Magnetic Bearing Actuator
Group 6
1. List of symbols:
 B
Flux Density
 H
Field Intensity
 Θ
Magneto-motive Force (MMF)
 Rc
Resistance of the coil
 Rext
Resistance of the external circuit
 R
Total resistance
 E
Electro-motive force (EMF)
 I
Current
 lav
Average length of the wire
 N
Number of turns
 Acond
Cross-Sectional Area of the conductor
 Acoil
Cross-Sectional Area of the coil
 j
Current Density
 r
Radius to the centre of the coil
 ρ
Resistivity
 ρOT
Resistivity at operating temperature
 µo
Permeability of air
 ROT
Resistance at operating temperature
1
Magnetic Bearing Actuator
Group 6
2. Introduction:
This report is to explain the necessary steps that were taken to achieve the task of theoretically building
a Magnetic Bearing Actuator. This specific report entails the design details of a radial 8-pole, heteropolar magnetic bearing actuator. The design had to be within certain specifications had to adhere to.
The bearing had to be optimized in accordance to certain design criteria (such as coil area, resultant
force on the journal, minimum core volume etc).
There are two parts to the design a magneto-statics component which was used to obtain the load
capacity and a thermal component that determines the temperature operating range of the bearing
depending on the insulation class given.
The main aim of the design was to make sure that:
-
The bearing develops the required load capacity (slightly higher) – result must be confirmed by
FE model and relevant calculations.
The winding temperature was within the acceptable range for the required insulator class.
2
Magnetic Bearing Actuator
Group 6
3. Theory:
Magnetic Bearings:
Magnetic bearings are used to in lieu of rolling element or fluid film journal bearings in some high
performance turbo machinery applications. Specific applications include pumps for hazardous/caustic
fluids, precision machining spindles, energy storage flywheels, and high reliability pumps and
compressors.
Magnetic bearings yield several advantages. Since there is no mechanical contact in magnetic bearings,
mechanical friction losses are eliminated. In addition, reliability can be increased because there is no
mechanical wear.
Besides the obvious benefits of eliminating friction, magnetic bearings also allow some perhaps less
obvious improvements in performance. Magnetic bearings are generally open loop unstable, which
means that active electronic feedback is required for the bearings to operate stably. However, the
requirement of feedback control actually brings great flexibility into the dynamic response of the
bearings. By changing controller gains or strategies, the bearings can be made to have virtually any
desired closed-loop characteristics. For example, flywheel bearings are extremely compliant, so that the
flywheel can spin about its inertial axis--the bearings serve only to correct large, low frequency
displacements.
Typical Bearing Geometry
Conceptually, the typical magnetic bearing is composed of eight of horseshoe-shaped electromagnets.
This configuration is shown in Figure 1. The eight magnets are arranged evenly around a circular piece of
iron mounted on the shaft that is to be levitated. Each of the electromagnets can only produce a force
that attracts the rotor iron to it, so all eight electromagnets must act in concert to produce a force of
arbitrary magnitude and direction on the rotor.
Fig.1: Eight Pole Magnetic Bearing with 4 poles active at any time
3
Magnetic Bearing Actuator
Group 6
4. Design Process – Electromagnetic (parts a-k)
4.1 Initial implementation of the design:
The design procedure involved several steps:
-
Bearing dimension calculations
Coil calculations
Thermal calculations
Bearing Dimension Calculations:
a) Selection of a reasonable flux density:
The example given from the lecture notes was 𝐵𝑗 of 1.6 – 1.7T. For the design of the model took the
average of the example value hence 𝐵𝑗 =1.65T. This then required steel that will provide the necessary
flux density. Through trial and error it was discovered that Steel M-14 would provide the best results for
our design.
