A Basic Procedure for FEM Analysis of BLDC Motor by Maxwell 2D

8/4/2019 A Basic Procedure for FEM Analysis of BLDC Motor by Maxwell 2D

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Problem Setup and Solution

Use these buttons to page forward and backward

This section will go through how to setup, solve, and post process a

sample problem Three Phase, Four Pole, Permanent MagnetBrushless DC Motor Using the Magnetostatic Solver.

Click on Slide Show/View Show to start the presentation. This is not a

full screen presentation, but rather it is shown in an individual windowwhich can be resized so that you can run the Maxwell software andview this presentation on the same screen.

A Basic Procedure for FEM Analysis of BLDC Motor By Maxwell 2D


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Create a New Project

Click on Projects to create a new Maxwell Project

Its recommended that you run the actual softwarewhile going through this tutorial.


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New Project

Select New

PM_Sync_3Ph_Motor Type in Name

Open the new project

Select Maxwell2D Version 8


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Executive Commands Area

This is the list of Executive Commands

Change Solver to Magnetostatic

Keep the drawing Plane to X-Y


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The Maxwell 2D Solvers

For this example, we are going to use the Magnetostatic solver


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Drawing Plane

A motor is best modeled by using the XY drawing Plane


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Define Model

The first step is todefine the geometry

In general, we will work down this list of

Executive Commands


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2D Modeler Toolbar

Use these icons as shortcuts to commonly used commands


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Define Problem Region

The drawing size should be3-5 times model size unlessthere is extreme fringing.

For this simulation most of

the flux will be contained inthe motor, so well use threetimes the model size.

The outside diameter of thismotor is 160 mm; well makethe problem region +/- 250 mm.

-250

-250

250

250


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Stator Slot Select Object/Polyline to create one half a slot. Use the Keyboard entryfields at the bottom left of the screen to enter the following coordinates

(make sure the mouse does not enter the black drawing region whenusing keyboard entry, or the focus is taken off the entry fields and ontothe screen):

First Point 1.25, 37.5Second Point 1.25, 38.0Third Point 2.4, 38.5Fourth Point 3.4, 46.5 click Enter twice to complete the

polyline command

Maxwell always tells you what to do; just look at the bottom of the screenfor instructions on the function of right and left mouse button.


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Stator Slot Zoom in and click on this object to highlight it. Next click onEdit/Duplicate/Mirror Duplicate and pick two points on the Y-Axis. Nextpick Object/Arc/Clockwise:

pick the midpoint .. (0, 46.5)the top of the left side of the slot .. (-3.4, 46.5)the top of the right side of the slot (3.4, 46.5)

change the number of segments of this arc to 6. With this arc we have nowdrawn one complete stator slot. Your geometry so far should look like this:

Show Me


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Stator Slot To finish creating this slot, we need to create the arc segment between twoadjacent slots, which will make up the inside diameter of the stator. Selectthe slot that was just created by clicking on it; you will notice that it willhighlight. Next, choose Edit/Duplicate/Along Arc , pick the (0,0) point asthe pivot point and duplicate along an angle 15 degrees with a total numberof two slots. Your geometry should look like this:


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Stator Slot Next, click on Object/Arc /Clockwise , and create an arc that has a centerat (0,0) and then snap to the bottom edge of the left slot and then thebottom edge of the right slot; using 11 segments, or one degree incrementof arc segments. Finally, click on Reshape/Edge/ Delete and delete all of the line segments that make up the second slot, leaving the arc segmentthat was just created. We now have one arc and one tooth drawn. Yourgeometry should look like this:


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Stator Slot

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Next we need to create the stator coil in the slot. The first step here is to turnon the hatches of the stator slot by clicking on Edit/Attributes/By Clicking ,select the stator slot and check Show Hatches . Make sure that the snap isset to Vertex and Grid ; Model/Snap to Mode . Next pick Object/Polylineand trace the inside of the slot to create the coil and then across the bottomof the slot to close off the coil; call this object Coil_1 and change its color toyellow; turn the hatches off. Your geometry should look like this:

Create the entire stator by selecting both the slot

and the coil. Click on Edit/Duplicate /Along Arc ,pick (0,0) as the pivot point and duplicate at a 15degree angle 24 times.


