International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 01, January 2019, pp. 1880-1896, Article ID: IJMET_10_01_186
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=1
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication Scopus Indexed
V. V. Kondaiah
Center for Design and Analysis, Department of Mechanical Engineering, CMR College of
Engineering & Technology, Kandlakoya, Hyderabad, Telangana-501401
Jagu S. Rao
Department of Mechanical Engineering, RGUKT, Nuzvid, Andhra Pradesh
V. V. Subba Rao
Department of Mechanical Engineering, Jawaharlal Nehru Technological University
Kakinada, Kakinada, Andhra Pradesh
ABSTRACT
Magnetic thrust bearing is a device which is used to support the object by controlling the magnetic field. Permanent magnets or electromagnets or both are used to produce magnetic field. The type of magnetic bearing discussed in this paper is a single acting active magnetic thrust bearing. A prototype magnetic thrust bearing is made to study the thrust capability. The measured values of force are compared with theoretical values. A leakage factor is estimated. The experiments are done at different air gaps from 1mm to 5 mm in steps of 0.5 mm. The variation of leakage factor is plotted at different air gaps. An attempt is made to find the optimum air gap between the stator and rotor of AMTB.
Keywords : Active magnetic thrust bearings (AMTB), leakage factor, Dynamic stiffness.
Cite this Article : V. V. Kondaiah, Jagu S. Rao and V. V. Subba Rao, Estimation of
Leakage Factor for Active Magnetic Thrust Bearing, International Journal of
Mechanical Engineering and Technology , 10(1), 2019, pp. 1880-1896. http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=1
An active magnetic bearing works on the principle of electromagnetic suspension. It consists of an electromagnet assembly, a set of power amplifiers which supply current to the electromagnets, a controller, and gap sensors with associated electronics to provide the feedback required to control the position of the rotor within the gap.
A Magnetic thrust bearing has an electromagnetic stator and a rotor. Allaire et al. [1] presented the design of a prototype of thrust magnetic bearing for the high load-to-weight
http://www.iaeme.com/IJMET/index.asp 1880 editor@iaeme.com

V. V. Kondaiah, Jagu S. Rao and V. V. Subba Rao ratio. Groom and Bloodgood [2] proposed a model by adding the loss and leakage factors to ideal models with and without bias permanent magnets. Subsequently, Bloodgood et al. [3] applied the theory for the optimal design of a thrust magnetic bearing with bias permanent magnets. Rao and Tiwari [4] implemented multi-objective genetic algorithms (MOGAs) for the optimization of active magnetic thrust bearings (AMTB) with pure electro magnets considering the power-loss and the weight as minimization type objective functions. David et al. [5] explained the leakage, fringing and eddy current effects in design of magnetic bearings.
Bekinal et al. [6] Experimented on permanent magnet thrust bearing and compared the theoretical and practical force generated in their test setup. Kondaiah et al. [7] experimented on active magnetic thrust bearing on a universal testing machine for an air gap of 3mm and measured the actual force between stator and rotor of bearing. In this work the bearing is made with laminated CRGO sheets
In the present work, a prototype of single acting active magnetic thrust bearing has been made and tested for thrust capability on the own fabricated test setup. The stator and rotor of the bearing is made with the solid metal of mild steel. The solid metal is used because the eddy current losses in the thrust applications are negligible [1]. The attractive force between stator and rotor has been measured on the test setup. The measured values of force are validated with theoretical values computed using Lorentz principle. The experiments are done at different current inputs and varying the gap between stator and rotor from 1 mm to 5 mm in steps of
0.5 mm. The average leakage factor is calculated at different air gaps. The variation of leakage factor is plotted with respect to air gap. A comparison of theoretical, actual and predicted forces has been discussed at different air gaps.
A Area of air gap g
B Magnetic flux density
F a
Actual Force developed
F p
Force on one pole face
F pre
Predicted force
F th
Theoretical force
R Total reluctance of magnetic circuit
R g
Reluctance of air gap
R f
Reluctance of iron path h c
Axial length of stator h t
Axial length of stator pole with base i Current in coil k Leakage factor k av
Average leakage factor l Effective magnetic circuit gap l b
Axial length of stator base l d
Axial length of thrust rotor l f
Length of iron path http://www.iaeme.com/IJMET/index.asp 1881 editor@iaeme.com