b) Estimate the flux density in the air gap𝐵𝑔 . Assuming 10% leakage:
𝐵𝑔 = 0.9𝐵𝑗
∴ 𝐵𝑔 = 0.9(1.65) = 1.485𝑇
c) From the known load capacity (LC or F) calculate force per/pole F1:
For the design the decision was taken to make three active poles:
Pole Pitch: 𝜏 =
360
𝑝
=
360
8
= 450
Hence 𝐹 = 𝐹1 + 2𝐹1 𝑐𝑜𝑠45 = 2.41𝐹1
∴ 𝐹 = 2.41𝐹1
𝐹1 =
𝐹
1000
=
= 414.214𝑁
2.41 2.41
d) Using the approximate expression for force/pole,
𝐹1 =
1 2
𝐵 𝐴
2𝜇0 𝑔 𝑔
Calculate the required cross-sectional are of the stator pole 𝐴𝑔 , to do this make 𝐴𝑔 the subject of the
formula:
4
Magnetic Bearing Actuator
Hence 𝐴𝑔 =
2𝐹1 𝜇0
𝐵𝑔2
=
Group 6
414.214(4𝜋𝑥10−7 )
1.4852
= 472.1𝑚𝑚2
e, f) Calculation of the width of the pole𝑊𝑝 , journal thickness 𝑊𝑗 and journal outside diameter𝐷𝑗 :
2𝑊𝑗 =
𝜋
𝜋
(115𝑥10−3 + 2𝑊𝑗 )
(𝐷𝑠 + 2𝑊𝑗 ) =
16
16
∴ 2𝑊𝑗 = 0.0226 + 0.393𝑊𝑗
𝑊𝑗 =
0.0226
= 14.1𝑚𝑚
(2 − 0.393)
Therefore the width of pole: 𝑊𝑝 = 2𝑊𝑗 = 2(14.1) = 28.2𝑚𝑚
Hence to obtain the journal OD: 𝐷𝑗 = 𝐷𝑠 + 2𝑊𝑗
𝐷𝑗 = (115𝑥10−3 ) + 2(14.1) = 143.2𝑚𝑚
g) Calculate the axial length of the bearing𝐿𝑏 :
𝐴𝑔 472.1
=
= 16.74𝑚𝑚
𝑊𝑝
28.2
𝐿𝑏 =
h) Estimate the pole (radial) length𝐿𝑝 :
Used 1.25 as it was the average between the 1 and 1.5.
𝐿𝑝 = (1 𝑡𝑜 1.5)𝑊𝑝 = 1.25(28.2) = 35.3𝑚𝑚
i)
Calculate back iron (radial) width:
𝑊𝑏𝑖 = 0.5𝑊𝑝
𝑊𝑏𝑖 = 0.5(28.2) = 14.1𝑚𝑚
j) Calculate the stator outside diameter OD:
𝑂𝐷 = 𝐷𝑗 + 2(𝑔 + 𝐿𝑝 + 𝑊𝑏𝑖 )
𝑂𝐷 = 143.2 + 2(0.3 + 35.3 + 14.1) = 242.6𝑚𝑚
k) Calculate the required MMF/pole; assuming (20-25) % leakage and infinite permeability of the
steel:
𝜗 = (1.2 − 1.25)
𝜗 = 1.225
𝐵𝑔
(𝑔)
𝜇0
1.485
(0.3𝑥10−3 ) = 434.284 𝐴𝑡
4𝜋𝑥10−7
5
Magnetic Bearing Actuator
Group 6
l) The area of the coil was assumed to be quite small for the initial calculations and had to be optimized
in the process of achieving the specified load capacity.
m) Calculate number of turns and wire diameter:
To obtain this value required the calculation of𝑙𝑎𝑣 ,this was done by assuming the shape of the coil
to be a trapezium.
The value of 𝑍𝑦 is taken as the distance between the centroid (point were the diagonals intersect) and
the line DC.
For this model𝑍𝑦 = 5.567, taken from the FE model.
∴ 𝑙𝑎𝑣 = 2(𝑊𝑝 + 𝑍𝑦 ) + 2(𝐿𝑏 + 𝑍𝑦 )
= 2(28.2 + 5.567) + 2(16.74 + 5.567) = 112.148𝑚𝑚
Standard copper wire is to be used: resistivity at 20C is 20
coefficient  = 0.0039 1/C.
=
0.17241*10-7 m and temperature
Due to the class H insulation maximum operation temperature was 1800C. Assuming an acceptable
temperature range means winding temperature between 65% and 80%.
