Ansoft 2D教程13_2D_section13_transient_pendulum

Maxwell 2D Application NoteA Swinging Pendulum ProblemA simple 2D Transient example can be used to demonstrate motion induced eddy currents. Two small puck magnets (NdFe35) are mounted on a base directly below a swinging aluminum plate which is two inches square by a quarter- inch thick. In one case, a solid plate is used, while in a second case, a slotted plate is used. It can be seen that the swinging motion of the solid plate is quickly dampened due to the motion induced eddy currents, while the slotted plate swings more freely. In a third case, a glass plate is used to show that swinging continues essentially undamped and that the period of oscillation is very close to the theoretical value for an ideal pendulum.Create the ProjectAccess the Maxwell Project Manager and create a new Maxwell 2D project called swing1. Open the project and select Transient as the Solver with an XY drawing plane.Set Up the Model¾Define the model settings:1. Choose Define Model/Draw Model to access the Maxwell 2D Modeler.2. Change the units to inches.3. Choose Model/Drawing Size and define the drawing size as follows:• Xmimima = -20• Ymimima = -20• Xmaxima = 20• Ymaxima = 20Create the BandChoose Object/Circle/2-point and create the band object by drawing a circle with its center at the origin and a radius of 10.1 inches. Use 360 segments, name the object band and color it dark green.Create the Slotted Plate¾Create the slotted plate:1. Choose Object/Rectangle and create a bar with the first corner at (-1,-10) and opposite corner at (-0.785, -9.75). Notice that dU=0.215 and dV=0.25. Name the object bar_1 and color it red.2. Zoom in on bar_1 and choose Edit/Deselect All to deselect any objects that may be selected.3. Select bar_1 by clicking inside of it.4. Create the remaining seven bars by choosing Edit/Duplicate/Along Line with an anchor point of(0,0) and dU=0.255 inches. There are now eight bars in the model.Create the Magnet¾Create the magnet:1. Choose Object/Rectangle and create the magnet with the first corner at (-0.5, -10.75) and itsopposite corner at (0.5, -10.25). Notice that dU=1 and dV=0.5 are automatically changed, whichshows the size of the magnet. Name the object magnet and color it light blue.2. Deselect any objects that may be selected. Press f on the keyboard to fit all the objects in thewindow and then hit CTRL-F on the keyboard to fill the objects with color.3. Save the model and exit the Maxwell 2D Modeler.Group the ObjectsGroup the objects together to save time when defining the materials and sources for the objects.¾Group the objects:1. Choose Define Model/Group Objects, and create a group containing all eight bars.2. Name the new group bars.3. Choose Exit to exit the Group Objects window and save the changes as you exit.Assign the Materials¾Assign the materials:1. Access the Material Manager and assign the following materials:• Assign vacuum to the band and background.• Assign aluminum to the [bars] group.• Assign NdFe35 to the magnet. Align this with a given direction of 90 degrees.2. Choose Exit to exit the Material Manager, and save the changes as you exit.Assign the Boundaries and Sources¾Assign the boundaries and sources:1. Choose Setup Boundaries/Sources and access the 2D Boundary/Source Manager.2. Choose Edit/Select/Object/By Clicking and select the background object. Click the right mousebutton to stop selecting objects.3. Choose Assign/Boundary/Balloon and assign a balloon boundary to the background.4. Choose Window/Change View/Zoom In and zoom in on the bars.5. Choose Edit/Select/Object/By Clicking and select the group of bars. Click the right mouse buttonto stop selecting objects.6. Choose Assign/Source/Solid and assign a solid source with 0 current to these objects. Thisindicates that the bars have a finite length and that current flow does not have a return path other than the inside of the object itself.7. Choose File/Exit to exit the Boundary Manager. Save the changes as you exit.Set Up the Solution Options¾Define the solution options:1. Choose Setup Solution/Options. When the Solve Setup window appears, choose Manual Mesh toaccess the 2D Meshmaker. In the transient solver, the mesh must always be created manually. You should already have a basic understanding of the mesh density that is required for an accuratesolution.2. Choose Mesh/Seed/Quadtree.3. Enter 7 as the seeding level and choose OK. This automatically creates a fine seed pattern for themodel.4. Choose Mesh/Make to create the mesh.2. Choose File/Exit and save the changes as you exit the Meshmaker.3. Enter the following Transient Analysis parameters in their respective fields:• Stop time: 5 sec• Time step: 0.01 sec• Save fields time step: Setup... Add Sweep... 