# · Web view1. List of symbols: BFlux Density HField Intensity ΘMagneto-motive Force...

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Magnetic Bearing ActuatorGroup 6

1. List of symbols:

BFlux Density

HField Intensity

Magneto-motive Force (MMF)

RcResistance of the coil

RextResistance of the external circuit

RTotal resistance

EElectro-motive force (EMF)

ICurrent

lavAverage length of the wire

NNumber of turns

AcondCross-Sectional Area of the conductor

AcoilCross-Sectional Area of the coil

jCurrent Density

rRadius to the centre of the coil

Resistivity

OTResistivity at operating temperature

oPermeability of air

ROTResistance at operating temperature

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 by FE model and relevant calculations.

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

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

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 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 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 the formula:

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:

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 coil to be a trapezium.

The value of is taken as the distance between the centroid (point were the diagonals intersect) and the 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 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:

Assuming J=A/m2

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 best results.

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

Figure 1: Schematic of the initial design implementation

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 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 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 the formula:

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.

ii) 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:

Coil design Calculations

l) Calculate the cross-sectional area of the coil:

This value was not calculated but was done using trial and error until the maximum or optimal load capacity was achieved.

, this is obtained from the FE model.

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 coil to be a trapezium.

The value of is taken as the distance between the centroid (point were the diagonals intersect) and the 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 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:

Assuming J=A/m2

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 best results.

It can be seen that the coil filling factor was low

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 1