Therefore class H would be (0.65 to 0.8)*180 = 1170C to 1440C
To obtain resistivity at maximum operating temperature is as follows:
𝜌144 = 0.17241𝑥10−7 [1 + (144 − 20)0.0039] = 2.55𝑥10−8 Ω𝑚
Assuming J=4.5𝑥106 A/m2
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Magnetic Bearing Actuator
Group 6
∴𝑁=
=
𝑉
𝑗𝜌144 𝑙𝑎𝑣
60
= 4662.373 𝑡𝑢𝑟𝑛𝑠
4.5𝑥106 (2.55𝑥10−8 )(112.148𝑥10−3 )
𝐴𝑐𝑜𝑛𝑑 =
𝜗
434.284
=
= 0.02069𝑚𝑚2
𝑁𝑗 4662.373(4.5𝑥106 )
Therefore actual 𝐴𝑐𝑜𝑛𝑑 taken from the standard metric wire sizes = 0.02270𝑚𝑚2
Coil filling co-efficient 𝑘𝑓 was not assumed but was calculated and then adjust to produce the best
results.
𝑘𝑓 =
𝑁𝐴𝑐𝑜𝑛𝑑 4(0.02270)
=
= 0.83
𝐴𝑐𝑜𝑖𝑙
126.27
𝜋
4
𝑘𝑓 (Max) = =0.78
The coil filling factor is too high and this was unacceptable (𝑘𝑓 > 0.78)
n) Calculate resistance and current
At the actual area of conductor = 0.02270mm2 the corresponding nominal resistance at 200C is
0.7596Ω/m.
Therefore at 1440C the nominal resistance is:
𝑅Ω⁄ = 0.7596[1 + (144 − 20)0.0039] = 1.1269 Ω⁄𝑚
𝑚
The resistance at 1440C is:
𝑅144 = 𝑅Ω⁄ ∗ 𝑁 ∗ 𝑙𝑎𝑣
𝑚
= 1.1269 ∗ 4662.373 ∗ (112.148𝑥10−3 ) = 589.22Ω
𝐼=
𝑉
60
=
= 0.102𝐴
𝑅144 589.22
o) Calculation of Actual MMF and MMF density
𝐴𝑐𝑡𝑢𝑎𝑙 𝜗 = 𝑁 ∗ 𝐼 = 4662.373 ∗ 0.102 = 475.562𝐴𝑡
𝜗 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 =
𝐴𝑐𝑡𝑢𝑎𝑙 𝜗 442.086
=
= 3.766𝑥106 𝐴𝑡⁄ 2
𝑚
𝐴𝑐𝑜𝑖𝑙
126.27
7
Magnetic Bearing Actuator
Group 6
Figure 1: Schematic of the initial design implementation
8
Magnetic Bearing Actuator
Group 6
4.2 Final Optimization of Design:
a) Selection of a reasonable flux density:
The example given from the lecture notes was 𝐵𝑗 of 1.6 – 1.7T. For the design of the model took the
average of the example value hence 𝐵𝑗 =1.65T. This then required steel that will provide the necessary
flux density. Through trial and error we discovered that Steel M-14 would provide the best results for
our design.
