Brushless DC Motor
Calculations
Copyright 2005 Magsoft Corporation
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Cover illustration: Color shade plot of flux density on rotor, magnet, and stator from simulationof motor at constant speed with external circuit coupling
1 About this document xv
What this document contains xv
Chapters to complete for the different simulations xvi
For experienced users xvi
1 Enter the materials 3
Start Flux2D 3
Open the materials database 5
Add the magnetic material 6
Add the nonlinear steel material 9
Close the materials database 11
2 Cogging torque computation 15
Special considerations for simulation 15
Enter the physical properties 17
Start Preflu 9.1 17
Open the 3-layer airgap problem 18
Save your project with a new name 20
Define as Transient Magnetic 22
Change to the Physics context 23
iii
Contents
Physics context toolbars 24
Import materials from the materials database 25
Assign materials and sources to the regions 27
Assign the windings of the stator slots 27
Assign WEDGE, AIR, STATOR_AIR, AIRGAP and SHAFT regions 31
Assign STATOR and ROTOR regions 33
Assign the MAGNET 35
Creating and Assigning Mechanical Sets 38
Creating Mechanical Sets 38
Create the MOVING_ROTOR Mechanical Set . . . . . . . . . . . . . . . . . . . . 39
Create the FIXED_STATOR Mechanical Set. . . . . . . . . . . . . . . . . . . . . 43
Create the ROTATING_AIRGAP Mechanical Set. . . . . . . . . . . . . . . . . . . 44
Assigning Mechanical Sets 45
Boundary conditions (Periodicity) 49
Check the physical model 51
Close Preflu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Solve (batch mode) 54
Prepare the batch file 54
Close the solver 61
Start the batch computation 62
Results 66
Display the full geometry 69
Displaying isovalues (equiflux) lines at t = 1 s 71
Change the default isovalues display . . . . . . . . . . . . . . . . . . . . . . . 71
Change the time to 1 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Display the isovalues plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Contentsiv
Color shade of flux density on a group of regions 75
Change the geometry display. . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Change the time to 0.5 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Create a group of the three regions . . . . . . . . . . . . . . . . . . . . . . . . 77
Display a color shade plot on the group of regions . . . . . . . . . . . . . . . . . 78
Create a path through the airgap 81
Normal component of flux density along the air gap path 86
Superimpose the curves display 88
Spectrum analysis 91
Axis torque (full cycle) 95
Save your analyses 98
Close PostPro_2D 99
3 Back EMF computation 102
Create the back EMF external circuit model 102
Conventions 102
Back EMF circuit 104
Start ELECTRIFLUX 105
Open a new circuit problem 106
Using the icon in the toolbar. . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Using the menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
ELECTRIFLUX toolbar 109
ELECTRIFLUX menus 110
File menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Edit menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
View menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Circuit menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Sheet menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Contents v
Window menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
? (Help) menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Change the size of the sheet 113
Add coils for stator windings 117
Place the 4 coil components on the sheet . . . . . . . . . . . . . . . . . . . . 119
Rotate the 4 coils for proper orientation of the hot point. . . . . . . . . . . . . . 122
Add inductors 125
Place the 3 inductors on the sheet . . . . . . . . . . . . . . . . . . . . . . . . 126
Rotate the 3 inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Add the open circuit loads 130
Place the 3 resistors on the sheet . . . . . . . . . . . . . . . . . . . . . . . . 132
Rotate the 3 resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Add the voltmeter 135
Place the voltmeter (R4) on the sheet . . . . . . . . . . . . . . . . . . . . . . 136
Rotate the voltmeter (R4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Save your circuit file 139
Connect (wire) the circuit components 140
Define the resistors and inductors 146
Define the resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Define the inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Rename the coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Analyze the circuit 152
Save and close the circuit file 154
Close ELECTRIFLUX 155
Enter the physical properties 156
Start Preflu 9.1 156
Open the 1-layer airgap problem 157
Save your project with a new name 159
Contentsvi
Define as Transient Magnetic 161
Change to the Physics context 162
Physics context toolbars 163
Import materials from the materials database 163
Import the problem circuit 165
Assign materials and sources to the regions 169
Assign the stator windings 169
Edit the PA region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Define the coil resistance 174
Assign WEDGE, AIR, AIRGAP and SHAFT regions 176
Assign STATOR and ROTOR regions 177
Assign the MAGNET 179
Creating and Assigning Mechanical Sets 181
Creating Mechanical Sets 181
Create the MOVING_ROTOR Mechanical Set . . . . . . . . . . . . . . . . . . . 182
Create the FIXED_STATOR Mechanical Set . . . . . . . . . . . . . . . . . . . . 186
Create the ROTATING_AIRGAP Mechanical Set . . . . . . . . . . . . . . . . . . 187
Assigning Mechanical Sets 188
Boundary conditions (Periodicity) 193
Check the physical model 194
Solve the back EMF problem 196
Check the version: Flux2D Standard 196
Start the solver 197
Start the solver 198
Close the solver 202
Contents vii
Results from the Back EMF computation 203
Display the back EMF in R4 (the voltmeter) 205
Display a spectrum of the back EMF in R4 208
Voltage and current in coil B_MC (MC) 213
Save and close PostPro_2D 214
4 Square wave motor: Constant speed (torque ripples) 217
Create the 3-phase bridge circuit 218
Start ELECTRIFLUX 219
Create a new circuit problem 221
Using the icon in the toolbar. . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Using the menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Change the size of the sheet 223
Add the 6 switches 226
Place the 6 switches on the sheet . . . . . . . . . . . . . . . . . . . . . . . . 228
Rotate the 6 switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Add the 6 series voltages 236
Place the 6 series voltages on the sheet . . . . . . . . . . . . . . . . . . . . . 238
Rotate the series voltages. . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
Add the main voltage source 243
Place the main voltage source . . . . . . . . . . . . . . . . . . . . . . . . . . 244
Rotate the main voltage source . . . . . . . . . . . . . . . . . . . . . . . . . 245
Add the 3 coils 246
Place the 3 coil components on the sheet . . . . . . . . . . . . . . . . . . . . 248
Rotate the coil components . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
Add the inductors 252
Place the 3 inductors on the sheet . . . . . . . . . . . . . . . . . . . . . . . . 254
Rotate the 3 inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
Contentsviii
Add the voltmeter 257
Save your circuit 260
Connect (wire) the circuit components 262
Define the circuit 266
Define the on/off resistance values for the switches . . . . . . . . . . . . . . . . 266
Define the inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
Define the voltmeter (R1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
Rename the coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
Analyze the circuit 273
Save and close the circuit file 275
Close ELECTRIFLUX 276
Assign the physical properties 277
Start Preflu 9.1 277
Open the Back EMF problem 278
Save your project with a new name 281
Change the coupled circuit 283
Delete the existing circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
Change to the Physics Context . . . . . . . . . . . . . . . . . . . . . . . . . 284
Import the Squarewave Circuit . . . . . . . . . . . . . . . . . . . . . . . . . 284
Assign face regions to the circuit 287
Assign the stator windings . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
Edit the PA region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
Edit the MA region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
Edit the PB region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
Edit the MC region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
Define the coil resistance 291
Define the Voltage Sources 293
Define the Main Voltage Source . . . . . . . . . . . . . . . . . . . . . . . . . 293
Define the Series Voltage Sources . . . . . . . . . . . . . . . . . . . . . . . . 294
Contents ix
Define the switches 295
Check the physical model 297
Close and save the model 298
Solve with user version 299
Select the user version 299
Start the solver 301
Verify the solving options 303
Start the computation 305
