CEME Tele-SeminarMonday, December 7, 2009
Considering Thermo-mechanical Modeling d D i f El t i l M hi
Prof. J. Rhett Mayor
and Design of Electrical Machines
yGeorgia Institute of Technology
Atlanta, GA
-0 04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
Temperature Distribution of Stator [C]
245
246
247
248
249
250
251
252
253
-2
0
2
4
6
8
10
12
14
x 10-3
Temperature Distribution of Half of the Tooth [C]
245
246
247
248
249
250
251
252
253
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
-0.05
-0.04
244
245
0.035 0.04 0.045 0.05 0.055
-4
2
244
245
Thermal Management of MPG’s
Key thermal management issues are related to internal gap control and magnetic circuit thermal managementI d i Increased temperatures on magnetic material and stator windings have deep impact on overall system performanceMagnet and Stator temperatures must be Magnet and Stator temperatures must be maintained at <150 to avoid large efficiency losses
1.60
R/Rn
0.80
1.00
1.20
1.40
n , N
/N0
η/η0
0.20
0.40
0.60
R/R
n
0.000 20 40 60 80 100 120 140 160
Temperature ('C)
Case 1: Benchmark study
Benchmarked thermal response of existing MPG design through thermal steady state effectiveness of coolingNatural convection cooling from all surfaces
Max Temps (˚C)
Component 1 2 3
Core 541
Swing Arm 695
Rotor/Stator 351
Case 2: Finned MICSE core
Average engine temperature drops by almost 200˚
Max Temps (˚C)
Component 1 2 3
Core 541 354
Swing Arm 695 516
Rotor/Stator 351 226
Transient Thermal Analysis Correlation Study
Transient coupled thermal-stress FEM models implemented in ALGOR FEA package are utilized to study the thermal response of the systemFLIR A20 Thermal imaging system has been used to determine IR signature of MPG-1 system during start-up transientsMPG-1 system during start-up transientsCorrelation studies between the thermographic data and ALGOR transient thermal analysis have validated the accuracy of the MPG-1 thermal models
IR temperature profile corresponds within 85% of ALGOR simulationT t l t t ithi ± 10˚CTemperatures correlate to within ± 10 C
Outline
1. Introduction2 Review of Machine Design2. Review of Machine Design
1. SM-PMAC Generator Case Study
3. Generic FD Thermal Modeling Approachg pp4. G-FD/FEA Benchmarking Studies5. Experimental Validationp6. Integrated Thermo-electromagnetic MDO 7. Summary & Conclusionsy
6
Conventional Machine Design Methodology
1
Machine Design(SM-PMAC Generator)Electromagnetic
S l t J EM Design T < Trial
No2
Select J EM Design T < Tlimit ? Design
YesThermo-mechanical
7
450W PMAC Generator Design Optimization
Generator scaling study included beneficial scaling effects to achieve optimal power density in 450W PMAC generator designMTD 1 t d i ti i d i hi h fid lit 5
6
7
8
Wi/W
)
LinearPower scaling
( ) ω⋅⋅∝ LDP 2 2
MTD-1 generator design was optimized using high-fidelity Maxwell™/PSPICE™ FEA to simulate expected no-load an loaded performanceExtensive materials selection study considered trade-offs 0
1
2
3
4
5
0 1 2 3 4 5
Nor
mal
ized
Pow
er (W
between high-frequency performance and high magnetic saturation limits for silicon, cobalt and amorphous ironsImproved thermal management of the rotor shaft enable implementation of NdFeB magnets, higher field strength
Gearing (x:1)
