Tutorial Brushless DC Motor Calculations

Brushless DC Motor

Calculations

Copyright © 2005 Magsoft Corporation

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www.magsoft-flux.com

Cover illustration: Color shade plot of flux density on rotor, magnet, and stator from simulation

of motor at constant speed with external circuit coupling

1 About this document xv

What this document contains · · · · · · · · · · · · · · · · · · · · · · · · · xv

Chapters to complete for the different simulations · · · · · · · · · · xvi

For experienced users· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · xvi

1 Enter the materials 3

Start Flux2D · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 3

Open the materials database · · · · · · · · · · · · · · · · · · · · · · · · · · 5

Add the magnetic material · · · · · · · · · · · · · · · · · · · · · · · · · · · 6

Add the nonlinear steel material· · · · · · · · · · · · · · · · · · · · · · · · 9

Close the materials database · · · · · · · · · · · · · · · · · · · · · · · · · 11

2 Cogging torque computation 15

Special considerations for simulation· · · · · · · · · · · · · · · · · · · · 15

Enter the physical properties · · · · · · · · · · · · · · · · · · · · · · · · · 17

Start Preflu 9.1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 17

Open the 3-layer airgap problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · 18

Save your project with a new name · · · · · · · · · · · · · · · · · · · · 20

Define as Transient Magnetic · · · · · · · · · · · · · · · · · · · · · · · · · 22

Change to the Physics context · · · · · · · · · · · · · · · · · · · · · · · · 23

iii

Contents

Physics context toolbars · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 24

Import materials from the materials database · · · · · · · · · · · · · 25

Assign materials and sources to the regions · · · · · · · · · · · · · · 27

Assign the windings of the stator slots · · · · · · · · · · · · · · · · · · · · · · · · 27

Assign WEDGE, AIR, STATOR_AIR, AIRGAP and SHAFT regions · · · · · · · 31

Assign STATOR and ROTOR regions · · · · · · · · · · · · · · · · · · · · · · · · · · 33

Assign the MAGNET · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 35

Creating and Assigning Mechanical Sets · · · · · · · · · · · · · · · · · 38

Creating Mechanical Sets· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 38

Create the MOVING_ROTOR Mechanical Set . . . . . . . . . . . . . . . . . . . . 39

Create the FIXED_STATOR Mechanical Set. . . . . . . . . . . . . . . . . . . . . 43

Create the ROTATING_AIRGAP Mechanical Set. . . . . . . . . . . . . . . . . . . 44

Assigning Mechanical Sets · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 45

Boundary conditions (Periodicity) · · · · · · · · · · · · · · · · · · · · · · 49

Check the physical model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 51

Close Preflu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Solve (batch mode) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 54

Prepare the batch file · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 54

Close the solver · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 61

Start the batch computation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 62

Results · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 66

Display the full geometry· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 69

Displaying isovalues (equiflux) lines at t = 1 s · · · · · · · · · · · · · · · · · · · 71

Change the default isovalues display . . . . . . . . . . . . . . . . . . . . . . . 71

Change the time to 1 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Display the isovalues plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Contentsiv

Color shade of flux density on a group of regions · · · · · · · · · · · · · · · · · 75

Change the geometry display. . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Change the time to 0.5 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Create a group of the three regions . . . . . . . . . . . . . . . . . . . . . . . . 77

Display a color shade plot on the group of regions . . . . . . . . . . . . . . . . . 78

Create a path through the airgap · · · · · · · · · · · · · · · · · · · · · · · · · · · · 81

Normal component of flux density along the air gap path · · · · · · · · · · · 86

Superimpose the curves display · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 88

Spectrum analysis · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 91

Axis torque (full cycle) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 95

Save your analyses · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 98

Close PostPro_2D · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 99

3 Back EMF computation 102

Create the back EMF external circuit model · · · · · · · · · · · · · · 102

Conventions· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 102

Back EMF circuit · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 104

Start ELECTRIFLUX · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 105

Open a new circuit problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 106

Using the icon in the toolbar. . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Using the menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

ELECTRIFLUX toolbar · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 109

ELECTRIFLUX menus· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 110

File menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Edit menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

View menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Circuit menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Sheet menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Contents v

Window menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

? (Help) menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Change the size of the sheet · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 113

Add coils for stator windings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 117

Place the 4 coil components on the sheet . . . . . . . . . . . . . . . . . . . . 119

Rotate the 4 coils for proper orientation of the hot point. . . . . . . . . . . . . . 122

Add inductors· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 125

Place the 3 inductors on the sheet . . . . . . . . . . . . . . . . . . . . . . . . 126

Rotate the 3 inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

Add the open circuit loads · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 130

Place the 3 resistors on the sheet . . . . . . . . . . . . . . . . . . . . . . . . 132

Rotate the 3 resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

Add the voltmeter· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 135

Place the voltmeter (R4) on the sheet . . . . . . . . . . . . . . . . . . . . . . 136

Rotate the voltmeter (R4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Save your circuit file · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 139

Connect (wire) the circuit components · · · · · · · · · · · · · · · · · · · · · · · 140

Define the resistors and inductors· · · · · · · · · · · · · · · · · · · · · · · · · · · 146

Define the resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Define the inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

Rename the coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Analyze the circuit · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 152

Save and close the circuit file · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 154

Close ELECTRIFLUX· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 155

Enter the physical properties · · · · · · · · · · · · · · · · · · · · · · · · 156

Start Preflu 9.1· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 156

Open the 1-layer airgap problem · · · · · · · · · · · · · · · · · · · · · · · · · · · 157

Save your project with a new name · · · · · · · · · · · · · · · · · · · 159

Contentsvi

Define as Transient Magnetic · · · · · · · · · · · · · · · · · · · · · · · · 161

Change to the Physics context · · · · · · · · · · · · · · · · · · · · · · · 162

Physics context toolbars · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 163

Import materials from the materials database · · · · · · · · · · · · 163

Import the problem circuit · · · · · · · · · · · · · · · · · · · · · · · · · · 165

Assign materials and sources to the regions· · · · · · · · · · · · · · 169

Assign the stator windings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 169

Edit the PA region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Define the coil resistance · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 174

Assign WEDGE, AIR, AIRGAP and SHAFT regions · · · · · · · · · · · · · · · · 176

Assign STATOR and ROTOR regions · · · · · · · · · · · · · · · · · · · · · · · · · 177

Assign the MAGNET· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 179

Creating and Assigning Mechanical Sets · · · · · · · · · · · · · · · · 181

Creating Mechanical Sets · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 181

Create the MOVING_ROTOR Mechanical Set . . . . . . . . . . . . . . . . . . . 182

Create the FIXED_STATOR Mechanical Set . . . . . . . . . . . . . . . . . . . . 186

Create the ROTATING_AIRGAP Mechanical Set . . . . . . . . . . . . . . . . . . 187

Assigning Mechanical Sets · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 188

Boundary conditions (Periodicity) · · · · · · · · · · · · · · · · · · · · · 193

Check the physical model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 194

Solve the back EMF problem · · · · · · · · · · · · · · · · · · · · · · · · 196

Check the version: Flux2D Standard · · · · · · · · · · · · · · · · · · · · · · · · · 196

Start the solver · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 197

Start the solver · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 198

Close the solver · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 202

Contents vii

Results from the Back EMF computation · · · · · · · · · · · · · · · · 203

Display the back EMF in R4 (the voltmeter) · · · · · · · · · · · · · · · · · · · · 205

Display a spectrum of the back EMF in R4 · · · · · · · · · · · · · · · · · · · · · 208

Voltage and current in coil B_MC (MC) · · · · · · · · · · · · · · · · · · · · · · · 213

Save and close PostPro_2D · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 214

4 Square wave motor: Constant speed (torque ripples) 217

Create the 3-phase bridge circuit · · · · · · · · · · · · · · · · · · · · · 218

Start ELECTRIFLUX · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 219

Create a new circuit problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 221

Using the icon in the toolbar. . . . . . . . . . . . . . . . . . . . . . . . . . . 221

Using the menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

Change the size of the sheet · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 223

Add the 6 switches · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 226

Place the 6 switches on the sheet . . . . . . . . . . . . . . . . . . . . . . . . 228

Rotate the 6 switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

Add the 6 series voltages· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 236

Place the 6 series voltages on the sheet . . . . . . . . . . . . . . . . . . . . . 238

Rotate the series voltages. . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

Add the main voltage source · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 243

Place the main voltage source . . . . . . . . . . . . . . . . . . . . . . . . . . 244

Rotate the main voltage source . . . . . . . . . . . . . . . . . . . . . . . . . 245

Add the 3 coils · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 246

Place the 3 coil components on the sheet . . . . . . . . . . . . . . . . . . . . 248

Rotate the coil components . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

Add the inductors · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 252

Place the 3 inductors on the sheet . . . . . . . . . . . . . . . . . . . . . . . . 254

Rotate the 3 inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

Contentsviii

Add the voltmeter· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 257

Save your circuit· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 260

Connect (wire) the circuit components · · · · · · · · · · · · · · · · · · · · · · · 262

Define the circuit · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 266

Define the on/off resistance values for the switches . . . . . . . . . . . . . . . . 266

Define the inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

Define the voltmeter (R1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

Rename the coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

Analyze the circuit · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 273

Save and close the circuit file · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 275

Close ELECTRIFLUX· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 276

Assign the physical properties · · · · · · · · · · · · · · · · · · · · · · · 277

Start Preflu 9.1· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 277

Open the Back EMF problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 278

Save your project with a new name · · · · · · · · · · · · · · · · · · · · · · · · · 281

Change the coupled circuit · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 283

Delete the existing circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

Change to the Physics Context . . . . . . . . . . . . . . . . . . . . . . . . . 284

Import the Squarewave Circuit . . . . . . . . . . . . . . . . . . . . . . . . . 284

Assign face regions to the circuit · · · · · · · · · · · · · · · · · · · · · · · · · · · 287

Assign the stator windings . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

Edit the PA region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

Edit the MA region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288

Edit the PB region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

Edit the MC region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290

Define the coil resistance · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 291

Define the Voltage Sources · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 293

Define the Main Voltage Source . . . . . . . . . . . . . . . . . . . . . . . . . 293

Define the Series Voltage Sources . . . . . . . . . . . . . . . . . . . . . . . . 294

Contents ix

Define the switches· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 295

Check the physical model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 297

Close and save the model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 298

Solve with user version · · · · · · · · · · · · · · · · · · · · · · · · · · · · 299

Select the user version · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 299

Start the solver · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 301

Verify the solving options· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 303

Start the computation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 305

Close the solver · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 307

Results: Constant speed computation · · · · · · · · · · · · · · · · · · 309

Display isovalues (equiflux) lines · · · · · · · · · · · · · · · · · · · · · · · · · · · 312

Set the properties for the display . . . . . . . . . . . . . . . . . . . . . . . . 312


Color shade plot on a group of regions · · · · · · · · · · · · · · · · · · · · · · · 318

Create the group of regions . . . . . . . . . . . . . . . . . . . . . . . . . . . 318

Set the properties for the display . . . . . . . . . . . . . . . . . . . . . . . . 319

Display the color shade plot . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

Create a path through the airgap · · · · · · · · · · · · · · · · · · · · · · · · · · · 323

Flux density along the airgap path · · · · · · · · · · · · · · · · · · · · · · · · · · 328

Flux density: Normal component . . . . . . . . . . . . . . . . . . . . . . . . 328

Flux density: Tangential component . . . . . . . . . . . . . . . . . . . . . . . 329

Superimpose the normal and tangential flux density curves . . . . . . . . . . . . 330

Spectrum analysis · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 334

Time variation curve of axis torque · · · · · · · · · · · · · · · · · · · · · · · · · · 338

Waveforms of the electric quantities · · · · · · · · · · · · · · · · · · · · · · · · · 342

Voltage and current in the main voltage source (V7) . . . . . . . . . . . . . . . 343

Current in Switch1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

Current in the B_COILA (PA) coil component . . . . . . . . . . . . . . . . . . . 348

Contentsx

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

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

Save and close PostPro_2D · · · · · · · · · · · · · · · · · · · · · · · · · 354

5 No load startup with electromechanical coupling 359

Modify the physical properties · · · · · · · · · · · · · · · · · · · · · · · 359

Start Preflu 9.1· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 360

Open the Constant Speed problem · · · · · · · · · · · · · · · · · · · · · · · · · · 361


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

Start the solver · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 372

Results from no load startup · · · · · · · · · · · · · · · · · · · · · · · · 380

Display the isovalues (equiflux) lines at time step 100 (t = 0.05 s) · · · · 382

Select the 100th time step (0.05 s) . . . . . . . . . . . . . . . . . . . . . . . 383

Set the display properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385


Time variation analysis (2D Curves) · · · · · · · · · · · · · · · · · · · · · · · · · 390

Axis torque curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391

Angular velocity curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

Rotor position curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396

Waveforms of electric quantities · · · · · · · · · · · · · · · · · · · · · · · · · · · · 399

Voltage and current in the main voltage source . . . . . . . . . . . . . . . . . . 400

Contents xi

Current in Switch1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403

Current in the B1 (PA) coil component . . . . . . . . . . . . . . . . . . . . . . 405

Voltage and current in the B2 (PB) coil component . . . . . . . . . . . . . . . . 407

Voltage and current in B3 (MC) coil component . . . . . . . . . . . . . . . . . . 409

Save and close PostPro_2D · · · · · · · · · · · · · · · · · · · · · · · · · 412

6 Servo action with electromechanical coupling 415

Modification of physical properties · · · · · · · · · · · · · · · · · · · · 415

Start Preflu 9.1· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 416

Open the No Load problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 417


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

Start the solver · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 429

Results from servo motor· · · · · · · · · · · · · · · · · · · · · · · · · · · 435

Display the isovalues (equiflux) lines· · · · · · · · · · · · · · · · · · · · · · · · · 438

Select the last time step (0.115 s) . . . . . . . . . . . . . . . . . . . . . . . . 438

Set properties for the isovalues display . . . . . . . . . . . . . . . . . . . . . 440


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 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 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 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

postprocessor settings for each problem.

xvi

Enter the materialsIn 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

1

Chapter 1

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.