0 to 5 with 21 samples. Accept and Ok.• Model depth: 2 inches• Symmetry multiplier: 14. Choose OK to save these parameters and exit the Solve Setup window.Set Up the Motion Parameters¾Define the motion solution options:1. Choose Setup Solution/Motion Setup.2. Select the band object and choose Set Band.3. Select Rotation limits and set the following value parameters:• Positive: 45 degrees• Negative: -45 degrees• Initial Pos: 45 degrees4. Verify that the Type of Motion is Rotation and that the Center of Rotation is (0,0).5. Choose Mechanical Setup to enter in the following mechanical parameters.6. Verify that Consider Mechanical Transient is selected.7. Choose Functions and define the following. Be sure to notice capital letters as functions are case-sensitive. The following values define the mechanical functions for the assembly:• Mass = 0.1• Force = Mass * 9.8• Radius = 0.254 (based on: 10/39.4 = 0.254 meters)• Torque = - Force * Radius * sin(P)Note:The mass is based on a value for both the plate and the basket where a 2” x 2” x 1/4” x1.639e- 5 (m3/in3) solid has a specific gravity of 2600 kg/m3 which yields a mass of 0.044kg. A basket, which is not modeled, holds the plate in place and is also taken intoaccount. The mass of this basket is approximately 0.056 kg.2. Choose Done to accept these functions.3. Choose Options and select Load so that a variable can be defined for the load torque. Choose OKto accept the setting.Enter the following mechanical properties:• Initial Angular Velocity: 0 rpm• Moment of Inertia: 0.0064 kg m2. This is based on the mass*(radius)2.• Damping: 0 M-m-sec/rad•2. Choose OK to accept these parameters and close the Mechanical Setup window.3. Choose Exit to accept the motion solution settings and exit.Generate a SolutionChoose Solve/Nominal problem to obtain a solution.View the Results¾Analyze the solutions:1. Choose Solutions/Transient Data and view the plots for Torque, Power Loss, Speed, and Position.Note that the plate swings back and forth past the magnets.2. Choose Post Process/Fields and post process the results at 0.75 sec. Choose Post Process.3. Zoom in on the magnet and the bars, and choose Plot/Field to create a flux plot.4. Select:••••••••••Plot Quantity: Flux Lines On Geometry: Surface -all- In Area: -all-okChoose ok to display the plot using the default plot settings.5. Use Plot/ Visibility to hide this plot before creating the next plot.Plot the Induced CurrentCreate a plot of induced current in the plate. Use the calculator to first load the current density, then plot its value in the z direction.¾Plot the current:1. First, create an object list which includes all of the bars as one group:GeometryCreateObject list …list1 and select all eight barsok2. Next, choose Data/Calculator, then select:•Quantity••••••••JScalarScalar_ZGeometrySurface: list1okPlotChoose ok to display the plot using the default plot settings.This completes the first part of the exercise. Exit the Post Processor and the project, and return to the Maxwell Project Manager.A Slotless PendulumCopy the project and solve it without the slots.In this simulation, the solution is a combination of mechanical and electromagnetic forces acting on the pendulum. Motion-induced eddy currents are prevalent in the solid plate.¾Copy the project:1. In the Maxwell Project Manager, select swing and choose Copy.2. Select Model Only to copy only the model and not the entire solution.3. Enter swing2 as the new project name.4. Choose OK.5. Choose Open to open the project.Modify the ModelModify the model such that it has a solid plate instead of a slotted one.¾Modify the model:1. Choose Define Model/Draw Model to access the Maxwell 2D Modeler.2. Zoom in on the eight bars and select all eight bars and delete them.3. Choose Object/Rectangle and create a rectangle with the first corner at (-1,-10) and its oppositecorner at (1, -9.75). Notice that dU=2 and dV=0.25, which is the size of the plate.4. Name the object plate and color it red.5. Exit the modeler and save the changes as you exit.Assign the Materials¾Assign the materials:1. Choose Setup Materials to access the Material Manager.2. Assign aluminum to plate.3. Exit the Material Manager and save the changes as you exit.Assign the Solid Source¾Assign the current source:1. Choose Setup Boundaries/Sources to access the 2D Boundary/Source Manager.2. Zoom in on the plate and choose Edit/Select/Object/By Clicking to select the plate.3. Click