Initial scaling studies based on 30W design using fundamental scaling laws
p g , g gover SmCo rotors => increased power density
Material Saturation Flux Density
Core Loss at 400Hz (@ 1T)
Maxwell™ FEA confirmed optimization of stator design for minimum mass
y ( )
M19 – 26 Gauge (0.47 mm) 1.7 T (17 kG) 24.48 W/kg
Cogent NO 005 (0.12 mm) 1.8 T (18 kG) 11.8 W/kg
Metglas™ 2605C0 (0.023 mm) 1.8 T (14 kG) 6.0 W/kg
Hi ® 50 2 2 T (22 kG) 17 64 W/k
8
of stator design for minimum mass without saturation (1.7T in teeth)
Hiperco® 50 2.2 T (22 kG) 17.64 W/kg
MTD-1Gx Swing-optimized PMAC Prototype
Thermo-mechanical design optimization studies resulted in integrated cooling fins and to allow >6A/mm2 current densitiesStator windings were potted with thermally conductive epoxyStator windings were potted with thermally conductive epoxy improve winding thermal management Two 450W PMAC swing-optimized generators were fabricated with different winding configurations for maximum copper fill factor Stator ring and
spider laminates
MTD-1G1 MTD-1G2
Stator outer diameter (mm) 62
spider laminates
( )Rotor outer diameter (mm) 32.5Axial length (mm) 40Rotor Inertia (kg.m2) 2.615 x 10-5
Air Gap (mm) 0.25Number of stator slots 30Number of poles 10Winding AWG 22 bifilarNo. turns per phase 130,130,130 140,130,140Phase Resistance at 100oC (Ω) 0.681 0.61,0.58Max. RMS current (A) 5
9
Mass (kg) 1.4
MTD-1Gx Oscillatory Performance
Oscillatory testing of the MTD-1Gx prototypes utilized a 4-bar linkage to approximate swing-engine motion
MTD 1G2: Maxwell 2D Back EMF vs Time
10
20
30Phase A Maxwell Phase B MaxwellPhase C Maxwell
MTD-1Gx Model Validation Oscillatory Power Testing
Actual power measured at frequencies up to 16Hz Estimated power at 55Hz is >700W based on FEA simulation
-30
-20
-10
0
Volta
ge (V
)
Test Freq. Vrms Power
1 2.15 2.5 3.8
2 4 5.0 15.1
simulation
0 0.02 0.04 0.06 0.08 0.1 0.12
Time (sec)
MTD-1G1 No-load 8.4Hz
20
30Phase APhase BPhase C
Simulated Back EMF at 8.66Hz3 8.66 10.3 63.2
4 16 18.9 213.5
55 ~700
-20
-10
0
10
Volta
ge (V
)
10
-300.000 0.020 0.040 0.060 0.080 0.100 0.120
Time (s)
Measured Back EMF at 8.4Hz (MTD-1G1)
MTD-1Gx Rotational Performance
M TD-1G1 Rotational Test
30
40
50Phase 1 Phase 2 Phase 3
MTD-1G2 Power vs Speed (5ohm)y = 5E-05x2 + 0.0249x
R2 = 0.9994
1000
1200
-30
-20
-10
0
10
20
Volta
ge (V
)
400
600
800
Pow
er (W
)
-50
-40
-0.010 -0.005 0.000 0.005 0.010Time (s)
MTD-1G2 Thermal response40.00 140.00
MTD-1G2 Cooling effect120.0
0
200
0 500 1000 1500 2000 2500 3000 3500 4000
Speed (rpm)
20.00
25.00
30.00
35.00
age
(V) 80.00
100.00
120.00
Tem
p (°
C)
Phase 1 rms voltageWinding Temp
60.0
80.0
100.0
mpe
ratu
re ('
C)
300W - Ambient300W - Cooling
300W400W
500W600W
0 00
5.00
10.00
15.00
Volta
0 00
20.00
40.00
60.00
Win
ding
0.0
20.0
40.0
Win
ding
Tem
11
0.000 1000 2000 3000 4000 5000 6000 7000 8000 9000
Time (sec)
0.000 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Time (s)
Generator Summary
MTD-1Gx Specifications
Rated Power (W) 600
Rated Current rms (A) 6.25
Max Power (W) 750( )
Max Current rms (A) 7.5
Power Factor 0.84
Efficiency 85%y
Max Winding Temp (ºC) 135
Dimensions (LxWxH) 5” x 3” x 3”
Mass (kg) 1.4
Max Specific Power (W/kg) 535.7
12
1
Machine DesignMachine Design(SM-PMAC Generator)Electromagnetic
2
Select J EM Design T < Tlimit ?
