1. Technical Report
General Design Data of a
Three Phase Induction Machine 90kW – Squirrel
Cage Rotor
Tasos Lazaridis
Electrical Engineer – CAD/CAE Engineer
tasoslazaridis13@gmail.com

2. Three-Phase Induction Machine Design
GENERAL DATA
Given Output Power (kW): 90
Rated Voltage (V): 380
Winding Connection: Wye
Number of Poles: 4
Given Speed (rpm): 1463
Frequency (Hz): 50
Stray Loss (W): 1620
Frictional Loss (W): 1000
Windage Loss (W): 2500
Operation Mode: Motor
Type of Load: Constant Power
Operating Temperature (C): 75
STATOR DATA
Number of Stator Slots: 48
Outer Diameter of Stator (mm): 349
Inner Diameter of Stator (mm): 235
Type of Stator Slot: 1
Stator Slot
hs0 (mm): 0.5
hs2 (mm): 21
bs0 (mm): 3
bs1 (mm): 9.3
bs2 (mm): 11.4
Top Tooth Width (mm): 6.72953
Bottom Tooth Width (mm): 7.38096
Length of Stator Core (mm): 300
Stacking Factor of Stator Core: 0.95
Type of Steel: D23_50
Number of lamination sectors 0
Press board thickness (mm): 2
Magnetic press board Yes
Number of Parallel Branches: 1
Type of Coils: 21
Coil Pitch: 4
Number of Conductors per Slot: 8
Number of Wires per Conductor: 1
Wire Diameter (mm): 4.62
Wire Wrap Thickness (mm): 0
Wedge Thickness (mm): 0
Slot Liner Thickness (mm): 0.3
Layer Insulation (mm): 0.3
Slot Area (mm^2): 303.35
Net Slot Area (mm^2): 251.069

3. Slot Fill Factor (%): 68.0113
Limited Slot Fill Factor (%): 75
Wire Resistivity (ohm.mm^2/m): 0.0217
Conductor Length Adjustment (mm): 0
End Length Correction Factor 1
End Leakage Reactance Correction Factor 1
ROTOR DATA
Number of Rotor Slots: 38
Air Gap (mm): 0.7
Inner Diameter of Rotor (mm): 70
Type of Rotor Slot: 1
Rotor Slot
hs0 (mm): 0.5
hs2 (mm): 22.5
bs0 (mm): 1.5
bs1 (mm): 7
bs2 (mm): 7
Cast Rotor: Yes
Half Slot: Yes
Length of Rotor (mm): 300
Stacking Factor of Rotor Core: 0.95
Type of Steel: D23_50
Skew Width: 0
End Length of Bar (mm): 0
Height of End Ring (mm): 32
Width of End Ring (mm): 23
Resistivity of Rotor Bar
at 75 Centigrade (ohm.mm^2/m): 0.0263158
Resistivity of Rotor Ring
at 75 Centigrade (ohm.mm^2/m): 0.0263158
Magnetic Shaft: Yes
MATERIAL CONSUMPTION
Armature Copper Density (kg/m^3): 8900
Rotor Bar Material Density (kg/m^3): 2689
Rotor Ring Material Density (kg/m^3): 2689
Armature Core Steel Density (kg/m^3): 7820
Rotor Core Steel Density (kg/m^3): 7820
Armature Copper Weight (kg): 23.3299
Rotor Bar Material Weight (kg): 3.01416
Rotor Ring Material Weight (kg): 2.49448
Armature Core Steel Weight (kg): 85.2642
Rotor Core Steel Weight (kg): 78.6141
Total Net Weight (kg): 192.717
Armature Core Steel Consumption (kg): 181.997
Rotor Core Steel Consumption (kg): 96.6668