Close the solver 307
Results: Constant speed computation 309
Display isovalues (equiflux) lines 312
Set the properties for the display . . . . . . . . . . . . . . . . . . . . . . . . 312
Display the isovalues plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
Color shade plot on a group of regions 318
Create the group of regions . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Set the properties for the display . . . . . . . . . . . . . . . . . . . . . . . . 319
Display the color shade plot . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
Create a path through the airgap 323
Flux density along the airgap path 328
Flux density: Normal component . . . . . . . . . . . . . . . . . . . . . . . . 328
Flux density: Tangential component . . . . . . . . . . . . . . . . . . . . . . . 329
Superimpose the normal and tangential flux density curves . . . . . . . . . . . . 330
Spectrum analysis 334
Time variation curve of axis torque 338
Waveforms of the electric quantities 342
Voltage and current in the main voltage source (V7) . . . . . . . . . . . . . . . 343
Current in Switch1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
Current in the B_COILA (PA) coil component . . . . . . . . . . . . . . . . . . . 348
Contentsx
Current in the B_COILB (PB) coil component . . . . . . . . . . . . . . . . . . . 350
Current in the B_COILC (MC) coil component . . . . . . . . . . . . . . . . . . . 352
Save and close PostPro_2D 354
5 No load startup with electromechanical coupling 359
Modify the physical properties 359
Start Preflu 9.1 360
Open the Constant Speed problem 361
Save your project with a new name 363
Define the no load characteristics 365
Edit the MOVING_ROTOR mechanical set . . . . . . . . . . . . . . . . . . . . . 365
Close and save the model 369
Verify the user version: brushlike_921 370
Solve the no load startup problem 372
Choosing a time step 372
Start the solver 372
Results from no load startup 380
Display the isovalues (equiflux) lines at time step 100 (t = 0.05 s) 382
Select the 100th time step (0.05 s) . . . . . . . . . . . . . . . . . . . . . . . 383
Set the display properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
Display the isovalues plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
Time variation analysis (2D Curves) 390
Axis torque curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
Angular velocity curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
Rotor position curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396
Waveforms of electric quantities 399
Voltage and current in the main voltage source . . . . . . . . . . . . . . . . . . 400
Contents xi
Current in Switch1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
Current in the B1 (PA) coil component . . . . . . . . . . . . . . . . . . . . . . 405
Voltage and current in the B2 (PB) coil component . . . . . . . . . . . . . . . . 407
Voltage and current in B3 (MC) coil component . . . . . . . . . . . . . . . . . . 409
Save and close PostPro_2D 412
6 Servo action with electromechanical coupling 415
Modification of physical properties 415
Start Preflu 9.1 416
Open the No Load problem 417
Save your project with a new name 419
Define the servo model characteristics 421
Edit the MOVING_ROTOR mechanical set . . . . . . . . . . . . . . . . . . . . . 421
Close and save the model 425
Transient startup of servo problem 426
Solve the servo simulation with user version 428
Start the solver 429
Results from servo motor 435
Display the isovalues (equiflux) lines 438
Select the last time step (0.115 s) . . . . . . . . . . . . . . . . . . . . . . . . 438
Set properties for the isovalues display . . . . . . . . . . . . . . . . . . . . . 440
Display the isovalues plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
Color shade plot for stator, rotor, and magnet 444
Create a group of regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444
Set the display properties for the color shade plot . . . . . . . . . . . . . . . . 446
Display the color shade plot . . . . . . . . . . . . . . . . . . . . . . . . . . . 448
Time variation results (2D curves) 449
Axis torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
Contentsxii
Angular velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
Rotor position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452
Voltage and current in the main voltage source (V7) . . . . . . . . . . . . . . . 454
Current in Switch 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
Current in B1 (PA) coil component . . . . . . . . . . . . . . . . . . . . . . . . 459
Voltage and current in B3 (MC) coil component . . . . . . . . . . . . . . . . . . 461
Close PostPro_2D 464
Close Flux2D 465
Contents xiii
About this document
This tutorial, Brushless DC Motor: Calculations, is the second in the series featuring the model ofthe brushless DC permanent magnet motor. The calculations presented in this document arebased on the models (geometry and mesh) created with Preflu, as explained in Brushless DCMotor: Constructing the Model. You should already have completed and have saved two geometryand mesh files for this model in your working directory.
For the first computation, the cogging torque (see Chapter 2), use the model with the 3-layerairgap (BRUSHLESS_3LAYER).
For all the other computations, use the model with the 1-layer airgap (BRUSHLESS_1LAYER).
What this document contains
This tutorial shows you how to enter the required materials into the materials database(CSLMAT) and then how to conduct a series of simulations with the brushless permanentmagnet motor.
In both Chapters 3 and 4, you create external circuits with the new ELECTRIFLUX module.
Chapter 1 Enter the materials into the materials database (CSLMAT)
Chapter 2 Cogging torque computation (with batch file solution)
Chapter 3 Back EMF computation, with a 3-phase Wye external circuit
Chapter 4 Square wave motor: Constant speed (Torque ripples), with a square waveexternal circuit
Chapter 5 No load startup with electromechanical coupling, with the square waveexternal circuit from Chapter 4
Chapter 6 Servo action with electromechanical coupling, with the square wave external circuit from Chapter 4
xv
Introduction
Chapters to complete for the different simulations
If you wish to do only some of the simulations described in this tutorial, the list below showswhich chapters to complete for each of the simulations.
Cogging torque computation Chapters 1 and 2
Back EMF computation Chapters 1 and 3
Constant speed computation Chapters 1 and 4
No load startup computation Chapters 1, 4 and 5
Servo action computation Chapters 1, 4, 5 and 6
The simulations in Chapters 4, 5 and 6 use the same external circuit, a square wave circuit shownon page 218. For Chapter 5, you modify the physical properties of the problem from Chapter 4to create and solve a new problem. For Chapter 6, you modify the physical properties for theproblem from Chapter 5 to create and solve a new problem.
For experienced users
If you are familiar with Flux2D, you may want to take advantage of the chapter summaries at thebeginning of each chapter. These sections list the physical properties and the solver andpostprocessor settings for each problem.
xvi
Enter the materialsIn this chapter you start Flux2D and use the Materials database module to create thematerials to be assigned to various parts of the model of the motor. These materials areadded to the materials database and can then be used for other problems also.
Start Flux2D
Open the Materials database (CSLMAT)
Add the magnetic materialiso MU
scalar constant relative permeability of 1.071
magnet scalar constant remanent flux density of 0.401
Add the nonlinear steel materialiso MUscalar a sat
Js = 1.99Initial relative slope a = 7500
Close CSLMAT
1
Chapter 1
2
Enter the materials
For the brushless DC motor, you create two materials: (1) a magnetic material for the magnetand (2) a nonlinear steel material for the rotor and stator laminations.
Start Flux2D
Start Flux2D from your Windows taskbar.
3
Chapter 1
Starting Flux2D
Choose Start, Programs, Cedrat (or your installation directory), Flux 9.1.
Program Input
StartProgramsCedratFlux 9.1
The Flux Supervisor opens:
Chapter Enter the materials
Start Flux2D4
1
Flux Supervisor
Open the materials database
To open the Materials database, in the Construction folder, double click Materials database.
Program Input
Double click Materials database
Enter the materials Chapter
Open the materials database 5
1
Opening the materials database (CSLMAT)
Add the magnetic material
Flux2D includes a linear model of magnets (constant permeability mr and constant remanent flux density Br).
Proceed as follows:
Program Input
Selected command 1 Add
Selected command 1 Material
Name of the material : magnetpm
Comment magnetic material for brushless dc motor
Chapter Enter the materials
Add the magnetic material6
1
CSLMAT menu
Your screen should resemble the following figure:
Next, enter two properties for the magnetic material:
1. the relative permeability (1.071) and
2. the remanent flux density (0.401).