Trial Design
No2
Sequential Design Process is fundamentally not suited to
coupled multi-physics problem
Advantage Disadvantage
limit
YesThermo-mechanical
coupled multi physics problem
13
Lower J Lower copper loss, cooler Thicker wire, need larger slot, larger weight
Higher J Thinner wire, less slot, less weight Larger copper loss, hotter,
Outline
1. Introduction2 Review of Machine Design2. Review of Machine Design
1. SM-PMAC Generator Case Study
3. Generic FD Thermal Modeling Approachg pp4. G-FD/FEA Benchmarking Studies5. Experimental Validationp6. Integrated Thermo-electromagnetic MDO 7. Summary & Conclusionsy
14
Rationale
• Thermal management in electric machines is a critical design issue
• Computational techniques to evaluate high fidelity temperature distributions in temperature sensitive electrical machines are required in thesensitive electrical machines are required in the design stage
• The proposed model uses a finite difference p papproach to accurately and quickly simulate steady state and transient heat transfer in electrical machineselectrical machines
• This study will consider PM machines where the rotor does not contribute to thermal effects
15
Transient Thermal Modeling Approaches
Quasi-Transient: Using an applied constant
t thi t i t
ture
Quasi-Transient
current this transient simulation type shows how the temperature changes with time
Tem
pera
t
Fully Transient
with time
Fully Transient:Using time varying current
Time
yUsing time varying current (defined by either IEC standards or user input) this simulation shows how the temperature changes with time
16
Existing Thermal Modeling Techniques
• Classical thermal electric machine design uses various simplifications to approximate the motor as a cylinder to carry out thermal analysisy y
• More recent advances in thermal modeling of electrical machines include Thermal Circuits and FEA
Thermal Circuits FEA
Ad tAdvantages
Disadvantages
17
Existing Thermal Modeling Techniques
18
[Boglietti, A.; Cavagnino, A.; Staton, D., "Determination of Critical Parameters in Electrical Machine Thermal Models," Industry Applications, IEEE Transactions on , vol.44, no.4, pp.1150-1159, July-Aug. 2008]
Case 3: Ducted Air Flow
Air flow ducted axially along body with flow at 2 m/s92mm cooling fan adds g1.18W power draw and 80 g to system massThermal management objectives are achieved with minimal power and mass penalties
Max Temps (˚C)
Component 1 2 3
Core 541 354 251
Swing Arm 695 516 412
Rotor/Stator 351 226 146
Existing Thermal Modeling Techniques
• Classical thermal electric machine design uses various simplifications to approximate the motor as a cylinder to carry out thermal analysisy y
• More recent advances in thermal modeling of electrical machines include Thermal Circuits and FEA
Thermal Circuits FEA
Ad t Mi i l C t ti l ti • High AccuracyAdvantages • Minimal Computational time High Accuracy• Generic
• Cumbersome setupDisadvantages • Requires experimental data fit
• Low Accuracy (within ± 5 °C)
• Cumbersome setup• Large computational
time
20
Generic Model Design Parameters
• Complete description of the geometry is achieved using parametric model that takes advantage ofusing parametric model that takes advantage of symmetry
• 8 parameters for modeling a PM machine8 parameters for modeling a PM machine
•ΘOuter•ΘToothΘTooth•Θfoot•RStator Outer •RSt t IRStator Inner •Rwinding bottom •Rfoot outer •R
half the tooth pitch
21
•RFoot Inner tooth pitch
Automated Mesh Generation
RStator Outer
RStator Inner
Rwinding
Rf
RFoot Inner
ΘOuter
Rfoot outer
• Start by modeling half the tooth pitch
ΘOuter
ΘTooth
Θfoot
22
Transformation of Conventional Stator Slot Design
Actual Slot Modeled Slot
Actual and Modeled Slot Overlay
[“Maxwell v11 user’s guide”, Ansoft Corporation, June. 2006]
23
Automated Mesh Generation
• 2D polar coordinate mesh is generated using a
Tinf outer , hinf outer RStator Outer
dθis generated using a center node distribution
• Mesh is segmented such th t th b d i f
RStator Inner
Statordθ
that the boundaries of nodes correspond to the parameters of the model
Rwinding
Rfoot outer
Windings
Air
dr
• Boundary conditions applied to mesh RFoot Inner
ΘOuter
Air
Tinf inner , hinf inner
ΘTooth
Θfoot
24
Finite Difference Approach
1st Law Energy Conservation
Steady State Polar Finite Difference Equation
Transient Polar Finite Difference Equation
Heat Generation in Windings Equation
25
Development of Generic Model
T1 CK1,1 K1,n
X =
1 C1
Tn CnKn nKn 1
26
n,nKn,1
Exterior Boundary Conditions
Smooth Natural Horizontal
Smooth Natural Vertical
Smooth ForcedT∞
R
tframe00
00 00
VRequivalent
tframe
0
tframe
0
Finned Natural Finned Natural Finned ForcedHorizontal VerticalFinned Forced
V
00 00
tframe
27
tframetframe
Exterior Boundary Conditions
Smooth Natural Horizontal
Smooth Natural Vertical
Smooth ForcedT∞
R
tframe00
00 00
VRequivalent
tframe
0
tframe
0
28
Exterior Boundary Conditions
T∞
RRequivalent
Finned Natural Finned Natural Finned ForcedHorizontal VerticalFinned Forced
V
00 00
tframe
29
tframetframe
Exterior Boundary Conditions
Smooth Equivalent Resistance
TTb
Requivalent
T∞
R T∞TbRequivalent
Finned Equivalent Resistance
T
Requivalent
T∞Tb
30
Frame Thickness
L00
FrameFace
Mount
LMotor
TMotor
Foot TMotorootMount
TMotor
LMotorLMotor /2Motor
TMotorTMotor /2
T /2 T /2 T /2
31
TMotor /2 TMotor /2 TMotor /2
Outline
1. Introduction2 Review of Machine Design2. Review of Machine Design
1. SM-PMAC Generator Case Study
3. Generic FD Thermal Modeling Approachg pp4. G-FD/FEA Benchmarking Studies5. Experimental Validationp6. Integrated Thermo-electromagnetic MDO 7. Summary & Conclusionsy
32
Numerical Validation of FD Technique
• Mesh convergence tests were performed on a wedge consisting of a single material and compared with results from FEA.