3

Chapter 1

Starting Flux2D

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

Program Input

Start

Programs

Cedrat

Flux 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)

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 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 property

Please select the property 1 iso MU

Select a model 1 scalar cst

Value =


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, 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 isto 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


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 Material

Name of the material nlsteelpm

Comment nonlinear steel for laminations in brushless pm motor

To register, define at leastone 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 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 max

command 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

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 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 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

13

Chapter 2

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

Save and close PostPro_2D

14

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.

15

Chapter 2

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).

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 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

Cogging torque computation Chapter

Enter the physical properties 17

2

Starting Preflu 9.1 to enter the physical properties

The Preflu 9.1 application opens.

Open the 3-layer airgap problem

You can open an existing project either with the toolbar icon or the menu.

Using the icon in the toolbar

To open a new Flux project, click the icon on the toolbar

Program Input

click


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 workingdirectory

brushless_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 for

cogging 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


Save your project with a new name 21

2

Saving the brushless 3-layer model as cogging

Define as Transient Magnetic

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

Program Input

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 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 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 23

2

The cogging problem after defining the physical model

The Physics context is shown in the following figure.

Physics context toolbars

The Physics context includes some of the same icons and commands as the Geometry and Mesh

contexts. 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, we

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

Program Input

Physics

Material

Import material


Import materials from the materials database 25

2

The import material dialog appears.

Click on the icon next to the material database name to display the list of materials in 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 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 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 27

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 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



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. First

select "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 as

a 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 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


OK



2

Setting a vacuum property for the air regions

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.



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 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



2

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.



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 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 thedisplacement 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 Sets38

2

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 axisparallel to Oz

Coordinate system MAIN

Pivot point

First coordinate 0


Creating and Assigning Mechanical Sets 39

2

Defining the Axis information for the MOVING_ROTOR

Mechanical Set

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 "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 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 coefficientsand spring

Moment of inertia 0

Constant friction coefficient 0

Viscous friction coefficient 0

Friction 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 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


Moment of inertia 0





2

Defining the External kinematics information for the



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 themodel

Type of mechanical set Fixed

OK



2

Defining the information for the FIXED_STATOR

Mechanical Set

Create the ROTATING_AIRGAP Mechanical Set


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 motioninto account

Remeshing of the air partsurrounding the moving body

OK



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 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.



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 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



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. 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



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.


Boundary conditions (Periodicity) 49

2

Setting the AIRGAP region to the ROTATING_AIRGAP

mechanical set

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


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 90

Offset 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 it

before 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.



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 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)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


Solve (batch mode) 55

2

Choosing the problem to solve

The solver opens as shown below.

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

Program Input

click



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 file

as follows:

Program Input

Restarting mode New computation

Time values

Initial value of the time step

0.5

Study time limit 100


Maximum 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 1

Ok

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 rotor

0. 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 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.



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 to

begin the batch computation:

Program Input

Files Ready

COGGING.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 to

close the Solver.

Program Input

Batch

COGGING.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 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


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 over

the geometry, click the Results properties button or choose Results, Properties from the

menu.

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

Isovalues

Analyzed quantity Equi flux

Support Graphic selection

Computing parameters

Quality Normal

Number 21


Results72

2

Results properties dialog for isovalues display

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 73

2

Parameters dialog

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


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 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 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 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


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 Region

Objects available STATOR

MAGNET

ROTOR

Add -->


Results 77

2

Group manager dialog

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


Results78

2


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]


Quality Normal

Scaling 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

Supports

Path 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 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.


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

Path

Name CenterGap [or your choice]

Discretization 200

[default color] [new color, if desired]

Graphic section Arc

Numerical 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 angle

Center point

X

Y

0

0

Origin point

X

Y

25.4

0

Length 180

OK


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 Curves

manager 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 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.


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 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.


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 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 91

2

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

1 s


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.


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 the

spectrum 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 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 95

2

Settings for curve of axis torque over the whole cycle


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



Results96

2

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 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 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 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)



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 ΩB_MC, B_PB: Resistance total value, 20 turns, 0.141 Ω

Solve with static initialization

Initial value of time step 0.00125s



Store 1 on 1 time steps


Waveforms of electric quantities (2D curves)

Voltage through resistor Res4

Spectrum analysis of Res4 voltage curve

Voltage for Res1


101

Chapter 3

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:

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 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.

Back EMF computation Chapter

Create the back EMF external circuit model 103

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 click

Circuit.

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.


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

File

New



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 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.



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 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.



3

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.



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 sheet

Sheet 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 delta

Squaring gap (pixels) 10

Line Width 1

Background color [white]

Line color [blue]

Selected line color [red]

Sheet Width 800

Sheet Height 600

OK



3

Modifying the sheet properties

When you click OK, the dialog closes. Adjust the sheet window (if necessary) to show your new

sheet 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 symbol

with 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 move

the 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 following

figure.

Program Input

click to place B2 directlybelow B1

click to place B3 below and tothe left of B2

click 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 arrow

shape).



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 coils

B2 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° clockwise

click B2 symbol

B2 turns red

click three (3) times


click B3 symbol

B3 turns red

click once


click B4 symbol

B4 turns red





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 B2

click to place L2 above B3

click 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 270°clockwise.

Proceed as follows:

Program Input

click L1 symbol

L1 turns red

click once

L1 rotates 90° clockwise

click L2 symbol

L2 turns red



click L3

L3 turns red





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 Ω) 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 sheet

click to place R2 to the rightof coil B4

click 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° clockwise

click R2 symbol

R2 turns red



click R3

R3 turns red





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




3

All the components should now be properly positioned on your sheet, as shown in the following

figure.



3

Components placed on sheet

Save your circuit file

Now is a good time to save your circuit file. Click the icon or choose File, Save from the

menu.

Program Input

File

Save

The "Choose a file name" dialog opens.



3

Saving the circuit file

The dialog shows your working directory in the "Save in" field (e.g., ours is "Brushless_V9" in the

previous figure). If you should wish to save the file to a different directory, click the button

and browse to the directory you wish.

When you are ready, proceed as follows:

Program Input

Save in Brushless_V9[working directory]

File name onedelta.ccs [or your name]

Save

Connect (wire) the circuit components

Now connect the components.

Place the cursor over the bottom pin of coil B1, so that the cursor changes to a bull's-eye

shape.



3

Starting to connect (wire) the components

Program Input

position cursor over bottom pin of coil B1

Drag the cursor down to the top pin of coil B2 and click to complete the first connection.

Program Input

click pin at top of B2 tocomplete the connection

Connect all the components in the same way.



3

Notice that with the "Automatic component skirting" option (the default option), you cannot

make an invalid connection, such as one that passes "through" or over a component. The cursor

changes to a hand as it passes over coil B2, as shown in the following figure.

You can make connections only when you see the bull's-eye cursor.



3

The following figure shows resistor R2 being connected to coil B4.



3

Connections for upper part of circuit

When you are making long connections, such as between resistor R3 and coil B3, you can click

on the grid itself (not on a component pin) to create an intermediate point or "corner" for the

connection, as shown in the following figure.



3

Adding an intermediate point for a connection

Such intermediate points may improve the legibility of your circuit diagram. For example, the

following figure shows what the connection might look like without the intermediate point.

You can also move connections. If necessary, click the icon in the toolbar to select entire

connections; the cursor changes to . Then click the connection line to select it and drag the

line until it assumes the shape you wish. For example, the following figure shows the last

connection selected (the lines of the connection are shown in red on the screen, and the number

5 is displayed over the line).



3

Connection selected (lines shown in red)

Connecting R3 to B3 without intermediate point

The following figure shows the connections for the whole circuit.

Define the resistors and inductors

Now define the values of the resistors and inductors. You may use scientific notation to enter

the resistance and inductance values.

Use 100,000 Ω as the resistance value for all the resistors.

The design sheet value for the end turn inductance per phase is 0.031 mH/phase.



3

Circuit connections complete

Define the resistors

Begin by defining the resistance value for each of the 4 resistors.

Double click R1, the symbol for the first of the open circuit loads.

Program Input

Double click R1

The symbol turns red, and the Resistor dialog opens.

If you wish, you can edit the name of the resistor and add a brief description in the Comment

field.

F The name of any resistor must begin with a capital R. The initial letter of any

component name cannot be changed.

In the dialog, enter or verify the following:

Program Input

Resistor

Name R1



3

Defining resistance for R1

Program Input

Characteristics

Name R(ohm)

Value 1e5

Ok

When you choose Ok, the dialog closes. Define the other 3 resistors, including the voltmeter, as

follows:

Program Input

Double click R2

1e5

Ok

Double click R3

1e5

Ok



3

Program Input

Double click R4

1e5

Ok

Define the inductors

In the same way, define the inductors. Double click L1, the symbol for the first inductor. The

symbol turns red and the Inductor dialog opens.



3

Defining inductance value for the first inductor (L1)

In the Inductor dialog, enter or verify the following:

Program Input

Inductor

Name L1

Characteristics

Name L(henry)

Value 3.1e-5

Ok

When you choose Ok, the dialog closes.

Define the other inductors as follows:

Program Input

Double click L2

3.1e-5

Ok

Double click L3

3.1e-5

Ok

Again, when you click Ok, the dialog closes.



3

Rename the coils

The coils can be named to reflect their use in the motor. Any name can be used for the coils as

long as the name starts with a "B". Rename the coils by editing each one (double clicking),

similar to the way the resistors and inductors were changed.

Program Input

Double click B1

B_PA

Ok

Double click B2

B_MA

Ok

Double click B3

B_MC

Ok



3

Double click B4

B_PB

Ok

Analyze the circuit

Analyze the circuit to check its connections and to create the *.CIF file to be used for

simulations. Choose Circuit, Analyse from the menu.

Program Input

Circuit

Analyse



3

The following dialog opens with a report of the analysis.

Click Exit to close the dialog.

Program Input

The circuit is connexe. Exit



3

Analysis of the circuit

Save and close the circuit file

The circuit and transmission files are now complete. Save the circuit file by clicking the icon

or by choosing File, Save from the menu.

Program Input

File

Save

Close the circuit by choosing File, Close.

Program Input

File

Close



3

The following dialog opens.

Click Yes to confirm:

Program Input

Close circuit? Yes

Close ELECTRIFLUX

Finally, close ELECTRIFLUX by choosing File, Exit.

Program Input

File

Exit




3

Confirming close of circuit

Enter the physical properties




Start Preflu 9.1


Program Input




3

Starting Preflu 9.1 to enter the physical properties


Open the 1-layer airgap problem



To open an existing Flux project, click the icon on the toolbar.

Program Input

click



3

Preflu 9.1 screen

Using the menu


Program Input

Project

Open project




3


Program Input

Look in Brushless_V9 [your workingdirectory]

File Name brushless_1layer.flu [yourname]

Open

The 1-layer geometry is shown in the following figure:


Save your project now with a specific name to indicate that you will be using this model for back

EMF calculations.


Save your project with a new name 159

3

The geometry (with 1-layer airgap) displayed in Preflu


Program Input

Project

Save As…



Program Input

Save In: Brushless_V9[working directory]

File Name: bemf [your name]

Save


Save your project with a new name160

3

Saving the brushless 1-layer model as bemf

Define as Transient Magnetic

Define bemf 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. First, click on the "Coils

Coefficient" tab. In previous versions of Flux, when linking a circuit to a problem that was not

completely modeled (like this one, where only ¼ of the motor is represented), the values of the

circuit components needed to be adjusted for the amount of the problem represented. For

example, in the past, the values of the circuit inductors in this problem would be divided by 4.

