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Optimizing Power Density and Efficiency of a Double-Halbach Array
Permanent-Magnet Ironless Axial-Flux Motor
Kirsten P. Duffy – University of Toledo / NASA GRC
7/26/2016 Joint Propulsion Conference 1
https://ntrs.nasa.gov/search.jsp?R=20170003042 2018-06-27T15:13:58+00:00Z
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BackgroundHybrid Electric and Turboelectric Aircraft Propulsion
Boeing SUGAR NASA STARC-ABL
NASA N3X
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From Jansen et al. “Turboelectric Aircraft Drive Key Performance Parametersand Functional Requirements”
BackgroundTurboelectric Propulsion Benefits
Electric drive = motor + generator + other electrical components
Each aircraft configuration will yield combinations of power
density and efficiency required to achieve net benefit
Break-Even on Weight
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• Example – HEIST (Hybrid-Electric Integrated Systems Testbed)
• 31-foot span wing section
• 18 fans directly driven by electric motors
• Motors powered by batteries
• Motor dimensions: 5.5” diameter, 2” length
• Target: 13 kW power at 7200 RPM
Our motor design: target 13 kW/kg and 1% loss
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Target Application
http://climate.nasa.gov/news/2286/leaptech-demonstrates-electric-propulsion-technologies/
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AnalysisDouble-Halbach PM ArrayIronless Axial Flux Motor
Upper Halbach ArrayRotor
Lower Halbach ArrayRotor
WindingsStator
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AnalysisDouble-Halbach PM ArrayIronless Axial Flux Motor
Upper Halbach Array
Lower Halbach Array
Windings
N
N
NNN
N
N
NN N
S
SSS
S
S
S
SSS
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AnalysisDouble-Halbach PM ArrayIronless Axial Flux Motor
Model as 2D Pole Pair
N
N
NNN
N
N
NN N
S
SSS
S
S
S
SSS
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AnalysisPole Pair Analysis
ym
xm
yc xc
xp
A+ A–B+ C+C– B–yg
2D magnetostatic pole pair model allows for simple equation-based analysis
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AnalysisPole Pair Analysis
k = 2p/xp
𝐵𝑦 = 2𝐵𝑅𝑒−𝑘𝑦𝑔 1 − 𝑒−𝑘𝑦𝑚sin 𝜖𝜋 𝑛𝑚
𝜋 𝑛𝑚cos 𝑘𝑥 cosh 𝑘𝑦
𝐹𝑐 = 𝐽Δ𝑟 𝑥1
𝑥2
𝑦1
𝑦2
𝐵𝑦 𝑑𝑥𝑑𝑦
x
y
By
ym
yg
xm
xp
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AnalysisPole Pair Analysis
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
0.0 0.2 0.4 0.6 0.8 1.0
Axi
al F
lux
in C
en
ter
of
Gap
, By
(T)
Circumferential Distance (x/xp)
2D FEA
Equation
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ym
xm
yc xc
xp
yg
7/26/2016 Joint Propulsion Conference 11
AnalysisForce/Torque/Power
𝐹𝑐 = 2𝐽𝐵𝑅∆𝑟𝑦𝑔𝑦𝑚
𝑒−𝑘𝑦𝑔
𝑘𝑦𝑔
1 − 𝑒−𝑘𝑦𝑚
𝑘𝑦𝑚
sin 𝜖𝜋 𝑛𝑚
𝜋 𝑛𝑚 sin 𝑘𝑥𝑥1
𝑥2 sinh 𝑘𝑦𝑦1
𝑦2
𝑇 = 𝑝𝑟𝑎𝐹𝑝 𝑃 = 𝑇 𝜔𝑟 = 𝑇 𝑅𝑃𝑀 𝜋 30𝐹𝑝 =
𝑐=1
6
𝐹𝑐
k = 2p/xp
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AnalysisPower Density – Based on Magnet Mass
𝑃
𝑚𝑚∝
𝐽𝐵𝑅𝑣𝑡𝑖𝑝
𝜌𝑚𝑒−𝑘𝑦𝑔
1 − 𝑒−𝑘𝑦𝑚
𝑘𝑦𝑚
sin 𝜖𝜋 𝑛𝑚
𝜋 𝑛𝑚
Ratio of gap to pole size
Large gap / pole sizelow power density
Small gap / pole sizehigh power density
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AnalysisPower Density – Based on Magnet Mass
𝑃
𝑚𝑚∝
𝐽𝐵𝑅𝑣𝑡𝑖𝑝
𝜌𝑚𝑒−𝑘𝑦𝑔
1 − 𝑒−𝑘𝑦𝑚
