Tutorial Brushless DC Motor Calculations

Brushless DC Motor

Calculations

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

Contents 1

About this document

xv

What this document contains · · · · · · · · · · · · · · · · · · · · · · · · · xv Chapters to complete for the different simulations · · · · · · · · · · xvi For experienced users· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · xvi

1

Enter the materials

3

Start Flux2D · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 3 Open the materials database · · · · · · · · · · · · · · · · · · · · · · · · · · 5 Add the magnetic material · · · · · · · · · · · · · · · · · · · · · · · · · · · 6 Add the nonlinear steel material· · · · · · · · · · · · · · · · · · · · · · · · 9 Close the materials database · · · · · · · · · · · · · · · · · · · · · · · · · 11

2

Cogging torque computation

15

Special considerations for simulation· · · · · · · · · · · · · · · · · · · · 15 Enter the physical properties · · · · · · · · · · · · · · · · · · · · · · · · · 17 Start Preflu 9.1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 17 Open the 3-layer airgap problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · 18

Save your project with a new name · · · · · · · · · · · · · · · · · · · · 20 Define as Transient Magnetic · · · · · · · · · · · · · · · · · · · · · · · · · 22 Change to the Physics context · · · · · · · · · · · · · · · · · · · · · · · · 23

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

Import materials from the materials database · · · · · · · · · · · · · 25 Assign materials and sources to the regions · · · · · · · · · · · · · · 27 Assign the windings of the stator slots · · · · · · · · · · · · · · · · · · · · · · · · 27 Assign WEDGE, AIR, STATOR_AIR, AIRGAP and SHAFT regions · · · · · · · 31 Assign STATOR and ROTOR regions · · · · · · · · · · · · · · · · · · · · · · · · · · 33 Assign the MAGNET · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 35

Creating and Assigning Mechanical Sets · · · · · · · · · · · · · · · · · 38 Creating Mechanical Sets· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 38 Create the MOVING_ROTOR Mechanical Set . . . . . . . . . . . . . . . . . . . . 39 Create the FIXED_STATOR Mechanical Set. . . . . . . . . . . . . . . . . . . . . 43 Create the ROTATING_AIRGAP Mechanical Set . . . . . . . . . . . . . . . . . . . 44

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

Boundary conditions (Periodicity) · · · · · · · · · · · · · · · · · · · · · · 49 Check the physical model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 51 Close Preflu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Solve (batch mode) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 54 Prepare the batch file · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 54 Close the solver · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 61 Start the batch computation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 62

Results · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 66 Display the full geometry· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 69 Displaying isovalues (equiflux) lines at t = 1 s · · · · · · · · · · · · · · · · · · · 71 Change the default isovalues display . . . . . . . . . . . . . . . . . . . . . . . 71 Change the time to 1 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Display the isovalues plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

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Color shade of flux density on a group of regions · · · · · · · · · · · · · · · · · 75 Change the geometry display . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Change the time to 0.5 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Create a group of the three regions . . . . . . . . . . . . . . . . . . . . . . . . 77 Display a color shade plot on the group of regions . . . . . . . . . . . . . . . . . 78

Create a path through the airgap · · · · · · · · · · · · · · · · · · · · · · · · · · · · 81 Normal component of flux density along the air gap path · · · · · · · · · · · 86 Superimpose the curves display · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 88 Spectrum analysis · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 91 Axis torque (full cycle) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 95

Save your analyses · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 98 Close PostPro_2D · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 99

3

Back EMF computation

102

Create the back EMF external circuit model · · · · · · · · · · · · · · 102 Conventions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 102 Back EMF circuit · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 104 Start ELECTRIFLUX · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 105 Open a new circuit problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 106 Using the icon in the toolbar. . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Using the menu

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

ELECTRIFLUX toolbar · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 109 ELECTRIFLUX menus · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 110 File menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Edit menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 View menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Circuit menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Sheet menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

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

Change the size of the sheet · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 113 Add coils for stator windings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 117 Place the 4 coil components on the sheet

. . . . . . . . . . . . . . . . . . . . 119

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

Add inductors · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 125 Place the 3 inductors on the sheet . . . . . . . . . . . . . . . . . . . . . . . . 126 Rotate the 3 inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

Add the open circuit loads · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 130 Place the 3 resistors on the sheet . . . . . . . . . . . . . . . . . . . . . . . . 132 Rotate the 3 resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

Add the voltmeter· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 135 Place the voltmeter (R4) on the sheet . . . . . . . . . . . . . . . . . . . . . . 136 Rotate the voltmeter (R4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Save your circuit file · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 139 Connect (wire) the circuit components · · · · · · · · · · · · · · · · · · · · · · · 140 Define the resistors and inductors· · · · · · · · · · · · · · · · · · · · · · · · · · · 146 Define the resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Define the inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Rename the coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Analyze the circuit · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 152 Save and close the circuit file · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 154 Close ELECTRIFLUX· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 155

Enter the physical properties · · · · · · · · · · · · · · · · · · · · · · · · 156 Start Preflu 9.1· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 156 Open the 1-layer airgap problem · · · · · · · · · · · · · · · · · · · · · · · · · · · 157

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

Contents

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Define as Transient Magnetic · · · · · · · · · · · · · · · · · · · · · · · · 161 Change to the Physics context · · · · · · · · · · · · · · · · · · · · · · · 162 Physics context toolbars · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 163

Import materials from the materials database · · · · · · · · · · · · 163 Import the problem circuit · · · · · · · · · · · · · · · · · · · · · · · · · · 165 Assign materials and sources to the regions· · · · · · · · · · · · · · 169 Assign the stator windings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 169 Edit the PA region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Define the coil resistance · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 174 Assign WEDGE, AIR, AIRGAP and SHAFT regions · · · · · · · · · · · · · · · · 176 Assign STATOR and ROTOR regions · · · · · · · · · · · · · · · · · · · · · · · · · 177 Assign the MAGNET· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 179

Creating and Assigning Mechanical Sets · · · · · · · · · · · · · · · · 181 Creating Mechanical Sets · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 181 Create the MOVING_ROTOR Mechanical Set . . . . . . . . . . . . . . . . . . . 182 Create the FIXED_STATOR Mechanical Set . . . . . . . . . . . . . . . . . . . . 186 Create the ROTATING_AIRGAP Mechanical Set . . . . . . . . . . . . . . . . . . 187

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

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

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Results from the Back EMF computation · · · · · · · · · · · · · · · · 203 Display the back EMF in R4 (the voltmeter) · · · · · · · · · · · · · · · · · · · · 205 Display a spectrum of the back EMF in R4 · · · · · · · · · · · · · · · · · · · · · 208 Voltage and current in coil B_MC (MC) · · · · · · · · · · · · · · · · · · · · · · · 213 Save and close PostPro_2D · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 214

4

Square wave motor: Constant speed (torque ripples) 217 Create the 3-phase bridge circuit · · · · · · · · · · · · · · · · · · · · · 218 Start ELECTRIFLUX · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 219 Create a new circuit problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 221 Using the icon in the toolbar. . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Using the menu

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

Change the size of the sheet · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 223 Add the 6 switches · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 226 Place the 6 switches on the sheet . . . . . . . . . . . . . . . . . . . . . . . . 228 Rotate the 6 switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

Add the 6 series voltages· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 236 Place the 6 series voltages on the sheet . . . . . . . . . . . . . . . . . . . . . 238 Rotate the series voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

Add the main voltage source · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 243 Place the main voltage source . . . . . . . . . . . . . . . . . . . . . . . . . . 244 Rotate the main voltage source . . . . . . . . . . . . . . . . . . . . . . . . . 245

Add the 3 coils · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 246 Place the 3 coil components on the sheet

. . . . . . . . . . . . . . . . . . . . 248

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

Add the inductors · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 252 Place the 3 inductors on the sheet . . . . . . . . . . . . . . . . . . . . . . . . 254 Rotate the 3 inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

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Add the voltmeter· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 257 Save your circuit· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 260 Connect (wire) the circuit components · · · · · · · · · · · · · · · · · · · · · · · 262 Define the circuit · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 266 Define the on/off resistance values for the switches . . . . . . . . . . . . . . . . 266 Define the inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Define the voltmeter (R1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 Rename the coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

Analyze the circuit · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 273 Save and close the circuit file · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 275 Close ELECTRIFLUX· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 276

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

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Define the switches· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 295 Check the physical model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 297 Close and save the model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 298

Solve with user version · · · · · · · · · · · · · · · · · · · · · · · · · · · · 299 Select the user version · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 299 Start the solver · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 301 Verify the solving options· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 303 Start the computation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 305 Close the solver · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 307

Results: Constant speed computation · · · · · · · · · · · · · · · · · · 309 Display isovalues (equiflux) lines · · · · · · · · · · · · · · · · · · · · · · · · · · · 312 Set the properties for the display . . . . . . . . . . . . . . . . . . . . . . . . 312 Display the isovalues plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314

Color shade plot on a group of regions · · · · · · · · · · · · · · · · · · · · · · · 318 Create the group of regions . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 Set the properties for the display . . . . . . . . . . . . . . . . . . . . . . . . 319 Display the color shade plot . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

Create a path through the airgap · · · · · · · · · · · · · · · · · · · · · · · · · · · 323 Flux density along the airgap path · · · · · · · · · · · · · · · · · · · · · · · · · · 328 Flux density: Normal component

. . . . . . . . . . . . . . . . . . . . . . . . 328

Flux density: Tangential component . . . . . . . . . . . . . . . . . . . . . . . 329 Superimpose the normal and tangential flux density curves . . . . . . . . . . . . 330

Spectrum analysis · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 334 Time variation curve of axis torque · · · · · · · · · · · · · · · · · · · · · · · · · · 338 Waveforms of the electric quantities · · · · · · · · · · · · · · · · · · · · · · · · · 342 Voltage and current in the main voltage source (V7) . . . . . . . . . . . . . . . 343 Current in Switch1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 Current in the B_COILA (PA) coil component . . . . . . . . . . . . . . . . . . . 348

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Current in the B_COILB (PB) coil component . . . . . . . . . . . . . . . . . . . 350 Current in the B_COILC (MC) coil component . . . . . . . . . . . . . . . . . . . 352

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

5

No load startup with electromechanical coupling

359

Modify the physical properties · · · · · · · · · · · · · · · · · · · · · · · 359 Start Preflu 9.1· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 360 Open the Constant Speed problem · · · · · · · · · · · · · · · · · · · · · · · · · · 361 Save your project with a new name · · · · · · · · · · · · · · · · · · · · · · · · · 363 Define the no load characteristics · · · · · · · · · · · · · · · · · · · · · · · · · · · 365 Edit the MOVING_ROTOR mechanical set . . . . . . . . . . . . . . . . . . . . . 365

Close and save the model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 369

Verify the user version: brushlike_921 · · · · · · · · · · · · · · · · · 370 Solve the no load startup problem · · · · · · · · · · · · · · · · · · · · 372 Choosing a time step· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 372 Start the solver · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 372

