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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


BackgroundHybrid Electric and Turboelectric Aircraft Propulsion

Boeing SUGAR NASA STARC-ABL

NASA N3X


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

• 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


Target Application

http://climate.nasa.gov/news/2286/leaptech-demonstrates-electric-propulsion-technologies/


AnalysisDouble-Halbach PM ArrayIronless Axial Flux Motor

Upper Halbach ArrayRotor

Lower Halbach ArrayRotor

WindingsStator



Upper Halbach Array

Lower Halbach Array

Windings

N

N

NNN

N

N

NN N

S

SSS

S

S

S

SSS



Model as 2D Pole Pair

N

N

NNN

N

N

NN N

S

SSS

S

S

S

SSS


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



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



-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

ym

xm

yc xc

xp

yg


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


AnalysisPower Density – Based on Magnet Mass

𝑃

𝑚𝑚∝

𝐽𝐵𝑅𝑣𝑡𝑖𝑝

𝜌𝑚𝑒−𝑘𝑦𝑔


𝑘𝑦𝑚


𝜋 𝑛𝑚

Ratio of gap to pole size

Large gap / pole sizelow power density

Small gap / pole sizehigh power density



𝑃

𝑚𝑚∝




𝑘𝑦𝑚


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

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



e = 1, nm = 2

e = 0.5, nm = 2

e = 1, nm = 8

𝑃

𝑚𝑚∝




𝑘𝑦𝑚


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


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

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


ResultsPower

yc = 3 mm, 16 pole pairs, magnet aspect ratio ym/xm = 116 pole pairs f = 1920 Hz

Low ID/OD

High ID/OD


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)


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

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 (

%)


J = 3 A/mm^2

J = 10 A/mm^2

J = 20 A/mm^2

J = 30 A/mm^2


ResultsI2R Loss Pc 𝑃𝑐 ∝

𝐽𝑟𝑚𝑠2 𝑉𝑐

𝜎𝜂

Low ID/OD

High ID/OD

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


d = 0.50 mm

d = 0.10 mm

d = 0.05 mm


ResultsConductor Eddy Loss Pe

𝑃𝑒 ∝ 𝜎𝑓2𝑑2𝐵𝑝𝑘2 𝑉𝑐

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


ResultsEffect of Magnet Aspect Ratio

Rotor ID/OD = 0.6, yc = 3 mm, 16 pole pairs


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


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


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

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


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


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

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


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


Results – Increasing Speed

13 kW

26 kW

52 kW Added weight of gearbox

53 m/s106 m/s

212 m/s

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 (%)


Results – Increasing SpeedRedesigned for 13 kW with Gearbox

53 m/s 106 m/s212 m/s


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)


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%

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