Example2 Torque Analysis of SPM Motor

General

Torque characteristics of SPM motor (Surface Permanent Magnet Motor) is analyzed when the electricity is applied.
The model is a permanent magnet synchronous motor with magnets attached on the surface of a rotor.
The analysis is coupled with the external circuit.
The homogenizing method is applied to simulate the layer structure of the electromagnetic plates of steel for the core.
The torque and the magnetic flux density are solved.
Unless specified in the list below, the default conditions will be applied.
In this exercise, the model is half period symmetric for your easy understanding.
Fast calculation is possible by making this model 1/4 period symmetric.
Obtain this session’s project file. (Save the project file before open)

Analysis Conditions

Item	Settings
Solvers	Magnetic Field Analysis [Luvens]
Analysis Space	2D
Analysis Type	Transient Analysis
Unit	mm
Options	Select External Circuit Coupling. Select Rotating machinery. [Conversion] Model Thickness: 30×10^-3[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 Constant Velocity.

Number of Rotations: 1800[r/min]

Rotor’s Initial Rotation Position: 0[deg]

Number of Slide Mesh Divisions

Circumferential Division Angle: 1.0[deg]

Rotation per Step: 1[mesh]

Number of Slide Mesh Layers: 3

External circuit is as follows.

60[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: 1[mm]

Ambient Air Creation

Select Create ambient air automatically.

Ambient Air Scale: 1.2

The Transient Analysis tab is set up as follows.

With the settings as below, number of steps is 180, circumferential division angle is 1.0[deg], and rotation per step is 1[mesh], the rotation up to 180 degrees (=180*1.0*1) is analyzed.

Tab

Setting Item

Setting

Transient Analysis

Time step

Automatic

Table

Number	Calculation steps	Output steps
1	180	1

Graphical Objects

A rotor core and magnet are placed in the center. A stator and coils are placed around them.

The motor has 4 poles.

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

Rotation period boundary (symmetric) is set.

“Ambient Air Creation” is selected.

In this exercise, the model is half period symmetric for your easy understanding. The calculation can be faster by making this model quarter period symmetric.
In the quarter model, the number of series in the circuit is 2 and the resistance value of FEM coil in the external circuit is half of the half model.

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
4/Sheet	Mag1	mag
5/Sheet	Mag2	mag
0/Sheet	Rotor	core
27/Sheet	Stator	core
29/Sheet	U1+	Cu
30/Sheet	U1+	Cu
31/Sheet	W1-	Cu
32/Sheet	W1-	Cu
33/Sheet	V1+	Cu
34/Sheet	V1+	Cu
35/Sheet	U1-	Cu
36/Sheet	U1-	Cu
37/Sheet	W1+	Cu
38/Sheet	W1+	Cu
39/Sheet	V1-	Cu
40/Sheet	V1-	Cu

The material properties are set up as follows:

The homogenizing method is applied to simulate the laminated plate of steel for the core.

Body Attribute Name	Tab	Setting
Mag1	Direction	Vector: X=1, Y=0, Z=1
Mag1	Stator/Rotor/Air	Rotor
Mag2	Direction	Vector: X=1, Y=0, Z=-1
Mag2	Stator/Rotor/Air	Rotor
Rotor	Layer	Select Take layer into account Space Factor: 97[%] Layer Direction Vector: X=0, Y=1, Z=0
Rotor	Stator/Rotor/Air	Rotor
Stator	Layer	Select Take layer into account Space Factor: 97[%] Layer Direction Vector: X=0, Y=1, Z=0
Stator	Stator/Rotor/Air	Stator
U1-	Current	Waveform: External Circuit Coupling Coil name on the circuit: U1 Turns: 35[Turns] Direction: – Y Direction
U1-	Stator/Rotor/Air	Stator
U1+	Current	Waveform: External Circuit Coupling Coil name on the circuit: U1 Turns: 35[Turns] Direction: +Y Direction
U1+	Stator/Rotor/Air	Stator
V1-	Current	Waveform: External Circuit Coupling Coil name on the circuit: V1 Turns: 35[Turns] Direction: – Y Direction
V1-	Stator/Rotor/Air	Stator
V1+	Current	Waveform: External Circuit Coupling Coil name on the circuit: V1 Turns: 35[Turns] Direction: +Y Direction
V1+	Stator/Rotor/Air	Stator
W1-	Current	Waveform: External Circuit Coupling Coil name on the circuit: W1 Turns: 35[Turns] Direction: – Y Direction
W1-	Stator/Rotor/Air	Stator
W1+	Current	Waveform: External Circuit Coupling Coil name on the circuit: W1 Turns: 35[Turns] Direction: +Y Direction
W1+	Stator/Rotor/Air	Stator

The material properties are set as follows.

Material Name

Tab

Properties

Conductivity

Conductivity Type: Conductor

Conductivity: 5.977×10^7[S/m]

mag

Relative permeability

Material Type: Permanent Magnet

Magnet

Magnetization Characteristic Type: Linear

Magnetization Strength: 1.25[T]

Relative Permeability: 1.05

core

Permeability

Magnetization Characteristic Type: Select B-H curve

B-H Curve Table

Magnetic Field [A/m]	Magnetic Flux Density [T]
0	0
58	0.42
90	0.8
180	1.19
380	1.37
1100	1.48
2000	1.55
3000	1.608
11000	1.81
20000	1.91

Boundary Conditions

Half period symmetric 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 at the rotation angle of 0[deg] is shown below.

The diagram below shows time-torque characteristics.

Transient state becomes stable at around 12[ms].

About 40[N*m] of torque is obtained.

See other Magnetic Analysis (Transient Analysis) examples.