• Comparative performance was evaluated based on accuracy• Comparative performance was evaluated based on accuracy, mesh size, and computational time
0.05
0.06
0.07
190
190.5
0 02
0.03
0.04
189
189.5
0.02 0.04 0.06 0.08 0.10
0.01
0.02
188.5
33
Numerical Validation of FD Technique
Number of Nodes
Computational Time [sec]
Min. Temp [C]
Max. Temp [C]
FEA
331.00 30.00 101.78 105.51562.00 180.00 101.82 105.55
1145.00 780.00 101.84 105.58
Proposed Model
315.00 0.40 101.47 105.20676.00 0.50 101.79 105.521173.00 1.10 101.63 105.37
Analysis
Number of Nodes ~320 ~600 ~1150320 600 1150
Precent error [%] 0.30 0.03 0.20
Time Reduction [%] 98 67 99 72 99 86
34
98.67 99.72 99.86
PM Simulation Studies: Case 1
• Steady State model run with a heat flux boundary condition imposed on the = 10 kW/m3condition imposed on the boundaries that contact the windings
• Maximum temperature
T∞ = 25 Ch = 100 W/m2-K
x 10-3
Temperature Distribution of Half of the Tooth [C]
252
253
Temperature Distribution of Stator [C]
252
253
• Maximum temperature within 0.2° C
• Minimum temperature within 0 1° C
q” = 10 kW/m2
247
248
249
250
251
252
247
248
249
250
251within 0.1 C
• Computational Times:• FEA: 60 Sec
T∞ = 225 Ch = 150 W/m2-K
244
245
246
244
245
246
Time red ction 95%
• Proposed Algorithm: 3 Sec
35
Time reduction: 95%
PM Simulation Studies: Case 2
• Transient model run with a50
55Winding Boundary Temperature vs Time
heat flux boundary condition imposed on the boundaries that contact the windings 45
50
e (C
)35
40
Tem
pera
ture
6 A/mm2 4 A/mm22 A/mm2• Transient temperatures
within 0.2° C Computational Times
T∞ = 25 Ch = 10 W/m2-K
= 10 kW/m3
25
30 Algor v19Proposed Algorithm
• Computational Times• FEA: 210 s• Proposed Algorithm:
FEA
0 50 100 150 200 250 30025
Time (min)
Time reduction: 98 5%
3 s
36
Time reduction: 98.5%
PM Simulation Studies: Case 3
• Steady model run with a uniform heat generation imposed on the windings and contact resistance between the windings and stator
T t f d t b ithi 0 1° C
Time reduction: 95.7%
• Temperature found to be within 0.1° C• Computational Times
• FEA: 35 s
T∞ = 25 Ch = 80 W/m2-K
= 10 kW/m3
• Proposed Algorithm: 1.5 s
= 64.8 kW/m3
R = 10-3 m2-K/WFEA - Typical Slot GeometryRt,c = 10 m -K/W
37
FEA - Modeled Slot Geometry
Summary of Results
Computational Time (sec)
FEAProposed
ETime
FEAp
AlgorithmError
Reduction
Case 1 60 3 ± 0 2° 95 00 %Case 1 60 3 ± 0.2 95.00 %Case 2 210 3 ± 0.2° 98.57 %Case 3 35 1.5 ± 0.2° 95.71 %
Average 96.43
38
Outline
1. Introduction2 Review of Machine Design2. Review of Machine Design
1. SM-PMAC Generator Case Study
3. Generic FD Thermal Modeling Approachg pp4. G-FD/FEA Benchmarking Studies5. Experimental Validationp6. Integrated Thermo-electromagnetic MDO 7. Summary & Conclusionsy
39
Class Item Unit Value
General
Pole Number [‐] 8Rated / Max Power [kW] 10 / 20Rated / Max Torque [Nm] 40 /80Rated / Max Speed [rpm] 2450 / 8000p p
Slot Number [EA] 12Core Type [‐] Separated
Core Thickness [mm] 0.35Core Material [‐] RM 8
Stator Core Length [mm] 80Winding Type [‐] Concentric
Stator
Winding Type [ ] ConcentricCoils per phase Winding [EA] 4
Turns per Coil [Turns] 24Resistance [mohm] 4.85
Leakage Inductance [uH] 33
Magnetizing Inductance [uH]L1: 198 L2: 73 3L2: ‐73.3