Estimation of Leakage Factor for Active Magnetic Thrust Bearing l g
Height of Air gap n Number of turns r ci
Inner radius of coil gap r co
Outer radius of coil gap r i
Inner radius of stator r o
Outer diameter of stator v Voltage supplied

% Percentage of error between theoretical force and actual force th

% Percentage of error between predicted force and actual force pre

, ni Magneto motive force
 r
Relative permeability of silicon steel

Magnetic flux
 g
Permeability of free space
4𝜋 × 10 −7
Web/amp-turn-meter
A magnetic thrust bearing has an electromagnetic stator and a rotor, which are separated by an air gap, as illustrated in Fig. 1. In its simplest form, the electromagnetic stator is formed by an inner and outer pole connected by a common base. The exploded view, in Fig. 1, clearly shows the stator, shaft, winding, and thrust collar of a single acting bearing. The stator and rotor disc are made up of mild steel. The mild steel discs are turned into the desired shapes on the lathe machine. The winding, which occupies the space between the inner and outer poles of the stator, produces the magnetic flux in the bearing. Magnetic flux paths are flowing through the inner and outer poles through the rotor disc. It is important to provide a good flux path to avoid leakage from the magnetic components [1].
Figure 1 Components of AMTB http://www.iaeme.com/IJMET/index.asp 1882 editor@iaeme.com

V. V. Kondaiah, Jagu S. Rao and V. V. Subba Rao
The model of the magnetic thrust bearing used is based on one dimensional electromagnetic theory. Several assumptions are made in this derivation for the sake of simplicity as given below.
1.
No leakage of flux takes place between the inner and outer poles.
2.
The intensity of flux is always below saturation level.
3.
Changes in the current input are small compared to the steady state level.
4.
Axial shaft motions are small compared to the steady state air gap.
5.
One dimensional model of the magnetic path was used.
Figure 2 Geometry of AMTB
The geometry of AMTB is shown in Fig.2, pole face area of air gap A g is given by
A g
 
 r
2 ci
 r i
2
  r r o
2  2 co

(1)
These areas of the outer and inner poles are made equal so that the magnetic flux density has the same level in each pole. The pole face area then equals the air gap area A g
. Thus the thickness of the base could be evaluated from
A g

2
 r t ci b (2)
The rotor disc thickness equals to back wall thickness. The reluctance of each air gap is given by
R g


0 l g
A g
And the reluctance of the iron path is
R f
 l f
 
0
A r g
Let the length of air gap magnetically be equal to the iron path with value
(3)
(4) http://www.iaeme.com/IJMET/index.asp 1883 editor@iaeme.com

Estimation of Leakage Factor for Active Magnetic Thrust Bearing l e
 l f
 r
The total reluctance of the magnetic circuit is
R

2 R g

R f


2 l g
 l e
 

0
A g

Thus the effective magnetic gap l is
(5)
(6) l

2 l g
 l e
Magneto Motive Force (ϑ) is equal to the number of turns in the coil times the current
  ni
The magnetic flux could be found from
(7)
(8)
 

R


A ni
0 g l
And the flux density in the path is given by
(9)
B


A g


A ni
0 g l
(10)
The magnetic flux density must not exceed the saturation level for the particular magnetic material involved. Typical values for silicon iron are 1.2 to 1.6 Tesla and for rare earth materials up to 2.0 Tesla. The attractive force developed at each pole face is
F p


2
2

A g

A g
2 l
2
2
(11)
The total force developed is
F th

2 F p


2

A g

 
0
A g
2 l
2
(12)
The actual force is reduced some extent due to leakage effects. A leakage parameter k , can be calculated for the thrust bearing geometry as k

F th
F a (13)
Having some practical values of F a
at a particular air gap, an average leakage factor, k av could be predicted that fits F th
with the practical results. And the thrust bearing load capacity is then modified to include as
F pre

2 2 l k av
2
Where F pre
is predicted force.
(14) http://www.iaeme.com/IJMET/index.asp 1884 editor@iaeme.com

