Example4 Starting Characteristics of Induction Motor

General

A cage structure three-phase induction motor is analyzed.
The magnetic field of coils on the stator generates eddy current at the conductor on the rotor.
The magnetic fields generated by eddy current and stator create the torque which rotates the asynchronous motor.
The motion coupled analysis is applied.
The analysis begins from the stationary state of the model. The rotation is gradually increased and reaches the stable state at about 1000[r/min].
The rotation velocity, torque and magnetic flux density are solved.
Unless specified in the list below, the default conditions will be applied.

Analysis Conditions

Item	Setting
Solver	Magnetic Field Analysis [Luvens]
Analysis Space	2D
Analysis Type	Transient Analysis
Unit	mm
Options	Select External Circuit Coupling. Select Rotating machinery. [Conversion] Model Thickness: 4.2×10^-2[m] Select Partial Model. Number of Divisions of the Whole Model: 2 Circuit Configuration Number of Series: 1 Circuit Configuration Number of parallels: 2 Select Convert the result to the whole model and output it.

The Rotating Machinery tab is set as follows.

Tab	Setting Item	Setting
Rotating Machinery	Rotational Movement	Select Motion Equation Coupling
Rotating Machinery	Number of Slide Mesh Divisions	Circumferential Division Angle: 0.5[deg] Number of Slide Mesh Layers: 3
Setting Motion Equation Coupling	Moment of Inertia	Inertial Moment of Rotor: 6.269×10^-4[kgm2] Inertial Moment of Load: 3.0×10^-3[kgm2]
	External Torque	Waveform: Constant 0[N*m]
	Coulomb Friction Torque	Waveform: Coefficient Coulomb Friction Torque: 0.5×10^-5[Nm] Viscous Friction Coefficient: 0[Nm/(r/min)] Squared Load Torque Coefficient: 1.226×10^-6[N・m/(r/min)2]
	Initial Time State	Number of Rotations: 0[r/min] Rotor’s Initial Rotation Position: 0[deg]

External circuit is as follows.

50[Hz] three-phase AC voltage is applied.

Set the Mesh Tab as follows.

Tab

Setting Item

Setting

Mesh

Meshing Setup

Automatically set the general mesh size: Deselect

General mesh size: 2[mm]

Ambient Air Creation

Select Create ambient air automatically

Ambient Air Scale: 1.2

The Transient Analysis tab is set up as follows.

One second is divided into 800 steps.

Tab

Setting Item

Setting

Transient Analysis

Time step

Manual

Table

Number	Calculation steps	Output steps	Time step [s]
1	800	1	1.0/800

Graphical Objects

A rotor cage consisted of conductor and rotor core is placed in the center. A stator core and coils are placed around it.

This is a 2D model analysis. By utilizing the symmetry of the analysis model, it is made to be a half period symmetric model.

“Ambient Air Creation” is selected.

Small mesh size is (0.3mm) is applied to the gap.

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
25/Sheet	Cage	Al
26/Sheet	Cage	Al
27/Sheet	Cage	Al
28/Sheet	Cage	Al
29/Sheet	Cage	Al
30/Sheet	Cage	Al
31/Sheet	Cage	Al
32/Sheet	Cage	Al
33/Sheet	Cage	Al
34/Sheet	Cage	Al
35/Sheet	Cage	Al
36/Sheet	Cage	Al
37/Sheet	Cage	Al
38/Sheet	Cage	Al
39/Sheet	Cage	Al
40/Sheet	Cage	Al
41/Sheet	Cage	Al
24/Sheet	Rotor	50A1300
65/Sheet	Stator	50A1300
67/Sheet	U1+	Cu
68/Sheet	U1+	Cu
69/Sheet	W1-	Cu
70/Sheet	W1-	Cu
71/Sheet	V1+	Cu
72/Sheet	V1+	Cu
73/Sheet	U1-	Cu
74/Sheet	U1-	Cu
75/Sheet	W1+	Cu
76/Sheet	W1+	Cu
77/Sheet	V1-	Cu
78/Sheet	V1-	Cu

The material properties are set up as follows:

Body Attribute Name	Tab	Settings
Cage	Stator/Rotor/Air	Rotor
Rotor	Stator/Rotor/Air	Rotor
Stator	Stator/Rotor/Air	Stator
U1-	Current	Waveform: External Circuit Coupling Coil name on the circuit: U1 Turns: 66[Turns] Direction: – Y Direction
U1-	Stator/Rotor/Air	Stator
U1+	Current	Waveform: External Circuit Coupling Coil name on the circuit: U1 Turns: 66[Turns] Direction: +Y Direction
U1+	Stator/Rotor/Air	Stator
V1-	Current	Waveform: External Circuit Coupling Coil name on the circuit: V1 Turns: 66[Turns] Direction: – Y Direction
V1-	Stator/Rotor/Air	Stator
V1+	Current	Waveform: External Circuit Coupling Coil name on the circuit: V1 Turns: 66[Turns] Direction: +Y Direction
V1+	Stator/Rotor/Air	Stator
W1-	Current	Waveform: External Circuit Coupling Coil name on the circuit: W1 Turns: 66[Turns] Direction: – Y Direction
W1-	Stator/Rotor/Air	Stator
W1+	Current	Waveform: External Circuit Coupling Coil name on the circuit: W1 Turns: 66[Turns] Direction: +Y Direction
W1+	Stator/Rotor/Air	Stator

The material properties are set as follows.

Material Name

Tab

Properties

Electric Conductivity

Conductivity Type: Conductor

Conductivity: 1.02×10^7[S/m]

Electric Conductivity

Conductivity Type: Conductor

Conductivity: 5.977×10^7[S/m]

50A1300

Permeability

Magnetization Characteristic Type: Select B-H curve

B-H Curve Table

Magnetic Field [A/m]	Magnetic Flux Density [T]
0	0
20	0.028
30	0.035
35	0.038
40	0.04
45	0.042
50	0.044
60	0.058
70	0.07
80	0.085
90	0.11
100	0.135
120	0.215
140	0.335
160	0.48
200	0.86
240	1.12
300	1.29
400	1.431
500	1.491
600	1.531
700	1.559
800	1.576
900	1.581
1000	1.591
1300	1.617
1600	1.63
2200	1.658
3000	1.689
4000	1.725
5000	1.756
7000	1.819
10000	1.888
16000	1.975
22000	2.026
30000	2.078
40000	2.122
50000	2.163
70000	2.238
80000	2.271

Boundary Conditions

Symmetric period boundary is set.

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Setting
Symmetric	Symmetry/Continuity	Periodic	Rotation Period (1 period)

Results

The distribution of the magnetic flux density right after the start is shown below.

The distribution of eddy current density is shown as follows.

Eddy current is generated at the cage conductor by the magnetic flux created by the coils.

The diagram below shows time-rotation velocity characteristic.

The rotation is gradually increased and reaches the stable state at about 1000[r/min].

The diagram below shows time-torque characteristics.

See other Magnetic Analysis (Transient Analysis) examples.