the right mouse button to stop selecting objects.4. Choose Assign/Source/Solid and assign a solid source with 0 amperes to the plate.5. Exit the Boundary Manager and ave the changes as you exit.Setup the Solution Options¾Define the solution options:1. Choose Setup Solution/Options. The Solve Setup window appears.2. Choose Manual Mesh to access the Meshmaker.3. Choose Mesh/Seed/Quadtree and perform an automatic seeding.4. Enter 7 as the seeding Level and then OK. This automatically creates fine seed pattern for the model.5. Choose Mesh/Seed/Surface. Select plate and enter a Seed Value = 0.1. Click on Seed and OK.6. C hoose Mesh/Make to create the mesh.7. Choose File/Exit and save the mesh as you exit the Meshmaker.8. Define the following Transient Analysis options:• Make certain that Start from time zero is selected.• Enter 0.7 seconds as the Stop time.• Enter 0.005 seconds as the Time step.• Save fields time step:: Setup... Add Sweep... 0 to 0.75 with 4 samples. Accept and Ok.• Enter 2 inches as the Model depth.• Enter 1 as the Symmetry multiplier.9. Select OK to accept these parameters and close the Solve Setup window.Solve the ProblemSelect Solve/Nominal Problem to obtain a solution.View the ResultsChoose Solutions/Transient Data and view the plots for Torque, Power Loss, Speed, and Position. It can be seen that the plate swings past the magnet once and then returns slowly to the resting position.Create a new position vs. time plotSince the position plot above is shown without using a negative angle (such as –45 degrees instead of 315 degrees), the plot will be modified assuming sin(angle) ~ angle.Select Post Process /Transient Data1.Open postion.dat2.Select Tools / Calculator3.Select: position.dat and click on Copy>> to load it into the calculator register4.Then, enter the following:• sin• Name/constant: 57.3• Enter• *• Name/constant: new• Enter5.Select: new and click on << Load to copy it to Loaded Signals register6.Finally, select:• Done• Plot• New• Select: new• ok7.The following plot shows position vs. angle, when the angle can be negative.This completes part two of the exercise. Exit the Post Processor and the project, and return to the Maxwell Project Manager.A Glass PendulumNow you can create a new project with a glass plate as its pendulum.In theory, an ideal pendulum will swing forever, provided that frictional and wind losses are zero. This behavior can be approximated by using a glass plate which has zero conductivity. Also, the period of an ideal pendulum can be calculated with the formula:where l is the length of pendulum in meters and G is the force of gravity, equal to 9.8 m/s2.In this simulation, the solution is purely mechanical. There are no magnetic forces acting on the system.¾Copy the project:n In the Maxwell Project Manager, copy only the model of swing2 and name the new project swing3.Assign the Materials¾Assign the materials:1. Enter the Material Manager and assign corning_glass to the plate.2. Exit the Material Manager and save changes as you exit.Set Up Boundaries and SourcesEnter the 2D Boundary Manager and remove the current source on the plate. Because this plate is made of glass, no current source should be used. Exit the 2D Boundary Manager and save the changes when the source condition has been removed.Set Up the Solution OptionsFor purely mechanical analysis, both the mesh and the time step must be extremely small.¾Define the solution options:1. Choose Setup Solution/Options. The Solve Setup window appears.2. Choose Manual Mesh.3. Choose Mesh/Seed/Quadtree and perform an automatic seeding.4. Enter 8 as the seeding Level. This automatically creates a fine seed pattern for the model.5. Choose OK.6. Choose Mesh/Make to create the mesh.7. Define the following Transient Analysis options:• Make certain that Start from time zero is selected.• Enter 1 second as the Stop time.• Enter 0.0025 seconds as the Time step.• Save fields time step:: Setup... Add Sweep... 0 to 1 with 2 samples. Accept and Ok.• Enter 2 inches as the Model depth.• Enter 1 as the Symmetry multiplier.8. Choose OK to accept these parameters and exit the Solve Setup window.Solve the ProblemChoose Solve/Nominal Problem to obtain a solution.View the ResultsOnce the solution has been generated, you can view the results.¾View the results:1. Choose Solutions/Transient Data from the top of the display window.2. Select Speed and Position to view their respective plots.Notice that the swinging of the glass plate continues essentially undamped with a period of oscillation that is very close to the theoretical value of 1.01 seconds.。