Proceed as follows:
Program Input
To register, define at leastone propertyPlease select the property 1 iso MUSelect a model 1 scalar cstValue =
Enter the materials Chapter
Add the magnetic material 7
1
Creating the magnet material (name and comment)
The field (a blue rectangle) where you enter the relative permeability is shown below:
On some screens, stars (******) may be shown instead of the solid blue field. In this case, clickon the stars and then enter the relative permeability of the magnet (1.071).
Proceed as follows:
Program Input
Value = 1.071Select the line whose value isto be changed
1 Validate
Please select the property 5 MagnetSelect a model 1 scalar cstValue = 0.401Select the line whose value isto be changed
1 Validate
Please select the property Quit
Chapter Enter the materials
Add the magnetic material8
1
Entering the relative permeability of the magnetic material
Add the nonlinear steel material
Next, add the nonlinear steel material. Proceed as follows:
Program Input
1 MaterialName of the material nlsteelpmComment nonlinear steel for laminations
in brushless pm motorTo register, define at leastone propertyPlease select the property 1 iso MUSelect a model B scalar a sat
The scalar a sat model features an arc tangent formula to model the B-H curve. Enter thesaturation magnetization value (Js) and the initial relative slope (a) of the relative permeability.
Program Input
Saturation magnetization Js = Tesla
1.99
Initial relative slope a =
7500
Select the line whose value isto be changed
1 Validate
Enter the materials Chapter
Add the nonlinear steel material 9
1
Entering the saturation magnetization (Js) and initial relative slope (a) for the nonlinear steel
When you choose Validate, a plot of the model is displayed:
If you wish, you can modify the maximum value along the X axis with the Mod abscissa maxcommand or read the values at specific points along the curve with the Pick command.
Chapter Enter the materials
Add the nonlinear steel material10
1
B-H plot of the nonlinear steel
For example, the following figure shows the values at a point near the "knee" of the curve.
Close the materials database
When you are ready, close the display and the materials database as follows:
Program Input
QuitQuit
Please select the property QuitSelected command QuitSelected command STOP
The Flux Supervisor is displayed.
You are now ready to begin creating the problem files to run the simulations.
Enter the materials Chapter
Close the materials database 11
1
Reading values on the B-H curve with "Pick" command
Cogging torque computationThis chapter explains how to compute the cogging torque for the brushless DC motor.
Assign physical propertiesPlane geometry, 50.308 depth, transient magnetic calculationMaterials and sources
All stator windings: vacuum, no sourceAirgap: rotating airgap, constant angular velocity of 0.16666666 rpm, 2 pole pairsWedge, air, shaft: vacuum, no sourceStator, rotor: nonlinear steel, no sourceMagnet: magnet material, constant direction 45 degrees, no source
Boundary conditions: Automatically assigned using periodicity
Solve with a batch fileCreate a batch file with the following data:
Time step 0.5 sStudy time limit 100 sLimit number of time steps 61Maximum value time step 0.5 sMinimum value time step 0.5 sStore automatically 1 on 1Initial position of the rotor: 0
Solve, Batch
13
Chapter 2
Analyze results with PostPro_2DIsovalues (equiflux) linesColor shade plot over rotor, magnet and stator onlyAnalysis of quantities along a path through the airgap
Normal component of the flux densitySpectrum analysis of normal component of flux density
Axis torque over full cycle of the motor
Save and close PostPro_2D
14
Cogging torque computation
The cogging torque in this brushless DC motor originates from variations in the reluctance ofthe magnetic circuit due to slotting as the rotor rotates. The cogging torque becomes detectablewhen the shaft is rotated slowly.
In other finite element packages, the cogging torque computation is generally performed as amulti-static computation with different rotor positions. The multi-static approach to the cogging torque computation requires a tremendous amount of effort in preparationa finite elementmesh and problem for each positionas well as long computation times and tediouspostprocessing.
With its rotating airgap feature, Flux easily computes the cogging torque. Only one finiteelement mesh is needed; only one problem is solved. Computation and postprocessing time isgreatly reduced compared to the multi-static method because in Flux, the rotor is rotatedautomatically. There is no need to modify the geometry, mesh or physical properties, and atorque value is stored for each position during the solving.
Special considerations for simulation
In general, cogging torque values are small. When one uses finite element methods to computethe cogging torque, special consideration is needed to limit the influence of finite elementnumerical errors due to the mesh.
With Flux2Ds moving airgap, you must make sure that the subdivisions on the boundaries ofthe moving airgap from the current time step overlap the subdivisions of the next time step inorder to keep the mesh topology constant in the airgap. Flux computes the torque with thevirtual work method, based on the energy in the moving airgap. Thus, by keeping the meshtopology the same at each position, the influence of finite element residual errors on the smalltorque values is minimized.
F Be sure to use the model with the 3-layer airgap for this problem.
Please do not confuse this special 3-layer geometric division of the airgap with the number oflayers required by the Maxwell Stress Method to accurately compute the torque.
15
Chapter 2
The reason for the three-layer structure, with the moving airgap placed between two outer layersof air, is to evenly subdivide the boundary of the moving airgap. In this example, for one pole ofthe motor, there are 180 subdivisions on the lower and upper boundaries of the airgap (0.5degrees/subdivision). Because the rotor moves by a multiple of 0.5 degrees, the mesh topologyremains the same. The nodes from the current time step are overlapped by the nodes of the nexttime step as the rotor rotates.
A constant speed of 1/6 or 0.16666666 rpm is specified for the rotation of the rotor, because 1second corresponds to 1 mechanical degree.
Before you proceed, be sure you have completed Chapter 1 and have added the two materials tothe Materials Database (CSLMAT).
Chapter Cogging torque computation
Special considerations for simulation16
2
The airgap subdivided into 3 layers
Enter the physical properties
To enter the physical properties, use the Preflu 9.1 application, the same application used tocreate the geometry and mesh (in previous versions of Flux, a separate application, the PhysicalProperties module, Prophy, was used).
Start Preflu 9.1
In the Flux Supervisor, in the Construction folder, double click Geometry & Physics:
Program Input
Double click Geometry & Physics
Cogging torque computation Chapter
Enter the physical properties 17
2
Starting Preflu 9.1 to enter the physical properties
The Preflu 9.1 application opens.
Open the 3-layer airgap problem
You can open an existing project either with the toolbar icon or the menu.
Using the icon in the toolbar
To open a new Flux project, click the icon on the toolbar
Program Input
click
Chapter Cogging torque computation
Enter the physical properties18
2
Preflu 9.1 screen
Using the menu
If you prefer, choose Project, Open project from the menu:
Program Input
Project
Open project
The Open project dialog opens.
Enter or verify the following:
Program Input
Look in
File Name
Brushless_V9 [your workingdirectorybrushless_3layer.flu [yourname]Open
Cogging torque computation Chapter
Enter the physical properties 19
2
The 3-layer geometry is shown in the following figure:
Save your project with a new name
Save your project now with a specific name to indicate that you will be using this model forcogging torque calculations.
Chapter Cogging torque computation
Save your project with a new name20
2
The geometry (with 3-layer airgap) displayed in Preflu
To save your project with a new name, choose Project, Save As from the menu:
Program Input
Project
Save As
The Save flux project dialog opens.
Enter or verify the following:
Program Input
Save In: Brushless_v9 [working directory]File Name: cogging [your name]
Save
Cogging torque computation Chapter
Save your project with a new name 21
2
Saving the brushless 3-layer model as cogging
Define as Transient Magnetic
Define cogging as a transient magnetic problem using the Application menu:
Program Input
ApplicationDefineMagnetic
Transient Magnetic 2D
The Define Transient Magnetic 2D application dialog opens.
Enter or verify the following:
Program Input
2D domain type 2D planeLength Unit MILLIMETERDepth of the domain 50.308
OK
Chapter Cogging torque computation
Define as Transient Magnetic22
2
Your screen should look like the following. Notice that there is a new context symbol,representing the Physical model context.
Change to the Physics context
The Physics commands are available only in the Physics context. The following figure shows thePhysics context selected.