b) Estimate the flux density in the air gap𝐵𝑔 . Assuming 10% leakage:
𝐵𝑔 = 0.9𝐵𝑗
∴ 𝐵𝑔 = 0.9(1.65) = 1.485𝑇
c) From the known load capacity (LC or F) calculate force per/pole F1:
For the design the decision was taken to make four active poles:
Pole Pitch: 𝜏 =
360
𝑝
=
360
8
= 450
Hence 𝐹 = 2𝐹1 𝑐𝑜𝑠22.5 + 2𝐹1 𝑐𝑜𝑠67.5 = 2.61𝐹1
∴ 𝐹 = 2.61𝐹1
𝐹1 =
𝐹
1000
=
= 383.14𝑁
2.61 2.61
d) Using the approximate expression for force/pole,
𝐹1 =
1 2
𝐵 𝐴
2𝜇0 𝑔 𝑔
Calculate the required cross-sectional are of the stator pole𝐴𝑔 , to do this make 𝐴𝑔 the subject of the
formula:
Hence 𝐴𝑔 =
2𝐹1 𝜇0
𝐵𝑔2
=
383.14(4𝜋𝑥10−7 )
1.4852
= 436.7𝑚𝑚2
e, f) Calculation of the width of the pole𝑊𝑝 , journal thickness 𝑊𝑗 and journal outside diameter𝐷𝑗 :
2𝑊𝑗 =
𝜋
𝜋
(115𝑥10−3 + 2𝑊𝑗 )
(𝐷𝑠 + 2𝑊𝑗 ) =
16
16
∴ 2𝑊𝑗 = 0.0226 + 0.393𝑊𝑗
9
Magnetic Bearing Actuator
Group 6
𝑊𝑗 =
0.0226
= 14.1𝑚𝑚
(2 − 0.393)
Therefore the width of pole: 𝑊𝑝 = 2𝑊𝑗 = 2(14.1) = 28.2𝑚𝑚
Hence to obtain the journal OD: 𝐷𝑗 = 𝐷𝑠 + 2𝑊𝑗
𝐷𝑗 = (115𝑥10−3 ) + 2(14.1) = 143.2𝑚𝑚
g) Calculate the axial length of the bearing𝐿𝑏 :
𝐿𝑏 =
𝐴𝑔 436.7
=
= 15.5𝑚𝑚
𝑊𝑝
28.2
h) Estimate the pole (radial) length𝐿𝑝 :
Used 1.25 as it was the average between the 1 and 1.5.
𝐿𝑝 = (1 𝑡𝑜 1.5)𝑊𝑝 = 1.25(28.2) = 35.3𝑚𝑚
ii)
Calculate back iron (radial) width:
𝑊𝑏𝑖 = 0.5𝑊𝑝
𝑊𝑏𝑖 = 0.5(28.2) = 14.1𝑚𝑚
j) Calculate the stator outside diameter OD:
𝑂𝐷 = 𝐷𝑗 + 2(𝑔 + 𝐿𝑝 + 𝑊𝑏𝑖 )
𝑂𝐷 = 143.2 + 2(0.3 + 35.3 + 14.1) = 242.6𝑚𝑚
k) Calculate the required MMF/pole; assuming (20-25) % leakage and infinite permeability of the
steel:
𝜗 = (1.2 − 1.25)
𝜗 = 1.225
𝐵𝑔
(𝑔)
𝜇0
1.485
(0.3𝑥10−3 ) = 434.284 𝐴𝑡
4𝜋𝑥10−7
Coil design Calculations
l) Calculate the cross-sectional area of the coil𝐴𝐶 :
This value was not calculated but was done using trial and error until the maximum or optimal load
capacity was achieved.
𝐴𝑐𝑜𝑖𝑙 = 545.73𝑚𝑚2 , this is obtained from the FE model.
10
Magnetic Bearing Actuator
Group 6
m) Calculate number of turns and wire diameter:
To obtain this value required the calculation of𝑙𝑎𝑣 , this was done by assuming the shape of the coil
to be a trapezium.
The value of 𝑍𝑦 is taken as the distance between the centroid (point were the diagonals intersect) and
the line DC.
For this model𝑍𝑦 = 8.266𝑚𝑚, taken from the FE model.
∴ 𝑙𝑎𝑣 = 2(𝑊𝑝 + 𝑍𝑦 ) + 2(𝐿𝑏 + 𝑍𝑦 )
= 2(28.2 + 8.266) + 2(15.5 + 8.266) = 120.64𝑚𝑚
Standard copper wire is to be used: resistivity at 20C is 20
coefficient  = 0.0039 1/C.
=
0.17241*10-7 m and temperature
Due to the class H insulation maximum operation temperature was 1800C. Assuming an acceptable
temperature range means winding temperature between 65% and 80%.