V. V. Kondaiah, Jagu S. Rao and V. V. Subba Rao
A prototype of single acting thrust bearing was constructed for testing of load capacity.
The rotor and stator parts separately are shown Fig. 3. The lead wires for the coil come out of holes in the stator base for connection to the control circuit. The dimensions of the prototype have been given in Table 1.
Table 1 Dimensions of prototype manufactured
Value
Parameter Symbol
(mm)
Inner diameter of stator r i
20
Inner diameter of coil gap, r ci
Outer diameter of coil gap, r co
30
45
Outer diameter of stator, r o
Depth of coil gap, d
Axial length of thrust runner, h t
Air gap, l g
52.5
3.8
10
1: 0.5: 5
(a) AMTB stator (b) AMTB rotor
Figure 3 Prototype of AMTB
The test setup used in this work, shown in Fig.4. is fabricated to measure the magnetic force between stator and rotor parts of the bearing. The frame holds the components of AMTB and load. The stator part of bearing is hold by upper horizontal bar of the frame and it has nut and bolt arrangement to move up and down. The rotor and load are hold by the middle horizontal bar. The rotor shaft is free to move in the middle horizontal bar. The shaft of rotor passes through the middle bar and dead weights are attached to it. http://www.iaeme.com/IJMET/index.asp 1885 editor@iaeme.com

Estimation of Leakage Factor for Active Magnetic Thrust Bearing
Figure 4 Test setup for AMTB
A variator is used to change the current input. An ammeter and a voltmeter are used to measure the input current and voltage respectively.
As the difference between the relative permeability of air and aluminum is negligible, the air gap between stator and rotor is maintained by keeping aluminum plates of desired thickness.
The thickness of aluminum plates ranging from 1mm to 5mm in the steps of 0.5mm. The voltage is varied from 50 V to 120 V. The input current is varied from 0 Amp to 6 Amp. At each value of current the attractive force is measured by applying equivalent force in the opposite direction. The experiment is repeated three times for each air gap and the average values have been taken as final values.
Though the experimentation has been done at different air gaps 1 mm to 5 mm in steps of 0.5 mm, the results of the AMTB at an air gap 1 mm have been shown in Table 2 for observation.
The actual force, theoretical force, predicted force, the percentage of error between actual force and theoretical force and percentage of error between predicted and actual force have been tabulated. http://www.iaeme.com/IJMET/index.asp 1886 editor@iaeme.com

V. V. Kondaiah, Jagu S. Rao and V. V. Subba Rao
V
Table 2 Results of AMTB when the air gap is 1 mm i F a
F th k F pre
90 2.16 65.95 199.09 1.74 58.14 66.87 -13.44
95 2.31 72.81 227.62 1.77 66.47 68.01 -9.53
100 2.45 78.22 254.58 1.81 74.34 69.28 -5.21
105 2.56 86.72 279.39 1.79 81.59 68.96 -6.29
110 2.73 94.65 316.86 1.83 92.53 70.13 -2.29
115 2.86 101.34 348.53 1.86 101.78 70.92 0.43
120 2.96 107.04 373.27 1.86 109.01 71.32 1.79 k av
= 1.85
Theoretical force and Predicted force has been calculated at each air gap between stator and rotor of AMTB, and these are compared with actual force measured.
400.00
350.00
300.00
250.00
200.00
150.00
100.00
50.00
0.00
Actual force(N)
Theoretical force(N)
Predicted force(N)
2.17 2.32 2.45 2.57 2.73 2.87 2.97
current(A)
Figure 5 Actual, Theoretical and Predicted force for 1mm airgap http://www.iaeme.com/IJMET/index.asp 1887 editor@iaeme.com

Estimation of Leakage Factor for Active Magnetic Thrust Bearing
300.00
250.00
200.00
150.00
100.00
Actual force(N)
Theoretical force(N)
Predicted force(N)
50.00
0.00
1.87 2.08 2.40 2.67 2.98 3.28 3.58 3.88
current(A)
Figure 6 Actual, Theoretical and Predicted force for 1.5 mm airgap
180.00
160.00
140.00
Actual force (N)
Theoreticalforce (N)
Predicted force (N)
120.00
100.00
80.00
60.00
40.00
20.00
0.00
1.88 2.13 2.50 2.78 3.15 3.37 3.67 3.85
current (A)
Figure 7 Actual, Theoretical and Predicted forces for air gap 2mm http://www.iaeme.com/IJMET/index.asp 1888 editor@iaeme.com

V. V. Kondaiah, Jagu S. Rao and V. V. Subba Rao
160.00
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
Actual force
Theoretical force
Predicted force current (A)
Figure 8 Actual, Theoretical and Predicted force for 2.5mm air gap
120.00
100.00
80.00
60.00
40.00
20.00
0.00
Actual force(N)
Theoretical force (N)
Predicted force(N)
Current(A)
Figure 9 Actual, Theoretical and Predicted forces for 3mm air gap http://www.iaeme.com/IJMET/index.asp 1889 editor@iaeme.com