Now, with Flux 9.1, the program takes the periodicity of the geometry into account and

internally divides the component values by 4. In this way, the same circuit can be used in

multiple models, regardless of how much of the problem is modeled.


Define as Transient Magnetic 161

3

Flux 9.1 automatically takes periodicity into account when using a circuit

Now click back on the Definition tab to define the domain .


Program Input

2D domain type 2D plane

Length Unit MILLIMETER

Depth of the domain 50.308

OK

Notice on your screen 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. At the top of the data Tree,

click the button to change to the Physics context.

Program Input

click


Change to the Physics context162

3

The Physics context is shown in the following figure.

Physics context toolbars

Please refer to Chapter 2 for an explanation of the icons on the toolbar when the program is in

the Physics context.

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.


Import materials from the materials database 163

3

The bemf problem after going to the Physics context

Program Input

Physics

Material

Import material

In the Import material dialog, click on the icon next to the material database 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.


Import materials from the materials database164

3

List of materials in the database displayed

Proceed as follows:

Program Input

Click MAGNETPM

Click NLSTEELPM + Ctrl

Import

After the import is complete, close the Import materials window.

Program Input

Close

Import the problem circuit

Before we can assign the coil conductors in the circuit we created earlier in this chapter to the

different regions of our model, we must import the circuit.

To import the circuit we created, click the icon on the toolbar.

Program Input

click


Import the problem circuit 165

3

If you prefer, choose Physics, Circuit, Import circuit from a CCS file from the menu:

Program Input

Physics

Circuit

Import circuit from a CCS file

The Import circuit dialog appears. Click on the browse file selector in the dialog box.

Program Input

click


Import the problem circuit166

3

The Open circuit dialog appears.


Program Input

Look In: Brushless_V9 [your workingdirectory]

File Name: onedelta.ccs [your name]

Open

The circuit file name is transferred to the Import Circuit dialog box.

Proceed as follows:

Program Input

Click OK


Import the problem circuit 167

3

Selected circuit ready for import

The circuit is displayed on the screen. If you expand the data Tree under the Electric Circuit

node, you will see the components from the imported circuit.

Click the GeometryFlux2DView tab at the bottom of the screen to return to the geometric view

of the model.

Program Input

Click GeometryFlux2DView


Import the problem circuit168

3

Imported circuit displayed as a new "tab" in the graphics area

Assign materials and sources to the regions

Material and/or source assignment is done region by region. You can assign the same properties

to several regions at the same time with the Edit Array command.

Assign the stator windings

Each winding region (PA, MA, MC, PB) must be linked to a coil conductor (B_PA, B_MA,

B_MC, B_PB) in the circuit you created. Each region will be changed individually.

Edit the PA region

Expand the Face Regions in the Data tree. Select the PA region and right-click the mouse to

select Edit.

Proceed as follows:

Program Input

Click PA

Right-click, Edit



3

The Edit Face Region dialog opens.


Program Input

Type of region Coil conductor region type

Positive orientation of thecurrent

Number of turns of theconductor

10

Coil conductor region component B_PA

Symmetries and periodicities All the symmetrical andperiodical conductors are inseries

OK



3

Similarly, select the MA region for editing (right-click on MA in the data Tree, select Edit)


Program Input




10

Coil conductor region component B_MA


OK



3

You can also select regions graphically. Click on one face of the MC region, then right-click and

select Edit.




3

Selecting the MC region for edit by selecting it graphically

The MC (B_MC) and PB (B_PB) regions each represent two windings. These regions are

considered compound surfaces. The number of turns for coils B_MC and B_PB is therefore

twice the value for one winding (20).Enter or verify the following:

Program Input




20

Coil conductor region component B_MC


OK

Finally select to edit the PB region (with either the tree or graphically).



3


Program Input




20

Coil conductor region component B_PB


OK

Define the coil resistance

According to the design sheet, the stator winding characteristics are 10 turns with a resistance

per phase value of 0.141Ω/phase.

For the PA (B_PA) and MA (B_MA) regions, the number of turns is 10. Their resistance must

be calculated, however. To obtain R/phase, divide 0.141Ω by 2 to obtain 0.0705Ω, because these

regions or coils represent only half of the complete winding. Since the B_PA and B_MA coils are

the same, we will use the Edit Array command to set the resistances to both coils at once.

Expand the data tree to display the coil conductors (under the Electric Circuit, then under the

Stranded Coil Conductor). Select the B_PA and B_MA coils using the mouse and Control key.

Proceed as follows:

Program Input

Click B_MA

Click B_PA + Ctrl

Right-click, Edit array



3

The Edit Stranded Coil dialog appears. In the Modify All column, enter the resistance.

Proceed as follows:

Program Input

Modify all - Resistance formula 0.0705

OK

Similarly, select the Edit Array command for the B_MC and B_PB coils.

The MC (B_MC) and PB (B_PB) regions each represent two windings. Their resistance is twice

the resistance for one winding. Thus, the resistance for B_MC and B_PB is 0.141 Ω. In the

Modify All column, enter the resistance.



3

Setting the resistance for coils B_MA & B_PA

Setting the resistance for coils B_MC & B_PB

Proceed as follows:

Program Input


OK

Assign WEDGE, AIR, AIRGAP and SHAFT regions

Assign properties to the WEDGE, AIR, AIRGAP and SHAFT regions as a group.

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 WEDGE + Ctrl


Under the Modify All column, we will set all these regions at once to a vacuum region.



3

Setting a vacuum property for the air regions

Proceed as follows:

Program Input


OK

Assign STATOR and ROTOR regions

Assign the NLSTEEL material to the STATOR and ROTOR regions.

Select the stator and rotor regions from the graphic. Make sure you hold the Control key when

making the second selection.



3

Selecting the Stator and Rotor regions graphically

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 NLSTEEL material.

Proceed as follows:

Program Input

Sub types: Select "Magnetic reg"

Material Select "NLSTEELPM"

OK



3

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.



3

Selecting the magnet region, then selecting Edit

Setting the magnet region to the MAGNETPM material

Proceed as follows:

Program Input

Type of region Magnetic region

Material of the region MAGNETPM

OK

Now you must set the magnet as a radial magnet. This is done by setting the magnet's

orientation. Select the icon from the toolbar.

Program Input

Click

The following figure shows the Orient Material window.

Proceed as follows:

Program Input

Magnet...Oriented type Radial Positif

OK

You have now assigned a material property to each region of the geometry.



3

Setting the magnet to a positive radial magnet

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 thedisplacement 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



3

Create the MOVING_ROTOR Mechanical Set

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


Proceed as follows:

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 axisparallel to Oz

Coordinate system MAIN

Pivot point

First coordinate 0



3

Defining the Axis information for the MOVING_ROTOR

Mechanical Set

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:

Program Input

Type of kinematics Imposed Speed

Velocity (rpm) 500

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

Click "Internalcharacteristics" tab



3

Defining the General kinematics information for the


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


Moment of inertia 0




0



3

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 kinematics

information, then click on OK button.

Proceed as follows to define the External characteristics information:

Program Input


Moment of inertia 0





3

Defining the External kinematics information for the



0

OK

Create the FIXED_STATOR Mechanical Set


the FIXED_STATOR mechanical set.

Proceed as follows:

Program Input

Mechanical set name fixed_stator

Comment the non-moving parts of themodel

Type of mechanical set Fixed

OK



3

Defining the information for the FIXED_STATOR

Mechanical Set

Create the ROTATING_AIRGAP Mechanical Set


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 motioninto account

Remeshing of the air partsurrounding the moving body

OK



3

Defining the information for the ROTATING_AIRGAP

Mechanical Set

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.

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.



3

Close the Mechanical set dialog

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

Now assign regions to the FIXED_STATOR mechanical set. Select the MA, MC, PA, PB,

STATOR and WEDGE regions from the tree by selecting their names. Make sure you hold the

Control key when making multiple selections.



3

Assigning regions to the MOVING_ROTOR mechanical set

Program Input

Click MA

Click MC + Ctrl

Click PA + Ctrl

Click PB + Ctrl

Click STATOR + Ctrl

Click WEDGE + Ctrl


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

mechanical set.



3

Assigning regions to the FIXED_STATOR mechanical set

Proceed as follows:

Program Input

MECHANICAL_SET Select "FIXED_STATOR"

OK

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



3

The Edit Face region dialog appears. Click on the Mechanical Set tab to assign the mechanical set

to the AIRGAP region.

Now select the ROTATING_AIRGAP mechanical set from the pull down menu.



3

Setting the AIRGAP region to the ROTATING_AIRGAP

mechanical set

Click on the Mechanical Set tab

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.

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

The New Periodicity dialog opens.



3

Defining a periodicity for the brushless DC motor

Proceed as follows:

Program Input

Geometrical type of theperiodicity

Rotation about Z axis withangle of the domain

Included angle of the domain 90

Offset angle with respect tothe X line

0

Physical aspects of periodicity Odd (anticyclic boundaryconditions)

OK





Program Input

Click




3

The model is ready for solving. Close the Preflu application.

Select Project, Exit from the menu.

Program Input

Project

Exit


Proceed as follows:

Program Input





3

Solve the back EMF problem

You are now ready to solve the back EMF problem. Because this problem includes saturation and

inductances and is voltage based, numerical transients may occur before the steady state is

reached. Thus the problem will be solved using Flux's ability to automatically come to a steady

state at the start.

Check the version: Flux2D Standard

In the Flux2D Supervisor, make sure that Flux2D: Standard is shown in the Program manager at

the top of the Supervisor window.

If you do not see "Flux2D: Standard," choose Versions, Standard from the menu.

Program Input

Versions

Standard


Solve the back EMF problem196

3

Start the solver

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

Program Input

Double click Direct


Solve the back EMF problem 197

3

Starting the solver

In the Open dialog, select the problem to be solved and click Open.

Program Input

Look in: Brushless_V9[working directory]

File name: BEMF.TRA [your name]

Open

Start the solver

The solver screen will appear.

Click the Solve button to begin the computation.

Program Input

click



3


The Definition of time data dialog opens:

Enter or verify the following information:

Program Input


initialised by static computation

Time values

Initial value of the timestep

0.00125



3

Definition of time data for back EMF computation

Program Input




one step on 1

OK

Click OK to close the time data dialog. The following dialog opens:

Do not change the initial position of the rotor. Click OK and watch as the solution proceeds.

Program Input


0. degrees

OK



3

When the computation stops, the following dialog opens:

Click OK to close the dialog.

Program Input

Stop the solving process OK



3

End of back EMF computation

Close the solver

Select File, Exit from the menu to close the solver.

Program Input

File

Exit




3

Results from the Back EMF computation

To see your results, in the Flux Supervisor, in the Analysis folder, double click Results.

Program Input



Results from the Back EMF computation 203

3

Starting Results analysis (PostPro_2D)

Select the problem to analyze and click Open:

Program Input


File name: BEMF.TRA [your name]

Open


Results from the Back EMF computation204

3

Choosing the problem to analyze with PostPro_2D

PostPro_2D opens:

Display the back EMF in R4 (the voltmeter)

Display a time variation curve of the back EMF or line to line no load voltage through the R4

resistor (the voltmeter).

Open the 2D curves manager with the button or choose Computation, 2D Curves

manager… from the menu:



3

Opening PostPro_2D

Program Input

Computation

2D curves manager…

The 2D curves manager opens.



3

2D curves manager: Settings for time variation curve of back emf in R4

Enter the data for the curve as follows:

Program Input

Curve description

Name VoltRes4


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Circuit

Components Voltage

Third data

Support R4

click




3

The voltage curve for the voltmeter (R4) is shown below:

To read specific values from the curve, in the 2D Curves menu, select New cursor….

Program Input

2D Curves

New cursor…

Then position the cursor as you wish. For instance, in the previous figure, the cursor is at X =

30.788E-3 s with a voltage value of Y = 3.379 Volts.

Display a spectrum of the back EMF in R4

To display a spectrum analysis of the voltage curve for R4, open the 2D Spectrum manager by

clicking the button or by choosing Computation, 2D spectrum manager… from the menu.



3

Time variation circuit display of voltage in R4

Program Input

Computation


The Spectrum manager opens, as shown in the following figure:



3

Settings for spectrum analysis of voltage curve for R4

Enter or verify the information as follows:

Program Input

Analyzed curve VoltRes4 [name of curve]

Between 1.25E-3

and 61.25E-3

Part of cycle described Full cycle [select]

Create this original curve [check to enable display of

voltage curve]

Spectrum

Harmonics number 30


Display the DC component line [check if desired]

Name SpectrVoltRes4


click

Clicking the button creates and displays the spectrum and the voltage curve at the same

time.



3

The spectrum and the voltage curve are shown below:



3

Time variation spectrum of voltage for R4

You can look at the back EMF or the line to line no load voltage through other components also.

Below, for example, is the voltage curve for Resis1:



3

Time variation voltage display for Resis1

Voltage and current in coil B_MC (MC)

You can also examine waveforms of electric quantities in any of the circuit components. For

example, the following figure shows both the voltage and current in coil B_MC (MC).