At the top of the data Tree, click the button to change to the Physics context.
Program Input
click
Cogging torque computation Chapter
Change to the Physics context 23
2
The cogging problem after defining the physical model
The Physics context is shown in the following figure.
Physics context toolbars
The Physics context includes some of the same icons and commands as the Geometry and Meshcontexts. Most of the Display and Select icons are the same.
The following figures show the Physics toolbar icons:
Chapter Cogging torque computation
Change to the Physics context24
2
The cogging problem after going to the Physics context
Physics toolbar icons: Add, Check
Physics toolbar icons: Display, Select
The following figures identify the Physics toolbar icons:
Import materials from the materials database
Before we can assign materials we created in Chapter 1 to the different regions of our model, wemust import them. Use the menu, Physics, Material, Import material.
Program Input
Physics
Material
Import material
Cogging torque computation Chapter
Import materials from the materials database 25
2
The import material dialog appears.
Click on the icon next to the material database name to display the list of materials in thedatabase.
Now scroll to find the two materials you want to import; MAGNETPM and NLSTEELPM.Select both with the mouse using the Control key.
Proceed as follows:
Program Input
Click MAGNETPMClick NLSTEELPM + Ctrl
Import
Chapter Cogging torque computation
Import materials from the materials database26
2
List of materials in the database displayed
Initial material import dialog
After the import is complete, close the Import materials window.
Program Input
Close
If you expand the Materials in the data tree, you will see the two materials now included in theproject.
Assign materials and sources to the regions
Material and/or source assignment is done region by region. You can select the regions from thescreen, or choose the region names from the data tree on the left. You can use the Edit Arraycommand to assign the same properties to several regions at the same time.
Assign the windings of the stator slots
Begin by assigning the winding areas of the stator slots to a "vacuum" state. We will select thestator slots from the data tree on the left. First expand the Face Region tree by clicking the
icon next to Physics, Regions, and Face region.
Cogging torque computation Chapter
Assign materials and sources to the regions 27
2
Materials imported into project
Proceed as follows:
Program Input
Click
Click
Click
Chapter Cogging torque computation
Assign materials and sources to the regions28
2
Next select the stator slots from the tree by selecting their names. Make sure you hold theControl key when making multiple selections.
Program Input
Click MA
Click MC + CtrlClick PA + CtrlClick PB + Ctrl
Now click the right mouse button and select Edit Array.
Program Input
Right click, Edit array
Cogging torque computation Chapter
Assign materials and sources to the regions 29
2
The Edit Face Region window appears, and the stator slots are highlighted on the graphic.
Under the Modify All column, we will set all the stator slots at once to a vacuum region. Firstselect "Air or vacuum" in the Modify All column.
Chapter Cogging torque computation
Assign materials and sources to the regions30
2
Select Air or Vacuum in the Modify All Column
Editing all stator slots using Edit Array function
Next, accept your input.
Proceed as follows:
Program Input
Sub types: Select "Air or vacuum"OK
Assign WEDGE, AIR, STATOR_AIR, AIRGAP and SHAFT regions
Next, assign properties to the WEDGE, AIR, STATOR_AIR, AIRGAP and SHAFT regions asa group:
Cogging torque computation Chapter
Assign materials and sources to the regions 31
2
Setting a vacuum property for the stator slots
Select the air regions from the tree by selecting their names. Make sure you hold the Control key when making multiple selections.
Program Input
Click AIRClick AIRGAP + CtrlClick SHAFT + CtrlClick STATOR_AIR + CtrlClick WEDGE + Ctrl
Right click, Edit array
Under the Modify All column, we will set all these regions at once to a vacuum region.
Proceed as follows:
Program Input
Sub types: Select "Air or vacuum"OK
Chapter Cogging torque computation
Assign materials and sources to the regions32
2
Setting a vacuum property for the air regions
Notice that the Console window displays a message confirming the assignment of the vacuumregion.
Assign STATOR and ROTOR regions
Assign the NLSTEELPM material to the STATOR and ROTOR regions.
Select the stator and rotor regions (shown below in orange) from the graphic. Make sure youhold the Control key when making the second selection.
Cogging torque computation Chapter
Assign materials and sources to the regions 33
2
Selecting the Stator and Rotor regions graphically
Console confirms region faces modified
Once the regions are selected, right click the mouse and select Edit Array.
Under the Modify All column, we will set both of these regions to the NLSTEELPM material.
Proceed as follows:
Program Input
Sub types: Select "Magnetic reg"Material Select "NLSTEELPM"
OK
Chapter Cogging torque computation
Assign materials and sources to the regions34
2
Setting the stator and rotor to NLSTEELPM
Edit the stator and rotor areas as a group
Assign the MAGNET
Finally, assign the MAGNETPM material to the MAGNET region.
Select the magnet region graphically with the mouse, then right click the mouse and select Edit.
The Edit Face Region window appears.
Cogging torque computation Chapter
Assign materials and sources to the regions 35
2
Selecting the magnet region, then selecting Edit
Setting the magnet region to the MAGNETPM material
Proceed as follows:
Program Input
Type of region Magnetic regionMaterial of the region MAGNETPM
OK
Now you must set the direction of the magnet. Select the icon from the toolbar to orient the magnet.
Program Input
Click
If you prefer, choose Physics, Material, Orient material for face region from the menu.
Program Input
Physics
Material
Orient material for face region
Chapter Cogging torque computation
Assign materials and sources to the regions36
2
The following figure shows the Orient Material window.
Proceed as follows:
Program Input
Magnet...Angle 45OK
You have now assigned a material property to each region of the geometry.
Your screen should resemble the following figure.
Cogging torque computation Chapter
Assign materials and sources to the regions 37
2
The physical properties are assigned
Setting the magnet to 45 degree orientation
Creating and Assigning Mechanical Sets
Creating Mechanical Sets
New with Flux 9.1 is the existence of Mechanical Sets. Mechanical Sets are used whenever youwant motion in the model (either rotating or translating). Whenever there is motion in themodel, you must define 3 mechanical sets;
Fixed - This defines the parts of the model that do not move
Moving- This defines the parts of the model that move (either rotating or translating)
Compressible- This defines the region between the moving and non-moving parts (and thedisplacement regions, in the case of a translating motion)
We will first create these mechanical sets. Select Physics, Mechanical Set and New from themenu.
Program Input
Physics
Mechanical setNew
Chapter Cogging torque computation
Creating and Assigning Mechanical Sets38
2
Create the MOVING_ROTOR Mechanical Set
The New Mechanical set dialog appears. Enter the information to create theMOVING_ROTOR mechanical set.
Proceed as follows to define the Axis information. Then go to the Kinematics tab.
Program Input
Mechanical set name moving_rotorComment the moving parts of the modelType of mechanical set Rotation around one axisRotation Axis Rotation around one axis
parallel to OzCoordinate system MAINPivot point First coordinate 0
Cogging torque computation Chapter
Creating and Assigning Mechanical Sets 39
2
Defining the Axis information for the MOVING_ROTOR
Mechanical Set
Second coordinate 0Click on "Kinematics" tab
The Kinematics tab opens. Enter the information to define the General kinematics, then click onthe Internal characteristics tab.
Proceed as follows to define the General kinematics information (rpm entered equals 1 degree ofrotation per second):
Program Input
Type of kinematics Imposed SpeedVelocity (rpm) 1/6Position at time t=0s. (deg) 0
Click "Internalcharacteristics" tab
Chapter Cogging torque computation
Creating and Assigning Mechanical Sets40
2
Defining the General kinematics information for the
MOVING_ROTOR Mechanical Set
The Internal characteristics tab opens. Enter the information to define the Internal kinematicsinformation, then click on the External characteristics tab.
