PMSM at the Cryogenic Temperature
Liping Zheng
11/03/2003
University of Central Florida
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).
Previous PMSM Design
Litz-wire:
1.78 mm x 2.27 mm
50 strands @ AWG 30
Gap : 0.5 mm
Stator Di: 25.5 mm
Do: 38 mm
Stator : Laminated Silicon Steel
Permanent magnet: NdFeB
Length: 25.4 mm
Shaft diameter: 16 mm
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.
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.
Magnet Properties
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
%/K
-0.047
-0.55
Thermal Expansion of Titanium:
4.8~5.6 x 10-6 /K
Stainless steel: 8.9~9.6 x 10-6 /K
Copper Loss- DC
 DC resistance
 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
Pcopper  I Rwire
2
Rwire
Lwire

S
Electrical Resistivity of Cu
  1.7 108 W  m
@ 300K
  0.2 10 W  m
8
@ 77K
Copper Loss - AC
 Skin effect can still be ignored
 Room temperature (300K)   5.8 107 (S )

2
 1.1(mm)

 Liquid nitrogen (77K)
  5 108 (S )
2

 0.37(mm)

 Litz-wire : 50 @ 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.
Stator Iron Loss
 The iron loss for electrical steel:
Ploss  k B f  Kc ( Bmax f )  Ke ( Bmax f )
2
h max
2
1.5
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.
Modified PMSM
 Permanent magnet:
NdFeB -> SmCo
 Wire size:
50 -> 20strands@AWG30
 Winding structure:
5 ->6 turns/phase/pole
 Gap length:
0.5 -> 1.0 mm
 Shaft thickness:
0.5mm -> 1.5mm
Simulated Flux
Flux Density Distribution
Flux Lines
Airgap Normal Flux
0.40
0.35
Flux Density (T)
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0
20
40
60
80
100
Angle (deg)
120
140
160
180
Simulated Core Loss
Simulated Torque
Loss Estimation
Unit
W
R. T
75.5
77K
7.2
Copper Loss
Stator Iron Loss W
4.6
36
Rotor Loss
W
3.8
1.0
Windage Loss
W
8.4
Filter Loss
W
11
Bearing Loss
W
10
Total Loss
W
114.3
73.6
Motor Efficiency:
m  2000 (2000 73.6)  96.5%
Control Efficiency:
Total Efficiency:
c  95%
  cm  91.6%