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JMAG Application NoteAnalysis of a Three Phase Induction Motor

CONTENTS

Overview........................................................................................................................................2

Appendix........................................................................................................................................2

1 Analysis Scope...........................................................................................................................3

2 Motor Specification.....................................................................................................................3

3 Analysis Results .........................................................................................................................6

3.1 Current Density Distribution.................................................................................................63.2 Speed-Torque Curve............................................................................................................7

4 Analysis Steps ............................................................................................................................8

5 FEM Model Creation ..................................................................................................................9

5.1 Mesh Model .........................................................................................................................9

5.1.1 2D Model ......................................................................................................................9

5.1.2 Partial Model.................................................................................................................9

5.1.3 Air Region .....................................................................................................................9

5.1.4 Mesh Generation ........................................................................................................10

5.2 Material Properties ............................................................................................................10

5.3 Analysis Conditions ........................................................................................................... 11

5.3.1 Analysis Control.......................................................................................................... 11

5.3.2 Full Model Conversion................................................................................................ 11

5.3.3 Circuit Conversion ...................................................................................................... 11

5.3.4 Step.............................................................................................................................12

5.3.5 Symmetry Boundary 2D..............................................................................................12

5.3.6 Periodic Boundary ......................................................................................................12

5.3.7 Motion .........................................................................................................................12

5.3.8 Electromagnetic Force and Torque Calculation..........................................................12

5.3.9 Slide............................................................................................................................12

5.3.10 FEM Coil ...................................................................................................................13

5.3.11 Circuit ........................................................................................................................14

6 Results Display.........................................................................................................................15

6.1 Current Density Distribution...............................................................................................15

6.2 Speed-Torque Curve..........................................................................................................15

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JMAG Application Note Analysis of a Three Phase Induction Motor -

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Overview

The purpose of this Application Note is to help JMAG users understand the steps and

settings used for a basic analysis of induction machines.The model data from the JMAG Application Catalog can be downloaded to view the

analysis model, settings and results described in this Application Note.

The organization is as follows:

Section 1 Analysis Scope

Presents the scope of the analysis.

Section 2 Motor Specification

Specifies the motor used for the analysis, including the motor geometry, the coil

arrangement and the material properties.

Section 3 Analysis Results

Shows the speed-torque relationship and rotor-current distribution results obtained

from the analysis.

Section 4 Analysis Steps

Describes the analysis steps used to obtain the results presented in Section 3.

Section 5 FEM Model Creation

Describes the analysis settings, including the mesh model, the material properties

and the condition settings.

Section 6 Results Display

Describes how to display the analysis results, such as creating graphs and showing

contour plots.

Appendix

Shows the JMAG mesh model and lists the settings, including material properties and

analysis conditions. The analysis settings are identical to the settings used in the model files

available from our Website.

Magnetic Field Analysis Rotation speed 0 rpm

The JMAG module(s) and the version used for the analysis are:

Module DP

Version Studio 10.0, Designer 10.4
http://jac001_im_02d.html/http://jac001_im_02d.html/

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1 Analysis Scope

This note presents how the current density distribution and the Speed-Torque curve of a

three-phase induction motor can be obtained.The motor analyzed has 4 poles, one coil perpole winding arrangement, and balanced three-phase currents are used in the stator coils.

This analysis inherently includes core saturation, space harmonics due to stator slots and

leakage paths. The rotor end-rings are approximated by adding an appropriate resistance to

each bar.

In the induction motor, current is induced in the rotor cage by the rotating magnetic field of

stator coils. Analyzing the current induced in the rotor bars is important since the induced

current essentially determines the performance of the induction motor.

2 Motor Specification

The specification of the induction motor used for the analysis is shown below.

Figure 2.1 Induction Motor

Coil

Rotor core

Stator coreBolt hole

Bar

Shaft

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Table 2.1 Specification

Number of poles 4

Number of stator slots 24Number of rotor slots 34

Excitation Three-phase AC

Frequency 50 HzPower supply

Current 4 A

Turns 66 turn/slotCoil

Resistance 1.48 /phase

Coil winding 1 coil per pole, 1 coil-side per slot: see Figure 2.2

Stator core (outside dimension) L 108 W 108 thickness 42 mm

Rotor core (outside dimension) R 34.7 thickness 42 mmEnd-ring cross-section 17.81 mm

2

Bar cross-section 13.34 mm2

Table 2.2 Material Magnetic Properties

Part Property

Bar Non-magnetic material

Rotor core Isotropic magnetic material: see Figure 2.3 for BH curve

Bolt hole Air

Stator core Isotropic magnetic material: see Figure 2.3 for BH curve

Shaft Isotropic magnetic material: see Figure 2.3 for BH curve

Coil Non-magnetic material

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Figure 2.2 Winding Pattern

0.0

0.5

1.0

1.5

2.0

2.5

0 10000 20000 30000 40000

Magnetic field, A/m

Flux

density,

T

Figure 2.3 BH Curve (rotor core, stator core and shaft)

U-phase

V-phase

W-phase

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3 Analysis Results

The current density distribution and the Speed-Torque curve can be obtained from analysis

of the induction motor described in Section 2.

