1、9.1 Maxwell v15Basic Exercises Electrostatic Solver Introduction on the Electrostatic Solver This note introduces the “Electrostatic Solver” based on some simple examples. This solver is meant to solve the static electric field without current flowing in conductors (conductors are in electrostatic e

2、quilibrium). The conductors are considered perfect such that there is no electric field inside conductors. Example 1 : Capacitance of a Cylindrical Capacitor Suppose we have a long coaxial line. We want to know what is the electric field distribution based on the potential (or the charges) that are

3、applied on each conductor. We also want to determine the capacitance. Create Design To Create Design Select the menu item Project Insert Maxwell 3D Design, or click on the icon Rename design as Coaxial Line Set Solution Type To set the Solution Type: Select the menu item Maxwell 3D Solution Type Sol

4、ution Type Window: 1. Choose Electric Electrostatic 2. Click the OK button Set Default Material To set the default material: Using the 3D Modeler Materials toolbar, choose Select In Select Definition window, 1. Type Copper in the Search by Name field 2. Click the OK button ANSYS Maxwell 3D Field Sim

5、ulator v15 Users Guide 9.1-# Create Geometry Create Regular Polyhedron Select the menu item Draw Regular Polyhedron 1. Using the coordinate entry fields, enter the center of the base X: 0, Y: 0, Z: -4, Press the Enter key 2. Using the coordinate entry fields, enter the radius dX: 0.6, dY: 0, dZ: 0,

6、Press the Enter key 3. Using the coordinate entry fields, enter the height dX: 0, dY: 0, dZ:25, Press the Enter key 4. Number of Segments: 24 Change the name of the Object to Inner Create Second Polyhedron Select the menu item Draw Regular Polyhedron 1. Using the coordinate entry fields, enter the c

7、enter of the base X: 0, Y: 0, Z: -4, Press the Enter key 2. Using the coordinate entry fields, enter the radius dX: 1, dY: 0, dZ: 0, Press the Enter key 3. Using the coordinate entry fields, enter the height dX: 0, dY: 0, dZ:25, Press the Enter key 4. Number of Segments: 24 Change the name of the Ob

8、ject to Gap Create Third Polyhedron Select the menu item Draw Regular Polyhedron 1. Using the coordinate entry fields, enter the center of the base X: 0, Y: 0, Z: -4, Press the Enter key 2. Using the coordinate entry fields, enter the radius dX: 1.2, dY: 0, dZ: 0, Press the Enter key 3. Using the co

9、ordinate entry fields, enter the height dX: 0, dY: 0, dZ:25, Press the Enter key 4. Number of Segments: 24 Change the name of the Object to Outer ANSYS Maxwell 3D Field Simulator v15 Users Guide 9.1-# Subtract Objects Press Ctrl and select the objects Outer and Gap from the history tree Select the m

10、enu item, Modeler Boolean Subtract 1. Blank Parts: Outer 2. Tool Parts: Gap 3. Click the OK button Define Region Create Simulation Region Select the menu item Draw Region or click on the icon In Region window, 1. Pad individual directions: Checked 2. Padding Type: Percentage Offset +X and -X = 300 +

11、Y and -Y = 300 +Z and -Z = 0 3. Press OK Assign Excitations Based on the assumptions that the conductors are in electrostatic equilibrium, we assign voltage potential on the object itself (and not on the surface of the object like in the other solvers). Assign Excitation for Inner Select the object

12、Inner from the history tree Select the menu item Maxwell 3D Excitations Assign Voltage In Voltage Excitation window, 1. Set Value to -1000 V 2. Press OK Assign Excitation for Outer Select the object Outer from the history tree Select the menu item Maxwell 3D Excitations Assign Voltage In Voltage Exc

13、itation window, 1. Set Value to 1000 V 2. Press OK ANSYS Maxwell 3D Field Simulator v15 Users Guide9.1-# Assign Parameters In addition to the field, we are interested by the Capacitance value as well as the force applied to the inner armature. Assign Matrix Parameter to Calculate Capacitance Select

14、the menu item Maxwell 3D Parameters Assign Matrix In Matrix window 1. Voltage1 and Voltage2 Include: Checked 2. Press OK Assign Force Parameter for Inner Select the Object Inner from the tree Select the menu item Maxwell 3D Parameters Assign Force In Force Setup window, 1. Type : Virtual 2. Press OK

15、 Analysis Setup To create an analysis setup: Select the menu item Maxwell 3D Analysis Setup Add Solution Setup Solution Setup Window: 1. General Tab Percent Error: 5 2. Convergence Tab Refinement Per Pass: 50% 3. Click the OK button Analyze To start the solution process: 1. Select the menu item Maxw

