comsol涡流模块Word文档格式.docx

1、coiljA + （0 r A） = -2- r-FO RC E SThe total electromagnetic force acting on region of space can be obtained by integrating Maxwells stress tensor on the delimiting boundary :F = T n dSThe Force Calculation feature automatically performs the integral along the boundaries of the desired region, consid

2、ering also the axisymmetric geometry of the problem. The computed force will be available in results processing as a global variable.Results and DiscussionIn the time-harmonic regime, the varying magnetic field induces electrical currents in the metallic plate. The currents, in turn, act as sources

3、of an opposing magnetic field “shielding” the plate from the magnetic field. As a result of this phenomenon, the region in which electrical currents are generated is confined in proximity of the surface and reduces in size with increasing frequency. Figure 1 and Figure 2 show the induced current den

4、sity at 10 Hz and 300 Hz, respectively.In this model, a time-domain study is performed to investigate the step response of the system. Figure 3 displays a snapshot of the induced current density and magnetic flux density for the transient solution in a combined surface and arrow plot.Finally, Figure

5、 4 shows the total axial force between the coils and the plate as a function of time computed by the Force Calculation feature. For the chosen current direction, the force is repulsive （negative）.Figure 1: The component of the induced current density for the time-harmonic solution plotted together w

6、ith a contour plot of the magnetic vector potential at a frequency of 10 Hz.Figure 2: Plot of the same quantities at a frequency of 300 Hz.Figure 3: Snapshot of the induced current density （surface plot） and the magnetic flux density （arrow plot） during the transient study.Figure 4: Total force acti

7、ng on the copper plate plotted as a function of time.Model Library path: ACDC_Module/Inductive_Devices_and_Coils/ coil_above_plateModeling InstructionsFrequency DomainFrom the File menu, choose New.NE W1 In the New window, click the Model Wizard button.MO DE L W I ZA R D1 In the Model Wizard window,

8、 click the 2D Axisymmetric button.2 In the Select physics tree, select AC/DCMagnetic Fields （mf）.4Click the Study button.5 In the tree, select Preset StudiesFrequency Domain.6 Click the Done button.GE OMETR Y 1Square 11 In the Model Builder window, under Component 1 right-click Geometry 1 and choose

9、Square.2In the Square settings window, locate the Size section.3In the Side length edit field, type 0.1.4Locate the Position section. In the z edit field, type -0.05.Rectangle 11 In the Model Builder window, right-click Geometry 1 and choose Rectangle.2In the Rectangle settings window, locate the Si

10、ze section.3In the Width edit field, type 0.08.4In the Height edit field, type 0.02.5Locate the Position section. In the z edit field, type -0.021.Circle 11 Right-click Geometry 1 and choose Circle.2 In the Circle settings window, locate the Size and Shape section.3In the Radius edit field, type 0.0

11、025.4Locate the Position section. In the r edit field, type 0.0125.5In the z edit field, type 0.0025.Circle 24Locate the Position section. In the r edit field, type 0.0185.6 Click the Build All Objects button.The geometry is now complete.Next, add the materials relevant to the model.MATER I A L SOn

12、the Home toolbar, click Add Material.AD D MA T E RI AL1 Go to the Add Material window.2 In the tree, select Built-InAir.3 In the Add Material window, click Add to Component.Copper.MA TERIALSCopper1 In the Model Builder window, under Component 1Materials click Copper.2 Select Domains 2 4 only.MA G N

13、E T I C FI E L DSSingle-Turn Coil 11 On the Physics toolbar, click Domains and choose Single-Turn Coil.2 Select Domains 3 and 4 only.3 In the Single-Turn Coil settings window, locate the Single-Turn Coil section.4 From the Coil excitation list, choose Voltage.5In the V coil edit field, type 0.1mV.Wi

14、th this setting, the Single-Turn Coil feature applies a loop voltage of 0.1 mV to each of the coil loops.Now, add a Force Calculation feature that computes the total force acting on the plate.Force Calculation 11 On the Physics toolbar, click Domains and choose Force Calculation.2 Select Domain 2 on

15、ly.3 In the Force Calculation settings window, locate the Force Calculation section.4 In the Force name edit field, type plate.S T UDY 1Step 1: Frequency Domain1 In the Model Builder window, under Study 1 click Step 1: Frequency Domain.2 In the Frequency Domain settings window, locate the Study Sett

16、ings section.3 In the Frequencies edit field, type 10Hz,100Hz,300Hz.Disable the automatic plot generation.4 In the Model Builder window, click Study 1.5 In the Study settings window, locate the Study Settings section.6 Clear the Generate default plots check box.7 On the Study toolbar, click Compute.

17、When the solution process is completed, create plot groups to visualize the results.RES U LTS2D Plot Group 11 On the Results toolbar, click 2D Plot Group.2 On the 2D Plot Group 1 toolbar, click Surface.3 In the Surface settings window, click Replace Expression in the upper-right corner of the Expres

18、sion section. From the menu, choose Magnetic FieldsCurrents and chargeInduced current densityInduced current density, phi component （mf.Jiphi）. Add a contour plot to show the field lines of the magnetic flux density. In axial symmetry, those lines can be obtained by plotting the isolines of the magn

19、etic vector potential multiplied by the radial coordinate, r.4 On the 2D Plot Group 1 toolbar, click Contour.5In the Contour settings window, locate the Expression section.6In the Expression edit field, type Aphi*r.7 In the Model Builder window, click 2D Plot Group 1.8In the 2D Plot Group settings w

20、indow, locate the Data section.9 From the Parameter value （freq） list, choose 10.10 On the 2D Plot Group 1 toolbar, click Plot.The plot shows the induced current density in the plate. Plotting the other solutions shows how the region in which the currents are induced decreases with increasing freque

21、ncy.11 From the Parameter value （freq） list, choose 100, then click Plot.12 From the Parameter value （freq） list, choose 300, then click Plot.Transient AnalysisTo set up a time-dependent study to investigate the step response of the system requires only a few additional steps. The Initial Values fea

22、ture automatically included in the Magnetic Fields interface specifies the initial value for the magnetic vector potential, defaulted to zero. At the beginning of the transient simulation （t = 0）, a 0.1 mV voltage is applied to the coil. This corresponds to exciting from an unexcited state the syste

23、m with a step function.A D D S T UDY1 Go to the Add Study window.2 Find the Studies subsection. In the tree, select Preset StudiesTime Dependent.3 In the Add study window, click Add Study.4 Close the Add Study window.S T UDY 2 Time Dependent1 In the Model Builder window, under Study 2 click Step 1:

24、Time Dependent.2 In the Time Dependent settings window, locate the Study Settings section.3 In the Times edit field, type 0,10（range（-4,1/3,-1）.4 Select the Relative tolerance check box.5 In the associated edit field, type 0.001.6 In the Model Builder window, click Study 2.7 In the Study settings wi

25、ndow, locate the Study Settings section.8 Clear the Generate default plots check box.9 On the Study toolbar, click Compute.RESUL T S2D Plot Group 22 In the 2D Plot Group settings window, locate the Data section.3 From the Data set list, choose Solution 2.4 From the Time （s） list, choose 0.002154.5 O

26、n the 2D Plot Group 2 toolbar, click Surface.6In the Surface settings window, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Magnetic FieldsInduced current density, phi component （mf.Jiphi）.7 In the Model Builder window, right-click 2D Plot Group 2 and choose Arrow Surface.8 In the Arrow Surface settings window, locate the Arrow Positioning section.9Find the r grid points subsection. In the Points edit