Magnetic Bearing Actuator

8/4/2019 Magnetic Bearing Actuator

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Magnetic Bearing Actuator Group 6

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1. List of symbols:

B Flux Density H Field Intensity 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 l

avAverage 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 Resistivity OT Resistivity at operating temperature o Permeability of air ROT Resistance at operating temperature


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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, hetero-

polar 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 byFE model and relevant calculations.

- The winding temperature was within the acceptable range for the required insulator class.


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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/causticfluids, 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 thebearings. 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 ofarbitrary magnitude and direction on the rotor.

Fig.1: Eight Pole Magnetic Bearing with 4 poles active at any time


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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 of 1.6 1.7T. For the design of the model took the

average of the example value hence =1.65T. This then required steel that will provide the necessaryflux density. Through trial and error it was discovered that Steel M-14 would provide the best results forour design.

b) Estimate the flux density in the air gap. Assuming 10% leakage:

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:

Hence

d)

Using the approximate expression for force/pole,

Calculate the required cross-sectional are of the stator pole , to do this make the subject of theformula:


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Hence

e, f) Calculation of the width of the pole, journal thickness and journal outside diameter:

( )

Therefore the width of pole:

Hence to obtain the journal OD:

g) Calculate the axial length of the bearing:

h) Estimate the pole (radial) length:

Used 1.25 as it was the average between the 1 and 1.5.

i) Calculate back iron (radial) width:

j) Calculate the stator outside diameter OD:

( )

k) Calculate the required MMF/pole; assuming (20-25) % leakage and infinite permeability of the

steel:


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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 of ,this was done by assuming the shape of the coilto be a trapezium.

The value of is taken as the distance between the centroid (point were the diagonals intersect) andthe line DC.

For this model , taken from the FE model. ( ) ( )

Standard copper wire is to be used: resistivity at 20C is 20= 0.17241*10-7 m and temperature

coefficient = 0.0039 1/C.

Due to the class H insulation maximum operation temperature was 180 0C. 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:

[ ]

Assuming J=A/m2


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Therefore actual taken from the standard metric wire sizes =

Coil filling co-efficient was not assumed but was calculated and then adjust to produce the bestresults.

Max) ==0.78

The coil filling factor is too high and this was unacceptable ( )

n) Calculate resistance and current

At the actual area of conductor = 0.02270mm2 the corresponding nominal resistance at 200C is

0.7596/m.

Therefore at 1440C the nominal resistance is:

[ ]

The resistance at 1440C is:

o) Calculation of Actual MMF and MMF density


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Figure 1: Schematic of the initial design implementation


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4.2 Final Optimization of Design:

a) Selection of a reasonable flux density:The example given from the lecture notes was of 1.6 1.7T. For the design of the model took the

average of the example value hence =1.65T. This then required steel that will provide the necessaryflux density. Through trial and error we discovered that Steel M-14 would provide the best results forour design.

b) Estimate the flux density in the air gap. Assuming 10% leakage:

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:

Hence

d) Using the approximate expression for force/pole,

Calculate the required cross-sectional are of the stator pole , to do this make the subject of theformula:

Hence

e, f) Calculation of the width of the pole, journal thickness and journal outside diameter:

( )


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m) Calculate number of turns and wire diameter:

To obtain this value required the calculation of, this was done by assuming the shape of the coilto be a trapezium.


For this model , taken from the FE model.

( ) ( )

Standard copper wire is to be used: resistivity at 20C is 20=

0.17241*10-7

m and temperature


Due to the class H insulation maximum operation temperature was 1800C. Assuming an acceptable




[ ]

Assuming J=A/m2


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Coil filling co-efficient

was not assumed but was calculated and then adjust to produce the best

results.

It can be seen that the coil filling factor was low


At the actual area of conductor = 0.02270mm2 the corresponding nominal resistance at 200C is

0.7596/m.


[ ]



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.

Chosen and the nominal resistance was


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m) The new is:

This value ofis higher than the original but is still lower than the expected value

n) [ ]



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.

Figure 2: Schematic of the Final design implementation


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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 temperaturefrom the maximum 180

oC.

RANGE DEGREES KELVIN(+273)

0.65*180OC 117OC 390K

0.8*180OC 144OC 417K

Copper loss in the winding (coil):

Hence

Volume of the coil:

Volume of Coil = 65836.867mm3, taken from the FE Model

Power density in the coil (in W/m3):


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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.


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5.2 Final design implementation:

Figure 6: Showing the final implementation of the design, with the correct flux flowing through the

journal

Figure 4: Showing the Force calculation interface

Selecting the x-component and

utilizing the equations to follow


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When setting the problem properties of the model on Quick-Field, we set the model class Plane-Parallel

value . By doing this the force obtained in Quick-field already accounted for thelength of the bearing. Thus the resultant force becomes:

But

This result is slightly higher then the required load capacity. The error obtained can be found below:

% Error =

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


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6. Summary of Final Design Parameters:

Parameter Unit Value

Winding No of turns - 4334.18

Wire diameter (std) mm 0.05515

Average length of turn mm 120.64Operating temp. resistance 242.49

Developed MMF A-t 1070.5

Coil volume mm3

65836.867

Power loss density W/m3

225558

Force per pole (based on FE model) N 383.14

Number of poles switched on - 4

Axial length of the bearing mm 15.5

Winding max. temperature (FE model)0C 119


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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

%Error =

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:

%Error =

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).


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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:

%Error =

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 co-

efficient.

On optimizing this model by increasing the area of conductor; the result was a large coil filling co-

efficient. 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

%Error =

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

%Error = 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).


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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 capacityand 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.


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9. References:

1. Lecture notes distributed by Professor M. Hippner , based on magneto-statics andmagnetic circuit analysis using Quick Field.

2. Electro-mechanics and Electric Machines , by S.A. Nasar and L.E. Unnewehr.


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10. Appendix:

10.1 Optimization 1:


For this model , taken from the FE model.

( ) ( )

Standard copper wire is to be used: resistivity at 20C is 20=

0.17241*10-7

m and temperature


Due to the class H insulation maximum operation temperature was 1800C. Assuming an acceptable




[ ]

Assuming J=A/m2


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Coil filling co-efficient was not assumed but was calculated and then adjusted to produce the bestresults.

Max) = =0.78

The coil filling factor was too low and unacceptable


At the actual area of conductor = 0.01767mm2

the corresponding nominal resistance at 200C is

0.9757/m.


[ ]




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Figure 8: Showing the actual flux density distribution, it can be noted that were not achieving approx.1.6T in the air gap

. The load capacity obtained wasunacceptable as the requirement was to produce the given load capacity of 1000N.

Selecting the x-component, the

required load capacity was not

achieved

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Magnetic Bearing Actuator