrasant Tukadoji Maharaj Nagpur University
Nagpur, Maharashtra
INDIA
Abstract: - Balancing process carried out in the thermal power station is very complex and complicated. The
complete unit is to be cooled down for balancing this takes nearly 10 to 15 days. After cooling the unit is
disassembled and the rotor is taken out for which again 10 to 15 days are required for balancing and assembly.
Rotor is placed on the balancing machines for balancing which is carried out by Engineers of the testing
department. Balancing of a bulky rotor is difficult and it is carried out step by step. After balancing, complete
rotor is to be placed in the turbo machine which is a most difficult task as it has to match the all alignment and
other conditions properly. The complete process takes period of nearly one and half month for balancing the
rotor, so balancing of the rotor is called to be the costly project in the thermal power station. After the balancing
procedure is completed, while starting the complete unit various parameters are to be controlled such as steam
inlet temperature, pressure, flow of the steam and rpm of the unit to avoid any type of danger. Loss of production
of power during the shutdown period is major loss of any power station. Paper details the automatic thermal
balancing of turbo machinery rotor using heating coils.
Key-Words: - Balancing, Heating Coil, Rotor, Turbo Machinery, Centrifugal force
Received: July 26, 2021. Revised: March 17, 2022. Accepted: April 21, 2022. Published: May 10, 2022.
1 Introduction
Experimental simulator is fabricated for
implementing balancing technique. Fabricated model
consists of two hollow shafts, heating coils, slip ring,
carbon brushes, pulley, journal bearing, wooden
platform, coupling and motor. In practice a rotor
weighting 20 tons or more and rotating at 1500 rpm
may be so well balanced that the motion except for
sound is just perceptible. The significance of this
statement may be appreciated, when it is realized that
if the same turbo machinery rotor were out of balance
to the extent of one lb at a radius of 4 feet. In other
words, if the CG of the rotor were displaced only
1/1000th part of an inch from the axis of an rotation,
then the periodic force tending to produce vibration
would be 3070 lb weight or 1.36 tons. The
unbalance of the particular zone is detected. The
heating coil opposite to that zone will be heated by
supplying suitable amount of current to the heating
coils through the slip ring and carbon brushes which
create the thermal condition such as temperature rises
and deformation. Heating of coil is carried out while
running condition produces thermal stresses in that
zone. Centrifugal force acting along the rotor in that
heated region is so effective that, these forces will
reduce the unbalance.
The new balancing method is the result of
attempts through current practice towards satisfying
the objective of an ideal balancing process. Balancing
of the rotor as it spins, does not generate debris,
simple, low cost and reliable.
2 Experimental Simulator
Experimental simulator is fabricated for
implementing this balancing technique. Fabricated
model consists of two hollow shafts, heating coils,
slip ring, carbon brushes, pulley, journal bearing,
wooden platform, coupling and motor. Heating coils
are placed between the gap of two hollow shafts with
the help of insulator, mica sheet and layer of asbestos
sheets. Heating coils are connected to the end
terminals of the slip rings. Slip rings are provided on
both ends of the shaft and carbon brushes are holding
over the slip rings. Shaft is placed in the journal
bearing and connected to the coupling with the
provision of bushes, which are provided to the shaft
and to rotate through the motor. Pulley is connected
to another end for creating the load through the rigid
coupling and extension of the shaft.
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2022.17.14
Pramod Belkhode
E-ISSN: 2224-3461
131
Volume 17, 2022
2.1 Selection of Rotor
Rotor diameter is selected on the basis of available
size of slip rings in the market. Minimum bore
diameter of the slip ring available in the market is 40
mm, so as per the standard size available, Rotor size
is selected.
2.1.1 Calculation of Heat Generation
Heating coils are directly connected between two slip
rings. Slip ring available in the market as per the size
have a four terminal, so four heating coils are
available (four zones are formed). Two ends of a
heating coil are attached to two terminals of two slip
rings. To avoid direct contact of heating coil with the
surface of the rotor insulated sheets and asbestos
sheets are wraps axially along the heating coil
respectively. In between these heating coils a layer of
asbestos sheet is placed for effective heating in that
particular zone.
