A Basic Procedure for FEM Analysis of BLDC Motor By Maxwell 2D
Problem Setup and Solution This section will go through how to setup, solve, and post process a sample problem – Three Phase, Four Pole, Permanent Magnet Brushless 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 window which can be resized so that you can run the Maxwell software and view this presentation on the same screen.
Use these buttons to page forward and backward
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Create a New Project
Click on Projects to create a new Maxwell Project It’s recommended that you run the actual software while going through this tutorial.
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New Project Type in Name
PM_Sync_3Ph_Motor
Select New Select Maxwell 2D Version 8
Open the new project
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Executive Commands Area Change Solver to Magnetostatic Keep the drawing Plane to X-Y
This is the list of Executive Commands
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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 to define 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 be 3-5 times model size unless there is extreme fringing.
For this simulation most of the flux will be contained in the motor, so we’ll use three times the model size.
-250 -250
The outside diameter of this motor is 160 mm; we’ll make the problem region +/- 250 mm.
250 250
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Stator Slot Select Object/Polyline to create one half a slot. Use the Keyboard entry fields at the bottom left of the screen to enter the following coordinates (make sure the mouse does not enter the black drawing region when using keyboard entry, or the focus is taken off the entry fields and onto the screen): First Point 1.25, 37.5 Second Point 1.25, 38.0 Third Point 2.4, 38.5 Fourth 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 screen for 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 on Edit/Duplicate/Mirror Duplicate and pick two points on the Y-Axis. Next pick 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 now drawn one complete stator slot. Your geometry so far should look like this:
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Stator Slot To finish creating this slot, we need to create the arc segment between two adjacent slots, which will make up the inside diameter of the stator. Select the slot that was just created by clicking on it; you will notice that it will highlight. Next, choose Edit/Duplicate/Along Arc, pick the (0,0) point as the pivot point and duplicate along an angle 15 degrees with a total number of 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 center at (0,0) and then snap to the bottom edge of the left slot and then the bottom edge of the right slot; using 11 segments, or one degree increment of arc segments. Finally, click on Reshape/Edge/ Delete and delete all of the line segments that make up the second slot, leaving the arc segment that was just created. We now have one arc and one tooth drawn. Your geometry should look like this:
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Stator Slot Next we need to create the stator coil in the slot. The first step here is to turn on 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 is set to Vertex and Grid; Model/Snap to Mode. Next pick Object/Polyline and trace the inside of the slot to create the coil and then across the bottom of the slot to close off the coil; call this object Coil_1 and change its color to yellow; 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 15 degree angle 24 times.
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Stator and Permanent Magnets The 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), accept the default of 36 segments; the stator OD is 120 mm. Rename this object Stator and change its color to green. Your geometry should look like this:
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Stator and Permanent Magnets Next create the permanent magnets by creating two straight lines and two arcs 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 as possible (the actual value in degrees will change to ensure an integer value for the number of segments), the inside arc segment can use the default value. Your geometry should look like this: Select this permanent magnet and click on Edit/Duplicate/Along Arc (90 degrees and a total of 4), to create the four permanent magnets. Save the work you’ve done so far by clicking of File/Save.
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Rotor Your geometry should look like this:
To create the rotor, we’ll use the inside arc segments of the permanent magnets. The first step is to copy the permanent magnets in the clipboard; select the four permanent magnets and click on Edit/Copy. Next, click on Reshape/Edge/Delete and delete all edges of the permanent magnets except the inside arc. Then use the Object/Arc command to connect the remaining arc segments and call this new object the Rotor. Choose Edit/Paste to place the permanent magnets back into the model. Click on Object/Circle (centered at the origin) to create the shaft which has a 26mm diameter.
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Rotor Assign different colors for the stator coils to represent the A_phase, A_return, B_phase, etc. windings. We’ll also use different colors for the permanent magnets to show different polarity. Change the name of the object between the permanent magnets and the stator from object1 to Air_Gap. Click on File/Save and then File/Exit. You won’t see A, C-, B, etc on your drawing. It’s shown here for information only.
A-
A- B B C-
C
CA
C B-
A
B-
B-
A
B-
A
C C-
C C-
B
B A-
A-
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Group Objects It is often helpful to group like objects. In this case we’ll group the A_phase, A_return, B_phase, etc. coils.
A-
A- B
B
C-
C
CA
C B-
A
B-
B-
A
B-
A
C C-
C C-
B
B A-
A-
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Group Objects Click on Define Model/Group Objects and select coil pairs to be used for phase 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 them together. 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 need to be included in the B-H curve, and it needs to be defined well into 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 equivalent current sheets on the surface of the magnets. When specifying coercivity Hc Maxwell uses the normal value, not the intrinsic value. The relationship between magnetic properties is: Br = µo * Mp = µo * µr * Hc
B Br Remanence
Hc - Coercivity
H
Br – Magnetic Retentivity or Remanence Hc – Magnetic Coercivity µr – Relative Permaebility µo – Permeability of Free Space 4πe-7 Mp – Permanent Dipole Magnetization
When defining a linear permanent magnet, you need to specify two quantities from the expression above.