𝑘𝑦𝑚
sin 𝜖𝜋 𝑛𝑚
𝜋 𝑛𝑚
Ratio of magnet thickness to pole size
Large magnet thicknessto pole size
low power density
Small magnet thicknessto pole size
high power density
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0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 5 10 15 20
Sin
(p/n
m)/
(p/n
m)
Number of magnets per pole pair, nm
e = 1.00
e = 0.75
e = 0.50
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AnalysisPower Density – Based on Magnet Mass
e = 1, nm = 2
e = 0.5, nm = 2
e = 1, nm = 8
𝑃
𝑚𝑚∝
𝐽𝐵𝑅𝑣𝑡𝑖𝑝
𝜌𝑚𝑒−𝑘𝑦𝑔
1 − 𝑒−𝑘𝑦𝑚
𝑘𝑦𝑚
sin 𝜖𝜋 𝑛𝑚
𝜋 𝑛𝑚
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 5 10 15 20
Sin
(p/n
m)/
(p/n
m)
Number of magnets per pole pair, nm
e = 1.00
e = 0.75
e = 0.50
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Analysis
Parameter Value
Target power 13 kW
Target power density13 kW/kgBased on magnet and winding mass only
Target loss< 1%Including magnet and winding losses only
Outer diameter 5.5 inches (140 mm)
Magnet remanence flux, BR 1.4 T (NdFeB)
Current density, J3 A/mm2 (natural convection)to 30 A/mm2 (liquid cooling)
Electrical frequency, f< 2000 Hz≤ 16 pole pairs at 7200 RPM
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0
5
10
15
20
25
0.2 0.4 0.6 0.8 1.0
Mo
tor
Po
we
r (k
W)
Ratio of Motor ID to OD
J = 3 A/mm^2
J = 10 A/mm^2
J = 20 A/mm^2
J = 30 A/mm^2
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ResultsPower
yc = 3 mm, 16 pole pairs, magnet aspect ratio ym/xm = 116 pole pairs f = 1920 Hz
Low ID/OD
High ID/OD
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ResultsPower Density
yc = 3 mm, 16 pole pairs, magnet aspect ratio ym/xm = 116 pole pairs f = 1920 Hz
0
5
10
15
20
25
0.2 0.4 0.6 0.8 1.0
Po
we
r D
en
sity
(kW
/kg)
Ratio of Motor ID to OD
J = 3 A/mm^2
J = 10 A/mm^2
J = 20 A/mm^2
J = 30 A/mm^2
Low ID/OD
High ID/OD
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0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
0.2 0.4 0.6 0.8 1.0
Re
sist
ive
Lo
ss (
%)
Ratio of Motor ID to OD
J = 3 A/mm^2
J = 10 A/mm^2
J = 20 A/mm^2
J = 30 A/mm^2
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ResultsI2R Loss Pc 𝑃𝑐 ∝
𝐽𝑟𝑚𝑠2 𝑉𝑐
𝜎𝜂
Low ID/OD
High ID/OD
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0.01%
0.10%
1.00%
10.00%
100.00%
0.2 0.4 0.6 0.8 1.0
Edd
y cu
rre
nt
loss
in c
on
du
cto
rs
Ratio of Motor ID to OD
d = 0.50 mm
d = 0.10 mm
d = 0.05 mm
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ResultsConductor Eddy Loss Pe
𝑃𝑒 ∝ 𝜎𝑓2𝑑2𝐵𝑝𝑘2 𝑉𝑐
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0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
0
5
10
15
20
25
0.0 0.5 1.0 1.5 2.0
Re
sist
ive
Lo
ss
Po
we
r D
en
sity
(kW
/kg)
Ratio of Magnet Axial to Average Circumferential Length
Power Density
Resistive Loss
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ResultsEffect of Magnet Aspect Ratio
Rotor ID/OD = 0.6, yc = 3 mm, 16 pole pairs
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ResultsEffect of Coil Thickness
Rotor ID/OD = 0.6, yc = 3 mm, 16 pole pairs
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
1.6%
0
2
4
6
8
10
12
14
16
0 2 4 6 8 10 12
Re
sist
ive
Lo
ss
Po
we
r D
en
sity
(kW
/kg)
Coil Thickness (mm)
Power Density
Resistive Loss
