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Magnetic Circuits (II)

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Example 3

5% cross-section increase for

fringing in airgap

Find: (a) total reluctance of the flux path;

(b) current required to produce B = 0.5 T in the air gap;

(c) inductance of the coil.

µr =2000

Φ

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Example 4

(1) How much is current required to produce 0.016Wb of flux in the core?

(2) What is core’s relative permeability at that current level?

(3) What is its reluctance and inductance at this level?

M5 Steel at DC

N = 400, A = 150 cm2

lc = 55 cm

Φ

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Example 5

2221212

2121111

I  L I  L

I  L I  L

+=

+=

λ

λ ∞→

r µ

N 1 turns

g

N 2 turns 0g

g

g

Aµ =R

(1) Let I 2 = 0

∞→r

µ

N 1 turns

I 1

N 2 turns

Find self and mutual inductances.

(2) Let I 1 = 0

+ _ 11

I  N

gR

Φ

∞→r

µ

N 1 turns

I 2

N 2 turns

+ _

22 I  N

gR

Φ

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Example 6

2221212

2121111

I  L I  L

I  L I  L

+=

+=

λ

λ

1g

2g

∞→r

µ

N 1 turns

I 1  N 2 turns

I 2

10

11

g

g Ag

µ =R

Find self and mutual inductances.

20

22

g

g Ag

µ =R

(1) Let I 2 = 0

ΦΦ   1gR

2gR

(2) Let I 1 = 0

ΦΦ

2gR

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Why Use Airgap for Inductor? (1)

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Why Use Airgap for Inductor? (2)

g =1 mm air gap

After opening an airgap

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Magnetic Fringing (More Accurate)

gg   R P    /1=  permeance

+++=   gd w

g

wd g   308.0)(52.00µ P

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Leakage Flux

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Magnetic Materials

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Hysteresis Loop for Ferromagnetic Materials

Br remnant flux or residue flux

H c coercive flux or coercivity

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Magnetization Curves for Hard Materials (I)

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Magnetization Curves for Hard Materials (II)

1T = 10 kGauss, 1A/m = 0.01257 Oe or 1 Oe = 79.6 A/m

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From Yeadon – Handbook of Small Electric Motors

Hard Magnetic Material Properties

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Hard Material Circuit Analysis (1)

Device line: Bm=( Br  /H c)( H m+H c)= µ 0µ r  H m +Br

mmm   d  H =F    g H gg  =F

0=+   gm   F F

0=+   g H d  H  gmm

mm

g   H g

d  H    −=

m

m

gg

H g

d  H  B

00

µ µ    −==

md

B

+

_

mF

Actual direction of H m

g

gr  B

c H − m H

gm   B B   =

H

B

cross section area Am

cross section area Ag

∞→µ

mmgg   A B A B   ==ΦFrom

m

g

gm  A

A

B B  =⇒ From magnetic circuit

m

m

gmm

H  A

A

g

d  B

0µ −=

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Hard Material Circuit Analysis (2)

mm

g   H g

B 0µ −=

gr  B

c H − m H

gm   B B   =

H

H

mmgg   A B A B   ==ΦFromg

mmg

A

A B B   =⇒

From   )(002

mm

g

mmgmmg   B H gA

Ad  B H g

d  B   −=−=⇒   µ µ

magVol

gapVol2

0

gap

mag)(

VolVol g

mm

B B H −

=⇒µ

The required volume of magnet can be minimized by operating the magnet at

the point of maximum BH (or energy) product.

Device line: Bm= µ 0µ r  H m +Br

md

B

+

_

mF

Actual direction of H m

g

cross section area Am

cross section area Ag

∞→µ

maximum BH product

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Maximum Energy Point

B

H c H −

r  B

r m m r

c

B B H B H

= +  2r

m m m r m

c

B B H H B H  H

⇒ = +

max

( )To get (- ) 0 ,

2 2

m m cr m m m m

m

B H H  B B H B H

H

∂⇒ = ⇒ = = −

m H

m B

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Soft Magnetic Materials

Ferrite materials Carbon steels

Silicon steels

High saturation alloys

Amorphous ferromagnetic alloys

Soft magnetic powder composites

Nanostructured materials

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Soft Magnetic Material Properties

From Yeadon – Handbook of Small Electric Motors

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Ferrite Materials (1)

3C81 is from Philips, USA.

Philips Components , 3C81Material Grade Specification, 1997

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Ferrite Materials (2)

3F3 is from Philips, USA.

Philips Components , 3F3Material Grade Specification, 2000

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Ferrite Materials (3)

4F1 is from Philips, USA.

Philips Components , 4F1Material Grade Specification, 2000

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Carbon Steel 1008

www.eng-tips.com Magnetic Engineering Forums

Maxwell SV Software

http://www.eng-tips.com/http://www.eng-tips.com/

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Carbon Steel 1010

www.eng-tips.com Magnetic Engineering Forums

Maxwell SV Software

http://www.eng-tips.com/http://www.eng-tips.com/

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Carbon Steel 1018

www.eng-tips.com Magnetic Engineering Forums

Maxwell SV Software

http://www.eng-tips.com/http://www.eng-tips.com/

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Nonoriented Silicon Steel

J. F. Gieras, Advancements in Electric Machines, Springer, 2008.

M-19 means core losses shall be below 1.9 W/lb at 1.5 T and 60 Hz.

Fe-Si alloys with random orientation of crystal cubes and practically have the same

properties in any direction in the plane of the sheet.

Armco M-19

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Armco M-27, 36 and 43

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High Frequency Electric Steel (1)

To reduce core loss, laminations with thin gauges are manufactured.

ArnonTM 5 is from Arnold Magnetic Technologies Corp., Rochester, NY, USA.

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High Frequency Electric Steel (2)

Cogent Power Ltd ., Newport, UK. www.cogent-power.com

J. F. Gieras, Advancements in Electric Machines, Springer, 2008.

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High Saturation Alloys

Fe-Co alloys with Co contents from 15 to 50% have the highest known

saturation flux density and highest Curie temperature of any alloy family..

Hiperco50 is from Carpenter , USA.

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Hiperco50 Core Loss

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Vacoflux50 B-H curveVacoflux50 is from Vacuumschmelze, Hanau, Germany.

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Amorphous Ferromagnetic Materials (1)

J. F. Gieras, Advancements in Electric Machines, Springer, 2008.

www.ammtechnologies.com

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Amorphous Ferromagnetic Materials (2)

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Soft Magnetic Powder Composites (1)

Soft magnetic powder composites are composed of iron powder, dielectric

(epoxy resin) and filler (glass or carbon fibers) for mechanical strengthening.

Accucore from TSC Ferrite International, Wadsworth, IL. www.tscinternational.com

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Soft Magnetic Powder Composites (2)

SomaloyTM 500 from Höganäs, Sweden.

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Soft Magnetic Powder Composites (3)

SomaloyTM 500 from Höganäs, Sweden.

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Soft Magnetic Nanocrystalline Composites

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