11-FEB-2020EIEN20 Design of Electrical Machines
7. Magnetic circuits Soft and hard magnetic materials Magnetic design
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L7: Magnetic circuits• Soft and hard magnetic materials• Design of magnetic core
– Torque expression– Main magnetizing flux path
• Permanent magnet machines – Assignment A4 (continuation of A3)– PMSM, BLDC and Dimensioning– Powder core machines
• Exploring single-fed machines: inductance and reluctance machines through FEMM and Ansys- RMxprt
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 3
Electromagnetically active parts• Coil or winding – to produce
variable magnetic flux• Permanent magnet – to
produce invariable magnetic flux
• Soft magnetic core – to provide an easy path for the flux
• Torque = excitation alignment torque + reluctance torque
– T=ψm isq +isd isq (Ld -Lq )
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 4
Analysis->synthesis->design• Specify magnetisation
arrangement B() and winding layout N()I(t)
– Magnetisation paths– Find induced voltage, forces
and torque and power loss mechanisms
• Interaction– Estimation of linking flux – Determination of current I– Deriving torque from I…
• Attraction– Estimation of gap
permeances G– Estimation of linking flux – Deriving torque from energy
B()F()
dMMFBrlT 2
0
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 5
Design Target
mech
T
el PTdttituT
P 0
1• Energy conversion
• Torque per rotor volume
• Air-gap shear stress
• Product of magnetic and electric loadings
B
l
r
wz K
T
F
222
gapRT AF
lrFr
VT
BKA
BKwzABIz
AF
gapgapgap
η - efficiency
σ=kBK
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 6
Forces on wire, slotting, leakage
• Force on current-carrying conductor in an uniform magnetic field Fx =By Iz z
• Slotted coils = mechanical support + reduced reluctance of the mutual flux path Fx =tx Axz =1/μ0 *Bx By xz
• Leakage flux, does not contribute gap (mutual) flux and torque generation
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 7
Electrical machine examples• Electrical machines with stator magnetization
– Induction machine– Reluctance machine
• Presence of magnetic core and very small air- gap are essential
• Same size, voltage and power
– Ø155/94-H120 mm– 2.2kW, 400V, 50Hz
-B-B
-B+A
+A+A
-C-C-C+B+B+B-A
-A-A
+C+C+C-B-B
-B+A
+A+A
-C -C -C +B +B +B-A
-A-A
+C+C+C47.3 7715.0
+A
-C
+C-B
+B
-A
+A
-C
+C -B
+B
-A
47.3 7715.0
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 8
Induction machine
• Induction machine is an electrical transformer– the magnetizing circuit is seen from no load test (NLT)– leakage inductances are found from locked rotor test (LRT)
• Load resistance Rr ’/s consists of equivalent electromechanical load resistance Rr ’(1-s)/s and actual winding resistance Rr ’
sRIsT rr
em
'2'3,
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 9© Avo R 9
Induction machine – 2SIE 100L4A
• FEMM quasi-static @ slip-frequency
• Ansys RMxprt – machine geometry library + ”non FE” models
Stator size Do /Di -H mm 155/95-100Power Pn , @50Hz W 2200Speed nn , @50Hz rpm 1440Current In , @400V A 4.5 (7 max)Efficiency η, % 84.7,85.5,84.6Power factor cosφ - 0.83Start current Ia /In - 7.3Start torque Ta /Tn - 2.4Knee torque Tkn /Tn - 2.8Inertia J kgm2 0.0070Weight w kg 25.5Cost* SEK 6840
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 10
• Geometry– Rotor and stator– Do/Di-H
• Windings– #Slots, #Poles,
#Phases• Materials
– BH-curve– Loss characterisation
• Operation point– Current distribution
Model specification
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 11
Semi-closed slots• Semi-closed slots are
most common for Ems• Slot geometry defined by
– Bredth b– Height h
• Slot can slightly vary in respect to slot opening and slot bed
b2
b1
b0
h2
h1
h0
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 12
Series of quasi-static analyses• Nominal current & slip
frequency
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FEMM Tω - characteristics• Expected ~15Nm @ 1440 rpm• Unstable operation point under
“knee”
1410 1420 1430 1440 1450 1460 1470 1480 1490 1500-18
-16
-14
-12
-10
-8
-6
-4
-2to
rque
, T [N
m]
1410 1420 1430 1440 1450 1460 1470 1480 1490 15000.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
indu
ctan
ce, L
[H]
speed, n [rpm]
Re(B)+Im(J) Im(B)+Re(J)
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 14
IM @ Ansys RMxprt
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Winding Layout