This concludes our analysis of the back EMF. We encourage you to explore other results in

PostPro_2D on your own.



3

Voltage and current curves for coil B_MC (MC)


When you finish, click the Save button to save your analysis (including all the curves you

have created).

Program Input

click

Close PostPro_2D by selecting File, Exit from the menu:

Program Input

File

Exit




3

Square wave motor: Constantspeed (torque ripples)This chapter shows you how to simulate constant speed operation of the motor at 500

rpm with inverter drives.

Create a 6-step inverter (3 phase bridge) circuit using ELECTRIFLUX



All stator windings: vacuum, external circuit

Airgap: rotating airgap, constant angular velocity of 500 rpm, 2 pole pairs

Wedge, air, shaft regions: vacuum, no source

Stator, rotor regions: nonlinear steel, no source

Magnet: magnet, radial +, no source

Boundary conditions: Accept default boundary conditions

Link the external circuit

Coil regions (PA, MA, MC, PB) to coil components (B_COILA, B_COILB,

B_COILC)

Define coil characteristics

B_COILA: Resistance total value, 10 turns, 0.141 ΩB_COILB, B_COILC: Resistance total value, 20 turns, 0.141 Ω

Define voltage source: Constant time variation, 24 volts

Define the switches: User define, Time, 3 coefficients

Coefficients for SWC1: 15, 75, 180






215

Chapter 4

Solve at constant speed

Select custom release (brushlike_921)

Solve, Direct

New computation

Initialized by static computation

Initial value of the time step 0.00125s



Store 1 on 1 time step

Initial rotor position 0


Isovalues (equi flux) lines at time step 1, 0.00125 s

Color shade plot on stator, rotor, magnet regions group

Analysis of quantities along a path through the air gap

Normal component of flux density

Tangential component of flux density

Spectrum analysis of normal component curve

Time variation of axis torque over one cycle

Waveforms of electric quantities

Voltage and current in voltage source

Current through Switch1

Current through B_COILA coil

Current through B_COILB coil

Current through B_COILC coil


216

Square wave motor: Constant speed (torque ripples)

For the square wave motor, you model a 3-phase bridge circuit (the freewheeling diodes are

neglected). Constant speed operation of the motor at 500 rpm with inverter drives is simulated

to yield motor torque ripples. The inverter switching scheme is rotor position dependent and is

modeled with switches that are controlled by the Flux2D user version "brushlike_921."

217

Chapter 4

Create the 3-phase bridge circuit

The following figure shows the complete circuit.

Chapter Square wave motor: Constant speed (torque ripples)

Create the 3-phase bridge circuit218

4

3-phase bridge circuit

Start ELECTRIFLUX

To start the circuit module, in the Construction folder, double click Circuit.

Program Input

Double click Circuit

Square wave motor: Constant speed (torque ripples) Chapter

Create the 3-phase bridge circuit 219

4

Starting the Circuit module (ELECTRIFLUX)

ELECTRIFLUX opens:



4

ELECTRIFLUX (Circuit) window

Create a new circuit problem

First, open a new circuit problem, either with the toolbar icon or the menu.


Click the icon in the toolbar.

Program Input

click

Using the menu

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

Program Input

File

New



4

New (blank) Circuit and Sheet windows open.

For a review of ELECTRIFLUX icons and menus, see page 109.



4

New Circuit and Sheet windows open

Change the size of the sheet

Before you proceed, if you wish, you can modify the size of the Sheet window.

Right click anywhere on the sheet to open the context menu and choose Sheet settings….

Program Input


Sheet settings…



4

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

The Sheet properties dialog opens.


Program Input

Sheet properties (Sheet_1)

Comment 6-step inverter, 3-phase bridge

Squaring gap (pixels) 10

Line Width 1

Background color [white]

Line color [blue]

Selected line color [red]

Sheet Width 800

Sheet Height 600

Ok

When you click OK, the dialog closes. Adjust the sheet window to show the new size.



4

Modifying the sheet properties

Now you are ready to begin placing the circuit components on the sheet. The following figure

shows all the components for the inverter circuit.



4

Inverter circuit components placed on circuit sheet

Add the 6 switches

First, add the 6 switches to the circuit sheet.

To add the switches, click Switch in the Components library.

Program Input

click Switch



4

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



4

Ready to place first switch component

Place the 6 switches on the sheet

Move your cursor over the switch symbol, but do not click on the symbol yet. Move the symbol

with the mouse until the switch is in the position shown in the following figure.

Then click to place the switch in that position (the switch symbol turns blue).

Program Input

click to place switch S1 atupper left of circuit sheet



4

Moving Switch 1 into position

The following figure shows Switch 1 in position.



4

Switch 1 in place

Move the cursor again and you will see Switch 2, as shown in the following figure.

Place switch S2 below and to the right of S1.

Program Input

click to place switch S2 belowand to the right of S1



4

Moving Switch 2 into position

Place the remaining 4 switches as shown (slightly enlarged) in the following figure.

Program Input

click to place switch S3 to the right of S1

click to place switch S4 belowS1

click to place switch S5 to the right of S3

click to place switch S6 belowS3



4

6 switches in place

After you have placed Switch 6, drag the cursor off the sheet to stop adding switch components.

The cursor takes the shape of an arrow.

Program Input

drag cursor off the circuitsheet



4

To stop adding switch components

Rotate the 6 switches

Now rotate each of the switches so that they are in the proper orientation. For each switch,

complete the two steps below:

1. Click Switch 1 to select it. The switch symbol turns red.

2. Then click the icon once.

Proceed as follows:

Program Input

click S1 symbol

S1 turns red

click once

S1 rotates 90° clockwise



4

To rotate Switch 1

The S1 symbol appears as shown (enlarged) here:

Notice that the "hot point" (the small square symbol) is at the upper right of the switch symbol.

This is the correct orientation for all 6 switches.

Follow the same procedure to rotate the remaining switches:

1. Select the switch (the symbol turns red).

2. Click the icon once (the symbol turns 90° clockwise).

Proceed as follows:

Program Input

click S3 symbol

S3 turns red

click once


click S5 symbol

S5 turns red

click once


click S4 symbol



4

Program Input

S4 turns red

click once


click S6 symbol

S6 turns red

click once


click S2 symbol

S2 turns red

click once




4

After you finish rotating the switches, your display should resemble the following figure:

Add the 6 series voltages

To model the commutation behavior of the switches, add 6 series voltages. A voltage source is

placed underneath each of the six switches, as shown in the following figure.



4

Six series voltages (placed under each switch)

Switches rotated

To add the first series voltage, click Voltage source in the Components library.

Program Input

click Voltage source

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



4

Ready to place the first series voltage

Place the 6 series voltages on the sheet

Move the symbol directly underneath the first switch, and click to place the voltage source

symbol:

Program Input

click to place V1 below S1



4

First series voltage in position

Move the cursor and place the 5 other series voltages, as shown in the following figure:

Program Input







When you have placed the last series voltage, drag the cursor off the sheet to stop adding voltages

for now.



4

Series voltages in position

Rotate the series voltages

Now rotate the series voltages. As you did for the switches, click the symbol to select it; the

symbol turns red; then click the icon once to rotate the symbol 90° clockwise.

Proceed as follows.

Program Input

click V1 symbol

V1 turns red

click once

V1 rotates 90° clockwise

The following figure shows V1 in the correct orientation.



4

Series voltage VS1 rotated

Rotate each series voltage 90° clockwise.

Program Input

click V3 symbol

click once

click V5 symbol

click once

click V4 symbol

click once

click V6 symbol

click once

click V2 symbol

click once



4

The following figure shows the series voltages in the proper orientation.



4

Six series voltages rotated

Add the main voltage source

Now add the main DC voltage source.

Click Voltage source in the Components library.

Program Input

click Voltage source

The red voltage source symbol is displayed in the upper left corner of the sheet, as before.



4

Place the main voltage source

Move the cursor and place the main voltage source to the left of the first switch, as shown in the

following figure.

Program Input

click to place V7 to the leftof S1


To stop adding voltage components, drag your cursor off the sheet.



4

Placing main voltage source (VS7) on the sheet

Rotate the main voltage source

Now rotate the main voltage source, as before.

Proceed as follows:

Program Input

click V7 symbol

V7 turns red

click once

V7 rotates 90° clockwise

The main voltage source V7 is correctly oriented in the following figure.



4

Main voltage source rotated

Add the 3 coils

Next, add 3 coils for the stator windings.

Click Coil conductor in the Components library.

Program Input

click Coil conductor



4

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



4

Ready to place the first coil component

Place the 3 coil components on the sheet

Move the coil component symbol to a position underneath and to the right of series voltage V4:

Program Input

click to place B1 below and tothe right of V4



4

Coil 1 (B1) placed on the sheet

Move the cursor to place the other 2 coils, as shown in the following figure.

Program Input

click to place B2 below andright of V6

click to place B3 below andright of V2


To stop adding coil components, drag the cursor off the sheet.



4

Three coils placed on sheet

Rotate the coil components

Now rotate the coil components. Each coil must be rotated 90 degrees; you will need to click the

Rotate icon once for the proper rotation, as shown in the following figure. Notice that the "hot

point" symbol is at the upper right of the coil.

Proceed as follows:

Program Input

click B1 symbol

B1 turns red

click once


click B2 symbol

B2 turns red

click once


click B3 symbol

B3 turns red



4

Program Input

click once


With the three coils properly oriented, your sheet should resemble the following figure:



4

Coils oriented (after rotation)

Add the inductors

Now add inductors to model the stator winding end turn inductances.

Click Inductor in the Components library.

Program Input

click Inductor



4

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



4

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.

Program Input

click to place L1 under coil B1




To stop adding inductors, drag the cursor off the sheet.



4

Placing 3rd inductor (L3) on the sheet

With the inductors added, your display should resemble the following figure:



4

Inductors placed on circuit sheet

Rotate the 3 inductors

Now rotate the 3 inductors for proper orientation.

Proceed as follows:

Program Input

click L1 symbol

L1 turns red

click once


click L2 symbol

L2 turns red

click once


click L3 symbol

L3 turns red

click once




4

With the inductors properly oriented, the lower part of your sheet should resemble the following

figure.

Add the voltmeter

Next, add a large resistor between V3 and V5. This resistor acts as a voltmeter to measure the

line to line voltage. The following figure shows the location for the resistor.



4

Resistor R1 (voltmeter) being placed on the sheet

Inductors oriented

To add the resistor, click Resistor in the Components library.

Program Input

click Resistor



4

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

Move the cursor over the resistor symbol and then place the symbol on the sheet, as shown in

the following figure.



4

Resistor R1 being placed on the sheet

Ready to place resistor on the sheet

Proceed as follows:

Program Input

click to place R1 between V3and V5


Drag the cursor off the sheet to stop adding resistors.

Save your circuit

Now is a good time to save your circuit. Click the icon or choose File, Save from the menu.

Program Input

File

Save



4



Program Input

Save in Brushless_V9 [working directory]

File name squarewave [or your name]

Save



4

Saving the circuit file

Connect (wire) the circuit components

Now connect the circuit components.

Place your cursor over the top pin of the main voltage source, V7, until the cursor changes to a

bull's-eye shape.

Program Input

position cursor over top pin of voltage source V7

Drag the cursor over to the top pin of switch S1 and click to complete the first connection.



4

Ready to start wiring the circuit

Program Input

click pin at top of S1 tocomplete the connection

Connect the remaining components as shown in the following figures.

The switches, series voltages, and voltmeter are connected as shown in the following figure.



4

Connections for upper part of circuit

The coils and inductors are connected as shown below.



4

Connections for lower part of circuit

The following figure shows the connections for the whole circuit:



4

Circuit connections completed

Define the circuit

The components that must be defined are the switches, the resistor, and the inductors.

According to the design sheet, the value of the end turn inductance per phase is 0.031 mH/phase.

Even though we are modeling only ¼ of the motor, we can define the components to their full

value and Flux will internally scale them to the correct value.

Define only the voltmeter (the resistor), the inductors, and the on/off resistance values for the

switches now. (These characteristics can also be defined or modified during the physical

properties definition. You will use the Preflu module to complete the definition of the circuit in

the next section.)

Define the on/off resistance values for the switches

Begin by defining the on/off resistance values for the switches.

Double click S1, the symbol for Switch 1.

Program Input

Double click S1

The symbol turns red, and the following dialog opens.



4

Defining on/off resistance for Switch 1 (S1)

If you wish, you can edit the name of the switch and add a description in the Comment field.

F The name of any switch must begin with a capital S. The initial letter of any

component name cannot be changed.

In the dialog, enter or verify the following:

Program Input

Switch

Name S1

Ron(ohm)

Value 1e-4

Roff(ohm)

Value 10000

Ok

When you choose Ok, the dialog closes.

F The default Roff value is 10000 Ω; you do not need to re-enter this value. You

should verify it, however.

