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

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

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

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

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

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

Διάγραμμα 1. Χαρακτηριςτική καμπφλη φαςικοφ ρεφματοσ – ταχφτητασ.

Διάγραμμα 2.Χαρακτηριςτική καμπφλη απόδοςησ – ταχήτητασ.

Διάγραμμα 3. Χαρακτηριςτική καμπφλη ςυντελεςτή ιςχφοσ – ταχφτητασ.

Διάγραμμα 4. Χαρακτηριςτική καμπφλη ιςχφοσ – ταχφτητασ.

Διάγραμμα 5. Χαρακτηριςτική καμπφλη ροπήσ – ταχφτητασ.

Διάγραμμα 6. Χαρακτηριςτική καμπφλη φαςικοφ ρεφματοσ – ιςχφοσ εξόδου.

Διάγραμμα 7. Χαρακτηριςτική καμπφλη απόδοςησ - ιςχφοσ εξόδου.

Διάγραμμα 8. Χαρακτηριςτική καμπφλη ςυντελεςτή ιςχφοσ - ιςχφοσ εξόδου.

Διάγραμμα 9. Χαρακτηριςτική καμπφλη ολίςθηςησ - ιςχφοσ εξόδου.

Διάγραμμα 10.Χαρακτηριςτική καμπφλη ροπήσ - ιςχφοσ εξόδου.

Διάγραμμα 11.Χαρακτηριςτική καμπφλη ροπήσ - ολίςθηςησ

Διάγραμμα 12. Το ςτιγμιότυπο ςτο οποίο λαμβάνονται οι μετρήςεισ τησ Ηλεκτρομαγνητικήσ προςομοίωςησ.

Διάγραμμα 13. Διάγραμμα του διανυςματικοφ δυναμικοφ ςτον κινητήρα.

Διάγραμμα 14.Διάγραμμα των δυναμικών γραμμών του διανυςματικοφ δυναμικοφ ςτον κινητήρα.

Διάγραμμα 15.Διάγραμμα του μαγνητικοφ πεδίου ςτον κινητήρα.

Διάγραμμα 16. Διάγραμμα του μζτρου του μαγνητικοφ πεδίου ςτον κινητήρα.

Διάγραμμα 17.Διαγράμματα ρευμάτων εκκίνηςησ – χρόνου.

Διάγραμμα 18.Διάγραμμα ροπήσ εκκίνηςησ – χρόνου.

Διάγραμμα 19. Διάγραμμα επαγώμενων τάςεων – χρόνου.

Διάγραμμα 20. Διάγραμμα ροών διαροήσ – χρόνου.

Διάγραμμα 21. Διαγράμματα ηλεκτρικήσ και μηχανικήσ ιςχφοσ – χρόνου.