Proceed as follows to define the Internal characteristics information:
Program Input
Type of load Inertia, friction coefficientsand spring
Moment of inertia 0Constant friction coefficient 0Viscous friction coefficient 0Friction coefficientproportional to the squarespeed
0
Cogging torque computation Chapter
Creating and Assigning Mechanical Sets 41
2
Defining the Internal kinematics information for the MOVING_ROTOR
Mechanical Set
Click "Externalcharacteristics" tab
The External characteristics tab opens. Enter the information to define the External kinematicsinformation, then click on OK button.
Proceed as follows to define the External characteristics information. Click OK at the end tocomplete the definition of the mechanical set:
Program Input
Type of load Inertia, friction coefficientsand spring
Moment of inertia 0Constant friction coefficient 0Viscous friction coefficient 0
Chapter Cogging torque computation
Creating and Assigning Mechanical Sets42
2
Defining the External kinematics information for the
MOVING_ROTOR Mechanical Set
Friction coefficientproportional to the squarespeed
0
OK
Create the FIXED_STATOR Mechanical Set
The New Mechanical set dialog closes briefly and then reappears. Enter the information to create the FIXED_STATOR mechanical set.
Proceed as follows:
Program Input
Mechanical set name fixed_statorComment the non-moving parts of the
modelType of mechanical set Fixed
OK
Cogging torque computation Chapter
Creating and Assigning Mechanical Sets 43
2
Defining the information for the FIXED_STATOR
Mechanical Set
Create the ROTATING_AIRGAP Mechanical Set
The New Mechanical set dialog closes briefly and then reappears. Enter the information to create the ROTATING_AIRGAP mechanical set.
Proceed as follows:
Program Input
Mechanical set name rotating_airgapComment the rotating airgapType of mechanical set CompressibleUsed method to take the motioninto account
Remeshing of the air partsurrounding the moving bodyOK
Chapter Cogging torque computation
Creating and Assigning Mechanical Sets44
2
Defining the information for the ROTATING_AIRGAP
Mechanical Set
The New Mechanical set dialog closes briefly and then reappears. Close the dialog by hitting theCancel button.
Proceed as follows:
Program Input
Cancel
Assigning Mechanical Sets
Now assign the mechanical sets to the regions of your model. First assign the appropriate regions to the MOVING_ROTOR mechanical set.
Cogging torque computation Chapter
Creating and Assigning Mechanical Sets 45
2
Close the Mechanical set dialog
Select the AIR, MAGNET, ROTOR and SHAFT regions from the tree by selecting their names. Make sure you hold the Control key when making multiple selections.
Program Input
Click AIRClick MAGNET + CtrlClick ROTOR + CtrlClick SHAFT + Ctrl
Right click, Edit array
Under the Modify All column, we will set all these regions at once to the MOVING_ROTORmechanical set.
Proceed as follows:
Program Input
MECHANICAL_SET Select "MOVING_ROTOR"OK
Chapter Cogging torque computation
Creating and Assigning Mechanical Sets46
2
Assigning regions to the MOVING_ROTOR mechanical set
Now assign regions to the FIXED_STATOR mechanical set. Select the MA, MC, PA, PB,STATOR, STATOR_AIR and WEDGE regions from the tree by selecting their names. Makesure you hold the Control key when making multiple selections.
Program Input
Click MAClick MC + CtrlClick PA + CtrlClick PB + CtrlClick STATOR + CtrlClick STATOR_AIR + CtrlClick WEDGE + Ctrl
Right click, Edit array
Under the Modify All column, we will set all these regions at once to the FIXED_STATORmechanical set.
Proceed as follows:
Program Input
MECHANICAL_SET Select "FIXED_STATOR"OK
Cogging torque computation Chapter
Creating and Assigning Mechanical Sets 47
2
Assigning regions to the FIXED_STATOR mechanical set
Now assign the airgap region to the ROTATING_AIRGAP mechanical set. Select the AIRGAP region from the tree by selecting its name.
Program Input
Click AIRGAP
Right click, Edit
The Edit Face region dialog appears. Click on the Mechanical Set tab to assign the mechanical set to the AIRGAP region.
Chapter Cogging torque computation
Creating and Assigning Mechanical Sets48
2
Click on the Mechanical Set tab
Now select the ROTATING_AIRGAP mechanical set from the pull down menu.
Proceed as follows:
Program Input
Select "ROTATING_AIRGAP"OK
Boundary conditions (Periodicity)
In previous versions of Flux, you needed to specify boundary conditions. With Flux 9.1,boundary conditions are automatically created based on symmetry and periodicity.
Cogging torque computation Chapter
Boundary conditions (Periodicity) 49
2
Setting the AIRGAP region to the ROTATING_AIRGAP
mechanical set
Since we have modeled one quarter, or 90 degrees, of the model, we need to define a periodicityreflecting this. Select the icon from the toolbar to create a new periodicity.
Program Input
Click
If you prefer, you can select Geometry, Periodicity, New from the menu.
Program Input
GeometryPeriodicityNew
Chapter Cogging torque computation
Boundary conditions (Periodicity)50
2
The New Periodicity dialog opens.
Proceed as follows:
Program Input
Geometrical type of theperiodicity
Rotation about Z axis withangle of the domain
Included angle of the domain 90Offset angle with respect tothe X line
0
Physical aspects of periodicity Odd (anticyclic boundaryconditions)OK
Check the physical model
Now that all physical attributes have been assigned to our model, we should have Flux check itbefore proceeding to solving.
Cogging torque computation Chapter
Boundary conditions (Periodicity) 51
2
Defining a periodicity for the brushless DC motor
Select the icon from the toolbar to start the Physical Check.
Program Input
Click
If you prefer, you can select Physics, Check physics from the menu.
Program Input
Physics
Check physics
The console indicates that the physical check is completed.
Close Preflu
The model is ready for solving. Close the Preflu application.
Chapter Cogging torque computation
Boundary conditions (Periodicity)52
2
Click on the icon in the toolbar to exit Preflu.
Program Input
Click
If you prefer, select Project, Exit from the menu.
Program Input
Project
Exit
When prompted, select to save your problem.
Proceed as follows:
Program Input
Save current project before Yes
The Flux Supervisor is displayed.
Cogging torque computation Chapter
Boundary conditions (Periodicity) 53
2
Solve (batch mode)
For the cogging torque computation, Flux2D generates the torque waveform of 2 slot pitches.For the 24-slot motor, 2 slot pitches corresponds to 30 mechanical degrees. The rotor rotates by0.5 degrees for each time step. This results in a total of 60 time steps or positions for the coggingtorque computation. With the rotor speed at 1/6 rpm, 1 second corresponds to 1 mechanicaldegree; thus the time step is 0.5 seconds.
Flux2D can solve directly (interactively) or in batch mode. For this problem, use batch mode toreduce the solution time.
Prepare the batch file
To open the Solver, in the Flux Supervisor, in the Solving process folder, double click Direct.
Chapter Cogging torque computation
Solve (batch mode)54
2
Starting the solver
Program Input
Double click Direct
In the Open dialog, select the problem to be solved and click Open
Program Input
Look in Brushless_V9[working directory]File name COGGING.TRA
Open
Cogging torque computation Chapter
Solve (batch mode) 55
2
Choosing the problem to solve
The solver opens as shown below.
Click the Prepare Batch button to prepare the file for batch mode.
Program Input
click
Chapter Cogging torque computation
Solve (batch mode)56
2
Solver: Main data
Your screen should resemble the following figure.
In the Definition of time data dialog, enter or verify the information to prepare the batch fileas follows:
Program Input
Restarting mode New computationTime valuesInitial value of the time step
0.5
Study time limit 100Limit number of time steps 61Maximum value of the timestep
0.5
Minimum value of the time step
0.5
Storage of time steps
Cogging torque computation Chapter
Solve (batch mode) 57
2
Ready to enter data for batch file
Program Input
one step on 1Ok
Your time data should be filled in as shown in the following figure:
Chapter Cogging torque computation
Solve (batch mode)58
2
Time data for the batch computation
After you click OK, the Rotating air gap dialog opens. Make sure that the initial position of the rotor is 0 degrees. Then click OK.
Program Input
Initial position of the rotor0. degrees
OK
Cogging torque computation Chapter
Solve (batch mode) 59
2
Verifying the initial position of the rotor (0 degrees)
Your screen should resemble the following figure. At the bottom of the screen, this message isdisplayed: COGGING: Preparation of the batch computation finished.
Flux2D has created a file called COGGING.DIF that will be used to start the batch solution.
Chapter Cogging torque computation
Solve (batch mode)60
2
Batch file completed
Close the solver
Choose File, Exit to close the solver.
Program Input
File
Exit
Cogging torque computation Chapter
Solve (batch mode) 61
2
Start the batch computation
In the Flux Supervisor, in the Solving process folder, double click Batch:
Program Input
Double click Batch
Chapter Cogging torque computation
Solve (batch mode)62
2
Starting the Solver for a batch computation
In the Batch window, problems with batch files prepared are indicated by Yes in the "Ready"column, as shown in figure below.
Select the problem you wish to solve, e.g., COGGING.TRA, and click the Start button tobegin the batch computation:
Program Input
Files ReadyCOGGING.TRA Yes COGGING.TRA
Start
Cogging torque computation Chapter
Solve (batch mode) 63
2
Starting the batch computation
The Solver window opens:
Chapter Cogging torque computation
Solve (batch mode)64
2
Batch computation in progress
When the problem has finished solving, the Batch window is displayed again. Choose Quit toclose the Solver.
Program Input
BatchCOGGING.TRA Quit
The Flux Supervisor should still be open.
Cogging torque computation Chapter
Solve (batch mode) 65
2
Closing the solver after batch computation
Results
To see your results, in the Flux2D Supervisor, in the Analysis folder, double click Results:
Program Input
Double click Results
Chapter Cogging torque computation
Results66
2
Starting Results analysis from the Supervisor
From the Open dialog, choose the problem you want to analyze and click Open:
Program Input
Look in Brushless_V9[working directory]File name COGGING.TRA
Open
Cogging torque computation Chapter
Results 67
2
Opening the cogging torque problem for results analysis
PostPro_2D opens with a display of the model geometry at the first time step, 0.5 s.
Chapter Cogging torque computation
Results68
2
Model open in PostPro_2D
Display the full geometry
You can display various quantities as plots on the model geometry. If you wish, instead of themodel ( of the motor, in this case), you can display the full geometry.
To see the full geometry, in the toolbar, click the Full Geometry icon or choose Geometry,Full Geometry from the menu:
Program Input
Geometry
Full geometry
Cogging torque computation Chapter
Results 69
2
Your screen should resemble the following.
Chapter Cogging torque computation
Results70
2
Model with full geometry displayed
Displaying isovalues (equiflux) lines at t = 1 s
It is often useful to begin analysis with a display of the isovalues (equiflux) lines.
Change the default isovalues display
By default, PostPro_2D displays 11 equiflux (isovalues) lines. To display 21 isovalue lines overthe geometry, click the Results properties button or choose Results, Properties from themenu.
Program Input
Results
Properties
Cogging torque computation Chapter
Results 71
2
The Display properties dialog opens.
Make sure the Isovalues tab is on top (this is the default).
Then enter or verify the information in the dialog as follows:
Program Input
IsovaluesAnalyzed quantity Equi fluxSupport Graphic selectionComputing parametersQuality NormalNumber 21
Chapter Cogging torque computation
Results72
2
Results properties dialog for isovalues display
Program Input
Scaling UniformOK
When you click OK, the properties dialog closes.
Change the time to 1 s
PostPro_2D opens with the model at the first time step, 0.5 s, and the rotor at 0 degrees. Look at the isovalues with the rotor position at 1 degree, or time 1 s.
To do so, open the Parameters manager dialog by clicking the icon or by choosingParameters, Manager from the menu.
Program Input
ParametersManager
The Parameters dialog opens, as shown in the following figure.
Cogging torque computation Chapter
Results 73
2
Parameters dialog
Choose 1 from the Values list and then close the Parameters dialog.
Program Input
ParametersValues 1
click
Display the isovalues plot
To display the isovalues lines, click the Isovalues button in the toolbar or choose Results,Isovalues from the menu.
Program Input
ResultsIsovalues
Chapter Cogging torque computation
Results74
2
The isovalues (equi flux) lines are displayed:
Color shade of flux density on a group of regions
Next, look at a color shade plot of the flux density over the stator, rotor, and magnet regions ofthe model only (not the full geometry) and at the initial time and position (0.5 s).
Change the geometry display
Click the Full Geometry button to deselect it.
Program Input
click
Cogging torque computation Chapter
Results 75
2
Display of the flux density lines on the full geometry at 1 s.
Change the time to 0.5 s
Now change the time back to the initial value, 0.5 s. Open the Parameters manager with thebutton, or choose Parameters, Manager from the menu.
Program Input
ParametersManager
In the Parameters dialog, choose 0.5 again and close the dialog.
Program Input
ParametersValues 0.5
click
Chapter Cogging torque computation
Results76
2
Choosing 0.5 s (initial time step)
Create a group of the three regions
To place the three regions in a group, click the icon or select Supports, Group manager from the menu.
Program Input
Supports
Group manager
The Group manager dialog opens.
In the Group manager, enter or verify the following:
Program Input
Filter RegionObjects available STATOR
MAGNETROTORAdd -->
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Results 77
2
Group manager dialog
Program Input
Current group STATORMAGNETROTOR
Group name Big3 [or your name]Create
When you click the Create button, the dialog closes and the group is added to the supports list in the problem's data tree.
Display a color shade plot on the group of regions
Now use the group for the display of the color shade plot.
Open the Results, Properties dialog by clicking the button or by choosing Results,Properties from the menu.
Program Input
Results
Properties
Chapter Cogging torque computation
Results78
2
The Display properties dialog opens.
Click the Color Shade tab to bring it to the front. In the Color shade dialog, enter or verify thefollowing:
Program Input
click Color Shade tabAnalyzed quantity |Flux density|Support Big3 [or your regions group]Computing parametersQuality NormalScaling Uniform
OK
The Display properties dialog closes.
Cogging torque computation Chapter
Results 79
2
Properties for color shade plot on regions group
To display the plot, click the color shade button in the toolbar.
Program Input
click
The plot on the group of regions is shown below:
Chapter Cogging torque computation
Results80
2
Color shade plot of flux density on a group of regions
Create a path through the airgap
Next examine the variation of several quantities along a path through the center of the airgap.The following figure shows the path:
To create this path through the airgap, open the Path manager.
Click the Path manager button or choose Supports, Path manager from the menu:
Program Input
SupportsPath manager
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Results 81
2
Location of path through airgap
The Path Manager dialog opens:
You will be creating an arc path of 180 degrees through the center of the airgap. To verify thecoordinates for the path, with the Path manager open, move your cursor over the geometrymodel.
The cursor looks like a cross with a trailing line or, when Arc is selected (as shown in theprevious figure), the cursor resembles a cross with a drawing compass .
Use the Zoom region button to enlarge the area around the bottom of the stator and theairgap and move the cursor into the center of the airgap. The X and Y coordinates are shown atthe bottom of the PostPro_2D window.
Chapter Cogging torque computation
Results82
2
Path manager
The following figure shows the Path manager, an enlargement of the airgap, and the coordinates(here, for example, X= 25.4, so we used 25.4 for the X value):
In the Path Manager dialog, enter or verify the following:
Program Input
PathName CenterGap [or your choice]Discretization 200[default color] [new color, if desired]
Graphic section ArcNumerical section New section
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2
Locating the coordinates for the center of the airgap path
When you click the New section button, the Section Editing dialog opens:
In the Section Editing dialog, enter or verify the following:
Program Input
Section type Arc start angleCenter pointXY
00
Origin pointXY
25.40
Length 180OK
Chapter Cogging torque computation
Results84
2
Section editing window to create paths
The Section editing dialog closes and the path is displayed on the geometry, as shown (enlarged)in the following figure.
In the Path manager dialog, click the button to create the path and open the 2D Curvesmanager at the same time.
Program Input
click
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Results 85
2
Path through airgap
Normal component of flux density along the air gap path
The 2D Curves manager is shown in the following figure.
With the 2D curves manager, you can create and display curves of various quantities along paths;with selected parameters (such as a series of time steps); or along shell (line) regions.
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Results86
2
Settings for flux density curves (normal component at 1 s, 2 s, and 3 s)
Begin with curves of the normal component of the flux density along the path through the airgap at times 1 s, 2 s, and 3 s.
F To select these times from the Parameter values list, click 1, hold down the Ctrlkey, and then select 2 and 3.
Enter the curve information as follows:
Program Input
Curve descriptionName FDNorm [or your choice][default color] [new color, if desired]
PathFirst axisX axis CenterGap
Second axisQuantity Flux densityComponents Normal component
Third dataParameter TimeParameter values 1 + Ctrl
23
Selection step 1
click
Clicking the button creates and displays the curve at the same time.
Cogging torque computation Chapter
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2
A 2D curves sheet opens with the 3 curves stacked, as shown in the following figure:
Superimpose the curves display
To superimpose the curves, right click on the curves sheet, as shown in the previous figure.From the context menu, choose Properties to open the properties dialog.
Program Input
Right click on curves sheet
Properties
The Curves properties dialog appears. Click the Display tab to bring it to the front.
Chapter Cogging torque computation
Results88
2
Normal component of the flux density through the air gap at time steps 1, 2, and 3 s
In the Display dialog, enter or verify the following:
Program Input
click Display tabDisplay SuperimposedGradations ONX AxisRangeScale
Automaticlinear
Y AxisRangeScale
AutomaticlinearOK
When you click OK, the dialog closes.
Cogging torque computation Chapter
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2
The following figure shows the curves superimposed:
Chapter Cogging torque computation
Results90
2
Superimposed curves of normal component of flux density at times 1, 2, and 3 s
Spectrum analysis
Next, use the Spectrum manager to display the harmonics of the normal component of the fluxdensity at 1 s.
Click the button or choose Computation, 2D Spectrum manager from the menu.
Program Input
Computation
2D spectrum manager
The Spectrum manager opens, as shown in the following figure:
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2
Spectrum manager with settings for analysis of normal component of flux density at
1 s
Enter or verify the following:
Program Input
Analyzed curve FDNormBetweenand
079.79644
Part of cycle described Full cycleCreate this original curve [check box to display flux
density curve with spectrum]SpectrumHarmonics number 30Spectrum scale LinearDisplay the DC component line [check to enable if desired]
Name SpectFDNorm [name][default color] [new color, if desired]
click
Clicking the button creates and displays the spectrum and the curve on a new sheet.
Chapter Cogging torque computation
Results92
2
The flux density curve and the spectrum are shown below:
To clarify the spectrum display, you can change its properties. Right click on the legend of thespectrum and choose Properties from the context menu.
Program Input
Right click on spectrum legend
Properties
Cogging torque computation Chapter
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2
Spectrum analysis of normal component of flux density at 1 s
The previous spectrum plot, for example, uses a line width of 3, entered as shown below.
Chapter Cogging torque computation
Results94
2
Properties dialog to modify individual curve settings, such as line form and width
Axis torque (full cycle)
Finally, display the axis torque of the motor over the whole cycle of 61 time steps. Open the 2Dcurves manager with the button, or choose Computation, 2D curves manager from themenu.
Program Input
click
The 2D curves manager for the axis torque curve is shown below:
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Settings for curve of axis torque over the whole cycle
Enter or verify the following:
Program Input
Curve descriptionName AxisTorq [or your choice][default color] [new color, if desired]
ParameterFirst AxisX axis TimeParameter values 0.5 - 30.5Selection step 1
Second axisQuantity MechanicsComponent Axis torque
click
Clicking the button creates and displays the curve at the same time.
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The axis torque curve is shown in the following figure:
F Note: Since only of the motor is being modeled, the torque displayed will be of the total motor torque.
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Time varying display of the axis torque
To read values from the curve, from the 2D curves menu, select New cursor and then positionthe cursor.
Program Input
2D curvesNew cursor
For instance, the cursor in the previous figure is at X = 13.56537, showing a value of Y =2.151964E-3 N.m for the axis torque.
Save your analyses
This concludes our analysis of the cogging torque. We encourage you to create other supports(groups, paths, grids), plots, and curves on your own.
When you are ready, click the Save button to save your analysis work (the path, group, andcurves you created). If you prefer, choose File, Save from the menu.
Program Input
File
Save
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Close PostPro_2D
Close PostPro_2D by selecting File, Exit from the menu:
Program Input
File
Exit
The Flux Supervisor is displayed.
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Back EMF computationThis chapter explains how to compute the back EMF of the stator winding.
Create a 3-phase Wye connected no load circuit using ELECTRIFLUX (see diagram on page 105)
Assign physical propertiesPlane geometry, 50.308 depth, transient magnetic calculationMaterials and sources
All stator windings: vacuum, external circuitAirgap: rotating air gap, constant angular velocity of 500 rpm, 2 pole pairsWedge, air, shaft regions: vacuum, no sourceStator, rotor: nonlinear steel, no sourceMagnet: magnet, radial +, no source
Boundary conditions: Accept default conditionsLink external circuit
Coil regions (PA, MA, MC, PB) to coil components (B_PA, B_MA, B_MC,B_PB)
Define coil characteristicsB_PA, B_MA: Resistance total value, 10 turns, 0.0705 WB_MC, B_PB: Resistance total value, 20 turns, 0.141 W
Solve with static initializationInitial value of time step 0.00125sStudy time limit 100 sLimit number of time steps 49Store 1 on 1 time steps
Analyze results with PostPro_2DWaveforms of electric quantities (2D curves)
Voltage through resistor Res4Spectrum analysis of Res4 voltage curveVoltage for Res1
Save and close PostPro_2D
101
Chapter 3
Back EMF computation
Flux2D computes the back EMF of the stator winding by connecting the stator winding powersupply to an open circuit load and rotating the rotor over one electric cycle. Line to line andphase voltages with harmonics fully taken into account are readily available through the externalcircuit model.
F For this simulation and for those described in Chapters 4, 5 and 6, be sure to usethe 1-layer airgap model.
Create the back EMF external circuit model
Conventions
The following conventions are used for the external circuit model.
The stator winding connections for the model ( of the motor, or 1 pole) are 3-phase Wyeconnected. The phase diagram is shown in the following figure:
102
Phase diagram for the 3-phase Wye
connected windings
For the circuit model, the hot point convention is also used .
The small squares beside the components indicate the hot points, shown in the following figure at the top right of the coil.
The hot point shows the side through which the current should enter the component to give apositive voltage drop. The components must be oriented so that these hot points are on theproper side. Thus, the position of the hot point is essential for the coils.
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Coil with "hot" point
at upper right
Back EMF circuit
The following figure shows the components of the circuit as they should be placed on the screen.
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Circuit components for back EMF simulation
Start ELECTRIFLUX
To start ELECTRIFLUX, in the Flux Supervisor, in the Construction folder, double clickCircuit.
Program Input
Double click Circuit
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Starting the Circuit module (ELECTRIFLUX)
ELECTRIFLUX opens, as shown below:
Open a new circuit problem
Open a new circuit problem, either with the toolbar icon or the menu.
Using the icon in the toolbar
Click the icon in the toolbar.