Estimation of Leakage Factor for Active Magnetic Thrust Bearing
80.00
70.00
60.00
50.00
40.00
30.00
20.00
10.00
0.00
Actual force(N)
Theoretical force(N)
Predicted force(N)
3.13 3.33 3.53 3.72 3.87 4.05 4.22 4.35 4.55
Current(A)
Figure 10 Actual, Theoretical and Predicted force for 3.5mm
80.00
70.00
60.00
Actual force(N)
Theoretical force(N)
Predicted force(N)
50.00
40.00
30.00
20.00
10.00
0.00
current(A)
Figure 11 Actual, Theoretical and Predicted force for air gap 4mm http://www.iaeme.com/IJMET/index.asp 1890 editor@iaeme.com

V. V. Kondaiah, Jagu S. Rao and V. V. Subba Rao
80.00
70.00
60.00
50.00
40.00
30.00
20.00
10.00
0.00
Actual force(N)
Theoretical force(N)
Predicted force(N)
4.70 4.93 5.13 5.30 5.42 5.57 5.68 5.78
current(A)
Figure 12 Actual, Theoretical and Predicted force for air gap 4.5mm
60.00
50.00
40.00
30.00
20.00
10.00
0.00
Actual force(N)
Theoretical force(N)
Predicted force(N)
5.23
5.38
5.52
current(A)
5.65
Figure 13 Actual, Theoretical and Predicted force for air gap 5mm
In Fig. 5 to Fig. 13 the actual force, theoretical force and predicted force have been shown at different air gaps from 1 mm to 5mm in steps of 0.5 mm. From these plots it can be observed that there is large differences between theoretical force and actual force, however after introducing leakage factor, the difference between the predicted force and actual force drastically reduced for all the air gaps. The percentage of error between theoretical force and actual force is ranging from 77 to 266 and the percentage of error between predicted force and actual force is ranging from 13.25 to 0.16 http://www.iaeme.com/IJMET/index.asp 1891 editor@iaeme.com

Estimation of Leakage Factor for Active Magnetic Thrust Bearing
Table 3 Change of leakage factor and max % of error with respect to air gap
Air Average Max % of
Gap
(mm)
1
Leakage factor
(k av
)
1.8505 error of predicted force
11.85
1.5
2
1.829
1.5475
10.84
10.89
2.5
3
3.5
4
4.5
5
1.5229
1.4149
1.4306
1.4232
1.655
1.6765
4.99
11.59
8.06
12.2
13.26
6.2
The average value of leakage factor and maximum percentage of error between actual and predicted forces has been calculated at all air gaps from 1 mm to 5 mm in the steps of 0.5 mm.
There are shown in Table 3. The variation of leakage factor with air gap has been plotted in
Fig.14. It is observed that the average value of leakage factor is minimum and almost equal from the air gaps 2 mm to 4 mm. The average leakage factor value is more when the distance between stator and rotor of AMTB is too close and too far.
The variation of leakage factor with air gap has been plotted in Fig 14. It is observed that it is almost equal from the air gaps 2 mm to 4 mm.
1
0.8
0.6
0.4
0.2
0
2
1.8
1.6
1.4
1.2
Average leakage factor
1 1.5
2 2.5
3 3.5
4 4.5
5
Air Gap (mm)
Figure 14 Average leakage factor vs air gap http://www.iaeme.com/IJMET/index.asp 1892 editor@iaeme.com

V. V. Kondaiah, Jagu S. Rao and V. V. Subba Rao
14
12
10
8
6
4
2
0 max % error
1 1.5
2 2.5
3 3.5
4 4.5
5
Air gap(mm)
Figure 15 change of max % of error with air gap
The maximum percentage of error between predicted force and actual force with air gap has plotted in Fig 15. It is observed that the maximum percentage of error is minimum between the air gaps of 2 mm to 3.5 mm. At an air gap of 4.5 mm percentage of error is maximum and is 13.26. The minimum percentage of error at an air gap of 2.5 mm and is 4.99.
Table 4 Variation of current with air gap (voltage constant)
Voltage
Current (A)
(V)
95 2.32 3.13 2.32 3.85 3.93 4.22 4.57 5.13 5.23
100 2.45 3.28 2.45 4.03 4.08 4.35 4.75 5.30 5.38
105 2.57 3.42 2.57 4.18 4.23 4.55 4.93 5.42 5.52
110 2.73 3.58 2.73 4.28 4.37 4.80 5.10 5.57 5.65
115 2.87 3.73 2.87 4.45 4.50 4.95 5.20 5.68 --
120 2.97 3.88 2.97 4.63 4.68 5.10 5.32 5.78 -- air gap
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
(mm) http://www.iaeme.com/IJMET/index.asp 1893 editor@iaeme.com