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Stator and Permanent MagnetsThe outside diameter of the stator will be drawn using a circle. Click on

Object/Circle/Two point and select the (0,0) point and point (0,60), acceptthe default of 36 segments; the stator OD is 120 mm. Rename this objectStator and change its color to green. Your geometry should look like this:


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Stator and Permanent Magnets

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Next create the permanent magnets by creating two straight lines and twoarcs to make up one magnet and then duplicating this four times:

First line: (-21.91, 29.81) and (-18.36, 24.98)Second line: (21.91, 29.81) and (18.36, 24.98)

The outside arc should have an arc segments as close to 1 degree aspossible (the actual value in degrees will change to ensure an integer value

for the number of segments), the inside arc segment can use the defaultvalue. Your geometry should look like this:

Select this permanent magnet and click onEdit/Duplicate/Along Arc (90 degrees anda total of 4), to create the four permanentmagnets. Save the work youve done so farby clicking of File/Save .


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Rotor Your geometry should look like this:

To create the rotor, well use the inside arc segments of the permanentmagnets. The first step is to copy the permanent magnets in the clipboard;select the four permanent magnets and click on Edit/Copy . Next, click onReshape/Edge/Delete and delete all edges of the permanent magnets exceptthe inside arc. Then use the Object/Arc command to connect the remainingarc segments and call this new object the Rotor . Choose Edit/Paste to placethe permanent magnets back into the model.

Click on Object/Circle (centered at the origin) to create theshaft which has a 26mm diameter.


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Rotor

Assign different colors for thestator coils to represent the

A_phase, A_return, B_phase, etc.windings. Well also use differentcolors for the permanent magnetsto show different polarity. Changethe name of the object between thepermanent magnets and the statorfrom object1 to Air_Gap .

A

A

A

A

C-C-

C-C-

BB

B B A-A-

A-A-

CC

C C

B-

B-B-

B-

Show Me

Click on File/Save and thenFile/Exit .

You wont see A, C-, B, etc onyour drawing. Its shown herefor information only.


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Group Objects

It is often helpful to group

like objects. In this casewell group the A_phase ,A_return , B_phase , etc.coils. A

A

A

A

C-C-

C-C-

BB

B B A-A-

A-A-C

C

C

C

B-

B-B-B-


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Group Objects

Click on Define Model/Group Objects and select coil pairs to be used forphase windings.

Permanent magnets cannot be grouped, because the direction of magnetization for each permanent magnet needs to be set individually.

Click on each object that represents the A_phase winding and group themtogether. Repeat this for A_return , B_phase , etc.

Exit and Save these changes.

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Materials B-H Curves

Relative incremental permeability

needs to be greater than 1.0

In general, at least 20 points needto be included in the B-H curve,

and it needs to be defined wellinto the saturation region.

Save all custom B-H curves to

home /maxwell/config/maxwelldb / filename .bh


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Materials Permanent Magnets

Permanent Magnets are modeled as a combination

surface and volume current densities.

Linear Magnets are modeled using equivalentcurrent sheets on the surface of the magnets.

When specifying coercivity H c Maxwell usesthe normal value, not the intrinsic value. Therelationship between magnetic properties is:

B r = o * M p = o * r * H c

B

B rRemanence

Hc - Coercivity H

B r Magnetic Retentivity or RemanenceHc Magnetic Coercivityr Relative Permaebilityo Permeability of Free Space 4 e-7Mp Permanent Dipole Magnetization

When defining a linear permanent magnet, you need tospecify two quantities from the expression above.


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Materials Permanent Magnets

Non-linear permanent magnets can also be modeled. The non-linear curveused in the simulation represents the recoil permeability, not the original

virgin curve.

The blue non-linear curverepresents the original virgincurve of the permanent magnetmaterial. Depending upon theshape of the magnet, it couldreside at different operatingpoints. The recoil curve willstart from that operating pointand intersect the B axis at alower value.