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• Torque, current and efficiency @ 400V from 50 to 100Hz
Characteristics
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Reluctance machine
0 20 40 60 80 100 120 140 160 180-25
-20
-15
-10
-5
0
5
10
15
20
25
torq
ue, T
[Nm
]
0 20 40 60 80 100 120 140 160 1800.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
indu
ctan
ce, L
[H]
position, e [deg]
Torque and flux linkage at nominal current 6.5Apk and at the doubled current level
0 20 40 60 80 100 120 140 160 180-40
-30
-20
-10
0
10
20
30
40
torq
ue, T
[Nm
]
0 20 40 60 80 100 120 140 160 1800
0.05
0.1
0.15
0.2
0.25
indu
ctan
ce, L
[H]
position, e [deg]
+A
-C
+C -B
+B
-A
47.3 7715.0
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 18
RM @ Ansys RMxprt
• Aligned and unaligned flux linkage
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 19
RM Tω - characteristics
IT
P
η
Home assignment A3Performance estimation for a three-
phase PM synchronous machine
B
Hc
Do
B A
[mch]=EMK_task_3(con)
[geom,mch]=EMK_geom_1(md,con)
EMK_gofem_1(geom,md,task)
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 21
Multi-phase winding distribution
• Multi-phase constant balanced instantaneous power• A sinusoidal generated voltage is desirable • A sinusoidal variation of flux density round the rotor• Magnetic cores, distributed and concentrated windings
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 22
Sinusoidally-fed PM motor• N-phase system: Nph =3• P-pole excitation: Np =2 (4,6..)• S-slot stator: Ns={3,6,9,12, …}• Sinusoidal distribution
tPiDNk
tPrPK
dd
rKdrK
iPNktP
eis
s
espis
s
sp
ississsp
sspespsp
2cosˆ6
2cos
2)(
)(1)()()(
ˆ423
2sin)(
1
1
2
0
111
s
s
F
FF
FFF
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 23
Total force in the gap• The force on a current carrying conductor in the
presence of a magnetic field
σshear
B
I
ssgmesgmeis
eisesegm
eissgm
iNkBlKBlD
dlrtPKtPB
dlrKBF
ˆ32
2cos
2cos
)()(
1111
2
011
2
0
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 24
Magnetic shear stress• Maximum force is when flux density B() and surface
current K() waves are coincident i.e. peak of Bgm1 and MMF Fs1 per pole are orthogonal
σshear
B
I
eisssgm
sgmeissgm
eisis
sgm
eis
sgmeis
avg
lDiNkB
KBlDKB
lDrT
mNKB
lD
KBlD
AF
ˆ23
42
/2
2
11
11211
21111
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 25
Magnetisation
• % magnetic dimensioning• mu0 = 4*pi*1e-7; % magnetic permeability in vacuum• K_C = 1.2; % Carter's coefficient• Bgm = 0.8; % maximum flux density in the air-gap• mu_pm = 1.219; % permeability of permanent magnet• Br = 1.1; % remanence flux ensity of permanent magnet• K_m=2/3; % relative width of magnet• % fundamental space component of gap magnet flux density• Bgm1=4/pi*Bgm*sin(K_m*pi/2);
000
C
gpm
pm
rpm kgB
hBB
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 26
Magnetic coupling & loadingE=Ψm ω
Ψm I=T
BmstBmsy
Ψm /A==PN/A<Bsat
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 27
Main flux path• A linear characteristics
can be assumed in materials
• μpm =1, μfe =∞,• The hysteresis and eddy
currents are neglected, if the study does not require them explicitly.
• The geometry is simplified by excluding small radii, holes etc
Φ½Φ
½Φ
½Φ½Φ
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 28
Choice of magnetic materials• Hard magnetic material
– Remanence flux density Br
– Stability: temperature dependence & risk of demagnetization
• Soft magnetic material– Relative permeability μr
– Specfic core loss pc
ΦR=BRApm
FCJ=HCJlpm F
permanent magnet
iron core air-gap 2 air-gap 1
load 2load 1
P2
P1
Φ
Φ
F
Φpm
FfeFpmFg
Φd
FCB
air-gap 2 iron core
common 2
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 29
Permanent magnet excitation I
• Surface mounted magnets (Lx≥Ly), inset magnets (Lx<Ly) or interior (buried) magnets (Lx<Ly)
• Rotor design: Mechanic strength, magnetic protection smaller mechanical air-gap
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 30
Permanent magnet excitation II• Single-piece magnet &
multi-pole magnetisation• Self-shielding, some
cases the back core is not needed
• Anisotropic magnet is magnetised during Injection moulding
• Isotropic magnet can be magnetised after compression moulding
M1() M2() M3() M4()
21 pN
p
p NN
sin62
1
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Hard magnetic materials
• Typical materials: Ferrite, Alnico, SmCo, NdFeB• Techniques: Sintered, compression or injection molded