Estimation of Leakage Factor for Active Magnetic Thrust Bearing
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
voltage 95 voltage 100 voltage 105 voltage 110 voltage 115
1 1.5 2 2.5 3 3.5 4 4.5 5
Air gap(mm)
Figure 16 Variation of current with air gap (voltage constant)
Next the results have been analyzed at constant voltage. The variation of current with air gap has been shown in Table 4. The variation of current with air gap at constant voltage has been plotted in Fig. 16. The plots are made at constant voltages from 95 V to 120 V in steps of 5 V. It is observed that current is increasing with increase of air gap.
Table 5 variation of force with air gap (voltage constant)
Voltage actual force (N)
(V)
95 72.81 53.69 45.98 43.39 36.43 30.61 29.17 18.84 15.57
100 78.22 56.24 49.21 48.13 39.98 33.65 30.98 20.80 17.00
105 86.72 61.49 51.06 52.45 41.77 35.09 34.56 22.91 19.05
110 94.65 66.12 53.66 54.05 45.11 41.94 36.61 24.72 20.34
115 101.34 73.17 59.82 57.85 46.50 43.41 37.20 27.62 --
120 107.04 78.97 62.78 59.82 49.12 46.11 38.67 29.48 -- air gap
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
(mm) http://www.iaeme.com/IJMET/index.asp 1894 editor@iaeme.com

V. V. Kondaiah, Jagu S. Rao and V. V. Subba Rao
120.00
100.00
80.00
60.00
40.00
20.00
voltage 95 voltage 100 voltage 105 voltage 110 voltage 115 voltage 120
0.00
1 2 3 4 5 6 7 8 9
Air gap(mm)
Figure 17 Variation of force with air gap (voltage constant)
The variation of force with air gap has been shown in Table 5. The variation of force with air gap at constant voltage has been plotted in Fig. 17. It is observed that force is decreasing with increase of air gap.
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
1.5
2 2.5
3 3.5
4 4.5
5 air gap (mm)
Figure 18 Average power loss/force/mm gap
The average power loss per unit force per unit mm air gap calculated at each air gap has been calculated. The variation of average power loss per unit force per unit mm air gap with air gap has been plotted in Fig. 18. It is observed that average power loss per unit force per unit mm air gap is minimum and almost equal between the air gaps 2 mm and 4 mm.
In this paper one dimensional magnetic flux theory is used to find the theoretical force between stator and rotor parts of AMTB. A test setup is designed and fabricated to find actual force between stator and rotor. A leakage factor is introduced to find the predicted force. The experiments are carried out at different air gaps from 1 mm to 5 mm in the steps of 0.5 mm. http://www.iaeme.com/IJMET/index.asp 1895 editor@iaeme.com

Estimation of Leakage Factor for Active Magnetic Thrust Bearing
The percentage of error between theoretical force and actual force is ranging from 77 to 266 and the percentage of error between predicted force and actual force is ranging from 0.16 to
13.25. It shows that the predicted force is more closure to the actual force and is helpful in design of AMTB. The variation of average leakage factor with air gap is minimum and almost equal between the air gaps 2 mm to 4 mm and the average power loss per unit force per unit mm air gap is also minimum and almost equal between the air gaps 2 mm and 4 mm. With these results it may be concluded that the optimum air gap between stator and rotor from 2 mm to 4 mm.
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[4] Rao. J. S., Tiwari. R., Optimum Design and Analysis of thrust Magnetic Bearings using
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32(4) July 1996.
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[7] Rao J. S., Kondaiah V. V. and Rao V. V. S., Validation of thrust capacity of active magnetic bearing, International Journal of Engineering Research , vol.
3 , 108-112,2014
[8] Mr.Vijay Shankar A Finite Difference Approach To Pressure Distribution On Fixed Pad
Thrust Bearing Under Isothermal Condition. International Journal of Mechanical
Engineering and Technology, 8(7), 2017, pp. 1837–1843. http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=7 http://www.iaeme.com/IJMET/index.asp 1896 editor@iaeme.com