Program Input
click
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ELECTRIFLUX (Circuit) window
Using the menu
If you prefer, choose File, New from the menu.
Program Input
FileNew
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New (blank) Circuit and Sheet windows open.
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New Circuit and Sheet windows open in ELECTRIFLUX
ELECTRIFLUX toolbar
The ELECTRIFLUX toolbar includes icons for project management (New, Open, Save), as wellas special icons for managing components, selecting components, and viewing the sheet.
The following figure shows the ELECTRIFLUX toolbar.
The figures below identify the toolbar icons.
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ELECTRIFLUX menus
Below are brief descriptions and illustrations of the ELECTRIFLUX menus.
File menu
The File menu includes commands to open, save, print, and import/export circuit files.
Edit menu
The Edit menu includes commands to manage components on the sheet, e.g., Cut, Copy, Paste,Delete.
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View menu
The View menu includes commands to change the appearance of the sheet. For example, you candisplay or hide the circuit grid with View, Grid.
The Zoom commands are also accessible through the View menu.
Circuit menu
The Circuit menu includes commands to arrange components and connections, e.g., to insertconnection points, rotate elements, insert space between components, etc.
F "Automatic component skirting" is a setting that prevents circuit connections frombeing made through or across components. This option is activated (checked) bydefault.
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Sheet menu
The Sheet menu includes commands to manage individual circuit sheetsto change the name ofthe sheet, the background colors, the size of the sheet, the grid spacing, and so on.
Window menu
The Window menu includes commands for the display of the Circuit window (which includesthe Sheet window).
? (Help) menu
The ? (Help) menu includes commands to link to Flux online help (including a searchableIndex), the Flux User's Guide, and other documentation.
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Change the size of the sheet
Before you proceed, if you wish, you can change the size of the sheet window.
Right click anywhere on the sheet to open the context menu. Choose Sheet settings.
Program Input
Right click on the sheetSheet settings
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To modify the sheet settings (size of sheet, etc.)
The Sheet properties dialog opens.
Enter or verify the following:
Program Input
Sheet properties (Sheet_1)Comment 3 phase wye deltaSquaring gap (pixels) 10Line Width 1Background color [white]Line color [blue]Selected line color [red]Sheet Width 800Sheet Height 600
OK
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Modifying the sheet properties
When you click OK, the dialog closes. Adjust the sheet window (if necessary) to show your newsheet size.
Now you are ready to begin placing the circuit components on the sheet.
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New (larger) sheet with grid
The following figure shows all the components in place for the circuit.
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Circuit components placed on the sheet
Add coils for stator windings
First, add the coils for the stator windings.
To add the coils, click Coil conductor in the Components library.
Program Input
click Coil conductor
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A red coil symbol is displayed in the upper left corner of the sheet.
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Ready to place the coil components (stator windings)
Place the 4 coil components on the sheet
Move your cursor over the coil symbol, but do not click on the symbol yet. Drag the symbolwith the mouse until the coil is in the position shown in the following figure.
Then click to place the coil in that position (the coil symbol turns blue). As soon as you movethe cursor again, you will see a second (red) coil symbol.
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Moving coil B2 into position
Moving Coil 1 into position
Move the cursor to place the three other coils, as shown (somewhat enlarged) in the followingfigure.
Program Input
click to place B2 directlybelow B1click to place B3 below and tothe left of B2click to place B4 to the rightof B3
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Four coils placed on the sheet
Move your cursor off the sheet to stop adding coil components (the pointer changes to an arrowshape).
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To stop adding coil components to the sheet
Rotate the 4 coils for proper orientation of the hot point
Now rotate the coil components. For each component, complete the two steps below:
1. Click the component to select it (the component turns red).
2. Click the Rotate icon the appropriate number of times to position the component.
Each time you click the Rotate icon , the component rotates 90 clockwise. Note that coilsB2 and B4 must be rotated a total of 270 clockwise; thus, you need to click the Rotate icon
three (3) times to obtain the proper rotation for coils B2 and B4.
For example, the following figure shows coil B2 after its rotation. Look closely to see that the"hot point" is at the lower left of the coil.
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To rotate coil B1
To rotate the coils, proceed as follows:
Program Input
click B1 symbol
B1 turns red
click once
B1 rotates 90 clockwiseclick B2 symbol
B2 turns red
click three (3) times
B2 rotates 270 clockwiseclick B3 symbol
B3 turns red
click once
B3 rotates 90 clockwiseclick B4 symbol
B4 turns red
click three (3) times
B4 rotates 270 clockwise
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With the four coils properly rotated, your sheet should resemble the following:
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Coils rotated (slightly enlarged)
Add inductors
Now add inductors to model the stator winding end turn inductances.
Click Inductor in the Components library.
Program Input
click Inductor
A red inductor symbol is displayed in the upper left corner of the sheet.
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Ready to position inductors
Place the 3 inductors on the sheet
Move the cursor and click to place the 3 inductors on the sheet as shown in the following figure.
Proceed as follows:
Program Input
click to place L1 below B2click to place L2 above B3click to place L3 above B4
drag cursor off the sheet
Drag the cursor off the sheet to stop adding inductors.
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Placing the third inductor (L3) on the sheet
With the inductors added, your sheet should resemble the following figure.
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Inductors placed on sheet
Rotate the 3 inductors
Now rotate the 3 inductors for proper orientation. Inductors L2 and L3 must be rotated 270clockwise.
Proceed as follows:
Program Input
click L1 symbol
L1 turns red
click once
L1 rotates 90 clockwiseclick L2 symbol
L2 turns red
click three (3) times
L2 rotates 270 clockwiseclick L3
L3 turns red
click three (3) times
L3 rotates 270 clockwise
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With the inductors properly rotated, your sheet should resemble the following figure.
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Inductors oriented
Add the open circuit loads
Next, add the open circuit loads. These are three large resistors (100,000 W) connected in Wye.
The following figure shows the location of these three resistors.
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Three resistors (open circuit loads) placed on the sheet
To add the resistors, click Resistor in the Components library.
Program Input
click Resistor
A red resistor symbol is displayed in the upper left corner of the sheet.
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Ready to place resistor on the sheet
Place the 3 resistors on the sheet
Move the cursor and click to place 3 resistors on the sheet as shown in the following figure.
Proceed as follows:
Program Input
click to place R1 at the topright of the sheetclick to place R2 to the rightof coil B4click to place R3 at the lowerright corner of the sheet
drag cursor off the sheet
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Resistors for open circuit loads placed on the sheet
Move your cursor off the sheet to stop adding resistors for now.
Rotate the 3 resistors
Now rotate the 3 resistors for proper orientation of the "hot" point. Proceed as follows:
Program Input
click R1 symbol
R1 turns red
click once
R1 rotates 90 clockwiseclick R2 symbol
R2 turns red
click three (3) times
R2 rotates 270 clockwiseclick R3
R3 turns red
click three (3) times
R3 rotates 270 clockwise
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With the three resistors properly rotated, your sheet should resemble the following.
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Open circuit load resistors oriented
Add the voltmeter
Finally, add a large resistor between the phase C coil (B3) and the phase B coil (B4). This resistor acts as a voltmeter to measure the line to line voltage.
Click Resistor again in the Components library.
Program Input
click Resistor
Again, the red resistor symbol is displayed in the upper left corner of your sheet.
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Place the voltmeter (R4) on the sheet
Move your cursor with the resistor symbol and place it as shown in the following figure.
Proceed as follows:
Program Input
click to place R4 between B3and B4
drag cursor off the sheet
Drag your cursor off the sheet to stop adding resistors.
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Placing the voltmeter (R4) on the sheet
Rotate the voltmeter (R4)
Now rotate the resistor (R4) as follows.
Program Input
click R4 symbol
R4 turns red
click twice
R4 rotates 180 clockwise
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All the comp