Rated / Max Current [Apeak] 120 / 250Winding Insulation [‐] H
Rotor
Magnet Material [‐] Nd‐Fe‐BrPM Flux [Wb] 0.0534
Core Thickness [mm] 0.35C M i l [ ] RM 8Core Material [‐] RM 8
Cooling ‐ ‐Natural
ConvectionFrame Material [‐] 6061 Al
DimensionsLength of Frame [mm] 167
Inner/Outer Radius of Frame [mm] 110 / 93.5
40
Inner/Outer Radius of Frame [mm] 110 / 93.5
[9]Youngkook Lee and T. G. Habetler, “Current-Based Condition Monitoring and Fault Tolerant Operation for Electric Machines in Automotive Applications,” International Conference on Electrical Machines and Systems, pp. 2011-2016, October 2007.
Thermal Circuit Approach
Psw – Stator Winding Loss
Psc – Stator Core Loss
41[9]Youngkook Lee and T. G. Habetler, “Current-Based Condition Monitoring and Fault Tolerant Operation for Electric Machines in Automotive Applications,” International Conference on Electrical Machines and Systems, pp. 2011-2016, October 2007.
Calculation of G-FD Model Parameters
Item Unit ValueAngle of Foot [rad] 1.09E‐02Angle of Tooth [rad] 1.20E‐01Outside Angle [rad] 0 2618Outside Angle [rad] 0.2618
Inner Radius of Foot [mm] 57.9Outer Radius of Foot [mm] 59.883Radius of Windings [mm] 60
Inner Radius of Stator [mm] 87.359
42
[ ]Outer Radius of Stator [mm] 100
G-FD Steady-State Temperature Results
Item Unit Case 1 Case 2
Rotating Speed [rpm] 500 1000
Load [Nm] 9 0
q‐axis current [A] 25.4 32.6 95
100
Temperature Distribution of Half of the Tooth [C]
37.06
37.08
d‐axis current [A] ‐1.05 1.8
Copper Loss [W] 5.034 0.072
Core Loss [W] 18 12 37 575
80
85
90
37.02
37.04
Core Loss [W] 18.12 37.5Θ Stator ‐Experimental
[K] 13 20.1
Θ Stator – FD l
[K] 16.6 26.160
65
70
36.98
37
Simulation[K] 16.6 26.1
Θ Stator – FD Simulation (h=10)
[K] 14.2 22.2
55-20-10010203040
36.96
43
G-FD Transient Solution
Case 1: 500rpm, zero load Transient Temp of Stator [C]
5
10
Del
Tem
pera
ture
Sta
tor
0 0.5 1 1.5 2
x 104
0
Time Sec
20
25Transient Temp of Stator [C]
Case 2: 1000rpm, ~20% Load
10
15
Del
Tem
pera
ture
Sta
tor
440 0.5 1 1.5 2
x 104
0
5
Time Sec
Outline
1. Introduction2 Review of Machine Design2. Review of Machine Design
1. SM-PMAC Generator Case Study
3. Generic FD Thermal Modeling Approachg pp4. G-FD/FEA Benchmarking Studies5. Experimental Validationp6. Integrated Thermo-electromagnetic MDO 7. Summary & Conclusionsy
45
Coupled Multi-physics Machine Design
Advantages:
Eliminates costly design iteration steps
Avoids heuristic parameter selection
Multi-physics solution accounts for power supply, ambient, thermal condition, material, and load
( ) 10210110 34 ⋅−⋅+⋅−++⋅=Ζ ANmmVol BHη
46
Temperature Constraint: T<90°C
Results from Preliminary Integrated Design
Machine design specification:
15 kW 1800 rpm 60 HzConv. PSO
15 kW, 1800 rpm, 60 Hz
Temp. Limit: 90 OC
Amb. Temp.: 30 OC
Diameter mm 80 104.7
Length mm 75 87.7
Magnet Length mm 6.5 6.83Forced cooling: 5 m/s
Orientation: Horizontal
Magnet Length mm 6.5 6.83
Volume cm3 440 410
Mass kg 40.4 32.7
C t D it A/ 2 6 5 6 83Current Density A/mm2 6.5 6.83
Efficiency % 94.7 94.8
Temperature C 79.4 89.4V
Torque/Ampere Nm/A 3.06 3.84
Power Density W/kg 371 459
tframe
00
47
frame
Outline
1. Introduction2 Review of Machine Design2. Review of Machine Design
1. SM-PMAC Generator Case Study
