tutorial brushless dc motor calculations

Brushless DC Motor

Calculations

Copyright 2005 Magsoft Corporation

All rights reserved. No part of this work may be reproduced or used in any form or by anymeansgraphic, electronic, or mechanical, including photocopying, recording, taping, Webdistribution or information storage and retrieval systemswithout the written permission of thepublisher.

www.magsoft-flux.com

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


Start Preflu 9.1 156

Open the 1-layer airgap problem 157


Contentsvi

Define as Transient Magnetic 161


Physics context toolbars 163


Import the problem circuit 165


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 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



Solve the back EMF problem 196

Check the version: Flux2D Standard 196

Start the solver 197


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


Open the Back EMF problem 278


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


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

Close the solver 307

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

Contentsx

Current in the B_COILB (PB) coil component . . . . . . . . . . . . . . . . . . . 350

Current in the B_COILC (MC) coil component . . . . . . . . . . . . . . . . . . . 352


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

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


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

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

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


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 =


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


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


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.


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.


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


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


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



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.


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.


Program Input

Save In: Brushless_v9 [working directory]File Name: cogging [your name]

Save



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.


Program Input

2D domain type 2D planeLength Unit MILLIMETERDepth of the domain 50.308

OK


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



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:


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



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


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.



2

Materials imported into project

Proceed as follows:

Program Input

Click

Click

Click


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



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.



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:



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


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



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.



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



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.



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



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.



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


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



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



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



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



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



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



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.



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


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



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


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



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.



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.



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


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.



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.


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




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.


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



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



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



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:



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



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.



2

Batch file completed

Close the solver

Choose File, Exit to close the solver.

Program Input

File

Exit



2

Start the batch computation

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

Program Input

Double click Batch



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



2

Starting the batch computation

The Solver window opens:



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.



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


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


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.


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


Results 69

2

Your screen should resemble the following.


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


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


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.


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


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


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


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 -->


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


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.


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:


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


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.


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


Results 83

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


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


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.


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.


Results 87

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.


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.


Results 89

2

The following figure shows the curves superimposed:


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:


Results 91

2

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

1 s


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.


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


Results 93

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.


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:


Results 95

2

Settings for curve of axis torque over the whole cycle


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.


Results96

2

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.


Results 97

2

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


Save your analyses 98

2

Close PostPro_2D

Close PostPro_2D by selecting File, Exit from the menu:

Program Input

File

Exit



Close PostPro_2D 99

2

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.

Back EMF computation Chapter


3

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.

Chapter Back EMF computation

Create the back EMF external circuit model104

3

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



3

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



3

ELECTRIFLUX (Circuit) window

Using the menu

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

Program Input

FileNew



3

New (blank) Circuit and Sheet windows open.



3

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.



3

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.



3

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.



3

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.



3

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



3

To modify the sheet settings (size of sheet, etc.)

The Sheet properties dialog opens.


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



3

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.



3

New (larger) sheet with grid

The following figure shows all the components in place for the circuit.



3

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



3

A red coil symbol is displayed in the upper left corner of the sheet.



3

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.



3

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



3

Four coils placed on the sheet

Move your cursor off the sheet to stop adding coil components (the pointer changes to an arrowshape).



3

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.



3

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


B3 turns red

click once


B4 turns red


B4 rotates 270 clockwise



3

With the four coils properly rotated, your sheet should resemble the following:



3

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.



3

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.



3

Placing the third inductor (L3) on the sheet

With the inductors added, your sheet should resemble the following figure.



3

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


L2 rotates 270 clockwiseclick L3

L3 turns red


L3 rotates 270 clockwise



3

With the inductors properly rotated, your sheet should resemble the following figure.



3

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.



3

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.



3

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




3

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


R2 rotates 270 clockwiseclick R3

R3 turns red


R3 rotates 270 clockwise



3

With the three resistors properly rotated, your sheet should resemble the following.



3

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.



3

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 your cursor off the sheet to stop adding resistors.



3

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



3

All the comp

tutorial brushless dc motor calculations

Documents