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 Length: 25.4 mm Shaft diameter: 16 mm Stator : Laminated Silicon Steel Permanent magnet: NdFeB

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 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: 4.8~5.6 x 10-6 /K Stainless steel: 8.9~9.6 x 10-6 /K

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

Electrical Resistivity of Cu @ 300K @ 77K

Copper Loss - AC Skin effect can still be ignored Room temperature (300K) Liquid nitrogen (77K) 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: 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

Simulated Core Loss

Simulated Torque

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: