Example Problem #2 Maxwell 2D Hall Sensor

T7_3D, pg. 2 7/21/02 Hall Sensor Description: The Hall sensor works similarly to the vr sensor, except that an integrated chip is used to measure the differential of the average normal component of flux density instead of flux linkage in a coil. Here again, we will solve for one position of the target wheel and calculate the average normal flux density across each cell of hall chip. The Hall Cells here are shown larger than typical. Target Wheel Permanent Magnet Pole Piece Cell Top Cell Bot Hall IC

T7_3D, pg. 3 7/21/02 Hall Sensor - 2D Modeler Step 1: From the Maxwell Control Panel, create a new project by clicking ‘Projects’ to open the projects window; click on ‘new’, assign the name ‘hall_mag’, and select ‘Maxwell 2D field Simulator Version 9’. The project will open automatically. Set the ‘Solver’ to ‘Magnetostatic’, set the ‘Drawing’ to ‘XY Plane’, and click on the ‘Define Model/Draw Model’. Click on ‘File/Import’ and go to the..\emprojects\floppy directory and select the file: hall_wheel.dxf In the file import window, check “Import drawing layers into single window/layer” and type “hall_mag” into the window name entry box.

T7_3D, pg. 4 7/21/02 Hall Sensor - 2D Modeler Step 2: Change the drawing size by clicking on ‘Model/Drawing Size’ and type in a padding percent of 400, click on ‘Fit All’ and then ‘Round Off’. Change the name of the target wheel by clicking on ‘Edit/Attributes/By Clicking’ and then clicking anywhere inside the target_wheel. Change the name from object1 to target_wheel, and change the color to green. The finite element solver only recognizes objects that are closed. To determine if an object is closed, just click anywhere inside the object and if that object highlights, then it is a closed object. When translating dxf files, all names associated with objects are lost; you need to change all of the names from object1, 2, 3 etc. to something more meaningful.

T7_3D, pg. 5 7/21/02 Hall Sensor - 2D Modeler Step 3: Draw the Hall IC, top and bottom cell, pole piece, and permanent magnet. All dimensions are mm using the x,y coordinate system. You can use polyline or rectangle to create these shapes. After creating ‘Cell_Top’, use the mirror duplicate to create ‘Cell_Bot’. Permanent Magnet Pole Piece Cell Top Cell Bot (42, 2) (44, -2) (44, 3) (45, -3)(48, -3) (45, 3) (43, 1) (42.5, 1.5) Hall IC Note: Decreasing the grid spacing by typing “G” on the keyboard will make the drawing operation easier

T7_3D, pg. 6 7/21/02 Hall Sensor - Model When finished with the drawing, click on ‘File/Save’ and then ‘File/Exit’; the model should look like this:

T7_3D, pg. 7 7/21/02 Hall Sensor - Materials Step 4: Enter the Material Manager and assign the objects the following material: Cell_Bot, Cell_Top, Hall_IC:graphite Perm_Mag:NdFe30 Pole_Piece, Target_Wheel:M19 Backgroundvacuum Since M19 isn’t part of the material database, it will need to be created. Click on ‘Material/ Add’ change the default name to ‘M19’ and click on ‘Nonlinear Material’ and then on ‘BH Curve’. Next click on ‘Import’ and select ‘bh Format’, open the file folder and select M19.bh from the..\emprojects\floppy directory. Notice how the curve is defined well into the saturation region, and there are many points along the knee of the curve. Also, if you zoom in, you’ll see two curves; one is the original data, and the second is a fitted curve using a bezier spline interpolation. ‘Exit’ out of this window and ‘Enter’ this material to the project specific database; it will say ‘Local’ next to the name instead of ‘Locked’. The magnetization of the NdFe30 Magnet is aligned with the x-axis, choose ‘Align with a given direction’ and input an angle of zero. Again, the arrow that is shown on the screen in the objects orientation, not the direction of magnetization! Exit and save these changes.

T7_3D, pg. 8 7/21/02 Hall Sensor Boundary & Sources Step 5: Click on ‘Setup Boundaries/Sources’. In the source manager window click on ‘Edit/Select/Object/By Clicking’ and select the background region, click on the right mouse button to end the selection (check the bottom of the screen for a description of what the right and left mouse button). Click on ‘Assign/Boundary/ Value’ and then assign a value zero boundary condition to the background by clicking on the ‘Assign’ button. The value boundary simulates an zero flux crossing boundary, where no flux can escape the boundary region. Click on ‘File/Save’ then ‘File/Exit’. Step 6: Click on ‘Setup Solution/Options’ and then on ‘Manual Mesh’. Click on ‘Mesh/Seed/Object’; select each object individually and click on ‘Suggested Value’ and then ‘Seed’; some objects will have a value of zero for the number of points. Do this for each object and then click on ‘OK’. Click on ‘Mesh/Seed/Surface’ and again, assign the default for each object. Zoom in and see the seed points and then click on ‘Mesh/Make’. ‘File/Save’ and then then ‘File/Exit’ the Manual Mesh window.

T7_3D, pg. 9 7/21/02 Hall Sensor - Solution Options Step 7: Since we require a very fine solution in the hall element, we need to make sure that the problem is well converged. Reduce the ‘Linear’ and ‘Nonlinear’ residual by one order of magnitude: Linear = 1e-4, and Nonlinear = 5e-4. Reduce the percent error by one order of magnitude: Percent Error = 0.1 % Click on ‘OK’ and then solve this problem: Solve/Nominal Problem Your results should look similar to these

T7_3D, pg. 10 7/21/02 Hall Sensor - Post Processor Step 8: Click on ‘Post Process/Nominal Problem’ and click on ‘Edit/Visibility/By Item and hide the background object. Click on ‘Data/Calculator’ to enter the field calculator and perform the following operations: Load B_x:Qty / BScal ? / ScalarX Integrate:Geometry / Surface / cell_top Integrate (choose the button with the integral symbol) Integrate:Number / Scalar / 1 Geometry / Surface / cell_top Integrate Divide:Divide (choose the division symbol “/” ) Evaluate The top value is the average normal component of flux density across the top cell; repeat this to calculate the average over the bottom cell. This completes the magnetostatic hall sensor example. This result is the total B_x in the top cell This result is the area of the top cell