Therefore class H would be (0.65 to 0.8)*180 = 1170C to 1440C
To obtain resistivity at maximum operating temperature is as follows:
𝜌144 = 0.17241𝑥10−7 [1 + (144 − 20)0.0039] = 2.55𝑥10−8 Ω𝑚
Assuming J=4.5𝑥106 A/m2
∴𝑁=
=
𝑉
𝑗𝜌144 𝑙𝑎𝑣
60
4.5𝑥106 (2.55𝑥10−8 )(120.64𝑥10−3 )
= 4334.18 𝑡𝑢𝑟𝑛𝑠
11
Magnetic Bearing Actuator
Group 6
𝐴𝑐𝑜𝑛𝑑 =
𝜗
434.284
=
= 0.0226𝑚𝑚2
𝑁𝑗 4334.18(4.5𝑥106 )
Therefore actual 𝐴𝑐𝑜𝑛𝑑 taken from the standard metric wire sizes = 0.02270𝑚𝑚2
Coil filling co-efficient 𝑘𝑓 was not assumed but was calculated and then adjust to produce the best
results.
𝑘𝑓 =
𝑁𝐴𝑐𝑜𝑛𝑑 4334.18(0.02270)
=
= 0.18
𝐴𝑐𝑜𝑖𝑙
545.73
It can be seen that the coil filling factor was low 𝑘𝑓 < 0.78
n) Calculate resistance and current
At the actual area of conductor = 0.02270mm2 the corresponding nominal resistance at 200C is
0.7596Ω/m.
Therefore at 1440C the nominal resistance is:
𝑅Ω⁄ = 0.7596[1 + (144 − 20)0.0039] = 1.1269 Ω⁄𝑚
𝑚
The resistance at 1440C is:
𝑅144 = 𝑅Ω⁄𝑚 ∗ 𝑁 ∗ 𝑙𝑎𝑣
= 1.1269 ∗ 4334.18 ∗ (120.64𝑥10−3 ) = 589.22Ω
𝐼=
𝑉
60
=
= 0.102𝐴
𝑅144 589.22
o) Calculation of Actual MMF and MMF density
𝐴𝑐𝑡𝑢𝑎𝑙 𝜗 = 𝑁 ∗ 𝐼 = 4334.18 ∗ 0.102 = 442.086𝐴𝑡
𝜗 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 =
𝐴𝑐𝑡𝑢𝑎𝑙 𝜗
442.086
=
= 0.81𝑥106 𝐴𝑡⁄ 2
𝑚
𝐴𝑐𝑜𝑖𝑙
545.73𝑥10−6
The value of mmf density that was used in Quick-Field did not produce the required force and required
further optimization.
This was done by recalculating with a thicker wire diameter but keeping the same number of turns.
Chosen𝐴𝑐𝑜𝑛𝑑 = 0.05515𝑚𝑚2 and the nominal resistance was 0.3126 Ω⁄𝑚
12
Magnetic Bearing Actuator
Group 6
m) The new 𝑘𝑓 is:
𝑘𝑓 =
4334.18(0.05515)
= 0.64
545.73
This value of 𝑘𝑓 is higher than the original but is still lower than the expected value
𝑅Ω⁄𝑚 = 0.3126[1 + (144 − 20)0.0039] = 0.464 Ω⁄𝑚
n)
The resistance at 1440C is:
𝑅144 = 𝑅Ω⁄𝑚 ∗ 𝑁 ∗ 𝑙𝑎𝑣
= 0.464 ∗ 4334.18 ∗ (120.64𝑥10−3 ) = 242.49Ω
𝐼=
𝑉
60
=
= 0.247𝐴
𝑅144 242.49
o) Calculation of Actual MMF and MMF density
𝐴𝑐𝑡𝑢𝑎𝑙 𝜗 = 𝑁 ∗ 𝐼 = 4334.18 ∗ 0.247 = 1070.5𝐴𝑡
The actual MMF is higher than the initial MMF but at this value we were able to obtain the correct
MMF density to be used in the simulation.
𝜗 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 =
𝐴𝑐𝑡𝑢𝑎𝑙 𝜗
1070.5
=
= 1.96𝑥106 𝐴𝑡⁄ 2
𝑚
𝐴𝑐𝑜𝑖𝑙
545.73𝑥10−6
Figure 2: Schematic of the Final design implementation
13
Magnetic Bearing Actuator
Group 6
4.3 Thermal design:
Using the maximum allowable temperature for class H insulation of 1800C, ambient temperature of the
shaft is 400C and of the air is 200C
The temperature operating range for class H insulation assuming (65 to 80)%of the winding temperature
from the maximum 180oC.