Results from no load startup · · · · · · · · · · · · · · · · · · · · · · · · 380 Display the isovalues (equiflux) lines at time step 100 (t = 0.05 s) · · · · 382 Select the 100th time step (0.05 s) . . . . . . . . . . . . . . . . . . . . . . . 383 Set the display properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 Display the isovalues plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387

Time variation analysis (2D Curves) · · · · · · · · · · · · · · · · · · · · · · · · · 390 Axis torque curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 Angular velocity curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 Rotor position curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396

Waveforms of electric quantities · · · · · · · · · · · · · · · · · · · · · · · · · · · · 399 Voltage and current in the main voltage source . . . . . . . . . . . . . . . . . . 400

xii

Contents

Current in Switch1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 Current in the B1 (PA) coil component . . . . . . . . . . . . . . . . . . . . . . 405 Voltage and current in the B2 (PB) coil component . . . . . . . . . . . . . . . . 407 Voltage and current in B3 (MC) coil component . . . . . . . . . . . . . . . . . . 409

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

6

Servo action with electromechanical coupling

415

Modification of physical properties · · · · · · · · · · · · · · · · · · · · 415 Start Preflu 9.1· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 416 Open the No Load problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 417 Save your project with a new name · · · · · · · · · · · · · · · · · · · · · · · · · 419 Define the servo model characteristics · · · · · · · · · · · · · · · · · · · · · · · 421 Edit the MOVING_ROTOR mechanical set . . . . . . . . . . . . . . . . . . . . . 421

Close and save the model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 425

Transient startup of servo problem · · · · · · · · · · · · · · · · · · · · 426 Solve the servo simulation with user version · · · · · · · · · · · · · 428 Start the solver · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 429

Results from servo motor· · · · · · · · · · · · · · · · · · · · · · · · · · · 435 Display the isovalues (equiflux) lines· · · · · · · · · · · · · · · · · · · · · · · · · 438 Select the last time step (0.115 s) . . . . . . . . . . . . . . . . . . . . . . . . 438 Set properties for the isovalues display

. . . . . . . . . . . . . . . . . . . . . 440

Display the isovalues plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442

Color shade plot for stator, rotor, and magnet · · · · · · · · · · · · · · · · · · 444 Create a group of regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 Set the display properties for the color shade plot . . . . . . . . . . . . . . . . 446 Display the color shade plot . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

Time variation results (2D curves) · · · · · · · · · · · · · · · · · · · · · · · · · · 449 Axis torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449

Contents

xiii 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

Introduction About this document This tutorial, Brushless DC Motor: Calculations, is the second in the series featuring the model of the brushless DC permanent magnet motor. The calculations presented in this document are based on the models (geometry and mesh) created with Preflu, as explained in Brushless DC Motor: Constructing the Model. You should already have completed and have saved two geometry and mesh files for this model in your working directory. For the first computation, the cogging torque (see Chapter 2), use the model with the 3-layer airgap (BRUSHLESS_3LAYER). For all the other computations, use the model with the 1-layer airgap (BRUSHLESS_1LAYER).

What this document contains This tutorial shows you how to enter the required materials into the materials database (CSLMAT) and then how to conduct a series of simulations with the brushless permanent magnet motor. In both Chapters 3 and 4, you create external circuits with the new ELECTRIFLUX module. Chapter 1

Enter the materials into the materials database (CSLMAT)

Chapter 2

Cogging torque computation (with batch file solution)

Chapter 3

Back EMF computation, with a 3-phase Wye external circuit

Chapter 4

Square wave motor: Constant speed (Torque ripples), with a square wave external circuit

Chapter 5

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

Chapter 6

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

xv

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

Chapter 1 Enter the materials In this chapter you start Flux2D and use the Materials database module to create the materials to be assigned to various parts of the model of the motor. These materials are added to the materials database and can then be used for other problems also.

Start Flux2D Open the Materials database (CSLMAT) Add the magnetic material iso MU scalar constant relative permeability of 1.071 magnet scalar constant remanent flux density of 0.401

Add the nonlinear steel material iso MU scalar a sat Js = 1.99 Initial relative slope a = 7500

Close CSLMAT

1

2

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.

Starting Flux2D

3

4

Start Flux2D

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

Input Start Programs Cedrat Flux 9.1

The Flux Supervisor opens:

Flux Supervisor

Chapter

1

Enter the materials

5

Open the materials database

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

Opening the materials database (CSLMAT)

Program

Input Double click Materials database

Enter the materials

Chapter

1

6

Add the magnetic material

The Materials database (CSLMAT) opens:

CSLMAT menu

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

Chapter

1

Enter the materials

7

Add the magnetic material

Your screen should resemble the following figure:

Creating the magnet material (name and comment)

Next, enter two properties for the magnetic material: 1. the relative permeability (1.071) and 2. the remanent flux density (0.401). Proceed as follows: Program

Input

To register, define at least one property Please select the property

1 iso MU

Select a model

1 scalar cst

Value =

Enter the materials

Chapter

1

8

Add the magnetic material

The field (a blue rectangle) where you enter the relative permeability is shown below:

Entering the relative permeability of the magnetic material

On some screens, stars (******) may be shown instead of the solid blue field. In this case, click on the stars and then enter the relative permeability of the magnet (1.071). Proceed as follows: Program

Input

Value =

1.071

Select the line whose value is to be changed

1 Validate

Please select the property

5 Magnet

Select a model

1 scalar cst

Value =

0.401

Select the line whose value is to be changed

1 Validate

Please select the property

Quit

Chapter

1

Enter the materials

9

Add the nonlinear steel 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 least one property Please select the property

1 iso MU

Select a model

B scalar a sat

The scalar a sat model features an arc tangent formula to model the B-H curve. Enter the saturation magnetization value (Js) and the initial relative slope (a) of the relative permeability.

Entering the saturation magnetization (Js) and initial relative slope (a) for the nonlinear steel

Program

Input

Saturation magnetization Js = Tesla

1.99

Initial relative slope a =

7500

Select the line whose value is to be changed

1 Validate

Enter the materials

Chapter

1

10

Add the nonlinear steel material

When you choose Validate, a plot of the model is displayed:

B-H plot of the nonlinear steel

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.

Chapter

1

Enter the materials

11

Close the materials database

For example, the following figure shows the values at a point near the "knee" of the curve.

Reading values on the B-H curve with "Pick" command

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.

Enter the materials

Chapter

1

Chapter 2 Cogging torque computation This chapter explains how to compute the cogging torque for the brushless DC motor.

Assign physical properties Plane geometry, 50.308 depth, transient magnetic calculation Materials and sources All stator windings: vacuum, no source Airgap: rotating airgap, constant angular velocity of 0.16666666 rpm, 2 pole pairs Wedge, air, shaft: vacuum, no source Stator, rotor: nonlinear steel, no source Magnet: magnet material, constant direction 45 degrees, no source Boundary conditions: Automatically assigned using periodicity

Solve with a batch file Create a batch file with the following data: Time step 0.5 s Study time limit 100 s Limit number of time steps Maximum value time step 0.5 s Minimum value time step 0.5 s Store automatically 1 on 1 Initial position of the rotor: Solve, Batch

61

0

13

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

Chapter 2 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

16

Special considerations for simulation

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.

The airgap subdivided into 3 layers

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

2

Cogging torque computation

17

Enter the physical properties

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:

Starting Preflu 9.1 to enter the physical properties

Program

Input Double click Geometry & Physics

Cogging torque computation

Chapter

2

18

Enter the physical properties

The Preflu 9.1 application opens.

Preflu 9.1 screen

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 Program

icon on the toolbar Input click

Chapter

2

Cogging torque computation

19

Enter the physical properties

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

Brushless_V9 [your working directory brushless_3layer.flu [your name] Open

File Name

Cogging torque computation

Chapter

2

20

Save your project with a new name

The 3-layer geometry is shown in the following figure:

The geometry (with 3-layer airgap) displayed in Preflu

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.

Chapter

2

Cogging torque computation

21

Save your project with a new name

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.

Saving the brushless 3-layer model as cogging

Enter or verify the following: Program

Input

Save In:

Brushless_v9 [working directory]

File Name:

cogging [your name] Save

Cogging torque computation

Chapter

2

22

Define as Transient Magnetic

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.

Enter or verify the following: Program

Input

2D domain type

2D plane

Length Unit

MILLIMETER

Depth of the domain

50.308 OK

Chapter

2

Cogging torque computation

23

Change to the Physics context

Your screen should look like the following. Notice that there is a new context symbol, representing the Physical model context.

The cogging problem after defining the physical model

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 Program

button to change to the Physics context. Input click

Cogging torque computation

Chapter

2

24

Change to the Physics context

The Physics context is shown in the following figure.

The cogging problem after going to the Physics context

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:

Physics toolbar icons: Add, Check

Physics toolbar icons: Display, Select

Chapter

2

Cogging torque computation

25

Import materials from the materials database

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

Cogging torque computation

Chapter

2

26

Import materials from the materials database

The import material dialog appears.

Initial material import dialog

Click on the database.

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

List of materials in the database displayed

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

Chapter

2

Cogging torque computation

27

Assign materials and sources to the regions

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.

Materials imported into 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.

Cogging torque computation

Chapter

2

28

Assign materials and sources to the regions

Proceed as follows: Program

Input

Click

Click

Click

Chapter

2

Cogging torque computation

29

Assign materials and sources to the regions

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

Cogging torque computation

Chapter

2

30

Assign materials and sources to the regions

The Edit Face Region window appears, and the stator slots are highlighted on the graphic.

Editing all stator slots using Edit Array function

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.

Select Air or Vacuum in the Modify All Column

Chapter

2

Cogging torque computation

31

Assign materials and sources to the regions

Next, accept your input.

Setting a vacuum property for the stator slots

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:

Cogging torque computation

Chapter

2

32

Assign materials and sources to the regions

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 Click Click Click Click

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

Right click, Edit array

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

Setting a vacuum property for the air regions

Proceed as follows: Program

Input

Sub types:

Select "Air or vacuum" OK

Chapter

2

Cogging torque computation

33

Assign materials and sources to the regions

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

Console confirms region faces modified

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.

Selecting the Stator and Rotor regions graphically

Cogging torque computation

Chapter

2

34

Assign materials and sources to the regions

Once the regions are selected, right click the mouse and select Edit Array.

Edit the stator and rotor areas as a group

Under the Modify All column, we will set both of these regions to the NLSTEELPM material.

Setting the stator and rotor to NLSTEELPM

Proceed as follows: Program

Input

Sub types:

Select "Magnetic reg"

Material

Select "NLSTEELPM" OK

Chapter

2

Cogging torque computation

35

Assign materials and sources to the regions

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.

Selecting the magnet region, then selecting Edit

The Edit Face Region window appears.

Setting the magnet region to the MAGNETPM material

Cogging torque computation

Chapter

2

36

Assign materials and sources to the regions

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 magnet. Program

icon from the toolbar to orient the

Input Click

If you prefer, choose Physics, Material, Orient material for face region from the menu. Program

Input

Physics Material Orient material for face region

Chapter

2

Cogging torque computation

37

Assign materials and sources to the regions

The following figure shows the Orient Material window.

Setting the magnet to 45 degree orientation

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.