3.1 Current Density Distribution

At each speed, the current density in the rotor bars is calculated for every motion step of

rotor position.

The current density distribution at 1050 rpm is shown in Figure 3.1 for two different instants

in time, i.e., two different positions.

Figure 3.1 Current Density Distribution of the Cage Conductor Bars (rotation speed: 1050 rpm)

(upper: 0.11 seconds, lower: 0.14 seconds)

(Unit: A/m2)

(Unit: A/m2)

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3.2 Speed-Torque Curve

Figure 3.2 shows the Speed-Torque curve obtained for this induction motor model. The

maximum torque is found to be near 1000rpm. In the range labeled b in Figure 3.2, the speedchange is only about 5%, with a 100% change in the torque, therefore the motor is considered

to be essentially a constant speed machine with a fixed frequency power supply.

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

0 150 300 450 600 750 900 1050 1200 1350 1500

Rotation speed, rpm

Torque,

Nm

Figure 3.2 Speed versus Torque

a b

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4 Analysis Steps

A number of transient response magnetic field analyses are required to obtain the

Speed-Torque curve. The average torque is calculated at each speed, including the effects ofthe slip, and then the data is exported to a spreadsheet to create the Speed-Torque graph.

The current density can be viewed and evaluated inside JMAG with PLOT files that contain

the analysis results.

The steps to calculate the current density distribution are:

STEP 1: Create the FEM model

STEP 2: Run the analysis for each load point

The steps to obtain the Speed-Torque curve of the induction motor are:

STEPS 1 & 2: Same as above

STEP 3: Calculate the average torque at the specified speed

STEP 4: Repeat STEPS through 1 to 3 at different speeds

STEP 5: Evaluate the results using a spreadsheet

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5 FEM Model Creation

The FEM model, required to run the magnetic field analysis, is composed of a mesh model,

the material properties, and the analysis conditions.

5.1 Mesh Model

Some notes on the creation of the mesh model are provided below.

5.1.1 2D Model

The 2D analysis of JMAG's DP solver module is a good starting point for induction machine

analysis because it is easier and faster than 3D, yet gives sufficiently accurate results. 2D

analysis can be used when the stack length of the rotor and the stator are the same and the

two cores are aligned axially.

In this analysis, the magnetic flux in the axial direction, such as fringing at the ends of the

stack, is ignored.

5.1.2 Partial Model

Ahalf model can be used when the geometry and the magnetic field of the motor have a

periodicity of 180 degrees. The analysis runs faster with a partial model because it reduces

the time for data creation and calculation, as well as the CPU load of the computer.

A partial model requires periodic boundary condition settings, which are done during a later

step. For details, see 5.3.6 Periodic Boundary.

5.1.3 Air Region

The air region is required even if the magnetic circuit is closed within the motor, because of

some flux leakage, usually caused by saturation. An adequate size of the air region is 1.05 to

2.5 times the outer radius of the stator core, and the optimum value varies with the severity of

the saturation.

In this analysis, the mesh model of the air region is set to 1.25 times the radius of the motor.

A symmetry boundary condition specifies the outer circumference of the mesh model. See

5.3.5 Symmetry Boundary.

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5.1.4 Mesh Generation

Since the rotor has the rotational motion, the cylindrical slide mesh option can be used to

efficiently generate the mesh in the gap between the stator and the rotor for each increment ofrotation.

The number of divisions is set so there are at least 8 divisions in one period of the torque.

Generally, the divisions needed for accurate calculation vary with motor geometry. For this

analysis, one division has about 10 divisions in the circumferential direction. The number of

divisions in the radial direction is set to 5 because the flux in the gap of the induction motor

changes significantly as the stator current changes and as the rotor moves.

.

5.2 Material Properties

The material properties of the parts are specified with reference to the motor specification

list. See Figure 2.1 and Table 2.1.

In this analysis, the electric conductivity of the bar (3.0107S/m) is corrected to include the

effect of the current flowing in the end rings. Values used for the calculation are listed in Table

5.1. The resistance R2 of the corrected bar is calculated using the equation (1.1) and (1.2).

The inductance of the end rings is ignored in this method; however, there is no problem to

evaluate the Speed-Torque curve.

b

b

b

S

lR

1 (1.1)

r

r

r

S

lR

12 (1.2)

22

2

P

NRRR

rb (1.3)

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Table 5.1 Values Used for Calculating Correction Values of Electric Conductivity

Parameter Value

bR

: Resistance of the bar Calculated using theequation 1.1

rR :Resistance of the end ring Calculated using the

equation 1.2

2R : Correctedresistance of the bar Calculated using the

equation 1.3

2N : Number of rotor slots 34

P: Number of poles 4

b

l : Length of bar 42 mm

bS : Cross-section of the bar 13.34 mm2

rl : Length of the end ring circumference 188.5 mm

rS : Cross-section of the end ring 17.81mm2

: Conductivity of the conductor 3.0107S/m

5.3 Analysis Conditions

Some note about the analysis conditions are provided below.