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Materials – Permanent Magnets Non-linear permanent magnets can also be modeled. The non-linear curve used in the simulation represents the recoil permeability, not the original virgin curve. The blue non-linear curve represents the original virgin curve of the permanent magnet material. Depending upon the shape of the magnet, it could reside at different operating points. The recoil curve will start from that operating point and intersect the B axis at a lower value.
Original curve
Recoil curve
You need to input this red recoil curve into Maxwell
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Materials – Create New Magnet Create a new linear permanent magnet material. Click on Setup/Materials to enter the Material Manager. Click on Material/Add to add a new material and change the name (here we’ll just call it test_mag). Next click on Options, deselect µ and select Br,using the following definition: Br = 1.25 Tesla Hc = -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 be asked to choose the direction of magnetization, i.e. the north pole. Here you have three options: Align with object’s orientation Align with a given direction Align relative to object’s 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 is the object’s orientation, if you choose Align with object’s orientation this will be the direction of magnetization. If you choose Align with a given direction you will be asked to choose an angle. This angle is measured from the X-Axis in the counter clock-wise direction. If you choose Align relative to object’s orientation you can define an angle relative to the white arrow you see on the screen. You may also choose to make this a function, we’ll discuss functions later on in this tutorial. Click on View Angle and then the magnet to see if the direction of magnetization is set correctly. For now, choose Align with a given direction and alternate each permanent magnet North – South – North – South. North is pointing out from the rotor, and South is pointing 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 on Material/Add to add a new material and change the name to M19_Steel. Click on Nonlinear Material and then the button B H curve. Click on Add Point and use the entry fields in the bottom left to specify this bh curve. H (Amps/Meter) B (Tesla) We don’t enter the entire bh loop. You need to 0.0 0.0 start at (0,0) and define the normal curve well into 27.06 0.2 saturation. You may need to change the maximum 42.98 0.4 value of H. Click twice on the last point to finish 68.46 0.6 entering the data. Exit out of the B-H window and 107.46 0.8 Enter this new material into the local list of 175.12 1.0 materials. Assign this material to the Rotor and 302.48 1.2 the Stator. 746.12 1.4 3582 1.6 Assign copper to the coils and air to all other 11144 1.8 objects. Exit from the Material Manager 39800 2.0 119400 2.10003
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Full zoom
Zoom out
Zoom in
Measure
View attributes
Set default color for new boundary
De-select boundary
Delete boundary assignment
Assign source to outer boundary
Assign solid source
Assign balloon boundary
Assign symmetry boundary
Assign value boundary
Pick by intersection two objects
Pick by tracing on a polyline
Pick by clicking on an edge
Pick by clicking on object
Boundaries & Sources Toolbar
Begin “picking” by left mouse click; Finish “picking” by right mouse click
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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 region must always be specified unless background is excluded
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Boundaries & Sources Electrostatic Boundaries
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Boundaries & Sources Magnetostatic Boundaries
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Boundaries & Sources Eddy Current Boundaries
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Boundaries & Sources 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 the material manager, there is no assignment needed in the boundaries and sources manager
NOTE: Every problem needs at least ONE source of excitation
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Boundaries & Sources Electrostatic Sources
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Boundaries & Sources Magnetostatic Sources
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Boundaries & Sources Eddy Current Sources
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Boundaries & Sources In our example, we’re using the magnetostatic solver and we have two different types of sources: Permanent Magnets and Current Sources. The permanent magnets have already been defined, so we need to define the current sources. Pick the A_phase winding by clicking on the icon or using the menu Edit/Select/Object/By Clicking. Use the icon
or click on Assign/Source/Solid to assign this group of
Coils a solid current source. The value of this source will be 100 Amps
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Boundaries & Sources These four objects make up the A_phase winding When objects are grouped, as they are in this case, the solver will treat these four objects as though they were in parallel; thus the value of current in each of these objects is: 100 = 25 Amps 4 Also, since we model strands of coils as one object, the value of coil current we enter here is expressed in Amp-Turns. The solver will use 25 Amp-Turns in each of the four objects as the excitation for that object.
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Boundaries & Sources Using the same method as above, assign solid sources to the remaining coil groups. Use positive 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 into the screen. It’s 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: A_phase = 100 Amp-Turns B_Phase = -50 Amp-Turns C_Phase = -50 Amp-Turns
A_Return = -100 Amp-Turns B_Return = 50 Amp-Turns C_Return = 50 Amp-Turns
Finally, assign a Value boundary to the background region which is equal to zero. For most motor problems, there is very little flux leakage so a balloon boundary is not needed. Once finished, Save these settings and Exit the boundary/sources manager.
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Executive Parameters - Torque When computing the force or torque on an object, you want to select all objects that actually rotate or move. In our example, we’ll choose the rotor, shaft, and permanent magnets. First click on Setup Executive Parameters/Torque, select the rotating objects and then click on Include Selected Objects.
