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EM.Ferma Tutorial Lesson 5: Modeling Solenoids & Toroidal Coils

1,133 bytes added, 13:06, 16 September 2019
{{projectinfo|Tutorial| Modeling Solenoids & Toroidal Coils |Ferma L5 Fig_title.png|In this project, you will build helical solenoids and toroidal coils and will analyze their magnetic fields.|
*[[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]
*Curve Object
*Curve Generator
== What You Will Learn ==
In this tutorial you will learn about another type of magnetic source called wire current, which is used to model thin current-carrying wires with arbitrary curved shapes. You will use wizards to create solenoids and toroidal coil objects. You will also learn about [[EM.Cube]]'s variables as well as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]]'s versatile curve generator.
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== Getting Started ==
*Wire Currents
A volume current group is characterized by the three components of the current density vector, Jx, Jy and Jz, having units of A/m<sup>2</sup>. You learned about volume current sources in Tutorial Lesson 4. Under a volume current group, you can draw any solid geometric objects such as box, cylinder, cone, <i>etc</i>. A wire current is used to approximate a current filament, that is a current source flowing through a line or curve with a specified finite radius. A wire current group is characterized by its total current (I) having units of Amperes. In [[EM.Ferma]], only line and polyline objects can support wire currents. Under a wire current group, you can define any curve geometric object. However, before running a magnetostatic simulation, the program warns that all the curve object will be polygonized and replaced with polyline objects.
Since the governing differential equations only recognize the volume current density '''J''', and not I, as a valid source, [[EM.Ferma]] takes the linear current along a wire current source and converts it to a volume current density defined as
Solenoids are used to generate a uniform magnetic field. You can model a solenoid in [[EM.Ferma]] using a helix curve object. In this tutorial, however, you will use a wizard to create a solenoid geometry.
Click on the <b>Solenoid Wizard</b> [[Image:SolenoidWizardIconx.png]] button of the Wizard Toolbar or select the menu item '''Tools &rarr; Component Wizards &rarr; Solenoid'''.
<table>
== Examining the Geometry of the Parametric Curve ==
The wizard used [[CubeCAD]]'s '''Curve Generator''' to create a parametric curve to model the solenoid object. In this case, your solenoid is indeed a helix curve. However, the wizard's definition gives a more generalized helical coil object with '''Super-Quadratic''' cross section. Right-click on the name of you your solenoid in the navigation tree and select '''Properties...''' from the contextual menu. This opens up the "Curve Generator" dialog as shown in the figure below:
<table>
<tr>
<td> [[Image:Ferma L5 Fig9.png|thumb|left|640px|Thecurve The curve generator dialog showing the parametric definition of of the solenoid.]] </td>
</tr>
</table>
</table>
The definition of the three coordinate functions X(t), y(t) and z(t) also involves variables like "major_rad", "minor_rad", "height", <i>etc</i>. which you saw earlier in the variables dialog. To preserve the parameterization of your solenoid object, you should change its properties from the variables dialog rather than directly from its property dialog.
{{Note|[[CubeCAD]]'s curve generator always creates polyline objects. Unlike ordinary polylines that are characterized by their node sets, the ones created by the curve generator are characterized by mathematical expressions or Python functions.}}
== Running a Magnetostatic Analysis of the Solenoid ==
Note that the wizard also define defines two orthogonal, vertical, X- and Y-directed field sensor planes called "FSX" and "FSY", respectively. Change the settings of these observables as follows:
{| class="wikitable"
! scope="col"| Plot Type
! scope="col"| Max. Size
! scope="col"| Cone Length Ratio! scope="col"| Cone Radius Ratio
|-
! scope="row"| FSX
| (0, 0, 0)
| | Intensity
| -
| -
| -
| 0.5
| 0.75
| 0.25
|}
</table>
Run a magnetostatic simulation of your structure and visualize the field sensor plots. You can '''Hide''' any geometric objects to see other objects hidden behind, beneath or inside it. To hide an object, right-click on its surface in the project workspace or right-click on its name in the navigation tree and select '''Hide''' from the contextual menu. To show the object right-click on its surface in the project workspace or right-click on its name in the navigation tree and select '''Show''' from the contextual menu.
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</table>
Open the data manager and plot the data file "FSX_Z_HTotal.DAT" in EM.Grid as shown in the figure below. As you can see from this figure, the magnetic field along the central axis of the solenoid is almost constant (1191A/m) inside the solenoid in the region 12mm &le; z &le; 36mm.
<table>
== Building & Analyzing a Toroidal Coil ==
You may want to start a new blank project for this part of the tutorial lesson. You are going to create the geometry of a toroidal helix coil using one of [[EM.Cube]]'s convenient wizards. To do so, click on the <b>Coil Wizard</b> [[Image:CoilWizardIconx.png]] button of the Wizard Toolbar or select the menu item '''Tools &rarr; Component Wizards &rarr; Toroidal Coil'''.
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</table>
The geometry of a toroidal helix coil with a circular cross section appears at the center of the project workspace, and its name is added under a new group item called "WIRE_CURRENT" in the navigation tree. The wire current group has the same properties as in the last part.
<table>
</table>
The geometry of the toroidal helix coil object created by the wizard is fully parameterized. Open '''Variables Dialog''' and review the list of all the variables that have been used for the definition of the toroidal helix object.
<table>
<tr>
| 15
|-
| minor_h_radminor_rad_h
| 0.002*to_meters
| 5
|-
| minor_v_radminor_rad_v
| 0.002*to_meters
| 5
</table>
Open the property dialog of your coil object and examine the definition of toroidal helix coil in Curve Generator. The parameter "major_rad" determines the major radius of the torus. The cross section of this curve in a generalized super-quadratic curve with two horizontal and vertical radii: "minor_h_radminor_rad_h" and "minor_v_radminor_rad_v". The parameter t varies from zero to 2&pi;. For this project, you reduced the value of the variable "step" to 0.0025 to create a smoother polyline.
<table>
<tr>
<td> [[Image:Ferma L5 Fig24B.png|thumb|left|640px|The properties of the toroidal helix coil shown in CubeCAD's curve generator.]] </td>
</tr>
</table>
! scope="col"| Plot Type
! scope="col"| Max. Size
! scope="col"| Cone Length Ratio! scope="col"| Cone Radius Ratio
|-
! scope="row"| FSX
| (0, 0, 0)
| | Intensity
| -
| -
| -
| 1
| 0.5
| 0.25
|-
! scope="row"| FSZ
| 1
| 0.5
| 0.25
|}
<p>&nbsp;</p>
[[Image:Top_icon.png|30px]] '''[[#What_You_Will_Learn | Back to the Top of the Page]]''' [[Image:Back_icon.png|40px30px]] '''[[EM.Cube#EM.Ferma_Tutorial_Lessons Ferma_Documentation | Back to EM.Ferma Tutorial Gateway]]'''
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