Original curve

Recoil curve

You need to input this redrecoil curve into Maxwell


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Materials Create New Magnet

Create a new linear permanent magnet material. Click on Setup/Materials to enter theMaterial Manager.

Click on Material/Add to add a new material and change the name (here well just call ittest_mag). Next click on Options , deselect and select B r ,using the following definition:

Br = 1.25 TeslaH

c= -947,000 Amps/Meter

Click on Enter to add this material to the local database.

Choose one of the permanent magnets and Assign it this material property. You will beasked to choose the direction of magnetization, i.e. the north pole. Here you have three

options: Align with objects orientationAlign with a given directionAlign relative to objects orientation


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Materials Create New Magnet

You will notice that the permanent magnet selected has a white arrow near its center. This isthe objects orientation, if you choose Align with objects orientation this will be thedirection of magnetization.

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If you choose Align with a given direction you will be asked to choose an angle. Thisangle is measured from the X-Axis in the counter clock-wise direction.

If you choose Align relative to objects orientation you can define an angle relative tothe white arrow you see on the screen. You may also choose to make this a function, welldiscuss functions later on in this tutorial. Click on View Angle and then the magnet to seeif the direction of magnetization is set correctly.

For now, choose Align with a given direction and alternate each permanent magnetNorth South North South. North is pointing out from the rotor, and South ispointing in towards the rotor.


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Materials Create New Steel

We now need to create a non-linear bh curve for the steel we will use, M19. Click onMaterial/Add to add a new material and change the name to M19_Steel . Click onNonlinear Material and then the button B H curve. Click on Add Point and use the entryfields in the bottom left to specify this bh curve.

H (Amps/Meter) B (Tesla)0.0 0.027.06 0.242.98 0.468.46 0.6107.46 0.8175.12 1.0302.48 1.2746.12 1.43582 1.611144 1.839800 2.0119400 2.10003

We dont enter the entire bh loop. You need tostart at (0,0) and define the normal curve well intosaturation. You may need to change the maximumvalue of H. Click twice on the last point to finishentering the data. Exit out of the B-H window andEnter this new material into the local list of materials. Assign this material to the Rotor andthe Stator.

Assign copper to the coils and air to all otherobjects. Exit from the Material Manager

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Boundaries & Sources Toolbar

A s s

i g n s o u r c e

t o o u

t e r b o u n

d a r y

S e t d e f a u

l t c o

l o r f o r n e w

b o u n

d a r y

P i c k

b y c l i c k

i n g o n o b

j e c t

P i c k

b y c l i c k

i n g o n a n e d g e

P i c k

b y t r a c i n g o n a p o

l y l i n e

P i c k

b y i n t e r s e c t

i o n

t w o o b

j e c t s

D e l e t e

b o u n d a r y a s s i g n m e n

t

D e - s e

l e c t b o u n d a r y

V i e w a t

t r i b u t e s

M e a s u r e

Z o o m

i n

Z o o m o u t

F u l l z o o m

Begin picking by left mouse click; Finish picking by right mouse click

A s s

i g n v a l u e

b o u n

d a r y

A s s

i g n s y m

m e t r y

b o u n d a r y

A s s

i g n

b a l l o o n

b o u n

d a r y

A s s

i g n s o l

i d s o u r c e


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Boundaries & Sources

Typical Boundary Conditions

Balloon (for problems with fringing fields) Value A = 0, V = 0 (no fringing) Master/Slave (motor problems) Symmetry (periodic geometries - if possible, model entire model

first to see how fields behave)

NOTE: boundary condition on the outer edge of problem regionmust always be specified unless background is excluded


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Electrostatic Boundaries


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Magnetostatic Boundaries


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Eddy Current Boundaries


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Typical Source Conditions

Voltage or Charge (for electrostatic problems) Current (for magnetostatic and eddy problems) Permanent Magnet (for magnetostatic problems); the

permanent magnet characteristic is defined in thematerial manager, there is no assignment needed in theboundaries and sources manager

NOTE: Every problem needs at least ONE source of excitation


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Electrostatic Sources


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Magnetostatic Sources


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Eddy Current Sources


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In our example, were using the magnetostatic solver and we have twodifferent types of sources: Permanent Magnets and Current Sources. Thepermanent magnets have already been defined, so we need to define thecurrent sources. Pick the A_phase winding by clicking on the iconor using the menu Edit/Select/Object/By Clicking .

or click on Assign/Source/Solid to assign this group of Use the icon

Coils a solid current source. The value of this source will be 100 Amps

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These four objects makeup the A_phase winding

When objects are grouped, asthey are in this case, the solverwill treat these four objects as

though they were in parallel; thusthe value of current in each of these objects is:

Amps254100

=Also, since we model strands of coils as one object, the valueof coil current we enter here is expressed in Amp-Turns. The

solver will use 25 Amp-Turns in each of the four objects asthe excitation for that object.


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Using the same method as above, assign solid sources to the remaining coil groups. Usepositive or negative values to represent the direction of current; positive current is

represented as coming out of the screen, and negative current is represented as going intothe screen. Its important to use different colors and different names for each assignment.Since this is a three phase machine, the B and C phase will be 120 and 240 degrees out of phase respectfully:

Show Me

Finally, assign a Value boundary to the background region which is equal to zero. Formost motor problems, there is very little flux leakage so a balloon boundary is notneeded. Once finished, Save these settings and Exit the boundary/sources manager.

A_phase = 100 Amp-Turns A_Return = -100 Amp-TurnsB_Phase = -50 Amp-Turns B_Return = 50 Amp-TurnsC_Phase = -50 Amp-Turns C_Return = 50 Amp-Turns


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Executive Parameters - Torque

When computing the force or torque on an object, you want to select allobjects that actually rotate or move. In our example, well choose the rotor,shaft, and permanent magnets. First click on Setup ExecutiveParameters/Torque, select the rotating objects and then click on IncludeSelected Objects.

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Executive Parameters - Matrix

The inductance matrix can be expressed as:

333231

232221

131211

The inductance coupling conductors i and j is:

== d H BU L jiijij I 22 Note: The inductance calculation is

based on the apparent permeability inEACH triangle at the specified

excitation level

Where :

3223

3113

2112

=

==


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The energy stored in the magnetic field that couples two conductors is:

== d H B I LU jiij 21

21 2

U ij is the energy stored in the magnetic field linking conductor i with conductor j i is the current in conductor i. B i is the magnetic flux density associated with the case in which one amp is allowed

to flow through conductor i. H j is the magnetic field associated with case in which one amp is allowed to flow

through conductor j

Where:


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When calculating the inductance of an object or a group of objects, theyneed to be defined as a source in the Boundary/Source Manager ; for ourexample, this includes the A_phase, A_return, B_phase, B_return, C_phase,and C_return coil groups. To have Maxwell calculate the inductance for theentire A winding (A_phase and A_return) you need to choose A_phase andthen specify A_return as the return path. Maxwell needs to know what twogroups make up the entire A winding. Click on Setup ExecutiveParameters/Matrix-Flux and choose A_phase and then specify as thereturn path A_return. Repeat this for B and C winding.

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Setup Solution Options

Triangles are automatically refined to reduceenergy error

Solution continues until one of two stopping

criteria is met:1. the specified number of passes are

completed- OR -

2. percent error energy AND delta energy areless than specified

Start Field Solution

Generate InitialMesh

Compute Field

Perform ErrorAnalysis

HasStopping Criteria

been met?

Refine Mesh

No

Stop Field Solution

Yes

Change the percent error to 0.5% and solve thenominal problem

The important parameter here is the Percent Error.This is the value to which the software willconverge. Lowering the Percent Error will requiremore adaptive passes before convergence.


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Solutions - Convergence

Two passes to converge to anerror lower than 0.5%

Energy Error

Energy Error and DeltaEnergy are lower than 0.5%


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Solutions - Matrix

This is the inductance matrix. Thediagonal terms represent the self inductance, and the off diagonalterms represent the mutualinductance. Since we havent toldMaxwell how many turns are ineach winding, these values of

inductance are calculated for asingle turn with a depth of onemeter.

Click on Solutions/Matrix

The actual inductance will be : L tot = L 11 * N 2 * Depth

N is the number of turns in series calculated by: Total turns/No. Parallel pathsFor our example this value is 64. The depth of the motor is 94 mm. The total inductance forthe A_phase winding is:

L = (2.9048e-6) * (64) 2 * (0.096 meters)

L = 1.14 mH


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Solutions Flux Linkage

When the inductance matrix wascreated, the software automaticallyperforms a calculation for fluxlinkage.

Click on Solutions/Flux Linkage

Select one of the windings

Enter Actual Depth0.094

Enter turn number64

Updated Value


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Solutions - Torque

This is the value from the torquecalculation. This value for torque isbased on a one meter depth.

The actual torque will be : T tot = T * Depth

The depth of the motor is 94 mm. The total torque for this motor is:L = (8.24) * (0.096 meters)L = 0.791 N-m


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Solutions Post Process

Click on Post Process/Nominal Problem . Here we have a number of standard plots youcan examine.

To make make everything easier to read, remove the background by clicking onGlobal/Display , click on Next until you see background and change this from Yes to No .This will remove the background from the display window.

Next click on Post/Plot and select Flux Lines , keep the Plot_Type to Contour and changeSpectrum to Yes and Better Hardcopy to Yes .

The units for the flux lines are in Webers/meter, again based on one meter depth.

Show Me


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Solutions Post Process

Refresh this plot by clicking on Window/Refresh

Next lets plot the flux density by clicking on Post/Plot and choosing Mag B, make the plottype Shaded and again choose Spectrum and Better Hard Copy . The units here will beTesla. Maxwell solves all problems using the MKS units system:

Magnetic Flux Density B [Tesla]Magnetic Field Intensity H [Amps/meter]Magnetic Vector Potential A [Webers/meter]Current Density J [Amps/meter 2]Force [Newtons]Torque [Newton-meter]

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Post Process Plane Calculator

The two plots created, weremacro commands that

performed operations on thiscalculator. The plane calculatordrives the entire post processor.

This calculator has a stack and works on reverse polishnotation RPN

The first plot was the fluxwhich is represented byMagnetic vector potential A

The next plot was Magnitudeof the Flux Density Vector B

Post Process Air Gap


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Flux DensityLets calculate the flux density in air gap. This can be done by first creating a line in the airgap, then using the calculator determine the magnitude of the flux density on that line. Thefirst step is to turn off the snap to mode by clicking on Global/Defaults and turning Objectand Grid snap Off and turn the Keyboard Entry field On; click on Execute . Next click onPost/Line/Define and zoom into the air gap. Select Enter Arc and choose any point, modifythe entry fields to read (0,0), next pick a point in the air gap and then pick the point again,this will create a circle in the air gap. Next click on Calc/Plane and perform the following:

B_vector/Smooth/Magnitude . Mag BLine . Line calculatorEnter/Lineseg1/Yes . Enter circleValue/1000 .. Map the value on the top stack of the

plane calculator onto this lineReturn .. Exit the calculator

Next click on Post/Line/Plot to plot graphically display this value.

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Flux Density

The effects of the B fielddue to the stator slots are

easily seen here.


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Maxwell

This completes the training exercise for Maxwell 2D Problem Setup andSolution. Please refer to the training CD for other training examples:

Section 1 Intro FE Method.pptSection 2 Control Panel.pptSection 3 Problem Setup and Solution.ppt

Section 4 Parametric Solution.ppt

Or, you can browse our web site at www.ansoft.com . Select TechnicalSupport and register for an account. Here we have Tips and Tactics,

Frequently Asked Question, Application Notes and other example problems.

End Presentation


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A Basic Procedure for FEM Analysis of BLDC Motor by Maxwell 2D

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Transcript of A Basic Procedure for FEM Analysis of BLDC Motor by Maxwell 2D