16、ell 3D Analyze All (You will need to save your project before analyzing. Note that, the project is always saved before the simulation starts). ANSYS Maxwell 3D Field Simulator v15 Users Guide 9.1-# Create Vector Plot To Create Vector Plot Select the plane Global:XY from the history tree Select the m

17、enu item Maxwell 3D Fields Fields E E_Vector In Create Field Plot window 1. Press Done To adjust spacing and size of arrows, double click on the legend and then go to Marker/Arrow and Plots tabs ANSYS Maxwell 3D Field Simulator v15 Users Guide 9.1-# Solution Data To view the Solution Data: Select th

18、e menu item Maxwell 3D Results Solution Data 1. To view Capacitance Select the Matrix tab In our problem, we only have two conductors, therefore the capacitance values are symmetrical 2. To View Force Select the Force tab The analytical value of the capacitance per meter for an infinite long coaxial

19、 wire is given by the following formula: C = 20 / ln(b/a) (a and b being the inside and outside diameters) The analytical value would is therefore 1.089e-10 F/m (a =0.6mm, b=1mm) In our project, then length of the conductor is 25 mm, therefore the total capacitance is 2.72 pF. We obtain a good agree

20、ment with the obtained result. ANSYS Maxwell 3D Field Simulator v15 Users Guide9.1-# Example 2: Capacitance of a planar capacitor In this example we illustrate how to simulate a simple planar capacitor made of two parallel plates Create Design To Create Design Select the menu item Project Insert Max

21、well 3D Design Rename design as Plate Set Solution Type To set the Solution Type: Select the menu item Maxwell 3D Solution Type Solution Type Window: 1. Choose Electrostatic 2. Click the OK button Set Default Material To set the default material: Using the 3D Modeler Materials toolbar, choose Select

22、 In Select Definition window, 1. Type pec (Perfect Conductor) in the Search by Name field 2. Click the OK button Create Geometry Create Box Select the menu item Draw Box 1. Using the coordinate entry fields, enter the box position X: 0, Y: 0, Z: 0, Press the Enter key 2. Using the coordinate entry f

23、ields, enter the opposite corner dX: 25, dY: 25, dZ: 2, Press the Enter key Change the name of the Object to DownPlate Note: It is not needed to draw the plates; it is possible in this case just to apply a voltage to the surface of the gap. ANSYS Maxwell 3D Field Simulator v15 Users Guide9.1-# Creat

24、e Gap Select the menu item Draw Box 1. Using the coordinate entry fields, enter the box position X: 0, Y: 0, Z: 2, Press the Enter key 2. Using the coordinate entry fields, enter the opposite corner dX: 25, dY: 25, dZ: 1, Press the Enter key Change the name of the Object to Gap and material to Vacuu

25、m Create Second Box Select the menu item Draw Box 1. Using the coordinate entry fields, enter the box position X: 0, Y: 0, Z: 3, Press the Enter key 2. Using the coordinate entry fields, enter the opposite corner dX: 25, dY: 25, dZ: 2, Press the Enter key Change the name of the Object to UpPlate Cha

26、nge the colors of the objects if needed Assign Excitations Assign Excitation for DownPlate Select the object DownPlate from the history tree Select the menu item Maxwell 3D Excitations Assign Voltage In Voltage Excitation window, 1. Set Value to 0 V 2. Press OK Assign Excitation for UpPlate Select t

27、he object UpPlate from the history tree Select the menu item Maxwell 3D Excitations Assign Voltage In Voltage Excitation window, 1. Set Value to 1 V 2. Press OK Assign Parameters Assign Matrix Parameter to Calculate Capacitance Select the menu item Maxwell 3D Parameters Assign Matrix In Matrix windo

28、w 1. Voltage1 and Voltage2 Include: Checked ANSYS Maxwell 3D Field Simulator v 15 Users Guide 9.1-# Analysis Setup To create an analysis setup: Select the menu item Maxwell 3D Analysis Setup Add Solution Setup Solution Setup Window: 1. Convergence Tab Refinement Per Pass: 50% Maximum Number of Passe

29、s: 15 2. Click the OK button Analyze To start the solution process: 1. Select the menu item Maxwell 3D Analyze All Solution Data To view the Solution Data: Select the menu item Maxwell 3D Results Solution Data 1. To view Capacitance Select the Matrix tab The analytical value of the capacitance for t

30、wo parallel plates is given by: C = A/ d *0 (A is the area of the plate and d is the thickness of the dielectrics). Using this formula, we obtain 5.53 pF. This value matches the value obtain using the finite elements ANSYS Maxwell 3D Field Simulator v15 Users Guide9.1-# Example 3: Capacitance of planar capacitor with External Region Here we look at the consequence for the capac