FAM Project 2

Group: 1221EPopescu Andrei

Field Analysis and Modeling-Magnetostatics Project-

Professor: Drosu OanaStudent: Popescu AndreiGroup: 1221E

I. Purpose of the projectThe projects purpose is to describe, solve and analyze the results of a magnetostatics problem using QuickField Student for calculation of the flux density and magnetic strength.II. Problem FormulationThe magnetostatics problem to which QuickField program will provide a solution consists of the following: A square of 20 cm width and height with the center in the origin. Its points coordinates are (10, 10), (10, -10), (-10, -10), (-10, 10) Inside the square capacitor, 3 more squares, also centered in origin with the height and the width of 15, 10 and 8 cm. The last square is the ferromagnetic core. Inside the last square there are 2 air gaps (width 5 cm, height 1 cm), symmetrically placed with respect to the origin at 1.5 cm above and below. Symmetrically to the origin, we have 2 coils of width 5 cm and height 0.5 cm at 1 cm, and another 2 coils also of width 5 cm and height 0.5 cm at 4 cm above and below the origin. The coils (from top to bottom) have positive, negative, positive and negative polarity again, with, I=1 A and A=0.5cm * 5cm=2.5 * 10-4 m2. The ferromagnetic portion has the permittivity In rest, the block contains air with =1 The borders have the voltage U=0

III. Geometry(-10, 10)(10, 10)Border (A=0)

(-7.5, 7.5)(7.5, 7.5)

+J1(-5, 5)(5, 5)

(2.5, 4.5)(-2.5, 4.5)(4, 4)(-4, 4)

-J1(2.5, 3)(-2.5, 3)

+J2(2.5, 1.5)(-2.5, 1.5)(-2.5, 1)(2.5, 1)

(-2.5, -1.5)(-2.5, -1)(2.5, -1)(2.5, -1.5)(-2.5, -3)(2.5, -3)

-J2(-2.5, -4.5)(2.5, -4.5)(-4, -4)(4, -4)

(-5, -5)(5, -5)

(7.5, -7.5)(-7.5, -7.5)(-10, -10)(10, -10)

IV. Working ProcedureIn order to create a new problem you should go to File\New problem. Give a name to the file and choose a folder. The problem should be set to Magneto statics and you must use Centimeters as a Length Unit. After that, you can click Finish.

We start to place the coordinates of the points with the Add Vertices option from the Edit Menu. When we are done, we use the Insert Edges option to connect the edges.Afterwards, we double the desired edges/vertices and we label them. From the menu in left, we double click each label and we add their properties. We add the Mesh Spacing manually and we build the mesh in all blocks. Now we can select the Solve option in the Problem Menu.

Problem Description1. Edge Labels: Border - Contour of the largest square block2. Blocks: Green Portion The permittivity in the rest of the block

Selected PointsThe points chosen are the ones that are most relevant in noticing the changes that occur in the tests.

P1 (-3.5, 0) Left of the originP2 (0, 0) In the originP3 (3.5, 0) Right of the originP4 (0, -3.5) Below the originP5 (0, 3.5) Above the originP6 (-3.5, 3.5) Upper Left CornerP7 (-3.5, -3.5) Lower Left CornerP8 (3.5, 3.5) Upper Right CornerP9 (3.5, -3.5) Lower Right Corner

V. Test 1 Mesh InfluenceThe purpose of the first test is to show how the mesh density (number of nodes) influences the magnetic flux density and strength. I used 3 different meshes: approximately 50, 100 and 250 nodes. In order to achieve those numbers, I modified the spacing of each square. For a greater spacing, I obtained a less dense mesh. For this test we will use i1 = i2 = 1A and ,i1 = i2 = 1A

Mesh 143 NodesMesh 299 NodesMesh 3217 Nodes

Magnetic Flux B[T]B10.00129530.00392050.0025082

B20.00540320.00739910.0079771

B37.5343e - 40.00402840.0026555

B40.0047460.00742010.0080012

B50.004746710.00742010.0079991

B60.00222210.00296220.0035035

B70.00227310.00312580.0035004

B80.00239070.00312580.0034978

B90.00197190.00296220.0034897

Magnetic Field Strength H[A/m]H11.03083.11991.996

H24.22975.8886.348

H30.599563.20572.1211

H43.79155.90476.3671

H53.79365.90476.3655

H61.76832.35732.788

H71.80892.48742.7856

H81.90242.48742.7835

H91.56922.35732.777

Mesh 1 - Flux Density & Strength

Mesh 2 Flux Density & Strength

Mesh 3 Flux Density & Strength

Conclusion and ObservationsWe observe that using a denser mesh with more nodes, the picture is more precise and gives more detail. Because of this, the best approximation of the flux density and strength is found with use of the third mesh.The number of nodes varies directly proportional with the degree of accuracy of the picture and results. Thats why, for the following tests, I have used only the third mesh (217 nodes).The greatest values of the flux density were obtained on the Ox axis, between the two coils and the lowest values were obtained for the points near the upper and the lower coils. The strength varies inversely proportional with the distance from the origin. As we move farther, we obtain lower strengths and potentials.

VI. Test 2 PermeabilityThe second test emphasizes the way in which the values of permeability of the ferromagnetic core affect the magnetic field strength, as well as the flux density. The test was conducted on Mesh 3.

i1 = i2 = 1A

Magnetic Flux B[T]B13.6169e - 50.003920539.245

B27.9676e - 50.007399173.92

B33.7139e - 50.004028440.326

B49.5003e - 50.007420173.92

B59.5005e - 50.007420173.92

B62.6972e - 50.002962229.671

B72.9678e - 50.003125831.296

B82.968e - 50.003125831.296

B92.6973 - 50.002962229.671


H26.34045.8886.3435

H33.95543.20573.209

H47.56015.90475.8824

H57.56035.90475.8824

H62.14632.35732.3611

H72.36172.48742.4904

H82.36192.48742.4904

H92.14642.35732.3611

Flux Density & Strength



Conclusion and ObservationsThe variation of the flux density is directly proportional with the variation of values of the magnetic strength and potential. This is caused, due to the fact that the magnetic flux density B=H (magnetic permeability * magnetic field strength).As it can be easily observed from the pictures, the field lines escape more easily from the ferromagnetic core for the smaller permeability values and the strength has smaller and smaller values as the permeability increases.

VII. Test 3 Variation of Current Density J1This test shows the influence of the variation of current density of one coil on the values of the magnetic field strength and flux density. In this test we will change in order to be able to see the influence of its variation.

i2 = 1A00

Magnetic Flux[T]B10.00355810.00344580.0039205

B20.00371590.00406970.0073991

B30.0061610.00350640.0040284

B40.00939250.00921320.0074201

B50.00191070.00105510.0074201

B67.6295e - 44.234e - 40.0029622

B70.00396150.00388550.0031258

B88.0446e - 44.471e - 40.0031258

B90.00375480.00368270.0029622


H23.2063.23855.888

H32.87662.79033.2057

H47.47437.33165.9047

H51.52050.836645.9047

H60.607140.337652.3573

H73.15253.0922.4874

H80.640170.355852.4874

H92.9882.93062.3573




Conclusions and observationsIt can be easily observed from the table and the pictures that as we increase the first current, the magnetic field tends to cover the whole system. When the current through the lower coils is bigger, the flux density and the strength tend to concentrate around them due to the increase in the current flow in that area.

VIII. Test 4 Variation of Current Density J2This test shows the influence of the variation of current density of one coil on the values of the magnetic field strength and flux density. In this test we will change in order to be able to see the influence of its variation.

I1 = 1A00

Magnetic Flux[T]B10.00355710.00344470.0039205

B20.00371740.00406970.0073991

B30.00361720.00350750.0040284

B40.00191070.00105110.0074201

B50.00939250.00921320.0074201

B60.00375480.00368270.0029622

B78.0446e 44.4716e - 40.0031258

B80.00396150.00388550.0031258

B97.6296e - 44.2431e - 40.0029622


H22.95823.23855.888

H32.87842.79123.2057

H41.52050.836445.9047

H57.47437.33165.9047

H62.9882.93062.3573

H70.640170.355842.4874

H83.15253.0922.4874

H90.607150.337662.3573




Conclusions and observationsIt can be easily observed from the table and the pictures that as we increase the second current, the magnetic field tends to cover the whole system. When the current through the upper coils is bigger, the flux density and the strength tend to concentrate around them due to the increase in the current flow in that area.

IX. Test 5 Variation of PolarityFinally, this test shows the influence of the variation of the polarity of current through the coils on the values of the magnetic field strength and flux density. In this test we will change the signs of and in order to be able to see their influence.

I1 = 1A00

Magnetic Flux[T]B10.00392050.00597130.00597130.0039205

B20.00739918.5392e - 58.5392e - 50.0073991

B30.00402840.00604080.00604080.0040284

B40.00742010.0114050.0114050.0074201

B50.00742010.0114050.0114050.0074201

B60.00296220.00456340.00456340.0029622

B70.00312580.00481410.00481410.0031258

B80.00312580.00481410.00481410.0031258

B90.00296220.00456340.00456340.0029622

Magnetic Field Strength H[A/m]H13.11994.75184.75183.1199

H25.8880.0679530.0679535.888

H33.20574.80714.80713.2057

H45.90479.07569.07565.9047

H55.90479.07569.07565.9047

H62.35733.63143.63142.3573

H72.48743.83093.83092.4874

H82.48743.83093.83092.4874

H92.35733.63143.63142.3573

, Flux Density & Strength



,

Conclusions and observationsThe variation of the currents sense is clearly visible on the pictures. When the currents have the same sign the values for the magnetic flux density and for the magnetic field strength stay the same, but the direction of vectors are opposite. The same is true when the currents have opposite signs. As opposed to the currents with the same sign, for the currents with opposite signs we have bigger values for the magnetic flux density and field strength in the point of origin and lower values when moving away from the origin.

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FAM Project 2