RANGE
0.65*180OC
0.8*180OC
DEGREES
117OC
144OC
KELVIN(+273)
390K
417K
Copper loss in the winding (coil):
Δ𝑃𝑐𝑢 =
𝑉2
𝑅144
𝑅 = 𝑁𝑙𝑎𝑣 𝜌144
=
1
𝐴𝑐𝑜𝑛𝑑
4334.18(120.64𝑥10−3 )(2.55𝑥10−8 )
= 241,79Ω
0.05515𝑥10−6
Hence
Δ𝑃𝑐𝑢 =
602
= 14.85𝑊
242
Volume of the coil:
𝑉𝑜𝑙 = 𝐴𝑐𝑜𝑖𝑙 𝑙𝑎𝑣 =
𝑁𝐴𝑐𝑜𝑛𝑑
𝑙𝑎𝑣 = (545.73𝑥10−6 )(120.64𝑥10−3 ) = 65836.867𝑚𝑚3
𝑘𝑓
Volume of Coil = 65836.867mm3, taken from the FE Model
Power density in the coil (in W/m3):
𝑝=
𝑉 2 𝑘𝑓
ΔPcu
14.85
=
=
= 225557.5 𝑊⁄ 3
2
2
𝑚
𝑉𝑜𝑙
𝜌144 𝑁 𝑙𝑎𝑣 65836.867𝑥10−9
14
Magnetic Bearing Actuator
Group 6
5. Simulation Results:
5.1 Initial design implementation:
Figure 3: Showing the initial implementation, where we obtained a less than required flux density in the
core (1.45T as compared to 1.6T)
This was the initial simulation of the magnetic bearing actuator design. Please note that the actual load
capacity for this model was 767.92N. This was unacceptable as the specified load capacity was given to
be 1000N. Further optimization was necessary.
15
Magnetic Bearing Actuator
Group 6
5.2 Final design implementation:
Figure 6: Showing the final implementation of the design, with the correct flux flowing through the
journal
Selecting the x-component and
utilizing the equations to follow
Figure 4: Showing the Force calculation interface
16
Magnetic Bearing Actuator
Group 6
When setting the problem properties of the model on Quick-Field, we set the model class Plane-Parallel
value𝐿𝑧 = 𝐿𝑏 = 15.5𝑚𝑚. By doing this the force obtained in Quick-field already accounted for the
length of the bearing. Thus the resultant force becomes:
Fqf = 0.5 ∗ F1
𝐹 = 2.61 ∗ 𝐹1
But
𝐹 (𝑜𝑟 𝐿𝐶) = 2.61 ∗ 2 ∗ 𝐹𝑞𝑓 = 2.61 ∗ 2 ∗ 194.25 = 1013.985𝑁
This result is slightly higher then the required load capacity. The error obtained can be found below:
1013.985−1000
) 100
1000
% Error =(
= 1.3985%
The load capacity obtained is acceptable as the requirement was to produce the load capacity given or
produce slightly higher.
5.3 Thermal design results:
Figure 5: Showing the thermal response of the model
17
Magnetic Bearing Actuator
Group 6
6. Summary of Final Design Parameters:
Parameter
Winding
No of turns
Wire diameter (std)
Average length of turn
Operating temp. resistance
Developed MMF
Coil volume
Power loss density
Force per pole (based on FE model)
Number of poles switched on
Axial length of the bearing
Winding max. temperature (FE model)
Unit
mm
mm
Ω
A-t
mm3
W/m3
N
mm
0C
Value
4334.18
0.05515
120.64
242.49
1070.5
65836.867
225558
383.14
4
15.5
119
18
Magnetic Bearing Actuator
Group 6
7. Discussion of results:
The simulation design of the magnetic bearing was to achieve the maximum load capacity that was
initially given and for the thermal properties of the bearing to in the range of the maximum
temperature.