Fig 1: Arrangement for Heating Coil over Inner
Pipe with asbestos sheet
Length of the rotor is selected on the basis of
taking L/D scale ratio of Turbo machinery rotor of
unit No. 3 Thermal Power Station. Propose to work
on same type of condition.
L / D = 565/68.43 = 8.25
There is the availability of slip rings in market
with 40 mm inner bore therefore diameter of rotor is
selected as 40cm, corresponding length of the rotor
as per L/D ratio is 34.3 cm.
Finally, length of the rotor is selected considering
length of slip ring, journal bearing and clearance as
72.5 cm
2.1.2 Deformation of Rotor
As unbalance increases rotor will start to spin about
its mid position as shown in figure. Here y is rotor
deflection, taking small element of this rotor for
calculating the change in length of rotor.
BC/AB = dy/dx
AC = { AB2 + BC2 } 1/2
= { (dx)2 + [x(y/x)]2 } 1/2
= {(x)2 + x2(y/x)2 } ½
AC = (x) {1 + (dy/dx)2 } 1/2
x = 0
l = AC
x = L
x = 0
l = (x) {1 + (dy/dx)2 } 1/2
x = L
x = 0
l = {1 + (dy/dx)2 } ½ dx
x = L
where y = f( x )
2.1.3 Temperature Effect
Thermal stresses occur due to change in
temperature of a body, which results in the
change of its dimensions. If the body is
unrestrained, no stresses will be developed. But
if it is restrained, a compressive stress will be
induced which is given by delta.
Delta is function of coefficient of linear
expansion is mm/mm o c and the change of
length over the length L is l.
T = l / * L
Slip Ring
Heating Coil
dx
dy
y
dx
dy
A
B
C
e
L
R1
R2
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2.1.4 Heat Flow Equation
A hollow pipe with a thermal conductivity k,
inner pipe radius r1is held at temperature t1and
outer pipe radius r2 is held at temperature t 2.
Electrical energy is dissipated with the pipe at
the qg per unit volume.
The appropriate form of heat flow equation is,
d2t / dr2 + 1/r dt/dr + qg / k = 0
Or d/dr{rdt/dr}= - r{qg / k }
Upon integration
dt/dr = - r{qg / 2k }+ c1/r ….. eq (1)
Another integration gives the general solution for
temperature distribution
t = - r2{qg / 4k }+ c1loger + c2 …… eq. (2)
The constant of integration is determined from the
relevant boundary conditions are:
1. r = r1, the pipe region is perfectly
insulated and heat flow is zero
2. r = r2 at t = t2
From Fourier’s law Q = -kA dt/dr, and accordingly
the temperature derivative must be zero at r = r1.
Hence using expression (1)
c1 = (qg / 2k) r12
Applying the boundary condition r = r2 at t = t2 to
expression (2)
c2 = t2 + r22{qg / 4k }- (qg / 2k) r12 loger2
t = t2 + (qg / 2k) r12 loger/ r2 + (r22- r2){qg / 4k }
tmax - t2 = (qg / 2k) r12 loger/ r2 + (r22- r2){qg / 4k }
T = (qg / 2k) r12 loger/ r2 + (r22- r2){qg / 4k }
T = (qg / 2k) { r12 loger/ r2 + (r22- r2)/2}
Inserting the appropriate values calculate qg
Therefore, Heat generated qg is in w/m3
Total volumetric heat generation:
Qg = qg x Area of hallow pipe
In term of electrical quantities,
Heat generated = I2 x R
Hence the maximum allowable current can be
calculated to thermally balance the rotor.