Define Ron and Roff for the remaining switches as follows:

Program Input

Double click S2

1e-4

10000

Ok



4

Program Input

Double click S3

1e-4

10000

Ok

Double click S4

1e-4

10000

Ok

Double click S5

1e-4

10000

Ok



4

Program Input

Double click S6

1e-4

10000

Ok

Define the inductors

In the same way, define the inductors. Double click L1, the symbol for the first inductor.

Program Input

Double click L1

The symbol turns red, and the Inductor dialog opens.



4

Defining inductance value for the first inductor (L1)

In the Inductor dialog, enter or verify the following:

Program Input

Name L1

Characteristics

Name L(henry)

Value 3.1e-5

Ok

Define the other inductors as follows:

Program Input

Double click L2

3.1e-5

Ok

Double click L3

3.1e-5

Ok



4

Define the voltmeter (R1)

Finally, define the voltmeter, the resistor R1. Double click the R1 symbol.

Program Input

Double click R1

The resistor symbol turns red, and the Resistor dialog opens.

In the Resistor dialog, enter or verify the following:

Program Input

Name R1

Comment voltmeter

Characteristics

Name R(ohm)

Value 1e5

Ok

When you click Ok, the dialog closes.



4

Defining the voltmeter (resistor R1)

Rename the coils

The coils can be named to reflect their use in the motor. Any name can be used for the coils as

long as the name starts with a "B". Rename the coils by editing each one (double clicking),

similar to the way the resistors and inductors were changed.

Program Input

Double click B1

B_COILA

Ok

Double click B2

B_COILB

Ok

Double click B3

B_COILC

Ok



4

Analyze the circuit

Analyze the circuit to check its connections and to create the *.CIF file to be used for

simulation.

Choose Circuit, Analyse from the menu.

Program Input

Circuit

Analyse



4

The following dialog opens with a report of the analysis.

Click Exit to close the dialog.

Program Input

The circuit is connexe. Exit



4

Analysis of the circuit

Save and close the circuit file

The circuit and transmission files are now complete. Save the circuit by clicking the icon or

choosing File, Save from the menu.

Program Input

File

Save

Close the circuit by choosing File, Close.

Program Input

File

Close



4


Click Yes to confirm the close of the circuit:

Program Input

Close circuit? Yes

Close ELECTRIFLUX

Finally, close ELECTRIFLUX by choosing File, Exit.

Program Input

File

Exit




4

Confirmation to close circuit

Assign the physical properties




Start Preflu 9.1



Assign the physical properties 277

4

Starting the Preflu module

Program Input



Open the Back EMF problem

This constant speed model is similar to the model generated in the previous chapter to study

back EMF. The geometry, materials and mechanical sets are the same; just the drive circuit is

different. It will be easiest to start with the back EMF model to create this new model of a

constant speed brushless motor.



Assign the physical properties278

4

Preflu 9.1 screen



Program Input

click

Using the menu


Program Input

Project

Open project



4



Program Input


File Name bemf.flu [your name]

Open



4

Opening the Back EMF project

The geometry of the Back EMF model (1 layer airgap) is displayed:


Save your project now with a specific name to indicate that you will be using this model for

constant speed analysis.




4

Back EMF project is opened

Program Input

Project

Save As…



Program Input


File Name: constspeed [your name]

Save



4

Saving the bemf model as constspeed

Change the coupled circuit

The constant speed model is identical to the Back EMF model except for the circuit coupled to

the geometry. To create this model, you need to delete the current circuit, import the new

circuit, and assign the new circuit to regions in the model.

Delete the existing circuit

To delete the circuit currently coupled to the problem (onedelta.ccs), choose Physics, Circuit,

Delete electrical circuit from the menu.

Program Input

Physics

Circuit

Delete electrical circuit

A confirmation dialog appears. Click OK to delete the circuit.

Program Input

Delete electrical circuit? OK



4

Confirmation to delete the circuit

Change to the Physics Context

The Physics commands are available only in the Physics context. At the top of the data Tree,

click the button to change to the Physics context.

Program Input

Click

Import the Squarewave Circuit

To import the circuit we created, click the icon on the toolbar.

Program Input

Click

If you prefer, choose Physics, Circuit, Import circuit from a CCS file from the menu:

Program Input

Physics

Circuit

Import circuit from a CCS file



4

The Import circuit dialog appears. Click on the browse file selector in the dialog box.

Program Input

Click

The Open circuit dialog appears.


Program Input

Look In: Brushless_V9 [your workingdirectory]

File Name: squarewave.ccs [your name]

Open



4

Selecting the squarewave circuit to import

The circuit file name is transferred to the Import Circuit dialog box.

Proceed as follows:

Program Input

Click OK

The squarewave circuit appears. Your display should resemble the following:



4

The constspeed problem after importing the squarewave circuit

Selected circuit ready for import

Assign face regions to the circuit

Assign the stator windings

Each winding region (PA, MA, MC, PB) must be linked to a coil conductor (B_COILA,

B_COILB, B_COILC) in the circuit you created. Each region will be changed individually.

Edit the PA region

Expand the Face Regions in the Data tree (under Physics, Regions). Select the PA region and

right-click the mouse to select Edit.

Proceed as follows:

Program Input

Click PA

Right-click, Edit




4


Program Input


Material of the region <verify selection is blank>



10

Coil conductor region component B_COILA


OK

Edit the MA region

Similarly, select the MA region for editing (right-click on MA in the data Tree, select Edit)



4

Enter or verify the following. Note that the MA ("minus A") region uses the same coil conductor

(B_COILA) as the PA region, but the orientation of the current is set to Negative:

Program Input



Negative orientation of thecurrent


10

Coil conductor region component B_COILA


OK

Edit the PB region

Now, select the PB region for editing (right-click on PB in the data Tree, select Edit).



4


Program Input





20

Coil conductor region component B_COILB


OK

Edit the MC region

Now, select the MC region for editing (right-click on MC in the data Tree, select Edit).



4

Enter or verify the following. Note that the current orientation needs to be set to Negative, since

the orientation of all the coil conductors are the same in relation to the voltage sources in the

circuit.

Program Input



Negative orientation of thecurrent


20

Coil conductor region component B_COILC


OK

Define the coil resistance

According to the design sheet, the stator winding characteristics are 10 turns with a resistance

per phase value of 0.141Ω/phase. Since the B_COILA, B_COILB and B_COILC coils are the

same, we will use the Edit Array command to set the resistances to all coils at once.

Expand the data tree to display the coil conductors (under the Electric Circuit, then under FE

Coupling Components, then under the Stranded Coil Conductor). Select the B_COILA,

B_COILB and B_COILC coils using the mouse and Shift key.



4

Proceed as follows:

Program Input

Click B_COILA

Click B_COILC + Shift


The Edit Stranded Coil dialog appears. In the Modify All column, enter the resistance.

Proceed as follows:

Program Input


OK



4

Setting the resistance of all the coils

Define the Voltage Sources

Define the Main Voltage Source

The design value for the power supply is 24 volts. Expand the data tree to display the voltage

sources (under the Electric Circuit, then under the Voltage/current sources). Select the voltage

source, V7, from the data tree to set this voltage.

Proceed as follows:

Program Input

Click V7

Right click, Edit

The Edit voltage source dialog appears.



4

Changing the power supply voltage to 24v.

Proceed as follows:

Program Input

Value 24

OK

Define the Series Voltage Sources

The design value for the series voltages is 3.2 volts. Since they are all the same, we will use the

Edit Array command to set all voltage sources at once.

Select the V1 to V6 voltage sources using the mouse and Shift key.

Proceed as follows:

Program Input

Click V1

Click V6 + Shift


The Edit Voltage Source dialog appears. In the Modify All column, enter the voltage.



4

Setting all series voltages supplies

Proceed as follows:

Program Input

Modify all - RMS_MODULUS 3.2

OK

Define the switches

Next, define the switches. They are on or off depending on the rotor position.

The switches are time dependent and are defined with 3 coefficients:

1. Coefficient 1: ON angle in mechanical degrees

2. Coefficient 2: OFF angle in mechanical degrees

3. Coefficient 3: switch’s cycle in mechanical degrees

Expand the data tree to display the switches (under the Electric Circuit, then under the

Switches/semiconductors). Select switch S1 from the tree to set the switch timing.

Proceed as follows:

Program Input

Click S1

Right click, Edit



4

The Edit switch dialog appears. To access the switch timing, click on the Turn On Command

tab.

Proceed as follows:

Program Input

Click Turn on command

Now change the switch timing using the format shown. Again, the first coefficient is the ON

angle in mechanical degrees, the second coefficient is the OFF angle, and the third coefficient is

the switch's cycle in degrees.



4

Setting the timing for switch S1

Clicking the tab to go set the switch timing.

Proceed as follows:

Program Input

Command by formula

Expression USER(15,75,180)

OK

The other 5 switches can be defined similarly. The table below shows the characteristics for all 6

switches. You have already entered the characteristics for Switch 1, so that row is crosshatched.

Switch characteristics for user version brushlike_921

SW

No.

ON Angle OFF Angle Switch Cycle

1 15 75 180

2 45 105 180

3 75 135 180

4 105 165 180

5 135 15 180

6 165 45 180





Program Input

Click



4


Close and save the model

The model is ready for solving. Close the Preflu application. Select Project, Exit from the menu.

Program Input

Project

Exit


Proceed as follows:

Program Input





4

Solve with user version

You are now ready to solve the constant speed problem. Because this problem includes saturation

and inductances and is voltage based, numerical transients may occur before the steady state is

reached. Thus the problem will be solved using Flux's ability to automatically come to a steady

state at the start.

Select the user version

The switches of the external circuit are rotor position dependent and are controlled by the

Flux2D user version "brushlike_921."

To select the user version, choose Versions, brushlike_921 from the menu.

Program Input

Versions

brushlike_921


Solve with user version 299

4

You should see "Flux2D: brushlike_921" at the top of the Program manager, as shown in the

following figure:

F Make sure the appropriate user version (brushlike_921) is selected before you

start the solver.


Solve with user version300

4

Flux2D custom version (brushlike_921)

Start the solver

To start the solver, in the Solving process folder, double click Direct:

Program Input

Double click Direct



4

Starting the solver with a user version (includes user subroutine)

In the Open dialog, select the problem to be solved and click Open:

Program Input


File name: CONSTSPEED.TRA

Open



4


Verify the solving options

In the Solver window, click the Options tab to bring it to the front:

Enter or verify the options as follows:

Program Input

click Options tab

Magnetic, Electric iterations

Number of iterations 50

Requested precision 1.e-004

Thermal iterations


Required precision 1.e-004



4

Checking the solving options

Program Input

Magnetic updatings to coupledproblem

Minimal number of updatings 1

Maximal number of updatings 5


Progressive Newton Raphsonalgorithm

Disabled

Be sure that the Newton-Raphson algorithm is “Disabled,” as shown in the figure below:

Enter or verify the accuracy, solver type and priority for the computation, and click Apply to

apply the solving options.

Program Input

Accuracy definition Automatic accuracy

Solver type SuperLU (9.20)

Priority associated to thecomputation

Priority normal

Apply



4

Start the computation

Click the Solve button to begin the computation.

Program Input

click

The Definition of time data dialog opens, as shown in the following figure:



4

Definition of time data

Enter or verify the following information. Solve the problem with a time step that is 4 time steps

per slot pitch (1 time step every 3.75 degrees) over one electric cycle (180 mechanical degrees).

The resulting time step is 0.00125 seconds

Program Input


initialised by staticcomputation

Time values


0.00125




one step on 1

OK


Before the computation begins, the following dialog opens:

Do not change the initial position of the rotor. Click OK to close this dialog and watch as the

solution proceeds.



4

Verifying the initial position of the rotor (0)

Program Input


0. degrees

OK

When the computation is finished, the following dialog opens:


Program Input


Close the solver

Then close the solver by selecting File, Exit from the menu:



4

End of computation

Program Input

File

Exit




4

Results: Constant speed computation

In the Flux Supervisor, make sure the brushlike_921 version is still selected; otherwise, you will

not be able to proceed.

In the Supervisor, in the Analysis folder, double click Results.

Program Input



Results: Constant speed computation 309

4

Starting Results analysis from the Supervisor with user version (brushlike_921)

In the Open dialog, choose the problem to be analyzed and click open:

Program Input


File name: CONSTSPEED.TRA

Open


Results: Constant speed computation310

4

Choosing the problem to analyze

PostPro_2D opens with a display of the model geometry at the first time step (0.00125 s):



4

Constant speed problem ready for analysis in PostPro_2D

Display isovalues (equiflux) lines

Begin with an isovalues (equiflux) plot on the model geometry at time step 1 (0.00125 s).

Set the properties for the display

Open Results, Properties by clicking the icon or by choosing Results, Properties from the

menu:

Program Input

Results

Properties



4

The Display properties dialog opens, as shown in the following figure:

Make sure the Isovalues tab is on top. Then enter or verify the following settings:

Program Input

Isovalues




Quality Normal

Number 21

Scaling Uniform



4

Properties dialog for equiflux lines (Isovalues) display

Program Input

Display characteristics

Write numbers [check to enable, if desired]

OK

When you click OK, the properties dialog closes.