3. Generic FD Thermal Modeling Approachg pp4. G-FD/FEA Benchmarking Studies5. Experimental Validationp6. Integrated Thermo-electromagnetic MDO 7. Summary & Conclusionsy
48
Summary
DiaSGapLength
InductanceThichMag• Results have shown that the proposed algorithm is both
AirGap Flux Density
Number of turns per phase
Tooth WidthStator and Rotor Yoke Thickness
accurate and computationally efficient as compared with FEA
• Algorithm is also easy to use Back EMF
Output Power
with minimal setup time• Algorithm was designed for
easy integration with an Current
Current Desnity
Slot Fill Factor
electromagnetic optimization algorithm
• Heuristic current density Design
Parametersselection can be replaced with a fast computational thermal simulation
49
Weigth VolumeLoss
Conclusions
1. A Generic model for thermal analysis of electric machines has been developed
2. A technique for transforming typical stator geometries to a simplified geometry in polar coordinates was developed
3. When base lined against an FEA package, the proposed algorithm has shown an average time reduction of 96% and equivalent accuracy.
4. The direct integration of the thermo-mechanical and electromagnetic physics in the design process has been demonstrated
5. Results from PM design case study show a 20% increase in torque-density over existing techniques
50
References
[1] V. Subrahmanyam, Electric Drives: The McGraw-Hill Companies, INC., 1996.[2] A. Boglietti and A. Cavagnino, "TEFC Induction Motors Thermal Models: A Parameter Sensitivity
Analysis," IEEE Transactions on Industry Applications, vol. 41, pp. 756-763, May/June 2005.[3] M. Baggu and H. Hess, "Evaluation of an Existing Thermal Model of an Induction Motor and its [ ] gg , g
Further Application to an Advanced Cooling Topology," Proceedings of IEEE International Electric Machines and Drives Conference, vol. 2, pp. 1079-1083, May 2007.
[4] Y. K. Chin and D. A. Staton, "Transient Thermal Analysis using both Lumped-Circuit Approach and Finite Element Method of a permanent magnet traction motor," IEEE Africon, vol. 2, pp. 1027-1036 S t b 20041036, September 2004.
[5] S. K. Chowdhury, S. P. Chowdhury, and S. K. Pal, "An Interactive Software for the Analysis of Thermal Characteristics of Capacitor-Run Single-Phase Induction Motors," Electric Power Components and Systems, vol. 29, pp. 997-1011, October 2001.
[6] C Liao C L Chen and T Katcher "Thermal management of AC induction motors using[6] C. Liao, C.-L. Chen, and T. Katcher, Thermal management of AC induction motors using computational fluid dynamics modeling," Electric Machines and Drives, vol. 99, pp. 189 -191, May 1999.
[7] F. P. Incropera, D. P. Dewitt, T. L. Bergman, and A. S. Lavine, "Fundamentals of Heat and Mass Transfer," vol. 6, 2007., ,
[8] Harley, Y. Duan, " Method for Multi-objective Optimized Designs of Surface Mount Permanent Magnet Motors with Concentrated or Distributed Stator Windings." unpublished.
[9] Youngkook Lee and T. G. Habetler, “Current-Based Condition Monitoring and Fault Tolerant Operation for Electric Machines in Automotive Applications,” International Conference on Electrical Machines and Systems, pp. 2011-2016, October 2007.
51
Th k Thank you.
QUESTIONSQUESTIONS?
Temperature Distribution of Stator [C]
250
251
252
253
244
245
246
247
248
249
250
52
244