2.2 Analysis of Coil
Fig 2. Rotor pipe with heat coil
Outer shaft outer diameter = 87 mm
Outer shaft inner diameter = 82 mm
Inner shaft outer diameter = 38.6 mm
Inner shaft inner diameter = 35.6 mm
Heating coil diameter = 10 mm
Capacity of heating coil = 2000w
Length of heating coil = 45 cm
Thickness of insulation = 21 mm
Thermal conductivity of the shaft material = 45 w/mk
Thermal conductivity of insulation = 0.17 w/mk
Heating coil gap = inner radius of outer shaft – outer
radius of inner shaft
= 41 – 19.3 = 21.7 mm
Insulation thickness = heating coil gap – heating coil
diameter
= 21.7 – 10 = 11.7 mm
Insulation provided below and above the heating coil
diameter = 5.85 mm
Inner radius of heating coil, r1 = 5 mm
Radius of heating coil with insulation, r2 = 10.85 mm
Radius of outer shaft, r3 = 13.35 mm
Fig 3. Rotor with various radius
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Taking heat transfer coefficient from the outer
surface of the insulation to the surrounding = 10
w/m2k
Heat transfer , Q = (t1 – t4)/ (R1+R2+R3)
Where
R1 = loge r2/r1 / (2kl)
R2 = loge r3/r2 / (2kl)
R3 = 1 / (2r3lh)
t1- t4 =T = l / * L
substituting the above value, Q is calculated in Watt
under steady state all the heat produced on account of
current flow must be transferred to the surrounding.
Therefore,
Heat generated per unit volume, qg = Q / (r2l)
In terms of electric quantities, current density I and
electrical conductivity ke,
Heat generated per unit volume = i2/ke
Current required raising the temperature,
I = i*A
A = Area of heating coils, m2
This much amount of current I is to be supplied for
rising the temperature and mr2 is the centrifugal
force required for reducing the unbalance.
3 Experimental Simulator for
Balancing
Fig 4: Experimental Simulator for Automatic
Thermal Balancing of Turbo Machinery Rotor
Ba = Base of the Model, M = Motor, C = Coupling,
S1 = Inner shaft, S2 = Outer shaft, JB = Journal
Bearing, CR = Carbon Rod Assembly, S = Slip Ring,
D = Circular Disk, B = Blade.
During the balancing, unbalance is detected
as per the zone. Correspondingly heating coil
opposite to that zone will be activated. Coil will be
heated by supplying suitable amount of current to the
heating coils through the slip ring and carbon
brushes.
Thermal condition is formed such as elevated
temperature achieved and controlled amount of
incremental deformation is produced. Centrifugal
induced stresses are produced in that zone. The
centrifugal forces acting over the heated zone are so
effective that these forces will reduce the unbalance.
A physical balance assembly is schematically shown
in Fig 4. Four heating coils are connecting to four
terminals to a pair of slip ring, which is on both ends
of the rotor. On slip ring, carbon brushes are located
on both the ends of the respective slot of the copper
strip. Current is supplied to the respective heating
coils through the carbon brushes. Heating coils are
placed axially over the circumferential 90-degree
apart on the rotor. Between two heating coils a layer
of asbestos sheets, mica sheets, insulator sheets are
placed. So, the heat cannot be transferred over the
other zones of heating coils when particular heating
coil zone is activated.
4 Testing of Experimental Simulator
This testing is done using the instrument
vibroport 41. Connection between photocell,
accelerometer pickups and FFT analyzer is the one
set of connection. Other set of connection is the
connection between heating coils through the
switches on the switchboard, ammeter and
dimmerstat. Vibroport 41 measures the unbalance
reading on bearing1 and bearing 2 in micrometer.
Table 1 shows the readings taken on both bearings.
Level of unbalance is reducing due to the supply of
the current through the dimmerstat. In this case only
one heating coils is active were as other are at zero
voltage.
Table 1: Reading using Vibroport 41.
Current
(Amps)
Bearing1(µm)
Bearing2(µm)
At no voltage
380
341
1
316
330
3
316
320
8.3
304
284
9
289
279
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DOI: 10.37394/232012.2022.17.14
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Fig 5: Testing setup of the experimental simulator
when current supplied to the heating coils
5 Result and Discussion
The tests performed indicate the level of
unbalance decreases as current is supplied to the
heating coil. For quick balancing, current supply is to
be increase. So as to rises the temperature of the
heated portion to reduce the level of unbalance.
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WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2022.17.14
Pramod Belkhode
E-ISSN: 2224-3461
135
Volume 17, 2022
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