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Results
Effect of Number of Pole Pairs
Bmax = 1.0 T
11.0
11.5
12.0
12.5
13.0
13.5
0 10 20 30 40
Po
we
r D
en
sity
(kW
/kg)
Number of Pole Pairs
Series1
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Results
Effect of Number of Pole Pairs
Bmax = 1.0 T
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
0 10 20 30 40
Loss
Number of Pole Pairs
Resistive Loss Conductor Eddy Loss Resistive + Eddy Loss
Eddy current loss for0.05mm diameter wire
Small area of < 1% loss
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Parameter Value
Power 13 kW at 7200 RPM
Power density12.8 kW/kgBased on magnet and winding mass only
Loss0.85% - conductor resistive loss0.11% - conductor eddy current loss0.02% - magnet eddy current loss (3D FEA)
ID/OD = 0.6, Coil thickness = 3 mm, 16 pole pairs, 20 A/mm2 current density, and magnet aspect ratio = 1
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Results
Final Motor PerformanceVerified with Maxwell 3D FEA
• Difficult to achieve goal of 13 kW/kg and 1% loss in this configuration• Required 20 A/mm2 which will require cooling
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Conclusions/Future Work
• Continue to investigate configurations that will improve efficiency as well as power density
• Design, build and test
• Targets:• > 1 MW motor
• 13 kW/kg
• 96% efficiency
99% efficiency
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Thanks to the non-cryogenic motor team members from NASA:
• Yaritza de Jesus-Arce – team leader
• Cheryl Bowman
• Ryan Edwards
• Ralph Jansen
• Peter Kascak
• Andrew Provenza
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Acknowledgments
This work was funded by NASA:Advanced Air Vehicle Program
Advanced Air Transport Technology Project Hybrid Gas-Electric Propulsion Subproject
Amy Jankovsky subproject manager
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Results – Increasing Speed
13 kW
26 kW
52 kW Added weight of gearbox
53 m/s106 m/s
212 m/s
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0.0%
0.5%
1.0%
1.5%
2.0%
0
5
10
15
20
0 10000 20000 30000 40000
Re
sist
ive
Lo
ss (
%)
Po
we
r D
en
sity
(kW
/kg)
Rotor Speed (RPM)
Power Density Resistive Loss (%)
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Results – Increasing SpeedRedesigned for 13 kW with Gearbox
53 m/s 106 m/s212 m/s
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3D Transient vs 2D Static Results
0%1%2%3%4%5%6%7%8%9%
10%
Equation-basedmagnetostatic -optimal design
Equation-basedmagnetostatic -compact coils
Maxwell 3Dtransient -
compact coils
Res
isti
ve L
oss
0
2
4
6
8
10
12
14
Equation-basedmagnetostatic -optimal design
Equation-basedmagnetostatic -compact coils
Maxwell 3Dtransient -
compact coils
Pow
er D
ensi
ty (
kW/k
g)
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3D Transient vs 2D Static Results
AnalysisTorque(N-m)
Resistive Loss (%)
Eddy Current
Loss Conductors
(%)
Eddy Current
Loss Magnets
(%)Equation-based magnetostatic
large coils/optimal17.3 0.85% 0.11% -
Equation-based magnetostatic
compact coils/high J16.3 7.6% 0.06% -
Maxwell 3D magnetostatic
compact coils/high J16.6 - - -
Maxwell 3D transient
compact coils/high J16.9 8.1% - 0.02%