4. RATED-LOAD OPERATION
Stator Resistance (ohm): 0.0674703
Stator Resistance at 20C (ohm): 0.0554998
Stator Leakage Reactance (ohm): 0.126467
Rotor Resistance (ohm): 0.0270918
Rotor Leakage Reactance (ohm): 0.282897
Resistance Corresponding to
Iron-Core Loss (ohm): 86.3582
Magnetizing Reactance (ohm): 3.12506
Stator Phase Current (A): 196.241
Current Corresponding to
Iron-Core Loss (A): 2.253
Magnetizing Current (A): 62.2595
Rotor Phase Current (A): 169.394
Copper Loss of Stator Winding (W): 7794.93
Copper Loss of Rotor Winding (W): 2332.14
Iron-Core Loss (W): 1315.06
Frictional and Windage Loss (W): 3502.88
Stray Loss (W): 1620
Total Loss (W): 16565
Input Power (kW): 106.558
Output Power (kW): 89.9932
Mechanical Shaft Torque (N.m): 587.205
Efficiency (%): 84.4545
Power Factor: 0.812457
Rated Slip: 0.0243366
Rated Shaft Speed (rpm): 1463.5
NO-LOAD OPERATION
No-Load Stator Resistance (ohm): 0.0674703
No-Load Stator Leakage Reactance (ohm): 0.126973
No-Load Rotor Resistance (ohm): 0.0270573
No-Load Rotor Leakage Reactance (ohm): 0.288555
No-Load Stator Phase Current (A): 67.8374
No-Load Iron-Core Loss (W): 1535.74
No-Load Input Power (W): 7785.61
No-Load Power Factor: 0.13809
No-Load Slip: 0.000754578
No-Load Shaft Speed (rpm): 1498.87
BREAK-DOWN OPERATION
Break-Down Slip: 0.08
Break-Down Torque (N.m): 941.169
Break-Down Torque Ratio: 1.60279
Break-Down Phase Current (A): 418.008
LOCKED-ROTOR OPERATION
Locked-Rotor Torque (N.m): 474.54

5. Locked-Rotor Phase Current (A): 679.546
Locked-Rotor Torque Ratio: 0.808134
Locked-Rotor Current Ratio: 3.46282
Locked-Rotor Stator Resistance (ohm): 0.0674703
Locked-Rotor Stator
Leakage Reactance (ohm): 0.115617
Locked-Rotor Rotor Resistance (ohm): 0.0616147
Locked-Rotor Rotor
Leakage Reactance (ohm): 0.193633
DETAILED DATA AT RATED OPERATION
Stator Slot Leakage Reactance (ohm): 0.0881042
Stator End-Winding Leakage
Reactance (ohm): 0.0201604
Stator Differential Leakage
Reactance (ohm): 0.018202
Rotor Slot Leakage Reactance (ohm): 0.152883
Rotor End-Winding Leakage
Reactance (ohm): 0.00686664
Rotor Differential Leakage
Reactance (ohm): 0.123145
Skewing Leakage Reactance (ohm): 0
Stator Winding Factor: 0.478831
Stator-Teeth Flux Density (Tesla): 1.70722
Rotor-Teeth Flux Density (Tesla): 1.16603
Stator-Yoke Flux Density (Tesla): 1.87124
Rotor-Yoke Flux Density (Tesla): 0.588304
Air-Gap Flux Density (Tesla): 0.753862
Stator-Teeth Ampere Turns (A.T): 190.167
Rotor-Teeth Ampere Turns (A.T): 16.1044
Stator-Yoke Ampere Turns (A.T): 521.959
Rotor-Yoke Ampere Turns (A.T): 4.31289
Air-Gap Ampere Turns (A.T): 478.047
Correction Factor for Magnetic
Circuit Length of Stator Yoke: 0.246496
Correction Factor for Magnetic
Circuit Length of Rotor Yoke: 0.7
Saturation Factor for Teeth: 1.43149
Saturation Factor for Teeth & Yoke: 2.53236
Induced-Voltage Factor: 0.886832
Stator Current Density (A/mm^2): 11.7062
Specific Electric Loading (A/mm): 102.071
Stator Thermal Load (A^2/mm^3): 1194.86
Rotor Bar Current Density (A/mm^2): 8.33598
Rotor Ring Current Density (A/mm^2): 3.38302
Half-Turn Length of
Stator Winding (mm): 407.209