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Executive Parameters - Matrix The inductance matrix can be expressed as:
λ 11 λ 12 λ 13 λ 21 λ 22 λ 23 λ 31 λ 32 λ 33
Where : λ 12
= λ 21 λ 13 = λ 31
λ 23 = λ 32
The inductance coupling conductors i and j is:
Lij =
2 Uij
I
2
= ∫ Bi • Hj dΩ Ω
Note: The inductance calculation is based on the apparent permeability in EACH triangle at the specified excitation level
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Executive Parameters - Matrix The energy stored in the magnetic field that couples two conductors is:
1 1 2 Uij = L I = 2 2
∫
Ω
Bi • Hj dΩ
Where: • Uij is the energy stored in the magnetic field linking conductor i with conductor j • i is the current in conductor i. • Bi is the magnetic flux density associated with the case in which one amp is allowed to flow through conductor i. • Hj is the magnetic field associated with case in which one amp is allowed to flow through conductor j
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Executive Parameters - Matrix When calculating the inductance of an object or a group of objects, they need to be defined as a source in the Boundary/Source Manager; for our example, 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 the entire A winding (A_phase and A_return) you need to choose A_phase and then specify A_return as the return path. Maxwell needs to know what two groups make up the entire A winding. Click on Setup Executive Parameters/Matrix-Flux and choose A_phase and then specify as the return path A_return. Repeat this for B and C winding.
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Setup Solution Options • The important parameter here is the Percent Error. This is the value to which the software will converge. Lowering the Percent Error will require more adaptive passes before convergence. • Triangles are automatically refined to reduce energy 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 are less than specified Change the percent error to 0.5% and solve the nominal problem
Start Field Solution
Generate Initial Mesh
Compute Field
Perform Error Analysis Has Stopping Criteria been met?
Refine Mesh No
Yes Stop Field Solution
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Solutions - Convergence
Energy Error
Energy Error and Delta Energy are lower than 0.5%
Two passes to converge to an error lower than 0.5%
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Solutions - Matrix This is the inductance matrix. The diagonal terms represent the self inductance, and the off diagonal terms represent the mutual inductance. Since we haven’t told Maxwell how many turns are in each winding, these values of inductance are calculated for a single turn with a depth of one meter.
Click on Solutions/Matrix
The actual inductance will be: Ltot = L11 * N2 * Depth N is the number of turns in series calculated by: Total turns/No. Parallel paths For our example this value is 64. The depth of the motor is 94 mm. The total inductance for the A_phase winding is: L = (2.9048e-6) * (64)2 * (0.096 meters) L = 1.14 mH
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Solutions – Flux Linkage Click on Solutions/Flux Linkage
When the inductance matrix was created, the software automatically performs a calculation for flux linkage.
0.094
Enter Actual Depth
Select one of the windings
Updated Value
64
Enter turn number
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Solutions - Torque
This is the value from the torque calculation. This value for torque is based on a one meter depth.
The actual torque will be: Ttot = 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 you can examine. To make make everything easier to read, remove the background by clicking on Global/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 change Spectrum to Yes and Better Hardcopy to Yes. The units for the flux lines are in Webers/meter, again based on one meter depth.
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Solutions – Post Process Refresh this plot by clicking on Window/Refresh Next let’s plot the flux density by clicking on Post/Plot and choosing Mag B, make the plot type Shaded and again choose Spectrum and Better Hard Copy. The units here will be Tesla. 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/meter2] Force [Newtons] Torque [Newton-meter]
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Post Process – Plane Calculator The two plots created, were macro commands that performed operations on this calculator. The plane calculator drives the entire post processor. The first plot was the flux which is represented by Magnetic vector potential A The next plot was Magnitude of the Flux Density Vector B This calculator has a stack and works on reverse polish notation RPN
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Post Process – Air Gap Flux Density Let’s calculate the flux density in air gap. This can be done by first creating a line in the air gap, then using the calculator determine the magnitude of the flux density on that line. The first step is to turn off the snap to mode by clicking on Global/Defaults and turning Object and Grid snap Off and turn the Keyboard Entry field On; click on Execute. Next click on Post/Line/Define and zoom into the air gap. Select Enter Arc and choose any point, modify the 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 B Line ………………………………. Line calculator Enter/Lineseg1/Yes ………………. Enter circle Value/1000 ……………………….. Map the value on the top stack of the plane calculator onto this line Return …………………………….. Exit the calculator Next click on Post/Line/Plot to plot graphically display this value.
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Post Process – Air Gap Flux Density
The effects of the B field due to the stator slots are easily seen here.
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Maxwell This completes the training exercise for Maxwell 2D Problem Setup and Solution. Please refer to the training CD for other training examples: Section 1 Intro FE Method.ppt Section 2 Control Panel.ppt Section 3 Problem Setup and Solution.ppt Section 4 Parametric Solution.ppt Or, you can browse our web site at www.ansoft.com. Select Technical Support and register for an account. Here we have Tips and Tactics, Frequently Asked Question, Application Notes and other example problems.
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