1. PMSM at the Cryogenic Temperature
Liping Zheng
11/03/2003
University of Central Florida

2. Cryogenics
Cryogenics is generally defined when temperature is less than 120K.
The properties of most materials change significantly with the temperature.
Many materials are unsuitable for cryogenic applications.
Our motor will work at 77K (liquid nitrogen).

3. Previous PMSM Design Litz-wire: 1.78 mm x 2.27 mm 50 strands @ AWG 30
Gap : 0.5 mm
Stator Di: mm
Do: 38 mm
Length: 25.4 mm
Shaft diameter: 16 mm
Stator : Laminated Silicon Steel
Permanent magnet: NdFeB

4. Some Considerations
The PMSM need to operate at both room temperature and 77K. We consider:
Thermal stress
PM stability
Winding loss
Stator core loss
Some modifications will be made after the above consideration.

5. Permanent Magnet NdFeB (neodymium -iron-boron ) SmCo (samarium cobalt)
SmCo does quite well at cryogenic temperature.
NdFeB does well above 135K (-138 ºC). But it undergoes a spin reorientation below 135K.
Stanley R. Trout, “Using permanent magnets at low temperature,” Arnold TECHNotes.

6. Magnet Properties Thermal Expansion of Titanium: 4.8~5.6 x 10-6 /K
Material
SmCo
NdFeB
Density
g/cm3
8.4
7.5
Compressive Stress
Mpa
700~1000
1100
Thermal Conductivity
W/(m.K)
10.5 9
Coefficient of Thermal Expansion
// 10-6 /K
I 10-6 /K 11 8 3 -5
Specific Heat
J/(kg.K)
360
420
Electrical Resistivity
µW.cm
60~90
150
Temp. Coefficient of Br
%/K
-0.035
-0.11
Temp. Coefficient of Hc
-0.047
-0.55
Thermal Expansion of Titanium: ~5.6 x 10-6 /K
Stainless steel: 8.9~9.6 x 10-6 /K

7. Copper Loss- DC DC resistance Residue resistivity ratio (RRR)
Electrical resistivity reduces with temperature due to reduced phonon electron scattering.
Residue resistivity ratio (RRR)
Resistivity at 300K (room temperature) / resistivity at 4.2K (liquid helium).
The value showing the purity of a sample.
Copper loss

8. Electrical Resistivity of Cu
@ 300K
@ 77K

9. Copper Loss - AC Skin effect can still be ignored
Room temperature (300K)
Liquid nitrogen (77K)
Litz-wire : AWG 30 (D=0.01 in or 0.25 mm)
Proximity effect due to rotating flux can also be ignored because of the smaller size Litz-wire.

10. Stator Iron Loss The iron loss for electrical steel:
Where Kh is the hysteresis coefficient
Kc is the classical eddy coefficient
Ke is the excess eddy current coefficient.
F is the frequency.
Eddy current losses are proportional to electrical conductivity.
At low temperature, stator core loss will increase due to increased electrical conductivity.

11. Modified PMSM Permanent magnet: NdFeB -> SmCo Wire size:
50 ->
Winding structure:
5 ->6 turns/phase/pole
Gap length:
0.5 -> 1.0 mm
Shaft thickness:
0.5mm -> 1.5mm

12. Simulated Flux
Flux Density Distribution
Flux Lines

13. Airgap Normal Flux

14. Simulated Core Loss

15. Simulated Torque

16. Loss Estimation Unit R. T 77K Copper Loss W 75.5 7.2 Stator Iron Loss
4.6 36
Rotor Loss
3.8
1.0
Windage Loss
8.4
Filter Loss 11
Bearing Loss 10
Total Loss
114.3
73.6
Motor Efficiency:
Control Efficiency:
Total Efficiency: