Tutorial Brushless DC Motor Calculations

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Brushless DC Motor

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Cover illustration: Color shade plot of flux density on rotor, magnet, and stator from simulation of motor at constant speed with external circuit coupling

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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

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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

Contents

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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

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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

Contents

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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

Solve the back EMF problem · · · 196

Check the version: Flux2D Standard · · · 196

Start the solver · · · 197

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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

Contents

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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

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

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Define the switches· · · 295

Close and save the model · · · 298

Solve with user version · · · 299

Select the user version · · · 299

Verify the solving options· · · 303

Start the computation · · · 305

Results: Constant speed computation · · · 309

Display isovalues (equiflux) lines · · · 312

Set the properties for the display . . . 312

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

Contents

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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

Open the Constant Speed problem · · · 361

Define the no load characteristics · · · 365

Edit the MOVING_ROTOR mechanical set . . . 365

Verify the user version: brushlike_921 · · · 370

Solve the no load startup problem · · · 372

Choosing a time step· · · 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

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

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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

Open the No Load problem · · · 417

Define the servo model characteristics · · · 421

Edit the MOVING_ROTOR mechanical set . . . 421

Transient startup of servo problem · · · 426

Solve the servo simulation with user version · · · 428

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

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

Contents

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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

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About this document

This tutorial, Brushless DC Motor: Calculations, is the second in the series featuring the model of the brushless DC permanent magnet motor. The calculations presented in this document are based on the models (geometry and mesh) created with Preflu, as explained in Brushless DC

Motor: Constructing the Model. You should already have completed and have saved two geometry

and 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-layer airgap (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 permanent magnet 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 wave external circuit

Chapter 5 No load startup with electromechanical coupling, with the square wave external circuit from Chapter 4

Chapter 6 Servo action with electromechanical coupling, with the square wave external circuit from Chapter 4

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Chapters to complete for the different simulations

If you wish to do only some of the simulations described in this tutorial, the list below shows which 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 shown on page 218. For Chapter 5, you modify the physical properties of the problem from Chapter 4 to create and solve a new problem. For Chapter 6, you modify the physical properties for the problem 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 the beginning of each chapter. These sections list the physical properties and the solver and

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Enter the materials

In this chapter you start Flux2D and use the Materials database module to create the materials to be assigned to various parts of the model of the motor. These materials are added to the materials database and can then be used for other problems also.

Start Flux2D

Open the Materials database (CSLMAT)

Add the magnetic material

iso MU

scalar constant

relative permeability of 1.071 magnet

scalar constant

remanent flux density of 0.401

Add the nonlinear steel material

iso MU scalar a sat

Js = 1.99

Initial relative slope a = 7500

Close CSLMAT

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Enter the materials

For the brushless DC motor, you create two materials: (1) a magnetic material for the magnet and (2) a nonlinear steel material for the rotor and stator laminations.

Start Flux2D

Start Flux2D from your Windows taskbar.

Chapter 1

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Choose Start, Programs, Cedrat (or your installation directory), Flux 9.1. Program Input Start Programs Cedrat Flux 9.1

The Flux Supervisor opens:

Start Flux2D

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Open the materials database

To open the Materials database, in the Construction folder, double click Materials database.

Program Input

Double click Materials database

Open the materials database

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The Materials database (CSLMAT) opens:

Add the magnetic material

Flux2D includes a linear model of magnets (constant permeability µr 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

Add the magnetic material

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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 least one property

Please select the property 1 iso MU

Select a model 1 scalar cst

Value =

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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, click on the stars and then enter the relative permeability of the magnet (1.071).

Proceed as follows:

Program Input

Value = 1.071

Select the line whose value is to be changed

1 Validate

Please select the property 5 Magnet

Select a model 1 scalar cst

Value = 0.401

1 Validate

Please select the property Quit

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Add the nonlinear steel material

Next, add the nonlinear steel material. Proceed as follows:

Program Input

1 Material

Name of the material nlsteelpm

Comment nonlinear steel for laminations

in brushless pm motor To register, define at least

one property

Please select the property 1 iso MU

Select a model B scalar a sat

The scalar a sat model features an arc tangent formula to model the B-H curve. Enter the saturation 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

1 Validate

Add the nonlinear steel material

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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 max command or read the values at specific points along the curve with the Pick command.

Add the nonlinear steel material

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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

Quit Quit

Please select the property Quit

Selected command Quit

Selected command STOP

The Flux Supervisor is displayed.

You are now ready to begin creating the problem files to run the simulations.

Close the materials database

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Cogging torque computation

This chapter explains how to compute the cogging torque for the brushless DC motor.

Assign physical properties

Plane geometry, 50.308 depth, transient magnetic calculation Materials and sources

All stator windings: vacuum, no source

Airgap: rotating airgap, constant angular velocity of 0.16666666 rpm, 2 pole pairs Wedge, air, shaft: vacuum, no source

Stator, rotor: nonlinear steel, no source

Magnet: magnet material, constant direction 45 degrees, no source Boundary conditions: Automatically assigned using periodicity

Solve with a batch file

Create a batch file with the following data:

Time step 0.5 s

Study time limit 100 s

Limit number of time steps 61 Maximum value time step 0.5 s Minimum value time step 0.5 s Store automatically 1 on 1

Initial position of the rotor: 0 Solve, Batch

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Analyze results with PostPro_2D

Isovalues (equiflux) lines

Color shade plot over rotor, magnet and stator only Analysis of quantities along a path through the airgap

Normal component of the flux density

Spectrum analysis of normal component of flux density Axis torque over full cycle of the motor

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Cogging torque computation

The cogging torque in this brushless DC motor originates from variations in the reluctance of the magnetic circuit due to slotting as the rotor rotates. The cogging torque becomes detectable when the shaft is rotated slowly.

In other finite element packages, the cogging torque computation is generally performed as a multi-static computation with different rotor positions. The multi-static approach to the cogging torque computation requires a tremendous amount of effort in preparation—a finite element mesh and problem for each position—as well as long computation times and tedious

postprocessing.

With its rotating airgap feature, Flux easily computes the cogging torque. Only one finite element mesh is needed; only one problem is solved. Computation and postprocessing time is greatly reduced compared to the multi-static method because in Flux, the rotor is rotated automatically. There is no need to modify the geometry, mesh or physical properties, and a torque 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 compute the cogging torque, special consideration is needed to limit the influence of finite element numerical errors due to the mesh.

With Flux2D’s moving airgap, you must make sure that the subdivisions on the boundaries of the moving airgap from the current time step overlap the subdivisions of the next time step in order to keep the mesh topology constant in the airgap. Flux computes the torque with the virtual work method, based on the energy in the moving airgap. Thus, by keeping the mesh topology the same at each position, the influence of finite element residual errors on the small torque 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 of layers required by the Maxwell Stress Method to accurately compute the torque.

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The reason for the three-layer structure, with the moving airgap placed between two outer layers of air, is to evenly subdivide the boundary of the moving airgap. In this example, for one pole of the motor, there are 180 subdivisions on the lower and upper boundaries of the airgap (0.5 degrees/subdivision). Because the rotor moves by a multiple of 0.5 degrees, the mesh topology remains the same. The nodes from the current time step are overlapped by the nodes of the next time step as the rotor rotates.

A constant speed of 1/6 or 0.16666666 rpm is specified for the rotation of the rotor, because 1 second corresponds to 1 mechanical degree.

Before you proceed, be sure you have completed Chapter 1 and have added the two materials to the Materials Database (CSLMAT).

Special considerations for simulation

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Enter the physical properties

To enter the physical properties, use the Preflu 9.1 application, the same application used to create the geometry and mesh (in previous versions of Flux, a separate application, the Physical Properties 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

Enter the physical properties

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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

Enter the physical properties

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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 working directory

brushless_3layer.flu [your name]

Open

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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 for cogging torque calculations.

Save your project with a new name

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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.

Program Input

Save In: Brushless_v9 [working directory]

File Name: cogging [your name]

Save

Save your project with a new name

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Define as Transient Magnetic

Define cogging as a transient magnetic problem using the Application menu:

Program Input

Application Define Magnetic

Transient Magnetic 2D

The Define Transient Magnetic 2D application dialog opens.

Program Input

2D domain type 2D plane

Length Unit MILLIMETER

Depth of the domain 50.308

OK

Define as Transient Magnetic

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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 the Physics context selected.

At the top of the data Tree, click the button to change to the Physics context.

Program Input

click

Change to the Physics context

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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 Mesh contexts. Most of the Display and Select icons are the same.

The following figures show the Physics toolbar icons:

Change to the Physics context

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The cogging problem after going to the Physics context

Physics toolbar icons: Add, Check

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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, we must import them. Use the menu, Physics, Material, Import material.

Program Input

Physics

Material

Import material

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The import material dialog appears.

Click on the icon next to the material database name to display the list of materials in the database.

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 MAGNETPM

Click NLSTEELPM + Ctrl

Import

Import materials from the materials database

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List of materials in the database displayed Initial material import dialog

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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 the project.

Assign materials and sources to the regions

Material and/or source assignment is done region by region. You can select the regions from the screen, or choose the region names from the data tree on the left. You can use the Edit Array command 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 the stator 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.

Assign materials and sources to the regions

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Proceed as follows:

Program Input

Click

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Next select the stator slots from the tree by selecting their names. Make sure you hold the Control key when making multiple selections.

Program Input

Click MA

Click MC + Ctrl Click PA + Ctrl Click PB + Ctrl

Now click the right mouse button and select Edit Array.

Program Input

Right click, Edit array

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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. First select "Air or vacuum" in the Modify All column.

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Select Air or Vacuum in the Modify All Column Editing all stator slots using Edit Array function

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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 as a group:

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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 AIR Click AIRGAP + Ctrl Click SHAFT + Ctrl Click STATOR_AIR + Ctrl Click WEDGE + Ctrl

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

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Notice that the Console window displays a message confirming the assignment of the vacuum region.

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 you hold the Control key when making the second selection.

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Selecting the Stator and Rotor regions graphically Console confirms region faces modified

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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

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Setting the stator and rotor to NLSTEELPM Edit the stator and rotor areas as a group

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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.

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Selecting the magnet region, then selecting Edit

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Proceed as follows:

Program Input

Type of region Magnetic region

Material 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

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The following figure shows the Orient Material window.

Proceed as follows:

Program Input

Magnet...Angle 45

OK

You have now assigned a material property to each region of the geometry. Your screen should resemble the following figure.

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The physical properties are assigned Setting the magnet to 45 degree orientation

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Creating and Assigning Mechanical Sets

Creating Mechanical Sets

New with Flux 9.1 is the existence of Mechanical Sets. Mechanical Sets are used whenever you want motion in the model (either rotating or translating). Whenever there is motion in the model, 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 the

displacement regions, in the case of a translating motion)

We will first create these mechanical sets. Select Physics, Mechanical Set and New from the menu.

Program Input

Physics

Mechanical set New

Creating and Assigning Mechanical Sets

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Create the MOVING_ROTOR Mechanical Set

The New Mechanical set dialog appears. Enter the information to create the MOVING_ROTOR mechanical set.

Proceed as follows to define the Axis information. Then go to the Kinematics tab.

Program Input

Mechanical set name moving_rotor

Comment the moving parts of the model

Type of mechanical set Rotation around one axis

Rotation Axis Rotation around one axis

parallel to Oz

Coordinate system MAIN

Pivot point

First coordinate 0

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Defining the Axis information for the MOVING_ROTOR Mechanical Set

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Second coordinate 0

Click on "Kinematics" tab

The Kinematics tab opens. Enter the information to define the General kinematics, then click on the Internal characteristics tab.

Proceed as follows to define the General kinematics information (rpm entered equals 1 degree of rotation per second):

Program Input

Type of kinematics Imposed Speed

Velocity (rpm) 1/6

Position at time t=0s. (deg) 0

Click "Internal characteristics" tab

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Defining the General kinematics information for the MOVING_ROTOR Mechanical Set

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The Internal characteristics tab opens. Enter the information to define the Internal kinematics information, then click on the External characteristics tab.

Proceed as follows to define the Internal characteristics information:

Program Input

Type of load Inertia, friction coefficients

and spring

Moment of inertia 0

Constant friction coefficient 0

Viscous friction coefficient 0

Friction coefficient

proportional to the square speed

0

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Defining the Internal kinematics information for the MOVING_ROTOR Mechanical Set

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Click "External characteristics" tab

The External characteristics tab opens. Enter the information to define the External kinematics information, then click on OK button.

Proceed as follows to define the External characteristics information. Click OK at the end to complete the definition of the mechanical set:

Program Input

Type of load Inertia, friction coefficients

and spring

Moment of inertia 0

Constant friction coefficient 0

Viscous friction coefficient 0

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Defining the External kinematics information for the MOVING_ROTOR Mechanical Set

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Friction coefficient

proportional to the square speed

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_stator

Comment the non-moving parts of the

model

Type of mechanical set Fixed

OK

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Defining the information for the FIXED_STATOR Mechanical Set

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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_airgap

Comment the rotating airgap

Type of mechanical set Compressible

Used method to take the motion into account

Remeshing of the air part surrounding the moving body OK

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Defining the information for the ROTATING_AIRGAP Mechanical Set

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The New Mechanical set dialog closes briefly and then reappears. Close the dialog by hitting the Cancel 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.

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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 AIR

Click MAGNET + Ctrl Click ROTOR + Ctrl Click SHAFT + Ctrl

Under the Modify All column, we will set all these regions at once to the MOVING_ROTOR mechanical set.

Proceed as follows:

Program Input

MECHANICAL_SET Select "MOVING_ROTOR"

OK

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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. Make sure you hold the Control key when making multiple selections.

Program Input Click MA Click MC + Ctrl Click PA + Ctrl Click PB + Ctrl Click STATOR + Ctrl Click STATOR_AIR + Ctrl Click WEDGE + Ctrl

Under the Modify All column, we will set all these regions at once to the FIXED_STATOR mechanical set.

Proceed as follows:

Program Input

MECHANICAL_SET Select "FIXED_STATOR"

OK

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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.

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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.

Boundary conditions (Periodicity)

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Setting the AIRGAP region to the ROTATING_AIRGAP mechanical set

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Since we have modeled one quarter, or 90 degrees, of the model, we need to define a periodicity reflecting 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

Geometry Periodicity New

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The New Periodicity dialog opens.

Proceed as follows:

Program Input

Geometrical type of the periodicity

Rotation about Z axis with angle of the domain

Included angle of the domain 90

Offset angle with respect to the X line

0

Physical aspects of periodicity Odd (anticyclic boundary conditions)

OK

Check the physical model

Now that all physical attributes have been assigned to our model, we should have Flux check it before proceeding to solving.

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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.

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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

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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 by 0.5 degrees for each time step. This results in a total of 60 time steps or positions for the cogging torque computation. With the rotor speed at 1/6 rpm, 1 second corresponds to 1 mechanical degree; thus the time step is 0.5 seconds.

Flux2D can solve directly (interactively) or in batch mode. For this problem, use batch mode to reduce the solution time.

Prepare the batch file

To open the Solver, in the Flux Supervisor, in the Solving process folder, double click Direct.

Solve (batch mode)

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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

Solve (batch mode)

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The solver opens as shown below.

Click the Prepare Batch button to prepare the file for batch mode.

Program Input

click

Solve (batch mode)

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Your screen should resemble the following figure.

In the “Definition of time data” dialog, enter or verify the information to prepare the batch file as follows:

Program Input

Restarting mode New computation

Time values

Initial value of the time step

0.5

Study time limit 100

Limit number of time steps 61

Maximum value of the time step

0.5

Minimum value of the time step

0.5

Storage of time steps

Solve (batch mode)

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Program Input

one step on 1

Ok

Your time data should be filled in as shown in the following figure:

Solve (batch mode)

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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 rotor 0. degrees

OK

Solve (batch mode)

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Your screen should resemble the following figure. At the bottom of the screen, this message is displayed: “COGGING: Preparation of the batch computation finished.”

Flux2D has created a file called COGGING.DIF that will be used to start the batch solution.

Solve (batch mode)

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Close the solver

Choose File, Exit to close the solver.

Program Input

File

Exit

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Start the batch computation

In the Flux Supervisor, in the Solving process folder, double click Batch:

Program Input

Double click Batch

Solve (batch mode)

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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 to begin the batch computation:

Program Input

Files Ready

COGGING.TRA Yes COGGING.TRA

Start

Solve (batch mode)

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The Solver window opens:

Solve (batch mode)

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When the problem has finished solving, the Batch window is displayed again. Choose Quit to close the Solver.

Program Input

Batch

COGGING.TRA Quit

The Flux Supervisor should still be open.

Solve (batch mode)

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Results

To see your results, in the Flux2D Supervisor, in the Analysis folder, double click Results:

Program Input

Double click Results

Results

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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

Results

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PostPro_2D opens with a display of the model geometry at the first time step, 0.5 s.

Results

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Display the full geometry

You can display various quantities as plots on the model geometry. If you wish, instead of the model (¼ 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

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Your screen should resemble the following.

Results

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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 over the geometry, click the Results properties button or choose Results, Properties from the menu.

Program Input

Results

Properties

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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

Isovalues

Analyzed quantity Equi flux

Support Graphic selection

Computing parameters

Quality Normal

Number 21

Results

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Program Input

Scaling Uniform

OK

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 choosing Parameters, Manager from the menu.

Program Input

Parameters Manager

The Parameters dialog opens, as shown in the following figure.

Results

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Choose 1 from the Values list and then close the Parameters dialog.

Program Input

Parameters

Values 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

Results Isovalues

Results

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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 of the 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

Results

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Change the time to 0.5 s

Now change the time back to the initial value, 0.5 s. Open the Parameters manager with the button, or choose Parameters, Manager from the menu.

Program Input

Parameters Manager

In the Parameters dialog, choose 0.5 again and close the dialog.

Program Input Parameters Values 0.5 click Results

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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 Region

Objects available STATOR

MAGNET ROTOR Add -->

Results

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Program Input

Current group STATOR

MAGNET ROTOR

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

Results

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The Display properties dialog opens.

Click the Color Shade tab to bring it to the front. In the Color shade dialog, enter or verify the following:

Program Input

click Color Shade tab

Analyzed quantity |Flux density|

Support Big3 [or your regions group]

Computing parameters

Quality Normal

Scaling Uniform

OK

The Display properties dialog closes.

Results

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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:

Results

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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

Supports Path manager…

Results

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The Path Manager dialog opens:

You will be creating an arc path of 180 degrees through the center of the airgap. To verify the coordinates for the path, with the Path manager open, move your cursor over the geometry model.

The cursor looks like a cross with a trailing line or, when Arc is selected (as shown in the previous 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 the airgap and move the cursor into the center of the airgap. The X and Y coordinates are shown at the bottom of the PostPro_2D window.

Results

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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

Path

Name CenterGap [or your choice]

Discretization 200

[default color] [new color, if desired]

Graphic section Arc

Numerical section New section

Results

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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 angle

Center point X Y 0 0 Origin point X Y 25.4 0 Length 180 OK Results

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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 Curves manager at the same time.

Program Input

click

Results

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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.

Results

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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 Ctrl key, and then select 2 and 3.

Enter the curve information as follows:

Program Input

Curve description

Name FDNorm [or your choice]

Path First axis

X axis CenterGap

Second axis

Quantity Flux density

Components Normal component

Third data Parameter Time Parameter values 1 + Ctrl 2 3 Selection step 1 click

Clicking the button creates and displays the curve at the same time.

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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.

Results

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In the Display dialog, enter or verify the following:

Program Input

click Display tab

Display Superimposed Gradations ON X Axis Range Scale Automatic linear Y Axis Range Scale Automatic linear OK

When you click OK, the dialog closes.

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The following figure shows the curves superimposed:

Results

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Spectrum analysis

Next, use the Spectrum manager to display the harmonics of the normal component of the flux density 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:

Results

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Spectrum manager with settings for analysis of normal component of flux density at 1 s

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Program Input

Analyzed curve FDNorm

Between and

0

79.79644

Part of cycle described Full cycle

Create this original curve [check box to display flux

density curve with spectrum] Spectrum

Harmonics number 30

Spectrum scale Linear

Display the DC component line [check to enable if desired]

Name SpectFDNorm [name]

click

Clicking the button creates and displays the spectrum and the curve on a new sheet.

Results

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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 the spectrum and choose Properties from the context menu.

Program Input

Right click on spectrum legend

Properties

Results

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The previous spectrum plot, for example, uses a line width of 3, entered as shown below.

Results

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Axis torque (full cycle)

Finally, display the axis torque of the motor over the whole cycle of 61 time steps. Open the 2D curves manager with the button, or choose Computation, 2D curves manager… from the menu.

Program Input

click

The 2D curves manager for the axis torque curve is shown below:

Results

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Program Input

Curve description

Name AxisTorq [or your choice]

Parameter First Axis X axis Time Parameter values 0.5 - 30.5 Selection step 1 Second axis Quantity Mechanics

Component Axis torque

click

Clicking the button creates and displays the curve at the same time.

Results

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The axis torque curve is shown in the following figure:

F

Note: Since only ¼ of the motor is being modeled, the torque displayed will be ¼ of the total motor torque.

Results

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To read values from the curve, from the 2D curves menu, select New cursor… and then position the cursor.

Program Input

2D curves New 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, and curves you created). If you prefer, choose File, Save from the menu.

Program Input

File

Save

Save your analyses

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Close PostPro_2D

Close PostPro_2D by selecting File, Exit from the menu:

Program Input

File

Exit

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Back EMF computation

This 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 properties

Plane geometry, 50.308 depth, transient magnetic calculation Materials and sources

All stator windings: vacuum, external circuit

Airgap: rotating air gap, constant angular velocity of 500 rpm, 2 pole pairs Wedge, air, shaft regions: vacuum, no source

Stator, rotor: nonlinear steel, no source Magnet: magnet, radial +, no source

Boundary conditions: Accept default conditions Link external circuit

Coil regions (PA, MA, MC, PB) to coil components (B_PA, B_MA, B_MC, B_PB)

Define coil characteristics

B_PA, B_MA: Resistance total value, 10 turns, 0.0705 Ω B_MC, B_PB: Resistance total value, 20 turns, 0.141 Ω

Solve with static initialization

Initial value of time step 0.00125s

Study time limit 100 s

Limit number of time steps 49 Store 1 on 1 time steps

Analyze results with PostPro_2D

Waveforms of electric quantities (2D curves) Voltage through resistor Res4

Spectrum analysis of Res4 voltage curve Voltage for Res1

Save and close PostPro_2D

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Back EMF computation

Flux2D computes the back EMF of the stator winding by connecting the stator winding power supply to an open circuit load and rotating the rotor over one electric cycle. Line to line and phase voltages with harmonics fully taken into account are readily available through the external circuit model.

F

For this simulation and for those described in Chapters 4, 5 and 6, be sure to use the 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 (¼ of the motor, or 1 pole) are 3-phase Wye connected. The phase diagram is shown in the following figure:

Phase diagram for the 3-phase Wye connected windings

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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 a positive voltage drop. The components must be oriented so that these “hot” points are on the proper side. Thus, the position of the “hot” point is essential for the coils.

Create the back EMF external circuit model

103

Coil with "hot" point at upper right

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Back EMF circuit

The following figure shows the components of the circuit as they should be placed on the screen.

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Start ELECTRIFLUX

To start ELECTRIFLUX, in the Flux Supervisor, in the Construction folder, double click Circuit.

Program Input

Double click Circuit

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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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Using the menu

If you prefer, choose File, New from the menu.

Program Input

File New

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New (blank) Circuit and Sheet windows open.

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ELECTRIFLUX toolbar

The ELECTRIFLUX toolbar includes icons for project management (New, Open, Save), as well as 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 can display 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 insert connection points, rotate elements, insert space between components, etc.

F

"Automatic component skirting" is a setting that prevents circuit connections from being made through or across components. This option is activated (checked) by default.

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Sheet menu

The Sheet menu includes commands to manage individual circuit sheets—to change the name of the 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 includes the Sheet window).

? (Help) menu

The ? (Help) menu includes commands to link to Flux online help (including a searchable Index), the Flux User's Guide, and other documentation.