fam project 2
DESCRIPTION
famTRANSCRIPT
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
Magnetic Field Strength H[A/m]H12.87823.11993.123
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
Flux Density & Strength
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
Magnetic Field Strength H[A/m]H12.9572.74213.1199
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
Flux Density & Strength
Flux Density & Strength
Flux Density & Strength
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
Magnetic Field Strength H[A/m]H12.83062.74123.1199
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
Flux Density & Strength
Flux Density & Strength
Flux Density & Strength
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
, Flux Density & Strength
, 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.