5.3.1 Analysis Control

Transient response analysis is selected since the induced magnetomotive force and the

rotation motion of the rotor are time-varying phenomena, and the effects of eddy current need

to be included.

When a half (180 degrees) model is used for the analysis, the conversion factor for both the

FEM model and the circuit is 2.

Since the torque is constant at each rpm in the calculation of the Speed-Torque curve, the

dummy stationary analysis option may be used to shorten the initial transient state.

5.3.2 Full Model Conversion

The conversion factor is set to 2 because a half model is used for this analysis.

5.3.3 Circuit Conversion

The conversion factor is set to 2 because a half model is used for this analysis.

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5.3.4 Step

The rotor is set to rotate 1 degree per step in this analysis. The time interval is used to

specify the speed for each point on the Speed-Torque curve. When the analysis needs to runfor a mechanical angle, such as 720 degrees, the number of steps would be set to 721 to

include the initial starting position.

5.3.5 Symmetry Boundary 2D

The symmetry boundary sets the outer boundary of the entire mesh model, assuming all

magnetic flux stays inside this boundary.

5.3.6 Periodic Boundary

The periodic boundary needs to be specified when a half model is used. In this example,

both the model geometry and the direction of the magnetic field have a periodicity of 180

degrees in the circumferential direction. The model is 2D and the center is the origin, so the

point on the rotation axis is set to (0,0,0) and the direction of the rotation axis is set to

(X,Y,Z)=(0,0,1).

5.3.7 Motion

The motion condition is set on the rotating parts including the shaft, rotor core and rotor

bars. The center of the rotation is the origin and the rotation axis is Z-axis, sothe point on the

rotation axisis set to (0,0,0) and the direction of the rotation axis is set to (X,Y,Z)=(0,0,1).

To obtain the Speed-Torque curve, a number of analyses at different speeds will need to be

specified.

5.3.8 Electromagnetic Force and Torque Calculation

For this analysis, this condition is set on the shaft, rotor core, and the bars to calculate the

torque generated in the rotating parts. The nodal force method is used when the condition is

set on magnetic materials.

5.3.9 Slide

The cylindrical slide mesh option is used in this case to efficiently generate the mesh in the

air gap. With this option, the slide condition will be set automatically during the mesh

generation.

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5.3.10 FEM Coil

An FEM coil condition needs to be assigned to each phase. The coil regions for each phase

are connected in series, so only a single condition needs to be set to each phase.The directions of the current flow in the coil region are indicated in Figure 5.1.

Figure 5.1 Current Flow Directions Set by the FEM Coil Conditions (+ is upward, - is downward)

-V-V

+U

+U

-W

-W

+W+W

-U

-U

+V

+V

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5.3.11 Circuit

In this basic induction motor model, the currents in the stator coil are user-specified as input

values.The settings for the three-phase current sources and the FEM coil components will specify

the typical balanced three-phase operation of the motor.

For this analysis, amplitude is set to 4 A, frequency to 50 Hz, number of turns to 66 turns,

and resistance to 1.48 ohm as shown in the specification, Table 2-1. The U-phase current is

set to 0 degrees, the V-phase is set to +120 degrees (theta+120) and the W-phase is set to

-120 degrees (theta-120).

In JMAG, one FEM coil condition in the FEM model corresponds to one FEM coil

component in the circuit. The conditions defined in the circuit are run simultaneously with

magnetic field analysis.

Figure 5.2 Circuit Diagram (left: whole circuit, right: internal circuit of star connection block)

U-phase

V-phase

W-phase

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6 Results Display

After the analysis is complete, a results file is created, which is opened in a new window

with one click. Many parameters can be displayed, each with choices such as line plots orcolor contours. The display of the current density and the Speed-Torque curve is described

below.

6.1 Current Density Distribution

A contour plot of the current density distribution in the stator coils and the rotor bars of the

induction motor can be viewed.

6.2 Speed-Torque Curve

The Speed-Torque curve is displayed in a graph using the average torque at each rotation

speed in spreadsheet software. The electromagnetic force of the torque is exported from the

analysis results for each rotation speed to graph the Speed-Torque curve. The average torque

can be calculated by averaging one period of the torque in the steady state. The

Speed-Torque curve shown in Figure 3.2 was created by setting the average torque on the

vertical axis, and the speed on the horizontal axis.

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Engineering Technology Division, JMAG Support Team

[email protected]

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