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 32
Hard magnetic materialsFerrite
sint/moldSmCo
sint/moldNdFeB
sint/moldRemanence Br T 0.4/0.2 1.1/0.6 1.3/0.7
Temp dep KTB Br%/K -0.2 -0.03 -0.1/-0.1
Op temp max
0C /150 250/110 <180/110
Price Low High Moderate
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 33
PM loading
• Magnetic loading, demagnetisation• Temperature dependence
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 34
Soft magnetic core
• Magnetic core facilitate magnetic coupling and manufacturing of the machine
• Core (rot+sta) manufacturing: stamping + stacking• Insertion of electric insulation system: slot liner• Winding assembling: premade coils dragged into the stator slots • PM assembling: mounted or inserted on/into the rotor slots
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 35
Soft magnetic materials• Magnetic materials
– Bulky magnetic material,– Laminated electromagnetic
steel, – compressed molded
powder core– injection molded powder
core• Different material types
have their advantageous features at– Higher operational
frequency– Higher magnetic loading
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 36
Soft magnetic materials
laminated steel3% Si
Compressed iron powder
Injection moulded iron powder
Permeability μr.max
9250 200-700 10-20
Coercivity HC A/m 35 400 100-400
Thermal con λ W/mK 28 / 0.71 17 1-3
Specific loss pfe W/kg 1T 0.92 7 -
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 37
Soft magnetic materials development
• Material engineering = production engineering
• Saving energy vs reducing size
• Bs decreases / increases with decreasing / increasing core loss
A.Inoue 1997
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 38
Pre-study
• Material selection and suitability for different applications
• Magnetic EC based study– PMSM vs IM– Laminated core vs Powder core
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 39
PM machine with laminated core• 1-pole magnetic circuit
using laminated core (μ=2000)
• Surface mounted PMSM
Fpm=2240.9 A
fpm=605.2 A
Rpm
=366190 1/H
Fg=474.4 A
Rg=106204 1/H
Fst=10.0 A
Rst
=2230 1/H
Fwin=0.0 A
Fsy=51.9 A
Rsy
=11608 1/H
Fry=17.1 A
Rry
=3837 1/H
Bpm
=0.80 T
Bg=0.75 T
Bst
=1.75 T
Bsy
=1.71 T
Bry
=1.63 T
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 40
PM machine with powder core• 1-pole magnetic circuit
using powder core (μ=200)
• Powder core allows new design and production freedoms – advantageous if design is right
• Copper savings but slightly more iron
Fpm=2240.9 A
fpm=1168.6 A
Rpm
=366190 1/H
Fg=311.0 A
Rg=106204 1/H
Fst=65.3 A
Rst
=22304 1/H
Fwin=0.0 A
Fsy=339.9 A
Rsy
=116080 1/H
Fry=112.4 A
Rry
=38374 1/H
Bpm
=0.53 T
Bg=0.49 T
Bst
=1.15 T
Bsy
=1.12 T
Bry
=1.07 T
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 41
Induction machine with laminated core• 1-pole magnetic circuit
using laminated core (μ=2000)
• PM machine is usually smaller but more expensive than induction machine for the same performanceFpm=0.0 A
fpm=0.0 A
Rpm
=0 1/H
Fg=470.3 A
Rg=106204 1/H
Fst=9.9 A
Rst
=2230 1/H
Fwin=600.0 A
Fsy=51.4 A
Rsy
=11608 1/H
Fry=17.0 A
Rry
=3837 1/H
Bpm
=0.80 T
Bg=0.74 T
Bst
=1.74 T
Bsy
=1.70 T
Bry
=1.61 T
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 42
Induction machine with powder core• 1-pole magnetic circuit
using powder core (μ=200)
• Low permeability gives a high magnetising current
• Simply replacing a lamination stack is bound to be worse in performance and cost
Fpm=0.0 A
fpm=0.0 A
Rpm
=0 1/H
Fg=159.7 A
Rg=106204 1/H
Fst=33.5 A
Rst
=22304 1/H
Fwin=600.0 A
Fsy=174.5 A
Rsy
=116080 1/H
Fry=57.7 A
Rry
=38374 1/H
Bpm
=0.27 T
Bg=0.25 T
Bst
=0.59 T
Bsy
=0.58 T
Bry
=0.55 T
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 43
Assignment A4: step 1• Electromagnetic FE analysis of 3φ PMSM
– con.fem=1 - calculate loaded and unloaded machine
0 20 40 60 80 100 120 140 160 180-1.5
-1
-0.5
0
0.5
1
1.5
Mag
netic
flux
den
sity
inth
e ai
rgap
Bg, [
T]
BgnL(), [T]BgtL(), [T]Bgn0(), [T]Bgt0(), [T]
0 2 4 6 8 10 12 140
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
harmonic order, [-]
Mag
netic
flux
den
sity
in th
e ai
rgap
Bg, [
T]
BgnL(), [T]BgtL(), [T]Bgn0(), [T]Bgt0(), [T]
Lund University / LTH / IEA / Avo Reinap / EIEN20 / 2020-02-11 44
Assignment A4: step 2• Electromagnetic FE analysis of 3φ PMSM
– con.fem=2 – static characteristics
• Change rotor position and current vector accordingly• Record flux linkage of windings and flux density in
magnetic core parts