Magnetic Circuits (II)
Example 3
Φ
µr=2000
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.
Example 4
Φ
N = 400, A = 150 cm2
lc = 55 cm
M5 Steel at DC
(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?
Example 5
Find self and mutual inductances.
g
N2 turns
N1 turns
g
µ0 Ag
λ1 = L11 I1 + L12 I 2
λ2 = L21 I1 + L22 I 2
µr → ∞
(1) Let I2 = 0
I1
Rg =
Φ
Φ
N2 turns
N1 turns
Rg
N1 I1 +_
µr → ∞
Φ
(2) Let I1 = 0
Φ
I2
N2 turns
N1 turns
µr → ∞
Rg
_
+ N2I2
Example 6
Find self and mutual inductances.
g1
g2
R
=
R
=
N2 turns
g1
µ 0 Ag1 g 2 µ 0 Ag 2
I2
I1
g1
N1 turns
λ1 = L11 I1 + L12 I 2
λ2 = L21 I1 + L22 I 2
g2
µr → ∞
(1) Let I2 = 0
(2) Let I1 = 0
Φ
R g1
Rg 2
Φ
⇒
Φ
Rg 2
Φ
Why Use Airgap for Inductor? (1)
Why Use Airgap for Inductor? (2)
After opening an airgap
g =1 mm air gap
Magnetic Fringing (More Accurate)
 wd

+ 0.52( w + d ) + 0.308 g 
Pg = µ 0 
 g

Pg = 1 / R g
permeance
Leakage Flux
Magnetic Materials
Hysteresis Loop for Ferromagnetic Materials
Br remnant flux or residue flux
Hc coercive flux or coercivity
Magnetization Curves for Hard Materials (I)
Magnetization Curves for Hard Materials (II)
1T = 10 kGauss, 1A/m = 0.01257 Oe or 1 Oe = 79.6 A/m
Hard Magnetic Material Properties
From Yeadon – Handbook of Small Electric Motors
Hard Material Circuit Analysis (1)
g
cross section area Am
Φ
_
Fm
+
B
− Hc
µ →∞
Actual direction of Hm
From
cross section area Ag
Φ = Bg Ag = Bm Am
⇒ Bm = Bg
Ag
Am
Hm
H
Device line: Bm=(Br/Hc)(Hm+Hc)
= µ0µrHm +Br
Fm = H m d m
From magnetic circuit
Fg = H g g
Fm + Fg = 0
H mdm + H g g = 0
Hg = −
d m Ag
Hm
Load line: Bm = − µ 0
g Am
Br
Bm = Bg
g
dm
B
dm
Hm
g
dm
Bg = µ 0 H g = − µ 0
Hm
g
Hard Material Circuit Analysis (2)
cross section area Am
maximum BH product
Φ
_
Fm
+
B
− Hc
µ →∞
Actual direction of Hm
From
H
Br
Bm = Bg
g
dm
g
H
Device line: Bm= µ0µrHm +Br
cross section area Ag
Φ = Bg Ag = Bm Am
Hm
⇒ Bg = Bm
Am
Ag
Vol mag
dm
d A
d
From Bg = − µ 0
H m ⇒ Bg2 = − µ 0 m H m Bg = µ 0 m m (− H m Bm )
g
g
gAg
⇒ Vol mag =
Vol gap
µ 0 (− H m Bm )
B
2
g
Vol gap
The required volume of magnet can be minimized by operating the magnet at
the point of maximum BH (or energy) product.
Maximum Energy Point
B
Br
Bm
−Hc
=
Bm
Hm
Br
H m + Br
Hc
To get (- Bm H m ) max
H
Br
⇒ Bm H m =
H m2 + Br H m
Hc
∂ ( Bm H m )
Hc
Br
⇒
=
0 ⇒ Bm = , H m =
−
∂H m
2
2
Soft Magnetic Materials
 Ferrite materials
 Carbon steels
 Silicon steels
 High saturation alloys
 Amorphous ferromagnetic alloys
 Soft magnetic powder composites
 Nanostructured materials
Soft Magnetic Material Properties
From Yeadon – Handbook of Small Electric Motors
Ferrite Materials (1)
3C81 is from Philips, USA.
Philips Components, 3C81Material Grade Specification, 1997
Ferrite Materials (2)
3F3 is from Philips, USA.
Philips Components, 3F3Material Grade Specification, 2000
Ferrite Materials (3)
4F1 is from Philips, USA.
Philips Components, 4F1Material Grade Specification, 2000
Carbon Steel 1008
www.eng-tips.com Magnetic Engineering Forums
Maxwell SV Software
Carbon Steel 1010
www.eng-tips.com Magnetic Engineering Forums
Maxwell SV Software
Carbon Steel 1018
www.eng-tips.com Magnetic Engineering Forums
Maxwell SV Software
Nonoriented Silicon Steel
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
M-19 means core losses shall be below 1.9 W/lb at 1.5 T and 60 Hz.
J. F. Gieras, Advancements in Electric Machines, Springer, 2008.
Armco M-27, 36 and 43
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.
High Frequency Electric Steel (2)
Cogent Power Ltd., Newport, UK. www.cogent-power.com
J. F. Gieras, Advancements in Electric Machines, Springer, 2008.
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.
Hiperco50 Core Loss
Vacoflux50 B-H curve
Vacoflux50 is from Vacuumschmelze, Hanau, Germany.
Amorphous Ferromagnetic Materials (1)
www.ammtechnologies.com
J. F. Gieras, Advancements in Electric Machines, Springer, 2008.
Amorphous Ferromagnetic Materials (2)
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
Soft Magnetic Powder Composites (2)
SomaloyTM 500 from Höganäs, Sweden.
Soft Magnetic Powder Composites (3)
SomaloyTM 500 from Höganäs, Sweden.
Soft Magnetic Nanocrystalline Composites