Brushless PM

1
Brushless PM

• Magnet Modeling
• 1/18 ???

2
Introduction

• Brushless Permanent Magnet Motor? ??? ???? ??,
  ???? ??? ????? ??? ???.
• ???? ??? ?? ??
• ???????????? ??????
• ???????????? ???-gt???
• ?? ? ?? ?? ?? ??

3
Magnetic Circuit Concepts
Fig 1. Differential size block of magnetic
material

• B? ??? ??? ????? ???? ?????? H? Z???? ??? ???
  ???? ???? ?????? ????.
• B? H? ????? ??.
• B? H? ????? ?????? ??? ? ?????? ??? ?? ?? ?? ????.

4
Magnetic Circuit Concepts
Basic Relationships
Fig2. B-H Curve

• ???? H? ?? ????? ???? B? ????. ??? ?? ??? ???
  ????? ???? ??? ??? ???? ?? ??? ???.

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Magnetic Circuit Concepts
Fig 3. Magnetic material having a differential
length
If dxdyConstant
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Magnetic Circuit Concepts
Fig 4. A block of magnetic material
Where, F is defined as magnetomotive(MMF) A
HA/m
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Magnetic Circuit Concepts
Connecting above two fundamental equations
defined as the permeance Wb/A or H

• Permeability? ?? ????? permeance? ?? ??? ??? ???
  ? ? ??? ??.

Reluctance ( Inverse of Permeance )

• ????? ????? ???? ??? ?? ????? ???? ???? ????? ??
  ??? ??? ???? ????? ??.

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Magnetic Circuit Concepts
Comparasing to other systems
Table 1. Comparison to Other Physical systems
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Magnetic Circuit Concepts
Magnetic Field Sources
Amperes law
If C encloses I
Otherwise

• ??? ??? ???? ??? ???? ?? ???? ??? ??? ??? ?? ??.

Fig 5. A coil wrapped around a piece of magnetic
material
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Magnetic Circuit Concepts
Applying this equation to a coil wrapped around
magnetic material

• ??? ???? ???? ???? ?? ??? ???? ?? z?? ??? ??? ??.
  
• ???? ?????? ?? ???? ? ??? ?????? ?? ?? ???? ??
  ??? ????.

Finally,
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Magnetic Circuit Concepts

• Air Gap Modeling
• ?? ???? ??? ??? ??? ????? ???? ???.
• ??? ??? ??? ?? ? ???(MMF) ??? ????.
• ??? ???? ????? ????? ?? ????.
• ??? ??? ??? ?? ???? ?? ??? ?? ??? ??? ????
  ????.(?? ??? ??? ?? ??? ??? ?? ???? ??? ???
  ????.)
• ??? ???? Fig 6. ? ?? Fringing ??.

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Magnetic Circuit Concepts
Fig 6. Magnetic flux flow in an air gap between
two highly permeable structures
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Magnetic Circuit Concepts
Fig 7. Air gap permeance models
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Magnetic Circuit Concepts

• Fringing ??? ??
• Fringing ?? ??, ?? ?? ?? ???? ???
• Fringing ??? ??? ?? ??? ???? ?? ??? ???? ??? ??
  ??? ???? ??? ???
• -gt??? ?? ??? ???? ???? ?? ??? ??? ??? ?? ??
  ??? ?? ???. ?? ?? ????? ?? ? ??. ??? ?? ????
  ???? Fig 7-(c). ? ?? ? ???? ??? ???? ??? ??? ?
  ??? ? ? ??.

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Magnetic Circuit Concepts
Where dALdx Lthe depth of the block
Fig 8. Circular-arc straight-line permeance model
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Magnetic Circuit Concepts
Slot Modeling
Fig 9. A slotted structure
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Magnetic Circuit Concepts

• ??? ???? ??? ???? ??? ??-gt??? ??? ??
• ?? ???? ??? ??? ??? ??
• ?? ? ??? ?? ???? ??. ??? ?? ??? ?? ???? ???? ????
  ????.
• Carters Coefficient
• ???? ??? ???? ??? ??? ?? ???? ?? ??? ????
  ?? ? ? ??? ??? ?? ??

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Magnetic Circuit Concepts
Where, ge??????
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Magnetic Circuit Concepts
Fig 9. ?? ???? ??,
?? ?? ?????

• ?? ????? ?? ?? ??? ? ???? ?? ????.
• ??????? ? ????? ????.
• ???? ??? ?? ?? ??? ? ? ? ?? ??? ??

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Magnetic Circuit Concepts
Fig 10. A comparison of Carters coefficients
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Magnetic Circuit Concepts

• ???? ??? ?? ? ??? ??? ??? ????? ?? ?? ??? ?????
  ?? ?? ????? ?? ??? ?????? ???.
  ??? ??? ?? ?????? B? ? ???? ??.

Fig 11. Flux sqeezing at the base of a tooth
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Magnetic Circuit Concepts
Example
Fig 12. A simple magnetic structure and its
magnetic circuit model
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Magnetic Circuit Concepts

1. ???? ??, ??? ??, ??? ???? ??? ??? ????? ??
2. ??? ???? ?? ??? ???? ?? ?? ??? ????, ???? ???
   ????? ??? ??? ??.
3. ???? , (??? ??? ?? ??)
4. ????? ?? MMF? ??? ????, ??? ??? ????, ?? ??? ????
   ???? ????? Krichhoff? ??? ???.

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Magnetic Circuit Concepts

1. Fig 7 ? (a),(b),(c)? ?? ??? ??? ????? B? ??
   0.91T, 1.08T, 1.09? ??.( (C)? ?? X10g? ?? )
2. Ni400? MMF? ?? ??? ???? ? ??? ??? 90.5, 88.7,
   88.6? ??.
3. ??? ??? ?? ???? ?? (a)? ??? ? ?? (b),(c)??? ???
   ??.
4. ?? ?? ?? ?? ??? ???? ? 90? ??? ???? ??? ??? ????
   ??? ??? ??? ???? ??? ???? ?? ? ? ??.
5. ?? ????? ??? ??? ?? ????? ?? ??? ????? ??. -gt??
   ???? ?? ????