Initial Approach:
Initially it was decided to design the bearing using 3-pole activation. By activating three active poles it
produced a high force per pole (414.214N) as a result of the high force, the cross-sectional area of the
stator pole was large. Reason being the cross-sectional area of the stator pole is directly proportional to
the force per pole obtained. Since the cross-sectional are of the stator pole is high it resulted in the axial
length of the bearing to be high.
The actual value of MMF (475.562A-t) calculated, using the number of turns and current which was
calculated using the area of conductor and coil. Resulted in a higher value of MMF, although this value
was acceptable it produced an error of:
Initial value of MMF = 434.284A-t
475.562−434.284
) ∗ 100
434.284
%Error = (
= 9.5%
The MMF density that was produced using the actual MMF and the area of coil was relatively high.
However when used in the simulation of the model the MMF density did not produce the expected
results such as the force and flux density. The force produced using this design was 767.92 a value well
below the expected load capacity of 1000N, an error of:
1000−767.92
)∗
1000
%Error = (
100 = 23.2%
This was unacceptable, as the requirement for the design was to produce the given load capacity or
slightly higher.
The flux density was assumed to 1.65T but in the simulation at some points the flux density was 1.45T.
The coil filling co-efficient was 0.83, above the maximum of 0.78.
As a result of the results not meeting expectations, we decided to change the approach used.
Final Approach:
In this approach we decided to use 4-pole activation, although by doing this the value of the force per
pole would decrease, directly influencing both the cross-sectional area of the stator pole and the axial
length of the bearing (a decrease in both).
19
Magnetic Bearing Actuator
Group 6
This design produced an actual MMF closer to the initial calculations being 442.086A-t; the decrease was
a result of using a larger coil that dropped the average length. This decrease the number of turns used.
The error between the actual and initial is:
442.086−434.284
)∗
434.284
%Error = (
100 = 1.8%
The model produced a smaller MMF density as the area of coil was much larger and the MMF itself was
lower. When used in the FE model once again the load capacity was lower and so was the coil filling coefficient.
On optimizing this model by increasing the area of conductor; the result was a large coil filling coefficient. This changed caused a decrease in the resistance, producing a higher current. The number of
turns stayed the same.
A result of the above change produced an actual MMF considerably larger then the initial calculation, an
error of:
Actual MMF= 1070.5A-t
1070.5−434.284
) ∗ 100
434.284
%Error = (
= 146.5%
This is large error; however the MMF density that was calculated using this MMF produced a high value.
When used in the simulation the MMF density generated through the journal produced the required
load capacity although higher, the value is acceptable.
Load capacity achieved = 1013.985N
1013.985−1000
) ∗ 100
1000
%Error = (
= 1.4% a minimal error.
The thermal design used the design that was just discussed. The result of the simulation of thermal
design produced a temperature of 392K. The expected range of the winding temperature was 390K to
417K. The model produced a temperature in range of the insulation class H (1800C max).
20
Magnetic Bearing Actuator
Group 6
8. Conclusion:
The aim of the design was to simulate a magnetic bearing actuator using Quick-Field. The design had to
adhere to certain constraints whilst some could be optimized.
The results of our design had met the specifications asked such as the achievement of the load capacity
and the thermal properties.
With respect to the load capacity it required it to have a minimum volume to maximum force ratio.
Although we had not met this requirement to exact levels, we still produce a high load capacity. Another
aspect was the high MMF we achieved on the design, this value produced the required results.
The thermal design had utilized the same model used for magneto-statics, this allowed for maximum
expected results as the design had already been optimized. The difficulty was achieving the optimal
power density that would be used in the simulation. Once we obtained the correct power density and
boundary conditions we were able to produce the required temperature of the winding.
In all we had met most of the requirements, errors can be expected. We had worked through most
difficulties and produce required expectations.
21
Magnetic Bearing Actuator
Group 6
9. References:
1. Lecture notes distributed by Professor M. Hippner , based on magneto-statics and
magnetic circuit analysis using Quick Field.
2.
Electro-mechanics and Electric Machines , by S.A. Nasar and L.E. Unnewehr.