6. WINDING ARRANGEMENT
The 3-phase, 2-layer winding can be arranged in 12 slots as: AAAAZZZZBBBB
Angle per slot (elec. degrees): 15
Phase-A axis (elec. degrees): 52.5
First slot center (elec. degrees): 0
TRANSIENT FEA INPUT DATA
For one phase of the Stator Winding:
Number of Turns: 64
Parallel Branches: 1
Terminal Resistance (ohm): 0.0674703
End Leakage Inductance (H): 6.04158e-005
For Rotor End Ring Between Two Bars of One
Side:
Equivalent Ring Resistance (ohm): 5.92974e-007
Equivalent Ring Inductance (H): 3.99331e-009
2D Equivalent Value:
Equivalent Model Depth (mm): 300
Equivalent Stator Stacking Factor: 0.963333
Estimated Rotor Inertial Moment (kg m^2): 0.68408

7. Διάγραμμα 1. Χαρακτηριςτική καμπφλη φαςικοφ ρεφματοσ – ταχφτητασ.
Διάγραμμα 2.Χαρακτηριςτική καμπφλη απόδοςησ – ταχήτητασ.
Διάγραμμα 3. Χαρακτηριςτική καμπφλη ςυντελεςτή ιςχφοσ – ταχφτητασ.

8. Διάγραμμα 4. Χαρακτηριςτική καμπφλη ιςχφοσ – ταχφτητασ.
Διάγραμμα 5. Χαρακτηριςτική καμπφλη ροπήσ – ταχφτητασ.
Διάγραμμα 6. Χαρακτηριςτική καμπφλη φαςικοφ ρεφματοσ – ιςχφοσ εξόδου.

9. Διάγραμμα 7. Χαρακτηριςτική καμπφλη απόδοςησ - ιςχφοσ εξόδου.
Διάγραμμα 8. Χαρακτηριςτική καμπφλη ςυντελεςτή ιςχφοσ - ιςχφοσ εξόδου.
Διάγραμμα 9. Χαρακτηριςτική καμπφλη ολίςθηςησ - ιςχφοσ εξόδου.

10. Διάγραμμα 10.Χαρακτηριςτική καμπφλη ροπήσ - ιςχφοσ εξόδου.
Διάγραμμα 11.Χαρακτηριςτική καμπφλη ροπήσ - ολίςθηςησ

11. Διάγραμμα 12. Το ςτιγμιότυπο ςτο οποίο λαμβάνονται οι μετρήςεισ τησ Ηλεκτρομαγνητικήσ προςομοίωςησ.
Διάγραμμα 13. Διάγραμμα του διανυςματικοφ δυναμικοφ ςτον κινητήρα.

12. Διάγραμμα 14.Διάγραμμα των δυναμικών γραμμών του διανυςματικοφ δυναμικοφ ςτον κινητήρα.
Διάγραμμα 15.Διάγραμμα του μαγνητικοφ πεδίου ςτον κινητήρα.

13. Διάγραμμα 16. Διάγραμμα του μζτρου του μαγνητικοφ πεδίου ςτον κινητήρα.
Διάγραμμα 17.Διαγράμματα ρευμάτων εκκίνηςησ – χρόνου.

14. Διάγραμμα 18.Διάγραμμα ροπήσ εκκίνηςησ – χρόνου.
Διάγραμμα 19. Διάγραμμα επαγώμενων τάςεων – χρόνου.

15. Διάγραμμα 20. Διάγραμμα ροών διαροήσ – χρόνου.
Διάγραμμα 21. Διαγράμματα ηλεκτρικήσ και μηχανικήσ ιςχφοσ – χρόνου.