The physical properties are assigned

Cogging torque computation

Chapter

2

38

Creating and Assigning Mechanical Sets

Creating and Assigning Mechanical Sets Creating Mechanical Sets New with Flux 9.1 is the existence of Mechanical Sets. Mechanical Sets are used whenever you want motion in the model (either rotating or translating). Whenever there is motion in the model, you must define 3 mechanical sets; • Fixed - This defines the parts of the model that do not move • Moving- This defines the parts of the model that move (either rotating or translating) • Compressible- This defines the region between the moving and non-moving parts (and the displacement regions, in the case of a translating motion) We will first create these mechanical sets. Select Physics, Mechanical Set and New from the menu. Program

Input

Physics

Mechanical set New

Chapter

2

Cogging torque computation

39

Creating and Assigning Mechanical Sets

Create the MOVING_ROTOR Mechanical Set

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

Defining the Axis information for the MOVING_ROTOR Mechanical Set

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

Input

Mechanical set name

moving_rotor

Comment

the moving parts of the model

Type of mechanical set

Rotation around one axis

Rotation Axis

Rotation around one axis parallel to Oz

Coordinate system

MAIN

Pivot point First coordinate

0

Cogging torque computation

Chapter

2

40

Creating and Assigning Mechanical Sets

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.

Defining the General kinematics information for the MOVING_ROTOR Mechanical Set

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

Input

Type of kinematics

Imposed Speed

Velocity (rpm)

1/6

Position at time t=0s. (deg)

0 Click "Internal characteristics" tab

Chapter

2

Cogging torque computation

41

Creating and Assigning Mechanical Sets

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

Defining the Internal kinematics information for the MOVING_ROTOR Mechanical Set

Proceed as follows to define the Internal characteristics information: Program

Input

Type of load

Inertia, friction coefficients and spring

Moment of inertia

0

Constant friction coefficient

0

Viscous friction coefficient

0

Friction coefficient proportional to the square speed

0

Cogging torque computation

Chapter

2

42

Creating and Assigning Mechanical Sets

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

Defining the External kinematics information for the MOVING_ROTOR Mechanical Set

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

Input

Type of load

Inertia, friction coefficients and spring

Moment of inertia

0

Constant friction coefficient

0

Viscous friction coefficient

0

Chapter

2

Cogging torque computation

43

Creating and Assigning Mechanical Sets

Friction coefficient proportional to the square speed

0

OK Create the FIXED_STATOR Mechanical Set

The New Mechanical set dialog closes briefly and then reappears. Enter the information to create the FIXED_STATOR mechanical set.

Defining the information for the FIXED_STATOR Mechanical Set

Proceed as follows: Program

Input

Mechanical set name

fixed_stator

Comment

the non-moving parts of the model

Type of mechanical set

Fixed OK

Cogging torque computation

Chapter

2

44

Creating and Assigning Mechanical Sets

Create the ROTATING_AIRGAP Mechanical Set

The New Mechanical set dialog closes briefly and then reappears. Enter the information to create the ROTATING_AIRGAP mechanical set.

Defining the information for the ROTATING_AIRGAP Mechanical Set

Proceed as follows: Program

Input

Mechanical set name

rotating_airgap

Comment

the rotating airgap

Type of mechanical set

Compressible

Used method to take the motion into account

Remeshing of the air part surrounding the moving body OK

Chapter

2

Cogging torque computation

45

Creating and Assigning Mechanical Sets

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

Close the Mechanical set dialog

Proceed as follows: Program

Input Cancel

Assigning Mechanical Sets Now assign the mechanical sets to the regions of your model. First assign the appropriate regions to the MOVING_ROTOR mechanical set.

Cogging torque computation

Chapter

2

46

Creating and Assigning Mechanical Sets

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 Click Click Click

AIR MAGNET + Ctrl ROTOR + Ctrl SHAFT + Ctrl

Right click, Edit array

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

Assigning regions to the MOVING_ROTOR mechanical set

Proceed as follows: Program

Input

MECHANICAL_SET

Select "MOVING_ROTOR" OK

Chapter

2

Cogging torque computation

47

Creating and Assigning Mechanical Sets

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 Click Click Click Click Click Click

MA MC + Ctrl PA + Ctrl PB + Ctrl STATOR + Ctrl STATOR_AIR + Ctrl WEDGE + Ctrl

Right click, Edit array

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

Assigning regions to the FIXED_STATOR mechanical set

Proceed as follows: Program

Input

MECHANICAL_SET

Select "FIXED_STATOR" OK

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Creating and Assigning Mechanical Sets

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.

Click on the Mechanical Set tab

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Boundary conditions (Periodicity)

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

Setting the AIRGAP region to the ROTATING_AIRGAP mechanical set

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.

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Boundary conditions (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

If you prefer, you can select Geometry, Periodicity, New from the menu. Program

Input

Geometry Periodicity New

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Boundary conditions (Periodicity)

The New Periodicity dialog opens.

Defining a periodicity for the brushless DC motor

Proceed as follows: Program

Input

Geometrical type of the periodicity

Rotation about Z axis with angle of the domain

Included angle of the domain

90

Offset angle with respect to the X line

0

Physical aspects of periodicity

Odd (anticyclic boundary conditions) OK

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

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Boundary conditions (Periodicity)

Select the Program

icon from the toolbar to start the Physical Check. Input Click

If you prefer, you can select Physics, Check physics from the menu. Program

Input

Physics

Check physics

The console indicates that the physical check is completed.

Close Preflu

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

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Boundary conditions (Periodicity)

Click on the

icon in the toolbar to exit Preflu.

Program

Input Click

If you prefer, select Project, Exit from the menu. Program

Input

Project

Exit

When prompted, select to save your problem.

Proceed as follows: Program

Input

Save current project before

Yes

The Flux Supervisor is displayed.

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Solve (batch mode)

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.

Starting the solver

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Solve (batch mode)

Program

Input

Double click Direct

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

Choosing the problem to solve

Program

Input

Look in

Brushless_V9[working directory]

File name

COGGING.TRA Open

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Solve (batch mode)

The solver opens as shown below.

Solver: Main data

Click the Prepare Batch button Program

to prepare the file for batch mode. Input click

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Solve (batch mode)

Your screen should resemble the following figure.

Ready to enter data for batch file

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

Input

Restarting mode

New computation

Time values Initial value of the time step

0.5

Study time limit

100

Limit number of time steps

61

Maximum value of the time step

0.5

Minimum value of the time step

0.5

Storage of time steps

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Solve (batch mode)

Program one step on

Input 1 Ok

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

Time data for the batch computation

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Solve (batch mode)

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.

Verifying the initial position of the rotor (0 degrees)

Program

Input

Initial position of the rotor 0. degrees

OK

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Solve (batch mode)

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

Batch file completed

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

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Solve (batch mode)

Close the solver Choose File, Exit to close the solver. Program

Input File

Exit

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Solve (batch mode)

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

Starting the Solver for a batch computation

Program

Input Double click Batch

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Solve (batch mode)

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:

Starting the batch computation

Program

Input

Files

Ready

COGGING.TRA

Yes

COGGING.TRA Start

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Solve (batch mode)

The Solver window opens:

Batch computation in progress

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Solve (batch mode)

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

Closing the solver after batch computation

Program

Input

Batch COGGING.TRA

Quit

The Flux Supervisor should still be open.

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Results

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

Starting Results analysis from the Supervisor

Program

Input Double click Results

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Results

From the Open dialog, choose the problem you want to analyze and click Open:

Opening the cogging torque problem for results analysis

Program

Input

Look in

Brushless_V9[working directory]

File name

COGGING.TRA Open

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Results

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

Model open in PostPro_2D

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Results

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 Full Geometry from the menu: Program

or choose Geometry,

Input

Geometry

Full geometry

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Results

Your screen should resemble the following.

Model with full geometry displayed

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Results

Displaying isovalues (equiflux) lines at t = 1 s It is often useful to begin analysis with a display of the isovalues (equiflux) lines. Change the default isovalues display

By default, PostPro_2D displays 11 equiflux (isovalues) lines. To display 21 isovalue lines over the geometry, click the Results properties button or choose Results, Properties from the menu. Program

Input

Results

Properties

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Results

The Display properties dialog opens.

Results properties dialog for isovalues display

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

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Results

Program Scaling

Input 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 Parameters, Manager from the menu. Program

icon or by choosing

Input Parameters Manager

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

Parameters dialog

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Results

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 Isovalues from the menu. Program

in the toolbar or choose Results,

Input Results Isovalues

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Results

The isovalues (equi flux) lines are displayed:

Display of the flux density lines on the full geometry at 1 s.

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 Program

to deselect it. Input click

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Results

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.

Choosing 0.5 s (initial time step)

Program

Input

Parameters Values

0.5 click

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Results

Create a group of the three regions

To place the three regions in a group, click the the menu. Program

icon or select Supports, Group manager from

Input

Supports Group manager

The Group manager dialog opens.

Group manager dialog

In the Group manager, enter or verify the following: Program

Input

Filter

Region

Objects available

STATOR MAGNET ROTOR Add -->

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Results

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 Properties from the menu. Program

button or by choosing Results,

Input

Results

Properties

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Results

The Display properties dialog opens.

Properties for color shade plot on regions group

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

Input click Color Shade tab

Analyzed quantity

|Flux density|

Support

Big3 [or your regions group]

Computing parameters Quality

Normal

Scaling

Uniform OK

The Display properties dialog closes.

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Results

To display the plot, click the color shade button Program

in the toolbar. Input click

The plot on the group of regions is shown below:

Color shade plot of flux density on a group of regions

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Results

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:

Location of path through airgap

To create this path through the airgap, open the Path manager. Click the Path manager button Program

or choose Supports, Path manager… from the menu: Input Supports Path manager…

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Results

The Path Manager dialog opens:

Path manager

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.

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Results

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):

Locating the coordinates for the center of the airgap path

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

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Results

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

Section editing window to create paths

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

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Results

The Section editing dialog closes and the path is displayed on the geometry, as shown (enlarged) in the following figure.

Path through airgap

In the Path manager dialog, click the manager at the same time. Program

button to create the path and open the 2D Curves

Input click

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Normal component of flux density along the air gap path The 2D Curves manager is shown in the following figure.

Settings for flux density curves (normal component at 1 s, 2 s, and 3 s)

With the 2D curves manager, you can create and display curves of various quantities along paths; with selected parameters (such as a series of time steps); or along shell (line) regions.

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Results

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]

[default color]

[new color, if desired] Path

First axis X axis

CenterGap

Second axis Quantity

Flux density

Components

Normal component

Third data Parameter

Time

Parameter values

1 + Ctrl 2 3

Selection step

1 click

Clicking the

button creates and displays the curve at the same time.

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Results

A 2D curves sheet opens with the 3 curves “stacked,” as shown in the following figure:

Normal component of the flux density through the air gap at time steps 1, 2, and 3 s

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.

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Results

In the Display dialog, enter or verify the following: Program

Input click Display tab

Display

Superimposed

Gradations

ON

X Axis Range Scale

Automatic linear

Y Axis Range Scale

Automatic linear OK

When you click OK, the dialog closes.

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Results

The following figure shows the curves superimposed:

Superimposed curves of normal component of flux density at times 1, 2, and 3 s

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Results

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:

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

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Results

Enter or verify the following: 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]

[default color]

[new color, if desired] click

Clicking the

Chapter

2

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

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Results

The flux density curve and the spectrum are shown below:

Spectrum analysis of normal component of flux density at 1 s

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

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Results

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

Properties dialog to modify individual curve settings, such as line form and width

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Results

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:

Settings for curve of axis torque over the whole cycle

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Results

Enter or verify the following: Program

Input

Curve description Name

AxisTorq [or your choice]

[default color]

[new color, if desired] Parameter

First Axis X axis

Time

Parameter values

0.5 - 30.5

Selection step

1

Second axis Quantity

Mechanics

Component

Axis torque click

Clicking the

Chapter

2

button creates and displays the curve at the same time.

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Results

The axis torque curve is shown in the following figure:

Time varying display of the axis torque

F

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

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Save your analyses

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

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Close PostPro_2D

Close PostPro_2D Close PostPro_2D by selecting File, Exit from the menu: Program

Input

File

Exit The Flux Supervisor is displayed.

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Chapter 3 Back EMF computation This chapter explains how to compute the back EMF of the stator winding.

Create a 3-phase Wye connected no load circuit using ELECTRIFLUX (see diagram on page 105) Assign physical properties Plane geometry, 50.308 depth, transient magnetic calculation Materials and sources All stator windings: vacuum, external circuit Airgap: rotating air gap, constant angular velocity of 500 rpm, 2 pole pairs Wedge, air, shaft regions: vacuum, no source Stator, rotor: nonlinear steel, no source Magnet: magnet, radial +, no source Boundary conditions: Accept default conditions Link external circuit Coil regions (PA, MA, MC, PB) to coil components (B_PA, B_MA, B_MC, B_PB) Define coil characteristics B_PA, B_MA: Resistance total value, 10 turns, 0.0705 Ω B_MC, B_PB: Resistance total value, 20 turns, 0.141 Ω

Solve with static initialization Initial value of time step Study time limit Limit number of time steps Store 1 on 1 time steps

0.00125s 100 s 49

Analyze results with PostPro_2D Waveforms of electric quantities (2D curves) Voltage through resistor Res4 Spectrum analysis of Res4 voltage curve Voltage for Res1

Save and close PostPro_2D

101

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

F

For this simulation and for those described in Chapters 4, 5 and 6, be sure to use the 1-layer airgap model.

Create the back EMF external circuit model Conventions The following conventions are used for the external circuit model. The stator winding connections for the model (¼ of the motor, or 1 pole) are 3-phase Wye connected. The phase diagram is shown in the following figure:

Phase diagram for the 3-phase Wye connected windings

102

Create the back EMF external circuit model

103

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.

Coil with "hot" point at upper right

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.

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Create the back EMF external circuit model

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

Circuit components for back EMF simulation

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Create the back EMF external circuit model

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

Starting the Circuit module (ELECTRIFLUX)

Program

Input Double click Circuit

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ELECTRIFLUX opens, as shown below:

ELECTRIFLUX (Circuit) window

Open a new circuit problem Open a new circuit problem, either with the toolbar icon or the menu. Using the icon in the toolbar

Click the Program

icon in the toolbar. Input click

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Create the back EMF external circuit model

Using the menu

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

Input

File New

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Create the back EMF external circuit model

New (blank) Circuit and Sheet windows open.

New Circuit and Sheet windows open in ELECTRIFLUX

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ELECTRIFLUX toolbar The ELECTRIFLUX toolbar includes icons for project management (New, Open, Save), as well as special icons for managing components, selecting components, and viewing the sheet. The following figure shows the ELECTRIFLUX toolbar.

The figures below identify the toolbar icons.

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ELECTRIFLUX menus Below are brief descriptions and illustrations of the ELECTRIFLUX menus. File menu

The File menu includes commands to open, save, print, and import/export circuit files.

Edit menu

The Edit menu includes commands to manage components on the sheet, e.g., Cut, Copy, Paste, Delete.

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View menu

The View menu includes commands to change the appearance of the sheet. For example, you can display or hide the circuit grid with View, Grid.

The Zoom commands are also accessible through the View menu.

Circuit menu

The Circuit menu includes commands to arrange components and connections, e.g., to insert connection points, rotate elements, insert space between components, etc.

F

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

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Sheet menu

The Sheet menu includes commands to manage individual circuit sheets—to change the name of the sheet, the background colors, the size of the sheet, the grid spacing, and so on.

Window menu

The Window menu includes commands for the display of the Circuit window (which includes the Sheet window).

? (Help) menu

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

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Change the size of the sheet Before you proceed, if you wish, you can change the size of the sheet window.

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

Right click anywhere on the sheet to open the context menu. Choose Sheet settings…. Program

Input Right click on the sheet Sheet settings…

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The Sheet properties dialog opens.

Modifying the sheet properties

Enter or verify the following: 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

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115

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

New (larger) sheet with grid

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

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

Circuit components placed on the sheet

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Add coils for stator windings First, add the coils for the stator windings. To add the coils, click Coil conductor in the Components library. Program

Input click Coil conductor

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

Ready to place the coil components (stator windings)

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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.

Moving Coil 1 into position

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.

Moving coil B2 into position

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Move the cursor to place the three other coils, as shown (somewhat enlarged) in the following figure.

Four coils placed on the sheet

Program

Input click to below B1 click to the left click to of B3

Chapter

3

place B2 directly place B3 below and to of B2 place B4 to the right

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121

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

To stop adding coil components to the sheet

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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.

To rotate coil B1

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.

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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

B2 rotates 270° clockwise click B3 symbol

B3 turns red click

once

B3 rotates 90° clockwise click B4 symbol

B4 turns red click

three (3) times

B4 rotates 270° clockwise

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

Coils rotated (slightly enlarged)

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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.

Ready to position inductors

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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.

Placing the third inductor (L3) on the sheet

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.

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

Inductors placed on sheet

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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

three (3) times

L2 rotates 270° clockwise click L3

L3 turns red click

three (3) times

L3 rotates 270° clockwise

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

Inductors oriented

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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.

Three resistors (open circuit loads) placed on the sheet

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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.

Ready to place resistor on the sheet

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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.

Resistors for open circuit loads placed on the sheet

Proceed as follows: Program

Input click to place R1 at the top right of the sheet click to place R2 to the right of coil B4 click to place R3 at the lower right corner of the sheet drag cursor off the sheet

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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

three (3) times

R2 rotates 270° clockwise click R3

R3 turns red click

three (3) times

R3 rotates 270° clockwise

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

Open circuit load resistors oriented

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Add the voltmeter Finally, add a large resistor between the phase C coil (B3) and the phase B coil (B4). This resistor acts as a voltmeter to measure the line to line voltage. Click Resistor again in the Components library. Program

Input click Resistor

Again, the red resistor symbol is displayed in the upper left corner of your sheet.

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Place the voltmeter (R4) on the sheet

Move your cursor with the resistor symbol and place it as shown in the following figure.

Placing the voltmeter (R4) on the sheet

Proceed as follows: Program

Input click to place R4 between B3 and B4 drag cursor off the sheet

Drag your cursor off the sheet to stop adding resistors.

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Rotate the voltmeter (R4)

Now rotate the resistor (R4) as follows. Program

Input click R4 symbol

R4 turns red click

twice

R4 rotates 180° clockwise

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

Components placed on sheet

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Save your circuit file Now is a good time to save your circuit file. Click the menu. Program

icon or choose File, Save from the

Input File

Save

The "Choose a file name" dialog opens.

Saving the circuit file

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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.

Starting to connect (wire) the components

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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 to complete the connection

Connect all the components in the same way.

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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

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

Connections for upper part of circuit

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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.

Adding an intermediate point for a connection

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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.

Connecting R3 to B3 without 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).

Connection selected (lines shown in red)

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The following figure shows the connections for the whole circuit.

Circuit connections complete

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.

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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.

Defining resistance for R1

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

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R1

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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

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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.

Defining inductance value for the first inductor (L1)

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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.

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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

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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

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The following dialog opens with a report of the analysis.

Analysis of the circuit

Click Exit to close the dialog. Program

Input

The circuit is connexe.

Exit

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Save and close the circuit file The circuit and transmission files are now complete. Save the circuit file by clicking the or by choosing File, Save from the menu. Program

icon

Input File

Save

Close the circuit by choosing File, Close. Program

Input File

Close

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The following dialog opens.

Confirming close of circuit

Click Yes to confirm: Program

Input

Close circuit?

Yes

Close ELECTRIFLUX Finally, close ELECTRIFLUX by choosing File, Exit. Program

Input File

Exit

The Flux Supervisor is displayed.

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Enter the physical properties

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:

Starting Preflu 9.1 to enter the physical properties

Program

Input Double click Geometry & Physics

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The Preflu 9.1 application opens.

Preflu 9.1 screen

Open the 1-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 an existing Flux project, click the Program

icon on the toolbar. Input click

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Enter the physical properties

Using the menu If you prefer, choose Project, Open project from the menu: Program

Input

Project Open project

The Open project dialog opens.

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Save your project with a new name

Enter or verify the following: Program

Input

Look in

Brushless_V9 [your working directory]

File Name

brushless_1layer.flu [your name] Open

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

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

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 back EMF calculations.

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Save your project with a new name

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.

Saving the brushless 1-layer model as bemf

Enter or verify the following: Program

Input

Save In:

Brushless_V9[working directory]

File Name:

bemf [your name] Save

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Define as Transient Magnetic

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.

Flux 9.1 automatically takes periodicity into account when using a circuit

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Change to the Physics context

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

Enter or verify the following: 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, context.

representing the Physical model

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

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The Physics context is shown in the following figure.

The bemf problem after going to the Physics context

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.

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Import materials from the materials database

Program

Input

Physics Material

Import material

In the Import material dialog, click on the list of materials in the database.

icon next to the material database to display the

List of materials in the database displayed

Now scroll to find the two materials you want to import; MAGNETPM and NLSTEELPM. Select both with the mouse using the Control key.

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Import the problem circuit

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 Program

icon on the toolbar. Input click

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Import the problem circuit

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 Program

in the dialog box.

Input click

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Import the problem circuit

The Open circuit dialog appears.

Enter or verify the following: Program

Input

Look In:

Brushless_V9 [your working directory]

File Name:

onedelta.ccs [your name] Open

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

Selected circuit ready for import

Proceed as follows: Program

Input Click OK

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Import the problem circuit

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.

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

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

Input

Click GeometryFlux2DView

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Assign materials and sources to the regions

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

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The Edit Face Region dialog opens.

Enter or verify the following: Program

Input

Type of region

Coil conductor region type Positive orientation of the current

Number of turns of the conductor

10

Coil conductor region component

B_PA

Symmetries and periodicities

All the symmetrical and periodical conductors are in series OK

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

Enter or verify the following: Program

Input

Type of region

Coil conductor region type Positive orientation of the current

Number of turns of the conductor

10

Coil conductor region component

B_MA

Symmetries and periodicities

All the symmetrical and periodical conductors are in series OK

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

Selecting the MC region for edit by selecting it graphically

The Edit Face Region dialog opens.

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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

Type of region

Coil conductor region type Positive orientation of the current

Number of turns of the conductor

20

Coil conductor region component

B_MC

Symmetries and periodicities

All the symmetrical and periodical conductors are in series OK

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

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Enter or verify the following: Program

Input

Type of region

Coil conductor region type Positive orientation of the current

Number of turns of the conductor

20

Coil conductor region component

B_PB

Symmetries and periodicities

All the symmetrical and periodical conductors are in series 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

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

Setting the resistance for coils B_MA & B_PA

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.

Setting the resistance for coils B_MC & B_PB

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Proceed as follows: Program

Input

Modify all - Resistance formula

0.141 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 Click Click Click

AIR AIRGAP + Ctrl SHAFT + Ctrl WEDGE + Ctrl

Right click, Edit array

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

Setting a vacuum property for the air regions

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Proceed as follows: Program

Input

Sub types:

Select "Air or vacuum" 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.

Selecting the Stator and Rotor regions graphically

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Once the regions are selected, right click the mouse and select Edit Array.

Edit the stator and rotor areas as a group

Under the Modify All column, we will set both of these regions to the NLSTEEL material.

Setting the stator and rotor to NLSTEELPM

Proceed as follows: Program

Input

Sub types:

Select "Magnetic reg"

Material

Select "NLSTEELPM" OK

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Assign the MAGNET Finally, assign the MAGNETPM material to the MAGNET region. Select the magnet region graphically with the mouse, then right click the mouse and select Edit.

Selecting the magnet region, then selecting Edit

The Edit Face Region window appears.

Setting the magnet region to the MAGNETPM material

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Proceed as follows: Program

Input

Type of region

Magnetic region

Material of the region

MAGNETPM OK

Now you must set the 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.

Setting the magnet to a positive radial magnet

Proceed as follows: Program

Input

Magnet...Oriented type

Radial Positif OK

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

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Creating and Assigning Mechanical Sets

Creating and Assigning Mechanical Sets Creating Mechanical Sets New with Flux 9.1 is the existence of Mechanical Sets. Mechanical Sets are used whenever you want motion in the model (either rotating or translating). Whenever there is motion in the model, you must define 3 mechanical sets; • Fixed - This defines the parts of the model that do not move • Moving- This defines the parts of the model that move (either rotating or translating) • Compressible- This defines the region between the moving and non-moving parts (and the displacement regions, in the case of a translating motion) We will first create these mechanical sets. Select Physics, Mechanical Set and New from the menu. Program

Input

Physics

Mechanical set New

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Create the MOVING_ROTOR Mechanical Set

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

Defining the Axis information for the MOVING_ROTOR Mechanical Set

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 axis parallel to Oz

Coordinate system

MAIN

Pivot point First coordinate

0

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Second coordinate

0 Click on "Kinematics" tab

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

Defining the General kinematics information for the MOVING_ROTOR Mechanical Set

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 "Internal characteristics" tab

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

Defining the Internal kinematics information for the MOVING_ROTOR Mechanical Set

Proceed as follows to define the Internal characteristics information: Program

Input

Type of load

Inertia, friction coefficients and spring

Moment of inertia

0

Constant friction coefficient

0

Viscous friction coefficient

0

Friction coefficient proportional to the square speed

0

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

Defining the External kinematics information for the MOVING_ROTOR Mechanical Set

Proceed as follows to define the External characteristics information: Program

Input

Type of load

Inertia, friction coefficients and spring

Moment of inertia

0

Constant friction coefficient

0

Viscous friction coefficient

0

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Friction coefficient proportional to the square speed

0

OK Create the FIXED_STATOR Mechanical Set

The New Mechanical set dialog closes briefly and then reappears. Enter the information to create the FIXED_STATOR mechanical set.

Defining the information for the FIXED_STATOR Mechanical Set

Proceed as follows: Program

Input

Mechanical set name

fixed_stator

Comment

the non-moving parts of the model

Type of mechanical set

Fixed OK

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Create the ROTATING_AIRGAP Mechanical Set

The New Mechanical set dialog closes briefly and then reappears. Enter the information to create the ROTATING_AIRGAP mechanical set.

Defining the information for the ROTATING_AIRGAP Mechanical Set

Proceed as follows: Program

Input

Mechanical set name

rotating_airgap

Comment

the rotating airgap

Type of mechanical set

Compressible

Used method to take the motion into account

Remeshing of the air part surrounding the moving body OK

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

Close the Mechanical set dialog

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.

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Program

Input

Click Click Click Click

AIR MAGNET + Ctrl ROTOR + Ctrl SHAFT + Ctrl

Right click, Edit array

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

Assigning regions 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.

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Program

Input Click Click Click Click Click Click

MA MC + Ctrl PA + Ctrl PB + Ctrl STATOR + Ctrl WEDGE + Ctrl

Right click, Edit array

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

Assigning regions to the FIXED_STATOR mechanical set

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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

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

Click on the Mechanical Set tab

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

Setting the AIRGAP region to the ROTATING_AIRGAP mechanical set

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Boundary conditions (Periodicity)

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.

Defining a periodicity for the brushless DC motor

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Boundary conditions (Periodicity)

Proceed as follows: Program

Input

Geometrical type of the periodicity

Rotation about Z axis with angle of the domain

Included angle of the domain

90

Offset angle with respect to the X line

0

Physical aspects of periodicity

Odd (anticyclic boundary conditions) OK

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

icon from the toolbar to start the Physical Check. Input Click

The console indicates that the physical check is completed.

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Boundary conditions (Periodicity)

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

Input

Project

Exit

When prompted, select to save your problem.

Proceed as follows: Program

Input

Save current project before

Yes

The Flux Supervisor is displayed.

Back EMF computation

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Solve the back EMF problem

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

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Solve the back EMF problem

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

Starting the solver

Program

Input Double click Direct

Back EMF computation

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Solve the back EMF problem

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

Choosing the problem to solve

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 Program

to begin the computation. Input click

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Solve the back EMF problem

The Definition of time data dialog opens:

Definition of time data for back EMF computation

Enter or verify the following information: Program

Input

Restarting mode

New computation initialised by static computation

Time values Initial value of the time step

Back EMF computation

0.00125

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Program

Input

Study time limit

100

Limit number of time steps

49

Storage of time steps 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

Initial position of the rotor 0. degrees

OK

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Solve the back EMF problem

When the computation stops, the following dialog opens:

End of back EMF computation

Click OK to close the dialog. Program

Input

Stop the solving process

OK

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Solve the back EMF problem

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

Input File

Exit

The Flux Supervisor is displayed.

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Results from the Back EMF computation

Results from the Back EMF computation To see your results, in the Flux Supervisor, in the Analysis folder, double click Results.

Starting Results analysis (PostPro_2D)

Program

Input Double click Results

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Results from the Back EMF computation

Select the problem to analyze and click Open:

Choosing the problem to analyze with PostPro_2D

Program

Input

Look in:

Brushless_V9[working directory]

File name:

BEMF.TRA [your name] Open

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Results from the Back EMF computation

PostPro_2D opens:

Opening PostPro_2D

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 manager… from the menu:

Back EMF computation

button or choose Computation, 2D Curves

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Results from the Back EMF computation

Program

Input Computation

2D curves manager…

The 2D curves manager opens.

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

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Results from the Back EMF computation

Enter the data for the curve as follows: Program

Input

Curve description Name

VoltRes4

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.00125 - 0.06125

Selection step

1

Second axis Quantity

Circuit

Components

Voltage

Third data Support

R4 click

Clicking the

button creates and displays the curve at the same time.

Back EMF computation

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Results from the Back EMF computation

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

Time variation circuit display of voltage in R4

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.

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Results from the Back EMF computation

Program

Input Computation

2D spectrum manager…

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

Settings for spectrum analysis of voltage curve for R4

Back EMF computation

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Results from the Back EMF computation

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

Spectrum scale

Linear

Display the DC component line

[check if desired]

Name

SpectrVoltRes4

[default color]

[new color, if desired] click

Clicking the time.

Chapter

3

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

Back EMF computation

Results from the Back EMF computation

211

The spectrum and the voltage curve are shown below:

Time variation spectrum of voltage for R4

Back EMF computation

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Results from the Back EMF computation

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:

Time variation voltage display for Resis1

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213

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).

Voltage and current curves for 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.

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Results from the Back EMF computation

Save and close PostPro_2D When you finish, click the Save have created). Program

button to save your analysis (including all the curves you

Input click

Close PostPro_2D by selecting File, Exit from the menu: Program

Input

File

Exit

The Flux Supervisor is displayed.

Chapter

3

Back EMF computation

Chapter 4 Square wave motor: Constant speed (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 Assign physical properties Plane geometry, 50.308 depth, transient magnetic calculation 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 Ω B_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 Coefficients for SWC2: 45, 105, 180 Coefficients for SWC3: 75, 135, 180 Coefficients for SWC4: 105, 165, 180 Coefficients for SWC5: 135, 15, 180 Coefficients for SWC6: 165, 45, 180

215

Solve at constant speed Select custom release (brushlike_921) Solve, Direct New computation Initialized by static computation Initial value of the time step Study time limit Limit number of time steps Store 1 on 1 time step Initial rotor position

0.00125s 100 s 49 0

Analyze results with PostPro_2D 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

Save and close PostPro_2D

216

Chapter 4 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

218

Create the 3-phase bridge circuit

Create the 3-phase bridge circuit The following figure shows the complete circuit.

3-phase bridge circuit

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Create the 3-phase bridge circuit

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

Starting the Circuit module (ELECTRIFLUX)

Program

Input Double click Circuit

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ELECTRIFLUX opens:

ELECTRIFLUX (Circuit) window

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Create the 3-phase bridge circuit

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

Click the

icon in the toolbar.

Program

Input click

Using the menu

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

Input

File New

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New (blank) Circuit and Sheet windows open.

New Circuit and Sheet windows open

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

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Create the 3-phase bridge circuit

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

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

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

Input Right click on the sheet Sheet settings…

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The Sheet properties dialog opens.

Modifying the sheet properties

Enter or verify the following: 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.

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225

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

Inverter circuit components placed on circuit sheet

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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

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

Ready to place first switch component

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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.

Moving Switch 1 into position

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

Input click to place switch S1 at upper left of circuit sheet

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The following figure shows Switch 1 in position.

Switch 1 in place

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

Moving Switch 2 into position

Place switch S2 below and to the right of S1. Program

Input click to place switch S2 below and to the right of S1

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Create the 3-phase bridge circuit

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

6 switches in place

Program

Input click right click S1 click right click S3

Square wave motor: Constant speed (torque ripples)

to place switch S3 to the of S1 to place switch S4 below to place switch S5 to the of S3 to place switch S6 below

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Create the 3-phase bridge circuit

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.

To stop adding switch components

Program

Input drag cursor off the circuit sheet

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Create the 3-phase bridge circuit

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.

To rotate Switch 1

Proceed as follows: Program

Input click S1 symbol

S1 turns red click

once

S1 rotates 90° clockwise

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Create the 3-phase bridge circuit

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

S3 rotates 90° clockwise click S5 symbol

S5 turns red click

once

S5 rotates 90° clockwise click S4 symbol

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Create the 3-phase bridge circuit

Program

Input

S4 turns red click

once

S4 rotates 90° clockwise click S6 symbol

S6 turns red click

once

S6 rotates 90° clockwise click S2 symbol

S2 turns red click

once

S2 rotates 90° clockwise

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Create the 3-phase bridge circuit

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

Switches rotated

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.

Six series voltages (placed under each switch)

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Create the 3-phase bridge circuit

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.

Ready to place the first series voltage

Square wave motor: Constant speed (torque ripples)

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Create the 3-phase bridge circuit

Place the 6 series voltages on the sheet

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

First series voltage in position

Program

Input click to place V1 below S1

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Create the 3-phase bridge circuit

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

Series voltages in position

Program

Input click click click click click

to to to to to

place place place place place

V2 V3 V4 V5 V6

below below below below below

S2 S3 S4 S5 S6

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

Square wave motor: Constant speed (torque ripples)

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Create the 3-phase bridge circuit

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.

Series voltage VS1 rotated

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Create the 3-phase bridge circuit

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

Square wave motor: Constant speed (torque ripples)

once

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Create the 3-phase bridge circuit

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

Six series voltages rotated

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Create the 3-phase bridge circuit

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.

Square wave motor: Constant speed (torque ripples)

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Create the 3-phase bridge circuit

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.

Placing main voltage source (VS7) on the sheet

Program

Input click to place V7 to the left of S1 drag cursor off the sheet

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

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Create the 3-phase bridge circuit

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.

Main voltage source rotated

Square wave motor: Constant speed (torque ripples)

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Create the 3-phase bridge circuit

Add the 3 coils Next, add 3 coils for the stator windings. Click Coil conductor in the Components library. Program

Input click Coil conductor

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247

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

Ready to place the first coil component

Square wave motor: Constant speed (torque ripples)

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4

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Create the 3-phase bridge circuit

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:

Coil 1 (B1) placed on the sheet

Program

Input click to place B1 below and to the right of V4

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Create the 3-phase bridge circuit

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

Three coils placed on sheet

Program

Input click right click right

to of to of

place B2 below and V6 place B3 below and V2

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

Square wave motor: Constant speed (torque ripples)

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Create the 3-phase bridge circuit

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

B1 rotates 90° clockwise click B2 symbol

B2 turns red click

once

B2 rotates 90° clockwise click B3 symbol

B3 turns red

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Create the 3-phase bridge circuit

Program

Input click

once

B3 rotates 90° clockwise With the three coils properly oriented, your sheet should resemble the following figure:

Coils oriented (after rotation)

Square wave motor: Constant speed (torque ripples)

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4

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Create the 3-phase bridge circuit

Add the inductors Now add inductors to model the stator winding end turn inductances. Click Inductor in the Components library. Program

Input click Inductor

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253

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

Ready to position inductors

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4

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Create the 3-phase bridge circuit

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.

Placing 3rd inductor (L3) on the sheet

Program

Input

click to place L1 under coil B1 click to place L2 under coil B3 click to place L3 under coil B2 drag cursor off the sheet To stop adding inductors, drag the cursor off the sheet.

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255

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

Inductors placed on circuit sheet

Square wave motor: Constant speed (torque ripples)

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4

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Create the 3-phase bridge circuit

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

L1 rotates 90° clockwise click L2 symbol

L2 turns red click

once

L2 rotates 90° clockwise click L3 symbol

L3 turns red click

once

L3 rotates 90° clockwise

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257

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

Inductors oriented

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.

Resistor R1 (voltmeter) being placed on the sheet

Square wave motor: Constant speed (torque ripples)

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Create the 3-phase bridge circuit

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

Input click Resistor

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259

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

Ready to place resistor on the sheet

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

Resistor R1 being placed on the sheet

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Create the 3-phase bridge circuit

Proceed as follows: Program

Input click to place R1 between V3 and V5 drag cursor off the sheet

Drag the cursor off the sheet to stop adding resistors.

Save your circuit Now is a good time to save your circuit. Click the Program

icon or choose File, Save from the menu. Input

File

Save

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4

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Create the 3-phase bridge circuit

The following dialog opens.

Saving the circuit file

Enter or verify the following: Program

Input

Save in

Brushless_V9 [working directory]

File name

squarewave [or your name] Save

Square wave motor: Constant speed (torque ripples)

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4

262

Create the 3-phase bridge circuit

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.

Ready to start wiring the circuit

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.

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Create the 3-phase bridge circuit

Program

Input click pin at top of S1 to complete 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.

Connections for upper part of circuit

Square wave motor: Constant speed (torque ripples)

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Create the 3-phase bridge circuit

The coils and inductors are connected as shown below.

Connections for lower part of circuit

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265

The following figure shows the connections for the whole circuit:

Circuit connections completed

Square wave motor: Constant speed (torque ripples)

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4

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Create the 3-phase bridge circuit

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.

Defining on/off resistance for Switch 1 (S1)

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Create the 3-phase bridge circuit

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

Square wave motor: Constant speed (torque ripples)

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Create the 3-phase bridge circuit

Program

Input Double click S3

1e-4 10000

Ok

Double click S4

1e-4 10000

Ok

Double click S5

1e-4 10000

Ok

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Create the 3-phase bridge circuit

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.

Defining inductance value for the first inductor (L1)

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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

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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.

Defining the voltmeter (resistor R1)

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.

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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

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Create the 3-phase bridge circuit

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

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The following dialog opens with a report of the analysis.

Analysis of the circuit

Click Exit to close the dialog. Program

Input

The circuit is connexe.

Exit

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Create the 3-phase bridge circuit

Save and close the circuit file The circuit and transmission files are now complete. Save the circuit by clicking the choosing File, Save from the menu. Program

icon or

Input File

Save

Close the circuit by choosing File, Close. Program

Input File

Close

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The following dialog opens.

Confirmation to close circuit

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 The Flux Supervisor is displayed.

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Assign the physical properties

Assign 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:

Starting the Preflu module

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Program

Input Double click Geometry & Physics

The Preflu 9.1 application opens.

Preflu 9.1 screen

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

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Using the icon in the toolbar To open an existing Flux project, click the Program

icon on the toolbar. Input click

Using the menu If you prefer, choose Project, Open project from the menu: Program

Input

Project Open project

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The Open project dialog opens.

Opening the Back EMF project

Enter or verify the following: Program

Input

Look in

Brushless_V9 [your working directory]

File Name

bemf.flu [your name] Open

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

Back EMF project is opened

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 constant speed analysis. To save your project with a new name, choose Project, Save As… from the menu:

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Program

Input

Project

Save As…

The Save flux project dialog opens.

Saving the bemf model as constspeed

Enter or verify the following: Program

Input

Save In:

Brushless_V9[working directory]

File Name:

constspeed [your name] Save

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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.

Confirmation to delete the circuit

Program

Input

Delete electrical circuit?

OK

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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 Program

icon on the toolbar. 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

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

in the dialog box.

Input Click

The Open circuit dialog appears.

Selecting the squarewave circuit to import

Enter or verify the following: Program

Input

Look In:

Brushless_V9 [your working directory]

File Name:

squarewave.ccs [your name] Open

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

Selected circuit ready for import

Proceed as follows: Program

Input Click OK

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

The constspeed problem after importing the squarewave circuit

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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

The Edit Face Region dialog opens.

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Enter or verify the following: Program

Input

Type of region

Coil conductor region type

Material of the region

Positive orientation of the current

Number of turns of the conductor

10

Coil conductor region component

B_COILA

Symmetries and periodicities

All the symmetrical and periodical conductors are in series OK

Edit the MA region

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

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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

Type of region

Coil conductor region type

Material of the region

Negative orientation of the current

Number of turns of the conductor

10

Coil conductor region component

B_COILA

Symmetries and periodicities

All the symmetrical and periodical conductors are in series OK

Edit the PB region

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

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Enter or verify the following: Program

Input

Type of region

Coil conductor region type

Material of the region

Positive orientation of the current

Number of turns of the conductor

20

Coil conductor region component

B_COILB

Symmetries and periodicities

All the symmetrical and periodical conductors are in series OK

Edit the MC region

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

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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

Type of region

Coil conductor region type

Material of the region

Negative orientation of the current

Number of turns of the conductor

20

Coil conductor region component

B_COILC

Symmetries and periodicities

All the symmetrical and periodical conductors are in series 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.

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Proceed as follows: Program

Input

Click B_COILA Click B_COILC + Shift Right click, Edit array

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

Setting the resistance of all the coils

Proceed as follows: Program

Input

Modify all - Resistance formula

0.141 OK

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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.

Changing the power supply voltage to 24v.

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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 Right click, Edit array

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

Setting all series voltages supplies

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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

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

Clicking the tab to go set the switch timing.

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.

Setting the timing for switch S1

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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

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. Select the Program

icon from the toolbar to start the Physical Check. Input Click

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The console indicates that the physical check is completed.

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

When prompted, select to save your problem.

Proceed as follows: Program

Input

Save current project before

Yes

The Flux Supervisor is displayed.

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Solve with user version

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

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

Flux2D custom version (brushlike_921)

F

Chapter

Make sure the appropriate user version (brushlike_921) is selected before you start the solver.

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Solve with user version

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

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

Program

Input Double click Direct

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

Choosing the problem to solve

Program

Input

Look in:

Brushless_V9[working directory]

File name:

CONSTSPEED.TRA Open

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

Checking the solving options

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 Number of iterations

50

Required precision

1.e-004

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Program

Input

Magnetic updatings to coupled problem Minimal number of updatings

1

Maximal number of updatings

5

Requested precision

1.e-002

Progressive Newton Raphson algorithm

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 the computation

Priority normal Apply

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Start the computation Click the Solve button Program

to begin the computation. Input click

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

Definition of time data

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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

Restarting mode

New computation initialised by static computation

Time values Initial value of the time step

0.00125

Study time limit

100

Limit number of time steps

49

Storage of time steps one step on

1 OK

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

Verifying the initial position of the rotor (0)

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

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Program

Input

Initial position of the rotor 0. degrees

OK

When the computation is finished, the following dialog opens:

End of computation

Click OK to close the dialog. Program

Input

Stop the solving process

OK

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

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Program

Input File

Exit

The Flux Supervisor is displayed.

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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.

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

Program

Input Double click Results

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

Choosing the problem to analyze

Program

Input

Look in:

Brushless_V9[working directory]

File name:

CONSTSPEED.TRA Open

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

Constant speed problem ready for analysis in PostPro_2D

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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 menu: Program

icon or by choosing Results, Properties from the

Input Results

Properties

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

Properties dialog for equiflux lines (Isovalues) display

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

Input

Isovalues Analyzed quantity

Equi flux

Support

Graphic selection

Computing parameters Quality

Normal

Number

21

Scaling

Uniform

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Program

Input

Display characteristics Write numbers

[check to enable, if desired] OK

When you click OK, the properties dialog closes. Display the isovalues plot

To display the plot, click the Isovalues button from the menu. Program

in the toolbar, or choose Results, Isovalues

Input Results Isovalues

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The isovalues plot is shown below:

Display of flux density lines at time step 0.00125

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:

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Program

Input Right click on isovalues sheet

Properties

The Geometry properties dialog opens:

Removing the legend from the isovalues display

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.

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

Isovalues plot

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

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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:

Group manager dialog

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

Input

Filter

Region

Objects available

ROTOR MAGNET STATOR

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Program

Input Add ->

Current group:

ROTOR MAGNET STATOR

Group name

Big3 [or your name] 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

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The Display properties dialog opens.

Properties for color shade display

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

Input click Color Shade tab

Analyzed quantity

|Flux density|

Support

Big3 [group name]

Computing parameters Quality

Normal

Scaling

Uniform OK

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When you click OK, the Display properties dialog closes. Display the color shade plot

To display the plot, click the color shade button shade from the menu. Program

in the toolbar or choose Results, Colour

Input Results Colour shade

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

Color shade plot of flux density on a 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.

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Information about the iterations for each time step is available under the *log_res file tab at the bottom of the PostPro_2D screen.

Information about solving at time 0.055 s, Computation 44

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 Program

or choose Supports, Path manager… from the menu: Input Supports Path manager…

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The Path manager dialog opens.

Path manager

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 figure above).

Chapter

4

(when Arc is selected, as shown in the

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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).

Checking coordinates for path through airgap

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

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

Section Editing dialog to create path

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

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

Path through the airgap (enlarged)

In the Path manager dialog, click the manager at the same time. Program

button to create the path and open the 2D Curves

Input click

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Flux density along the airgap path The 2D curves manager is shown in the following figure.

Settings for flux density curve (normal component)

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

[default color]

[new color, if desired] Path

First axis X axis

CenterGap [path name]

Second axis

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Program

Input

Quantity

Flux density

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.

Normal component curve created

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

[default color]

[new color, if desired] Path

First axis X axis

CenterGap [path name]

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Program

Input

Second axis Quantity

Flux density

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 Program

icon to open a blank curves sheet. Input click

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

Input click Right click on the sheet

Properties

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

Curves properties Select dialog; choose curves to display

Enter or verify the following in the Selection dialog: Program

Input

Curves filter

Computation

Curves available

FDNorm FDTang Add -->

Displayed curves

FDNorm FDTang

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Click the Display tab to bring it to the front.

Settings for superimposed curves display

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

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Program Scale

Input linear OK

The two curves superimposed are shown below.

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

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

Input 2D Curves New cursor…

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Results: Constant speed computation

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

2D spectrum manager…

The Spectrum manager opens.

Spectrum manager

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Results: Constant speed computation

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

Spectrum scale

Linear

Display the DC component line

[check to enable if desired]

Name

SpectFDNorm [or other name]

[default color]

[new color, if desired] click

Clicking the

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

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The spectrum and the normal component curve are shown below:

Spectrum analysis of normal component of flux density

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

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The Curves properties dialog opens.

Sample of settings for spectrum display

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.

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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 manager… from the menu. Program

button or choose Computation, 2D curves

Input

Computation

2D curves manager…

The 2D Curves manager opens.

Settings for AxisTorque curve

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Enter or verify the following information: Program

Input

Curve description Name

AxisTorque

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.00125 - 0.06125

Selection step

1

Second axis Quantity

Mechanics

Components

Axis torque

Third data click Clicking the

button creates and displays the curve.

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The axis torque curve is shown below:

Axis torque over one cycle

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.

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Results: Constant speed computation

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.

Mean values from axis torque curve

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

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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

2D curves manager…

The 2D curves manager opens.

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

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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

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.00125 - 0.06125

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. Enter or verify the following: Program

Input

Curve description Name

V7Current

[default color]

[new color, if desired] Parameter

First axis

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Program

Input

X axis

Time

Parameter values

0.00125 - 0.06125

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 Program 2d curves manager

Chapter

4

button. Input click

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Superimpose the V7 voltage and current curves for a display like the following (we used the "Automatic" setting for the Y axis):

Voltage and current in the voltage source

Current in Switch1

Now create a curve of the current through Switch1. Click the Program

button to open the 2D curves manager. Input click

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Enter or verify the following: Program

Input

Curve description Name

CurrSW1

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.00125 - 0.06125

Second axis Quantity

Circuit

Components

Current

Third data Support

S1 click

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347

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

Current in Switch 1

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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

Enter or verify the following: Program

Input

Curve description Name

CurrB1(PA)

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.00125 - 0.06125

Second axis Quantity

Circuit

Components

Current

Third data Support

B_COILA click

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349

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

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

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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

Enter or verify the following information: Program

Input

Curve description Name

CurrB2(PB)

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.00125 - 0.06125

Second axis Quantity

Circuit

Components

Current

Third data Support

B_COILB click

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351

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

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

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Results: Constant speed computation

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

Enter or verify the following information: Program

Input

Curve description Name

CurrB3(MC)

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.00125 - 0.06125

Second axis Quantity

Circuit

Components

Current

Third data Support

B_COILC click

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4

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353

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

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

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Save and close PostPro_2D

Save and close PostPro_2D This concludes our analysis of the motor at constant speed. To save the analysis supports and the curves you have created, click the Save from the menu. Program

icon or choose File,

Input File Save

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Save and close PostPro_2D

Then close PostPro_2D by choosing File, Exit. Program

Input File

Exit The Flux Supervisor is displayed.

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4

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Chapter

Save and close PostPro_2D

4

Square wave motor: Constant speed (torque ripples)

Chapter 5 No load startup with electromechanical coupling In this chapter you modify the constant speed problem to simulate the no load startup.

Modify physical properties of constant speed problem Airgap 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 Study time limit Limit number of time steps Store 1 on Initial position of the rotor

5e-4 s 100 s 100 1 0

357

Analyze results with PostPro_2D Isovalues (equi flux) lines at time step 100 (time 0.05 s) Time variation analyses (2D curves) Axis torque Angular velocity Rotor position Waveforms of electric quantities Voltage and current in voltage source 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

Save and close PostPro_2D

358

Chapter 5 No load startup with electromechanical 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

360

Modify the physical properties

Start Preflu 9.1 In the Flux Supervisor, in the Construction folder, double click Geometry & Physics:

Starting the Preflu module

Program

Input Double click Geometry & Physics

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The Preflu 9.1 application opens.

The initial Preflu screen

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. You can open an existing project either with the toolbar icon or the menu. Using the icon in the toolbar To open an existing Flux project, click the Program

icon on the toolbar. Input click

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Using the menu If you prefer, choose Project, Open project from the menu: Program

Input

Project Open Project

The Open project dialog opens.

Opening the Constant Speed project

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Program

Input

Look in

Brushless_V9 [your working directory]

File Name

constspeed.flu [your name] Open

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

The constspeed project is opened

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 no load analysis. To save your project with a new name, choose Project, Save As… from the menu:

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Program

Input

Project

Save As…

The Save flux project dialog opens.

Saving the constspeed project as noload

Enter or verify the following: Program

Input

Save In:

Brushless_V9[working directory]

File Name:

noload [your name] Save

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Modify the physical properties

Define the no load characteristics The no load model is identical to the constant speed model except for the definition of the MOVING_ROTOR mechanical set. Edit the MOVING_ROTOR mechanical set

Expand the Mechanical Set in the Data tree. Select the MOVING_ROTOR mechanical set and right-click the mouse to select Edit. Proceed as follows: Program

Input

Click MOVING_ROTOR Right-click, Edit

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

Going to the Kinematics tab

Proceed as follows: Program

Input Click Kinematics

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Modify the physical properties

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

Going to the Internal Characteristics tab

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

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

Entering the No Load Internal Kinematic characteristics

Enter or verify the following: Program

Input

Type of load

Inertia, friction coefficients and spring

Moment of inertia

3.8675e-5

Constant friction coefficient

0

Viscous friction coefficient

0.005

Friction coefficient proport…

0 Click External characteristics

F

Chapter

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.

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Modify the physical properties

Enter the external kinematic characteristics.

Entering the No Load External Kinematic characteristics

Enter or verify the following: Program

Input

Type of load

Inertia, friction coefficients and spring

Moment of inertia

0

Constant friction coefficient

0

Viscous friction coefficient

0

Friction coefficient proport…

0 OK

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

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Verify the user version: brushlike_921

Program

Input

Project

Exit

When prompted, select to save your problem.

Proceed as follows: Program

Input

Save current project before

Yes

The Flux Supervisor is displayed.

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.

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Verify the user version: brushlike_921

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

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Solve the no load startup problem

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

Starting the solver with the brushlike_921 release (user subroutine)

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Solve the no load startup problem

Program

Input Double click Direct

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

Choosing the problem to solve

Program

Input

Look in:

Brushless_V9[working directory]

File name:

NOLOAD.TRA Open

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Solve the no load startup problem

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

Setting the general solving options

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 Number of iterations

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5

50

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Solve the no load startup problem

Program Requested precision

Input 1.e-004

Thermal iterations Number of iterations

50

Requested precision

1.e-004

Magnetic updatings for coupled problem Minimal number of updatings

1

Maximal number of updatings

5

Requested precision

1.e-002

Progressive Newton Raphson algorithm

Disabled

Accuracy definition

Automatic accuracy

Solver type

SuperLU (9.20)

Priority associated to the computation

Priority normal Apply

Click Apply to confirm the options.

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Then click the Solve icon

to begin the computation.

Program

Input click

The Definition of time data dialog opens:

Definition of time data for no load startup

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Enter or verify the following information: Program

Input

Restarting mode

New computation initialised by static computation

Time values Initial value of the time step

5e-4

Study time limit

100

Limit number of time steps

100

Storage of time steps one step on

1 OK

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

Initial rotor position for rotating air gap

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

Input

Initial position of the rotor 0. degrees

OK

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When the computation is finished, the following dialog opens:

End of solving (time steps completed)

Click OK to close the dialog and stop the computation. Program

Input

Stop the solving process

OK

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Solve the no load startup problem

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

Input File

Exit

The Flux Supervisor is displayed.

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Results from no load startup

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:

Starting Results analysis with customized release

Program

Input Double click Results

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Results from no load startup

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

Choosing no load problem to analyze

Program

Input

Look in:

Brushless_V9[working directory]

File name:

NOLOAD.TRA Open

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5

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Results from no load startup

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.

No load problem open in PostPro_2D

Begin your analysis with a display of the isovalues (equi flux) lines at time step 100, or time = 0.05 s.

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Results from no load startup

Select the 100th time step (0.05 s)

To select the 100th time step, click the Parameters manager button Manager… from the menu: Program

or choose Parameters,

Input Parameters Manager…

The Parameters dialog opens:

Choosing time step 100 from the Samples number list

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

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Results from no load startup

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

Rotor position at time step 100 (0.05 s)

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Results from no load startup

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

No load startup with electromechanical coupling

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The Display properties dialog opens:

Settings for display of 21 equiflux lines

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

Input

Isovalues Analyzed quantity

Equi flux

Support

Graphic selection

Computing parameters Quality

Normal

Number

21

Scaling

Uniform

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Results from no load startup

Program

Input

Display characteristics Write numbers

[check to enable if desired] OK

Click OK to apply the settings and close the dialog. Display the isovalues plot

To display the plot, click the Isovalues button Program

or choose Results, Isovalues from the menu. Input Results Isovalues

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

Isovalues at time step 100 (0.05 s)

If you wish, display this plot on the full geometry. Click the Geometry, Full geometry from the menu. Program

icon in the toolbar or choose

Input click

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389

The plot on the full geometry is shown below.

Isovalues plot on full geometry (t = 0.05 s)

No load startup with electromechanical coupling

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Results from no load startup

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 Curves manager… from the menu. Program

button or by choosing Computation, 2D

Input Computation

2D curves manager…

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Results from no load startup

The 2D curves manager opens:

Properties for time variation curve of axis torque

Axis torque curve

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

Input

Curve description Name

AxisTorque

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.0005 - 0.05

Selection step

1

Second axis

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5

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Results from no load startup

Program

Input

Quantity

Mechanics

Components

Axis torque click

Clicking the

icon creates and displays the curve.

The axis torque curve is shown below:

Axis torque

F

Chapter

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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Results from no load startup

Angular velocity curve

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

Input click

Enter or verify the following: Program

Input

Curve description Name

AngVel

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.0005 - 0.05

Selection step

1

Second axis Quantity

Mechanics

Component

Angular velocity click

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5

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The angular velocity curve is shown below:

Angular velocity curve

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5

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395

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:

Axis torque and angular velocity curves superimposed

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Rotor position curve

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

Input click

Enter or verify the following: Program

Input

Curve description Name

Position

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.0005 - 0.05

Selection step

1

Second axis Quantity

Mechanics

Components

Position click

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The curve of the rotor position is shown below:

Position curve

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5

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Results from no load startup

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

Position and angular velocity curves superimposed

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Results from no load startup

Waveforms of electric quantities Look next at the waveforms of the electric quantities. Click again. Program

to open the 2D curves manager

Input click

The 2D curves manager opens.

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

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5

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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

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.0005 - 0.05

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.

Curves listed in 2D Curves manager

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Results from no load startup

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

Input

Curve description Name

CurrV7

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.0005 - 0.05

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.

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Open a new 2D curves sheet and superimpose the V7 voltage and current curves (use the "Stretched" option for the Y axis):

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

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Results from no load startup

Current in Switch1

Now create a curve of the current in Switch1 (S1). Click Program

to open the 2D curves manager.

Input click

Enter or verify the following: Program

Input

Curve description Name

CurrS1

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.0005 - 0.05

Selection step

1

Second axis Quantity

Circuit

Component

Current

Third data Support

S1 click

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The curve of the current in SWITCH1 is shown below:

Current in Switch1

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Results from no load startup

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

Enter or verify the following: Program

Input

Curve description Name

CurrB1-PA

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.0005 - 0.05

Selection step

1

Second axis Quantity

Circuit

Component

Current

Third data Support

B_COILA click

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

Current in B1 (PA) coil component

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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

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.0005 - 0.05

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.

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

Input

Curve description Name

CurrB2-PB

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.0005 - 0.05

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.)

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

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

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

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

Input

Curve description Name

VoltB3-MC

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.0005 - 0.05

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

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.0005 - 0.05

Selection step

1

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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:

Superimposed display of voltage and current curves in B3 coil component

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

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Save and close PostPro_2D

Save and close PostPro_2D When you have finished your analysis, click the Save button and curves you have created. Program

to save the analysis supports

Input click

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

Input File

Exit

The Flux Supervisor is displayed.

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Chapter 6 Servo action with electromechanical coupling You 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

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 Study time limit 100 s Limit number of time steps 65 Store 1 on 1

Analyze results with PostPro_2D 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 Waveforms of electric quantities Voltage and current in voltage source Current in Switch1 Current in B1 coil component Voltage and current in B3 coil component

Save and close PostPro_2D Close Flux2D

414

Chapter 6 Servo action with electromechanical coupling 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.

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Modification of physical properties

Start Preflu 9.1 In the Flux Supervisor, in the Construction folder, double click Geometry & Physics:

Starting the Preflu module

Program

Input Double click Geometry & Physics

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The Preflu 9.1 application opens.

The initial Preflu screen

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. You can open an existing project either with the toolbar icon or the menu. Using the icon in the toolbar To open an existing Flux project, click the Program

icon on the toolbar. Input click

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Using the menu If you prefer, choose Project, Open project from the menu: Program

Input

Project Open Project

The Open Project dialog opens.

Opening the No Load project

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Program

Input

Look in

Brushless_V9 [your working directory]

File Name

noload.flu [your name] Open

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

The Noload project is opened.

Save your project with a new name Save your project now with a specific name to indicate that you will be using this model to simulate servo action. To save your project with a new name, choose Project, Save As… from the menu:

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Program

Input

Project

Save As…

The Save flux project dialog opens.

Saving the noload project as servo

Enter or verify the following: Program

Input

Save In:

Brushless_V9[working directory]

File Name:

servo [your name] Save

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Define the servo model characteristics The servo model is identical to the no load model except for the definition of the MOVING_ROTOR mechanical set. Edit the MOVING_ROTOR mechanical set

Expand the Mechanical Set in the Data tree. Select the MOVING_ROTOR mechanical set and right-click the mouse to select Edit. Proceed as follows: Program

Input

Click MOVING_ROTOR Right-click, Edit

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The Edit Mechanical Set dialog appears. To enter the servo characteristics, click on the Kinematics tab at the top.

Going to the Kinematics tab

Proceed as follows: Program

Input Click Kinematics

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Now go to define the Internal Characteristics of the kinematics.

Going to the Internal Characteristics tab

Proceed as follows: Program

Input Click Internal characteristics

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Change the constant friction coefficient value.

Defining MOVING_ROTOR for servo model

Enter or verify the following: Program

Input

Type of load

Inertia, friction coefficients and spring

Moment of inertia

3.8675e-5

Constant friction coefficient

0.3

Viscous friction coefficient

0.005

Friction coefficient proport…

0 OK

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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

When prompted, select to save your problem.

Proceed as follows: Program

Input

Save current project before

Yes

The Flux Supervisor is displayed. Now you can define the transient startup of the servo motor.

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Transient startup of servo problem

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:

Starting the Transient Startup module

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Transient startup of servo problem

Program

Input Double click Transient startup

The Transient starting (DEMEVO) module opens:

Transient startup (DEMEVO) screen

Prepare for the transient startup as follows:

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Solve the servo simulation with user version

Program

Input

Problem name

servo

Name of the problem containing the initialization (MS, MD, or ME) :

NOLOAD

looking for the number of time steps Number of time steps in the file: 100 Number of the time step to use as initial value (default 100_0.1)

100

Results are stored in the output 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.

User version of Flux2D

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.

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Solve the servo simulation with user version

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

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

Program

Input Double click Direct

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Solve the servo simulation with user version

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

Choosing the servo problem to solve

Program

Input

Look in:

Brushless_V9[working directory]

File name:

SERVO.TRA Open

In the Solver window, click the Solve icon Program

to start the computation. Input click

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Solve the servo simulation with user version

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

Notice of previous results for servo problem (transient startup)

Click Yes to continue. Program

Input

Do you want to continue ?

Yes

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The Definition of time data dialog opens:

Defining the time data for the SERVO problem

Enter or verify the following: 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

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Program

Input

Study time limit

100

Number of additional time steps

65

Storage of time steps one step on :

1 OK

Click OK to close the dialog and watch as the solution proceeds. When the computation is finished, the following dialog opens:

End of SERVO computation

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Click OK to close the dialog and stop the computation. Program

Input

Stop the solving process

OK

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

Input File

Exit

The Flux Supervisor is displayed.

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Results from servo motor

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:

Starting Results analysis with customized version

Program

Input Double click Results

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

Choosing SERVO problem to be analyzed

Program

Input

Look in:

Brushless_V9[working directory]

File name:

SERVO.TRA Open

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

Servo model open in PostPro_2D

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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 Manager from the menu: Program

button or choose Parameters,

Input Parameters Manager

The Parameters dialog opens:

Choosing time 0.115 in the Parameters dialog

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

Model at last time step, time 0.115 s

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Set properties for the isovalues display

Now set the display properties for 21 isovalue lines. Click the Results, Properties icon Program

or choose Results, Properties from the menu. Input Results

Properties

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The Display properties dialog opens:

Settings to display 21 equiflux lines

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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Display the isovalues plot

To display the plot, click the Isovalues icon Program

in the toolbar. Input click

The isovalues plot is shown below:

Equiflux (isovalues) lines at time 0.115 s

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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The isovalues plot over the full geometry is shown below:

Isovalues at t = 0.115 (full geometry)

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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 Group manager from the menu: Program

or choose Supports,

Input Supports Group Manager

The Group manager dialog opens:

Settings to create display group for color shade plot

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Enter or verify the following: Program

Input

Filter

Region

Objects available

ROTOR MAGNET STATOR Add -->

Current group

ROTOR MAGNET STATOR

Group name

Big3 [or your name]

These regions are displayed on the model geometry:

Creating a regions group for color shade display

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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 Program

or choose Results, Properties from the menu. Input Results

Properties

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The Display properties dialog opens:

Setting properties for color shade plot on group

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 click Color Shade tab

Support

Big3 [your regions group] OK

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Display the color shade plot

To display the plot, click the Color shade icon Program

in the toolbar. Input click

The color shade plot is shown below:

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

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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 manager… from the menu. Program

icon or by choosing Computation, 2D curves

Input Computation

2D curves manager…

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

Input

Curve description Name

AxisTorque

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.05 - 0.115

Selection step

1

Second axis Quantity

Mechanics

Components

Axis torque 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.

Settings for curve of angular velocity

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

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.05 - 0.115

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Program Selection step

Input 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:

Superimposed display of axis torque and angular velocity curves

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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Rotor position

Next, create a curve of the rotor position. Click Program

to open the 2D curves manager. Input click

Enter or verify the following: Program

Input

Curve description Name

Position

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.05 - 0.115

Selection step

1

Second axis Quantity

Mechanics

Component

Position click

Click the

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6

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:

Superimposed display of position and angular velocity curves

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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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

Enter or verify the following: Program

Input

Curve description Name

VoltV7

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.05 - 0.115

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

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.05 - 0.115

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:

Superimposed display of voltage and current curves for voltage source

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Current in Switch 1

Next, create a curve of the current in SWITCH1. Click Program

to open the 2D Curves manager.

Input click

Enter or verify the following: Program

Input

Curve description Name

CurrS1

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.05 - 0.115

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:

Current in Switch1

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Current in B1 (PA) coil component

Next look at a curve of the current in the B1 (PA) coil component. Click Curves manager. Program

to open the 2D

Input click

Enter or verify the following: Program

Input

Curve description Name

CurrB1-PA

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.05 - 0.115

Selection step

1

Second axis Quantity

Circuit

Component

Current

Third data Support

Electrical component B_COILA click

Click the

button to create and display the curve.

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The B1-PA current curve is shown below:

Current in the PA coil component (positive phase A)

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Voltage and current in B3 (MC) coil component

Finally, look at the voltage and current in the B3 (MC) coil component. Click 2D Curves manager. Program

to open the

Input click

Enter or verify the following: Program

Input

Curve description Name

VoltB3-MC

[default color]

[new color, if desired] Parameter

First axis X axis

Time

Parameter values

0.05 - 0.115

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

[default color]

[new color, if desired] 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

Chapter

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

MC voltage and current curves

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

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Close PostPro_2D

Close PostPro_2D When you are ready, close PostPro2D by choosing File, Exit from the menu: Program

Input File

Exit The following dialog opens.

Saving analysis file

Choose Yes to save your analysis. Program

Input

Do you want to save SERVO

Yes

The Flux Supervisor is displayed.

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Close Flux2D

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.

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