22
Magnetic Bearing Actuator
Group 6
10. Appendix:
10.1 Optimization 1:
The value of 𝑍𝑦 is taken as the distance between the centroid (point were the diagonals intersect) and
the line DC.
For this model𝑍𝑦 = 5.567, taken from the FE model.
∴ 𝑙𝑎𝑣 = 2(𝑊𝑝 + 𝑍𝑦 ) + 2(𝐿𝑏 + 𝑍𝑦 )
= 93.24𝑚𝑚
Standard copper wire is to be used: resistivity at 20C is 20
coefficient  = 0.0039 1/C.
=
0.17241*10-7 m and temperature
Due to the class H insulation maximum operation temperature was 1800C. Assuming an acceptable
temperature range means winding temperature between 65% and 80%.
Therefore class H would be (0.65 to 0.8)*180 = 1170C to 1440C
To obtain resistivity at maximum operating temperature is as follows:
𝜌144 = 0.17241𝑥10−7 [1 + (144 − 20)0.0039] = 2.55𝑥10−8 Ω𝑚
Assuming J=4.5𝑥106 A/m2
∴𝑁=
𝑉
𝑗𝜌144 𝑙𝑎𝑣
23
Magnetic Bearing Actuator
=
Group 6
60
4.5𝑥106 (2.55𝑥10−8 )(93.24𝑥10−3 )
𝐴𝑐𝑜𝑛𝑑 =
= 5607.84 𝑡𝑢𝑟𝑛𝑠
𝜗
434.284
=
= 0.01720𝑚𝑚2
𝑁𝑗 5607.84(4.5𝑥106 )
Therefore actual 𝐴𝑐𝑜𝑛𝑑 taken from the standard metric wire sizes = 0.01767𝑚𝑚2
Coil filling co-efficient 𝑘𝑓 was not assumed but was calculated and then adjusted to produce the best
results.
𝑘𝑓 =
𝑁𝐴𝑐𝑜𝑛𝑑 5607.84(0.01767)
=
= 0.27
𝐴𝑐𝑜𝑖𝑙
365.199
𝜋
𝑘𝑓 (Max) = 4 =0.78
The coil filling factor was too low and unacceptable
n) Calculate resistance and current
At the actual area of conductor = 0.01767mm2 the corresponding nominal resistance at 200C is
0.9757Ω/m.
Therefore at 1440C the nominal resistance is:
𝑅Ω⁄ = 0.9757[1 + (144 − 20)0.0039] = 1.4475 Ω⁄𝑚
𝑚
The resistance at 1440C is:
𝑅144 = 𝑅Ω⁄ ∗ 𝑁 ∗ 𝑙𝑎𝑣
𝑚
= 1.4475 ∗ 5607.24 ∗ (93.24𝑥10−3 ) = 756.80Ω
𝐼=
𝑉
60
=
= 0.0792𝐴
𝑅144 756.80
o) Calculation of Actual MMF and MMF density
𝐴𝑐𝑡𝑢𝑎𝑙 𝜗 = 𝑁 ∗ 𝐼 = 5607.24 ∗ 0.0792 = 444.093𝐴𝑡
𝜗 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 =
𝐴𝑐𝑡𝑢𝑎𝑙 𝜗 444.093
=
= 1.216𝑥106 𝐴𝑡⁄ 2
𝑚
𝐴𝑐𝑜𝑖𝑙
365.199
24
Magnetic Bearing Actuator
Group 6
Figure 6: Showing the Flux line distribution and hence flux density
Figure 7: Showing the schematic where we used a greater concentration of nodes on the core, rather
than the air gap in order to increase the accuracy of the force calculated on the journal
25
Magnetic Bearing Actuator
Group 6
Figure 8: Showing the actual flux density distribution, it can be noted that were not achieving approx.
1.6T in the air gap
Selecting the x-component, the
required load capacity was not
achieved
𝐹 (𝑜𝑟 𝐿𝐶) = 2.61 ∗ 2 ∗ 𝐹𝑞𝑓 = 2.61 ∗ 2 ∗ 144.18 = 752.619𝑁. The load capacity obtained was
unacceptable as the requirement was to produce the given load capacity of 1000N.
26