To display the plot, click the Isovalues button in the toolbar, or choose Results, Isovalues

from the menu.

Program Input

Results

Isovalues



4

The isovalues plot is shown below:

If you wish, you can change the display of the isovalues plot.

Right click anywhere on the sheet and choose Properties from the context menu:



4

Display of flux density lines at time step 0.00125

Program Input

Right click on isovalues sheet

Properties

The Geometry properties dialog opens:

For instance, to remove the legend from the sheet, click the Sheet tab to bring it to the front,

clear the “With legend” checkbox, and click OK to close the dialog.



4

Removing the legend from the isovalues display

You should then see the isovalues plot as shown in the following figure:

You can adjust the displays in many other ways. Remember to right click on the sheet to open

the properties dialog.



4

Isovalues plot

Color shade plot on a group of regions

Next, display a color shade plot for only the stator, rotor, and magnet regions.

Create the group of regions

Create a group of these three regions with the Group manager. Open the Group manager dialog

by clicking the button or by choosing Supports, Group manager from the menu:

Program Input

Supports

Group manager

The Group manager dialog opens:

Enter or verify the information in the Group manager as follows:

Program Input

Filter Region

Objects available ROTOR

MAGNET

STATOR



4

Group manager dialog

Program Input

Add ->

Current group: ROTOR

MAGNET

STATOR


Create

Click the Create button to create the group and close the Group manager dialog.

Set the properties for the display

Now use the group for the display of the color shade plot. Open the Results, Properties dialog

again by clicking the button or by choosing Results, Properties from the menu.

Program Input

Results

Properties



4


Click the Color shade tab to bring it to the front. Then enter or verify the information as

follows:

Program Input


Analyzed quantity |Flux density|

Support Big3 [group name]


Quality Normal

Scaling Uniform

OK



4

Properties for color shade display

When you click OK, the Display properties dialog closes.

Display the color shade plot

To display the plot, click the color shade button in the toolbar or choose Results, Colour

shade from the menu.

Program Input

Results

Colour shade



4

You will see the color shade plot on your group of regions:

The saturation values are not high (maximum of 1.5 T). These results are in the linear part of the

B-H curve, as can be seen during the solving process, where each time step requires only 2

Newton-Raphson iterations to achieve convergence—at an accuracy level of 1e-4.



4

Color shade plot of flux density on a group of regions

Information about the iterations for each time step is available under the *log_res file tab at the

bottom of the PostPro_2D screen.

Create a path through the airgap

To create a path through the center of the airgap, open the Path manager.

Click the Path manager icon or choose Supports, Path manager… from the menu:

Program Input

Supports

Path manager…



4

Information about solving at time 0.055 s, Computation 44

The Path manager dialog opens.

You will be creating an arc 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 appears in the shape of a drawing compass (when Arc is selected, as shown in the

figure above).



4

Path manager

Click the button and drag the cursor to enlarge the bottom of the airgap between the air and

the stator regions. Then position the cursor to see the coordinates (we used X=25.4).

Then in the Path manager dialog, enter or verify the information as follows:

Program Input

Name CenterGap [or your choice]

Discretization 200

[default color] [new color if desired]

Graphic section Arc

Numerical section New section



4

Checking coordinates for path through airgap

When you click the New section button, the Section Editing dialog opens.

In the Section Editing dialog, enter or verify the information as follows:

Program Input

Section type Arc start angle

Center point

X

Y

0

0

Origin point

X

Y

25.4

0

Length 180

OK



4

Section Editing dialog to create path

Click OK to close the Section Editing dialog. The path to be drawn through the airgap is

displayed:

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



4

Path through the airgap (enlarged)

Flux density along the airgap path

The 2D curves manager is shown in the following figure.

Flux density: Normal component

First, create a curve of the normal component of the flux density along the airgap path at the first

time step. Enter or verify the following:

Program Input

Curve description

Name FDNorm


Path

First axis

X axis CenterGap [path name]

Second axis



4

Settings for flux density curve (normal component)

Program Input


Components Normal component

Third axis

Parameter Time

Parameter values 0.00125

Selection step 1

Create

Click the Create button to create the curve of the normal component of the flux density. You

will not see the curve displayed, but you should see the name listed at the bottom of the 2D

Curves manager.

Flux density: Tangential component

Now create a similar curve for the tangential component of the flux density. The 2D Curves

manager should show a new default name for the curve and a new color. You should be able to

enter a new name (and color, if you wish), change the component, and create the second curve.

For the tangential component curve, enter or verify the information as follows:

Program Input

Curve description

Name FDTang


Path

First axis

X axis CenterGap [path name]



4

Normal component curve created

Program Input

Second axis


Components Tangent component

Third axis

Parameter Time

Parameter values 0.00125

Selection step 1

Create

When you click the Create button, the tangential component curve is added to the list, but you

will not see the curves yet.

Superimpose the normal and tangential flux density curves

To create a superimposed display of these two curves, proceed as follows:

Click the icon to open a blank curves sheet.

Program Input

click

Then right click anywhere on the blank curve sheet, and open the properties dialog.

Program Input

click


Properties



4

In the properties dialog, make sure the Selection tab is on top.

Enter or verify the following in the Selection dialog:

Program Input

Curves filter Computation

Curves available FDNorm

FDTang

Add -->

Displayed curves FDNorm

FDTang



4

Curves properties Select dialog; choose curves to display

Click the Display tab to bring it to the front.

Enter or verify the following information in the Display dialog:

Program Input

click Display tab

Display Superimposed

Gradations ON

X Axis

Range Automatic

Scale linear

Y Axis

Range Automatic



4

Settings for superimposed curves display

Program Input

Scale linear

OK

The two curves superimposed are shown below.

If you wish, display a cursor by choosing 2D curves, New cursor… from the menu.

Program Input

2D Curves

New cursor…



4

Superimposed curves of normal and tangential flux density (with cursor)

Spectrum analysis

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

density. Proceed as follows:

Click the button or choose Computation, 2D Spectrum manager… from the menu.

Program Input

Computation


The Spectrum manager opens.



4

Spectrum manager

Enter or verify the following for the spectrum analysis:

Program Input

Analyzed curve FDNorm

Between 0

and 79.79644

Part of cycle described Full cycle

Create this original curve [check box to enable display of normal component curve]

Spectrum

Harmonics number 30


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

Name SpectFDNorm [or other name]


click

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



4

The spectrum and the normal component curve 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



4

Spectrum analysis of normal component of flux density

The Curves properties dialog opens.

In the properties dialog, you can change, for example, the legend text, the form of the curve, the

line width and color. Make the settings you wish (our previous figure uses a line width of 3; the

default line width is 1). Click OK to apply your changes and close the dialog.



4

Sample of settings for spectrum display

Time variation curve of axis torque

Finally, display a curve of the axis torque of the motor over the whole cycle.

Open the 2D curves manager with the button or choose Computation, 2D curves

manager… from the menu.

Program Input

Computation


The 2D Curves manager opens.



4

Settings for AxisTorque curve


Program Input

Curve description

Name AxisTorque


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Mechanics

Components Axis torque

Third data

click

Clicking the button creates and displays the curve.



4

The axis torque curve is shown below:

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

Program Input

2D Curves

New cursor…

Position the cursor as you wish. For instance, in the figure above, the cursor is at X = 0.026 s,

and the axis torque value (Y) is 623.105 N.m.



4

Axis torque over one cycle

You can record the values from the curve in various ways. For example, from the 2D Curves

menu, choose Analysis, Write all mean values:

Program Input

2D Curves

Analysis

Write all mean values

The mean values are written into the “Review file” tab at the bottom of the window.

The average torque is given for all 1 pole (0.694 N.m.). The design value is 0.585 N.m.



4

Mean values from axis torque curve

Waveforms of the electric quantities

Next, look at curves of electric quantities. Use the 2D Curves manager, as before. Open the

curves manager by clicking the button or by choosing Computation, 2D curves manager…

from the menu.

Program Input

Computation





4

Settings for curve of voltage in the main voltage source (V7)

Voltage and current in the main voltage source (V7)

To create a curve of the voltage in the main voltage source (V7), enter or verify the settings as

follows:

Program Input

Curve description

Name V7Voltage


Parameter

First axis

X axis Time


Second axis

Quantity Circuit

Components Voltage

Third data

Support V7

Create

Click the Create button to create the curve. (The curve will not be displayed.)

In the same way, create a curve of the current in the voltage source. The 2D Curves manager

should still be open. You should be able to change only the name, the color (if you wish) and the

component to create the V7 current curve.


Program Input

Curve description

Name V7Current


Parameter

First axis



4

Program Input

X axis Time


Second axis

Quantity Circuit

Components Current

Third data

Support V7

Create

Click the Create button to create the time variation curve of the current in the voltage source.

(Remember, the curve will not be displayed.)

Close the 2D curves manager with the button.

Program Input

2d curves managerclick



4

Superimpose the V7 voltage and current curves for a display like the following (we used the

"Automatic" setting for the Y axis):

Current in Switch1

Now create a curve of the current through Switch1.

Click the button to open the 2D curves manager.

Program Input

click



4

Voltage and current in the voltage source


Program Input

Curve description

Name CurrSW1


Parameter

First axis

X axis Time


Second axis

Quantity Circuit

Components Current

Third data

Support S1

click



4

The curve of the current for Switch 1 is shown below.



4

Current in Switch 1

Current in the B_COILA (PA) coil component

Next, create and display a curve for the current in the B_COILA (PA) component. Click the

button to open the 2D curves manager.

Program Input

click


Program Input

Curve description

Name CurrB1(PA)


Parameter

First axis

X axis Time


Second axis

Quantity Circuit

Components Current

Third data

Support B_COILA

click



4

The curve of the current in the B_COILA coil component is shown below:



4

Current in coil component B_COILA (PA, positive phase A)

Current in the B_COILB (PB) coil component

In the same way, create a curve of the current in coil component B_COILB (PB, positive phase

B). Click the button to open the 2D curves manager.

Program Input

click


Program Input

Curve description

Name CurrB2(PB)


Parameter

First axis

X axis Time


Second axis

Quantity Circuit

Components Current

Third data

Support B_COILB

click



4

The curve of the current in coil component B_COILB (PB) is shown in the following figure:



4

Current in coil component B_COILB (PB, positive phase B)

Current in the B_COILC (MC) coil component

Finally, create a curve of the current in coil component B_COILC (MC, minus phase C). Click

the button to open the 2D curves manager.

Program Input

click


Program Input

Curve description

Name CurrB3(MC)


Parameter

First axis

X axis Time


Second axis

Quantity Circuit

Components Current

Third data

Support B_COILC

click



4

The curve of the current in B_COILC (MC) is shown below:



4

Current in coil component B_COILC (MC, negative phase C)


This concludes our analysis of the motor at constant speed.

To save the analysis supports and the curves you have created, click the icon or choose File,

Save from the menu.

Program Input

File

Save


Save and close PostPro_2D354

4

Then close PostPro_2D by choosing File, Exit.

Program Input

File

Exit



Save and close PostPro_2D 355

4



4

No load startup withelectromechanical couplingIn this chapter you modify the constant speed problem to simulate the no load startup.

Modify physical properties of constant speed problemAirgap

Rotating airgap

Mechanic values

Moment of inertia: 3.8675e-5

Viscous friction coefficient: 0.005

Keep "squarewave" circuit

Set release to custom (brushlike_921)

Solve, Direct

Time data

New computation

Initial value of time step 5e-4 s



Store 1 on 1

Initial position of the rotor 0

357

Chapter 5


Isovalues (equi flux) lines at time step 100 (time 0.05 s)

Time variation analyses (2D curves)

Axis torque

Angular velocity

Rotor position



Current in Switch1

Current in B_COILA coil component

Voltage and current in B_COILB coil component

Voltage and current in B_COILC coil component


358

No load startup withelectromechanical coupling

With the constant speed problem already defined, you can easily modify the physical properties

to simulate the no load startup.

F If you do not have the constant speed file, you must define all the physical

properties and link the external circuit as described in the previous chapter

(beginning on page 277). The only difference for this problem is in the definition of

the moving mechanical set.

Basically, for each time step, Flux2D computes the electromagnetic torque, solves the mechanical

equation to yield the angular acceleration, speed and displacement, then rotates the rotor and

repeats the process.

Modify the physical properties

Be sure you have the CONSTSPEED.TRA and squarewave.ccs files in your working directory.

To modify the physical properties, use the Preflu 9.1 application.

359

Chapter 5

Start Preflu 9.1


Program Input


Chapter No load startup with electromechanical coupling

Modify the physical properties360

5



Open the Constant Speed problem

This no load model is similar to the model generated in the previous chapter. We simply need to

modify the moving mechanical set.




Program Input

click

No load startup with electromechanical coupling Chapter

Modify the physical properties 361

5

The initial Preflu screen

Using the menu


Program Input

Project

Open Project




5

Opening the Constant Speed project

Program Input


File Name constspeed.flu [your name]

Open

The geometry of the Constant Speed model (1 layer airgap) is displayed.


Save your project now with a specific name to indicate that you will be using this model for no

load analysis.




5

The constspeed project is opened

Program Input

Project

Save As…



Program Input


File Name: noload [your name]

Save



5

Saving the constspeed project as noload

Define the no load characteristics

The no load model is identical to the constant speed model except for the definition of the


Edit the MOVING_ROTOR mechanical set

Expand the Mechanical Set in the Data tree. Select the MOVING_ROTOR mechanical set and


Proceed as follows:

Program Input

Click MOVING_ROTOR

Right-click, Edit



5

The Edit Mechanical Set dialog appears. To enter the no load characteristics, click on the

Kinematics tab at the top.

Proceed as follows:

Program Input

Click Kinematics



5

Going to the Kinematics tab

Change the type of kinematics problem to a "Coupled Load" problem. Then go to enter the

internal characteristics.

Proceed as follows:

Program Input

Type of kinematics Coupled load

Velocity at time t=0s (rpm) 0

Position at time t=0s (deg) 0

Click Internal characteristics



5

Going to the Internal Characteristics tab

Now enter the characteristics needed to do the No Load analysis.


Program Input


Moment of inertia 3.8675e-5


Viscous friction coefficient 0.005

Friction coefficient proport… 0

Click External characteristics

F Note: Since only ¼ of the motor is being modeled, the value you enter for the

moment of inertia is ¼ of the inertia of the entire motor.



5

Entering the No Load Internal Kinematic characteristics

Enter the external kinematic characteristics.


Program Input


Moment of inertia 0




OK





5

Entering the No Load External Kinematic characteristics

Program Input

Project

Exit


Proceed as follows:

Program Input



Verify the user version: brushlike_921

Because the motor has rotor position dependent switches, you must use the brushlike_921

custom version, as you did with the constant speed problem.


Verify the user version: brushlike_921370

5

Be sure you see Flux2D: brushlike_921 at the top of the Program manager.

If you do not, choose Versions, brushlike_921 from the menu.

Program Input

Versions

brushlike_921


Verify the user version: brushlike_921 371

5

Solve the no load startup problem

You are now ready to solve the motor at no load start up.

Choosing a time step

Choose a time step that is also valid at synchronous speed.

For example, if we estimate the synchronous speed to be 500 rpm, a time step of 0.5 ms will

rotate the rotor 6 degrees every time step (the slot pitch is 15 degrees). Therefore, a time step of

0.5 ms is appropriate for this problem.

Start the solver



Solve the no load startup problem372

5

Starting the solver with the brushlike_921 release (user subroutine)

Program Input

Double click Direct

In the Open dialog, select the problem to be solved and click Open:

Program Input


File name: NOLOAD.TRA

Open


Solve the no load startup problem 373

5


In the Solver window, click the Options tab to bring it to the front:

The most important option to check is that the Progressive Newton Raphson algorithm is

disabled, as shown below:

Verify the options as follows:

Program Input

click Options tab

Magnetic, Electric iterations




5

Setting the general solving options

Program Input


Thermal iterations



Magnetic updatings for coupledproblem

Minimal number of updatings 1

Maximal number of updatings 5


Progressive Newton Raphsonalgorithm

Disabled

Accuracy definition Automatic accuracy

Solver type SuperLU (9.20)

Priority associated to thecomputation

Priority normal

Apply

Click Apply to confirm the options.



5

Then click the Solve icon to begin the computation.

Program Input

click




5

Definition of time data for no load startup


Program Input


initialised by staticcomputation

Time values


5e-4




one step on 1

OK

Click OK to close the dialog. Before the computation begins, the following dialog opens:

Do not change the rotor position. Click OK to close the dialog and watch as the computation

proceeds.

Program Input


0. degrees

OK



5

Initial rotor position for rotating air gap


Click OK to close the dialog and stop the computation.

Program Input




5

End of solving (time steps completed)

Close the solver by selecting File, Exit from the menu:

Program Input

File

Exit




5

Results from no load startup

Make sure the Flux2D version is still brushlike_921; otherwise, you will not be able to proceed.

In the Flux Supervisor, in the Analysis folder, double click Results:

Program Input



Results from no load startup380

5

Starting Results analysis with customized release

In the Open dialog, choose the problem to be analyzed and click Open.

Program Input


File name: NOLOAD.TRA

Open


Results from no load startup 381

5

Choosing no load problem to analyze

Display the isovalues (equiflux) lines at time step 100 (t = 0.05 s)

PostPro_2D opens with the model geometry at the first time step, 0.0005 s.

Begin your analysis with a display of the isovalues (equi flux) lines at time step 100, or time =

0.05 s.



5

No load problem open in PostPro_2D

Select the 100th time step (0.05 s)

To select the 100th time step, click the Parameters manager button or choose Parameters,

Manager… from the menu:

Program Input

Parameters

Manager…

The Parameters dialog opens:

From the Values list, choose 0.05, the time at the 100th time step. Then close the Parameters

dialog.

Program Input

Parameters

Values 0.05

click



5

Choosing time step 100 from the Samples number list

You should see the model geometry with the rotor at approximately 256 degrees:



5

Rotor position at time step 100 (0.05 s)

Set the display properties

Set the display for 21 isovalue lines (the default is 11).

Click the Results, Properties icon or choose Results, Properties from the menu.

Program Input

Results

Properties



5

The Display properties dialog opens:

Make sure the Isovalues tab is on top. Then enter or verify the following:

Program Input

Isovalues




Quality Normal

Number 21

Scaling Uniform



5

Settings for display of 21 equiflux lines

Program Input

Display characteristics

Write numbers [check to enable if desired]

OK

Click OK to apply the settings and close the dialog.


To display the plot, click the Isovalues button or choose Results, Isovalues from the menu.

Program Input

Results

Isovalues



5

The isovalues plot at t = 0.05 s is shown below:

If you wish, display this plot on the full geometry. Click the icon in the toolbar or choose

Geometry, Full geometry from the menu.

Program Input

click



5

Isovalues at time step 100 (0.05 s)

The plot on the full geometry is shown below.



5

Isovalues plot on full geometry (t = 0.05 s)

Time variation analysis (2D Curves)

Now look at the time variation results, such as torque, speed, voltages, currents, etc. Look first at

a curve of the axis torque.

Open the 2D Curves manager by clicking the button or by choosing Computation, 2D

Curves manager… from the menu.

Program Input

Computation




5

The 2D curves manager opens:

Axis torque curve

Enter or verify the following to create a curve of the axis torque:

Program Input

Curve description

Name AxisTorque


Parameter

First axis

X axis Time


Selection step 1

Second axis



5

Properties for time variation curve of axis torque

Program Input

Quantity Mechanics


click

Clicking the icon creates and displays the curve.

The axis torque curve is shown below:

F The axis torque shown is the resulting torque from the electromagnetic torque,

friction torque and load torque. At synchronous speed, the average torque is

almost zero. The torque values you see during the solving process are the

electromagnetic torque computed by the virtual work method.



5

Axis torque

Angular velocity curve

Create a curve of the angular velocity next. Open the 2D curves manager again with the

button.

Program Input

click


Program Input

Curve description

Name AngVel


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Mechanics

Component Angular velocity

click



5

The angular velocity curve is shown below:



5

Angular velocity curve

Superimpose the axis torque and angular velocity curves on the same sheet. Use the “Stretched”

option for the Y axis.

Your curves display should resemble the following:



5

Axis torque and angular velocity curves superimposed

Rotor position curve

Look next at a curve of the rotor position. Open the 2D curves manager again with the

button.

Program Input

click


Program Input

Curve description

Name Position


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Mechanics

Components Position

click



5

The curve of the rotor position is shown below:



5

Position curve

Superimpose the position and angular velocity curves (with "Stretched" Y axis) for a display like

the following:



5

Position and angular velocity curves superimposed


Look next at the waveforms of the electric quantities. Click to open the 2D curves manager

again.

Program Input

click




5

To create a curve of the voltage in the main voltage source (V7)

Voltage and current in the main voltage source

To create a curve of the voltage in the main voltage source (V7), enter or verify the following:

Program Input

Curve description

Name VoltV7


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Circuit

Component Voltage

Third data

Support V7

Create

Click the Create button to create this curve. You will not see the curve displayed yet. The 2D

curve manager should remain open, with the new curve added to the list of curves in the Name

field at the bottom.



5

Curves listed in 2D Curves manager

For a curve of the current in the main voltage source, enter or verify the following:

Program Input

Curve description

Name CurrV7


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Circuit

Component Current

Third data

Support V7

Create

Click the Create button to create the current curve. Again, you will not see these curves

displayed yet.



5

Open a new 2D curves sheet and superimpose the V7 voltage and current curves (use the

"Stretched" option for the Y axis):



5

Superimposed display of voltage and current curves for V7 (main voltage source)

Current in Switch1

Now create a curve of the current in Switch1 (S1). Click to open the 2D curves manager.

Program Input

click


Program Input

Curve description

Name CurrS1


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Circuit

Component Current

Third data

Support S1

click



5

The curve of the current in SWITCH1 is shown below:



5

Current in Switch1

Current in the B1 (PA) coil component

Next create a curve of the current in the B1 (PA, positive phase A) coil component. Open the

2D Curves manager with the icon.

Program Input

click


Program Input

Curve description

Name CurrB1-PA


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Circuit

Component Current

Third data

Support B_COILA

click



5

The current curve for coil component B1 (PA) is shown below.



5

Current in B1 (PA) coil component

Voltage and current in the B2 (PB) coil component

Next create curves of the voltage and current in the B2 (PB, positive phase B) coil component.

Click the button to open the 2D Curves manager and

Program Input

click

Enter or verify the following for a curve of the voltage in B2:

Program Input

Curve description

Name VoltB2-PB


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Circuit

Component Voltage

Third data

Support B_COILB

Create

Click the Create button to create the voltage curve for the B2-PB component. Remember, you

will not see the curve displayed yet.

After the curve is created, the 2D Curves manager displays a new default curve name and color.

You should need only to enter a new name (and color, if you wish) for the curve and to select

Current as the Component.



5

Enter or verify the settings for the curve of the current in B2, as shown below.

Program Input

Curve description

Name CurrB2-PB


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Circuit

Component Current

Third data

Support B_COILB

Create

Click the Create button to create the current curve for coil B2. (Remember that the curve will

not be displayed.)



5

Superimpose the B2 voltage and current curves (with "Stretched" Y axis) for a display like the

following:

Voltage and current in B3 (MC) coil component

Next, create and superimpose voltage and current curves for coil component B3 (MC, minus

phase C).

Click to open the 2D curves manager once again.

Program Input

click



5

Superimposed display of voltage and current curves for coil component B2 (PB)

Enter or verify the following for the voltage curve for coil component B3:

Program Input

Curve description

Name VoltB3-MC


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Circuit

Component Voltage

Third data

Support B_COILC

Create

Click Create to create the B3 voltage curve (it will not be displayed yet).

With the 2D curves manager still open, enter or verify the following for the B3 current curve:

Program Input

Curve description

Name CurrB3-MC


Parameter

First axis

X axis Time


Selection step 1



5

Program Input

Second axis

Quantity Circuit

Component Current

Third data

Support B_COILC

Create

Again, click Create to create the B3 current curve.

Superimpose the curves on a new sheet ("Stretched" Y Axis) for a display like the following:

This concludes our analysis of the no load problem. We encourage you to explore other results

on your own.



5

Superimposed display of voltage and current curves in B3 coil component


When you have finished your analysis, click the Save button to save the analysis supports

and curves you have created.

Program Input

click

Close PostPro_2D by choosing from File, Exit from the menu:

Program Input

File

Exit




5

Servo action withelectromechanical couplingYou can easily modify the no load startup problem to simulate servo action, just by

adding a load.

Modify the physical properties of the no load startup problem

Plane geometry, 50, 308 depth

Airgap

Rotating airgap

Moment of inertia (default): 0.38765e-4

Viscous friction coefficient: 0.005

Constant friction coefficient: 0.3

Keep "squarewave" circuit

Solve, Transient startup

Problem: SERVO

Initialization: NOLOAD

Start from previous time step

Step to use: 100

Verify Flux version (brushlike_921)

413

Chapter 6

Solve with transient startup and user version

Restart at time step: Step1:time=0.05s

Keep previous time steps

Time data

Initial value of time step 1e-3 s



Store 1 on 1


Isovalues (equi flux) lines at last time step, 0.115 s

Color shade plot of flux density on stator, rotor, magnet regions group

Time variation analyses (2D curves)

Axis torque

Angular velocity

Rotor position



Current in Switch1

Current in B1 coil component

Voltage and current in B3 coil component


Close Flux2D

414

Servo action with electromechanicalcoupling

With the no load startup problem already defined, you can easily modify the physical properties

to simulate the servo action just by adding a load.

F You must have already solved the no load startup problem in order to modify it for

the servo simulation. The only difference between these two problems is that the

value of the load or "constant friction coefficient" for the servo problem is no

longer zero.

Once the servo problem is defined, use Flux2D’s transient startup feature to designate the last

time step of your no load startup as the initial time step of your servo problem. Then start the

simulation.

If you have not completed the no load problem, you must define all the physical properties as

described for the constant speed problem (see page 277). Then define the moving airgap

(mechanical coupling with constant friction coefficient of 0.3 N.m.) as described in this chapter

on page 424. Solve as for the no load problem (page 372).

Modification of physical properties

Make sure the no load problem files (NOLOAD.TRA and squarewave.ccs) are in your working

directory.

415

Chapter 6

Start Preflu 9.1


Program Input


Chapter Servo action with electromechanical coupling

Modification of physical properties416

6



Open the No Load problem

This Servo model is similar to the model generated in the previous chapter. We simply need to

modify the moving mechanical set.




Program Input

click

Servo action with electromechanical coupling Chapter

Modification of physical properties 417

6

The initial Preflu screen

Using the menu


Program Input

Project

Open Project

The Open Project dialog opens.



6

Opening the No Load project

Program Input


File Name noload.flu [your name]

Open

The geometry of the No Load model (1 layer airgap) is displayed.


Save your project now with a specific name to indicate that you will be using this model to

simulate servo action.




6

The Noload project is opened.

Program Input

Project

Save As…



Program Input


File Name: servo [your name]

Save



6

Saving the noload project as servo

Define the servo model characteristics

The servo model is identical to the no load model except for the definition of the


Edit the MOVING_ROTOR mechanical set

Expand the Mechanical Set in the Data tree. Select the MOVING_ROTOR mechanical set and


Proceed as follows:

Program Input

Click MOVING_ROTOR

Right-click, Edit



6

The Edit Mechanical Set dialog appears. To enter the servo characteristics, click on the

Kinematics tab at the top.

Proceed as follows:

Program Input

Click Kinematics



6

Going to the Kinematics tab

Now go to define the Internal Characteristics of the kinematics.

Proceed as follows:

Program Input

Click Internal characteristics



6

Going to the Internal Characteristics tab

Change the constant friction coefficient value.


Program Input


Moment of inertia 3.8675e-5

Constant friction coefficient 0.3

Viscous friction coefficient 0.005


OK



6

Defining MOVING_ROTOR for servo model



Program Input

Project

Exit


Proceed as follows:

Program Input



Now you can define the transient startup of the servo motor.



6

Transient startup of servo problem

The transient startup feature enables you to use a solution from one problem as the initial time

step of a transient problem. The necessary conditions are the same finite element mesh (number

of nodes, elements and regions); the same number of components (but not necessarily the same

circuit); and the same number of mechanical equations (whether they involve motion or not).

For the servo problem, the no load startup solution satisfies all the above conditions. Make sure

your servo problem and your no load startup problem are both in your working directory.

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


Transient startup of servo problem426

6

Starting the Transient Startup module

Program Input

Double click Transient startup

The Transient starting (DEMEVO) module opens:

Prepare for the transient startup as follows:


Transient startup of servo problem 427

6

Transient startup (DEMEVO) screen

Program Input

Problem name servo

Name of the problem containingthe initialization (MS, MD, orME) :

NOLOAD

looking for the number of timesteps

Number of time steps in thefile: 100

Number of the time step to useas initial value (default100_0.1)

100

Results are stored in theoutput file

Memory size reached 184 k.words

The Transient starting module closes and the Flux2D Supervisor is displayed. The solution at

time step 100 of the no load start up problem now becomes the first time step of the servo

problem.

Solve the servo simulation with user version

Now you are ready to solve the servo problem.

F Make sure the correct user version of Flux2D (brushlike_921) is shown at the

top of the supervisor window.

Choose a time step that is also valid at the new synchronous speed with the load. The no load

synchronous speed is 1200 rpm. With the load, the new speed is smaller, so a time step of 1 ms is

satisfactory for the computation.


Solve the servo simulation with user version428

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User version of Flux2D

Start the solver


Program Input

Double click Direct


Solve the servo simulation with user version 429

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Starting the solver for the servo problem (with customized release)

In the Open dialog, select the problem to be solved and click Open.

Program Input


File name: SERVO.TRA

Open

In the Solver window, click the Solve icon to start the computation.

Program Input

click



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Choosing the servo problem to solve

Because the transient startup is based on the no load problem, which has already been solved, the

following dialog opens.

Click Yes to continue.

Program Input

Do you want to continue ? Yes



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Notice of previous results for servo problem (transient startup)



Program Input

Restarting mode Restart at time step

Step1: time = 5.e-002 s

Keep the previous time steps

Time values

Value of the time step 1e-3



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Defining the time data for the SERVO problem

Program Input


Number of additional timesteps

65


one step on : 1

OK

Click OK to close the dialog and watch as the solution proceeds.




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End of SERVO computation

Click OK to close the dialog and stop the computation.

Program Input


Close the solver by selecting File, Exit from the menu:

Program Input

File

Exit




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Results from servo motor

Make sure the Flux version is still brushlike_921; otherwise, you will not be able to proceed.

In the Analysis folder, double click Results:

Program Input



Results from servo motor 435

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Starting Results analysis with customized version

In the Open dialog, choose the problem to be analyzed and click Open:

Program Input


File name: SERVO.TRA

Open


Results from servo motor436

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Choosing SERVO problem to be analyzed

PostPro_2D opens with a display of the model at the first time step (0.05 s).



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Servo model open in PostPro_2D

Display the isovalues (equiflux) lines

Begin your analysis with a display of 21 equiflux lines at the last time step, 0.115 s.

Select the last time step (0.115 s)

To select the last time step, click the Parameters manager button or choose Parameters,

Manager from the menu:

Program Input

Parameters

Manager

The Parameters dialog opens:

From the Samples number list, choose 0.115, the value of the last time step, and then close the

dialog.

Program Input

Parameters

Values 0.115

click



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Choosing time 0.115 in the Parameters dialog

You should see the geometry with the rotor at approximately 800 degrees:



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Model at last time step, time 0.115 s

Set properties for the isovalues display

Now set the display properties for 21 isovalue lines.

Click the Results, Properties icon or choose Results, Properties from the menu.

Program Input

Results

Properties



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Make sure the Isovalues tab is on top. Then enter 21 as the number of lines and click OK to close

the dialog.

Program Input

Isovalues

Number 21

OK



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Settings to display 21 equiflux lines


To display the plot, click the Isovalues icon in the toolbar.

Program Input

click

The isovalues plot is shown below:

F You may want to see this plot over the full geometry.

To display the full geometry, click the icon in the toolbar, or choose

Geometry, Full geometry from the menu.



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Equiflux (isovalues) lines at time 0.115 s

The isovalues plot over the full geometry is shown below:



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Isovalues at t = 0.115 (full geometry)

Color shade plot for stator, rotor, and magnet

Now display a color shade plot for only the stator, rotor, and magnet regions.

Display this plot over the full geometry. If you have not already done so, choose the Full

Geometry icon in the toolbar.

Program Input

click

Create a group of regions

First, create a group of the three regions. Click the Group manager icon or choose Supports,

Group manager from the menu:

Program Input

Supports

Group Manager

The Group manager dialog opens:



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Settings to create display group for color shade plot


Program Input

Filter Region

Objects available ROTOR

MAGNET

STATOR

Add -->

Current group ROTOR

MAGNET

STATOR


These regions are displayed on the model geometry:



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Creating a regions group for color shade display

Click Create to create the group and close the Group manager dialog.

Program Input

Create

Set the display properties for the color shade plot

Now click the properties icon or choose Results, Properties from the menu.

Program Input

Results

Properties



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Click the Color Shade tab to bring it to the front. Select the group you have just created as the

Support and click OK to close the dialog.

Program Input


Support Big3 [your regions group]

OK



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Setting properties for color shade plot on group

Display the color shade plot

To display the plot, click the Color shade icon in the toolbar.

Program Input

click

The color shade plot is shown below:



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Color shade plot of flux density on group of regions (rotor, magnet, and stator)

Time variation results (2D curves)

Now look at the time variation results such as torque, speed, voltages, currents, etc.

Axis torque

Begin by creating a curve of the axis torque.

Open the 2D curves manager by clicking the icon or by choosing Computation, 2D curves

manager… from the menu.

Program Input

Computation


The 2D curves manager opens. Enter or verify the following:

Program Input

Curve description

Name AxisTorque


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Mechanics


Create

Click Create to create the axis torque curve (you will not see the curve yet).



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The 2D curves manager should still be open with the Axis torque curve listed in the field at the

bottom.

Angular velocity

Enter or verify the following information to create a curve of the angular velocity. You should

need only to enter a new name for the curve and to choose Angular velocity from the

Components list:

Program Input

Curve description

Name AngVel


Parameter

First axis

X axis Time




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Settings for curve of angular velocity

Program Input

Selection step 1

Second axis

Quantity Mechanics

Components Angular velocity

click

Superimpose the axis torque and angular velocity curves using “Stretched” for the Y-axis. Your

display should resemble the following:

F The axis torque shown is the resulting torque from the electromagnetic torque,

friction torque and load torque. At synchronous speed, the average torque is

almost zero. The torque values you see during the solving process are the

electromagnetic torque computed by the virtual work method.



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Superimposed display of axis torque and angular velocity curves

Rotor position

Next, create a curve of the rotor position. Click to open the 2D curves manager.

Program Input

click


Program Input

Curve description

Name Position


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Mechanics

Component Position

click

Click the button to create and display the position curve.



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Superimpose the position and angular velocity curves ("Stretched" Y axis) for the following

display:

You can quickly see values on a curve by placing the arrow cursor on the curve and checking the

values at the bottom of the screen. The 2D Cursor feature, however, shows the values on both

curves at the cursor position, and offers the additional possibilities of writing the values to a file,

displaying the mean values, and so on.



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Superimposed display of position and angular velocity curves

Voltage and current in the main voltage source (V7)

Look now at waveforms of electric quantities. Begin with curves of the voltage and current in the

main voltage source, V7.

Click to open the 2D Curves manager.

Program Input

click


Program Input

Curve description

Name VoltV7


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Circuit

Component Voltage

Third data

Support V7

Create

Click Create to create the curve. The 2D Curves manager should remain open.



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For a curve of the current in the voltage source, enter or verify the following:

Program Input

Curve description

Name CurrV7


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Circuit

Component Current

Third data

Support V7

click

Click the button to create and display the V7 current curve.



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Superimpose the voltage and current curves (with "Stretched" Y axis) for a display like the

following:



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Superimposed display of voltage and current curves for voltage source

Current in Switch 1

Next, create a curve of the current in SWITCH1. Click to open the 2D Curves manager.

Program Input

click


Program Input

Curve description

Name CurrS1


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Circuit

Component Current

Third data

Support S1

click

Click the button to create and display the curve.



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The SWITCH1 current curve is shown below:



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Current in Switch1

Current in B1 (PA) coil component

Next look at a curve of the current in the B1 (PA) coil component. Click to open the 2D

Curves manager.

Program Input

click


Program Input

Curve description

Name CurrB1-PA


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Circuit

Component Current

Third data Electrical component

Support B_COILA

click

Click the button to create and display the curve.



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The B1-PA current curve is shown below:



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Current in the PA coil component (positive phase A)

Voltage and current in B3 (MC) coil component

Finally, look at the voltage and current in the B3 (MC) coil component. Click to open the

2D Curves manager.

Program Input

click


Program Input

Curve description

Name VoltB3-MC


Parameter

First axis

X axis Time


Selection step 1

Second axis

Quantity Circuit

Component Voltage

Third data

Support B_COILC

Create

Click Create to create the B3-MC voltage curve.



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Then, still in the 2D Curves manager, enter the information for the B3-MC current curve:

Program Input

Curve description

Name CurrB3-MC


Parameter

First axis

X axis Time

Parameter values 0.05 - 0.115 [select all]

Selection step 1

Second axis

Quantity Circuit

Component Current

Third data

Support B_COILC

click

Click to create and display the B3-MC current curve.



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Superimpose the B3-MC voltage curve ("Stretched" Y axis) for a display like the following:

This concludes our analysis of the servo motor. We encourage you to look at other results as you

wish.



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MC voltage and current curves

Close PostPro_2D

When you are ready, close PostPro2D by choosing File, Exit from the menu:

Program Input

File

Exit


Choose Yes to save your analysis.

Program Input

Do you want to save SERVO Yes



Close PostPro_2D464

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Saving analysis file

Close Flux2D

Choose File, Quit to close Flux2D:

Program Input

File

Quit

Congratulations! You have now completed the simulations for the brushless DC motor.

We hope you have enjoyed your analyses with Flux2D.


Close Flux2D 465

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Tutorial Brushless DC Motor Calculations

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Transcript of Tutorial Brushless DC Motor Calculations