Eddy Current Solver
• Solves sinusoidally-varying magnetic fields in frequency domain. Solves only for liner materials in 3D. It is a full wave solver thus considers displacement currents. Induced fields such as skin and proximity effects are also considered.
–涡流求解器
•解决频域中正弦变化的磁场。仅解决3D中的衬里材料。它是一个全波求解器，因此考虑位移电流。还考虑了感应场，例如趋肤和邻近效应。
【仿真介绍】
• Introduction to the Eddy Current Solver
– This workshop introduces the Eddy Current solver based on a simple example with a disk above a coil. This solver calculates the magnetic fields at a specified sinusoidal frequency. Both linear and nonlinear (for saturation effects) magnetic materials can be used. Also, eddy, skin and proximity effects are considered.
本仿真通过一个简单的线圈上带有一个磁盘（disk）的简单模型，介绍涡流解算器的使用。该计算器可以计算在特定频率正弦信号下的磁场。线性和非线性（饱和效应）的磁性材料均可以使用。此外，还考虑涡流，趋肤效应和邻近效应。
• 2D Geometry:
Iron Disk above a Spiral Coil – A sinusoidal 500 Hz current will be assigned to an eight turn spiral coil underneath of a cast iron disk. The coil induces eddy currents and losses in plate. The 2D model will be setup as shown below using the 2D RZ axisymmetric solver.
•2D几何：
螺旋线圈上方的铁盘–正弦500 Hz电流将分配给铸铁盘下面的八匝螺旋线圈。线圈在板中感应出涡流和损耗。如下所示，将使用2D RZ轴对称求解器建立2D模型。
【建模分析】
Step01 Create Design 创建设计文件
– Select the menu item Project -> Insert Maxwell 2D Design
Step02 Set Solution Type 设置解算器类型
– Select the menu item Maxwell 2D -> Solution Type
– Solution Type Window:
1. Geometry Mode: Cylindrical about Z
2. Choose Magnetic > Eddy Current
3. Click the OK button
如下图
Step03 Set Default Units 设置默认单位
– Select the menu item Modeler -> Units
• Set units to cm (centimeters) and press OK
Step04 Create Coil 创建线圈
大小为一个2*2cm的矩形，对角线坐标为(17,0,-1)和(19,0,1),颜色设置为黄色，材料设置为铜
– Select the menu item Draw-> Rectangle
1. Using the coordinate entry fields, enter the position of rectangle
– X: 17, Y: 0, Z: -1, Press the Enter key
2. Using the coordinate entry fields, enter the opposite corner
– dX: 2, dY: 0, dZ: 2, Press the Enter key
– Change the name of resulting sheet to Coil and color to Yellow
– Change the material of the object to Copper
根据模型可知，需要8个相同的矩形模型，所以接下来将对该Coil进行复制操作，方法如下，每个矩形的中心距为3.1
共需要8个
Duplicate Coil
– Select the sheet Coil from history tree
– Select the menu item Edit-> Duplicate -> Along Line 线性排列
1. Using the coordinate entry fields, enter the first point of duplicate vector
– X: 0, Y: 0, Z: 0, Press the Enter key
2. Using the coordinate entry fields, enter the second point
– dX: 3.1, dY: 0, dZ: 0, Press the Enter key
• Total Number: 8
• Press OK
Step05 Create Plate 创建 plate
Plate的大小为41*1，顶点坐标为(0,0,1.5)和(41,0,2.5)材料为cast_iron铸铁，颜色为橘黄色
– Select the menu item Draw -> Rectangle
1. Using the coordinate entry fields, enter the position of rectangle
– X: 0, Y: 0, Z: 1.5, Press the Enter key
2. Using the coordinate entry fields, enter the opposite corner
– dX: 41, dY: 0, dZ: 1, Press the Enter key
– Change the name of resulting sheet to Plate and color to Orange
– Change the material of the object to cast_iron
Step06 Create Solution Region 创建解算区域
– Select the menu item Draw-> Rectangle
1. Using the coordinate entry fields, enter the position of rectangle
– X: 0, Y: 0, Z: -100, Press the Enter key
2. Using the coordinate entry fields, enter the opposite corner
– dX: 120, dY: 0, dZ: 200, Press the Enter key
– Change the name of resulting sheet to Region
Step07 Assign Excitations 创建激励
• Assign Excitation
– Press Ctrl and select all Coils from history tree
– Select the menu item Maxwell 2D -> Excitations -> Assign -> Current
– In Current Excitation window,
• Base Name: Current
• Value: 125 A
• Type: Solid
• Ref. Direction: Positive
• Press OK
注意：选择"Solid "指定将考虑线圈中的涡流效应。另一方面，如果选择"Stranded "，则仅会计算出直流电阻，而不会考虑线圈中的交流电影响。当趋肤深度比绞合导体的厚度大得多时，例如使用利兹线时，绞合是合适的。注意，在两种情况下，都将计算板中的涡流效应。
Step08 Assign Boundary and Parameters 创建边界和参数
• Assign Boundary
– Select the object Region from history tree
– Select the menu item Edit -> Select ->All Object Edges
– Select the menu item Maxwell 2D -> Boundaries -> Assign -> Balloon
– In Balloon Boundary window,
• Press OK
注意：在对称轴上，将自动跳过"气球边界"分配，这也可以通过选择不在对称轴上的区域的边缘来实现。
• Assign Matrix Parameters
– Select the menu item Maxwell 2D -> Parameters -> Assign -> Matrix
– In Matrix window,
• For all current Sources
– Include: þ Checked
• Press OK
Step09 Analyze 分析
• Create an analysis setup:
– Select the menu item Maxwell 2D -> Analysis Setup -> Add Solution Setup
– Solution Setup Window:
1. General Tab
– Maximum Number of Passes: 15
2. Solver Tab
– Adaptive Frequency: 500 Hz
3. Click the OK button
•Start the solution process:
1. Select the menu item Maxwell 2D -> Analyze All
Step10 Solution Data 结果数据
• View Solution Information
– Select the menu item Maxwell 2D -> Results -> Solution Data
• To view Convergence
– Select the Convergence tab
• To View Impedance matrix
– Select Matrix tab
– By default, the results are displayed as [R,Z] but can be also shown as [R,L] or as coupling coefficients.
Convergence:收敛性
阻抗矩阵
RL矩阵
Flux Linkage 磁链
Inductive Coupling Coefficient:电感耦合系数
Step11 Compute Power Loss 计算功率损耗
• Compute Total Power Loss in the Plate
– Select the menu item Maxwell 2D > Fields > Calculator
– In Fields Calculator window,
• Select Input > Quantity > OhmicLoss
• Select Input > Geometry
– Select Volume
– Select Plate
– Press OK
• Select Scalar > Integral > RZ
• Select Output > Eval
所以在Plate上的损耗大约是260W
Step12 Create Field Plots 创建场图
• Plot Mesh
– Select the menu item Edit > Select All
– Select the menu item Maxwell 2D > Fields > Plot Mesh
– In Create Mesh Plot window, press Done
• Plot Flux Lines
– Select the menu item Edit > Select All
– Select the menu item Maxwell 2D > Fields > Fields > A > Flux _Lines
– In Create Field Plot window, Press Done
注意，由于磁力线是磁性的，因此磁力线被吸引到平板上。而且，由于板上有涡电流流动，因此在板上存在集肤效应。由图可以看出，极板上的磁力线分布不均匀，存在集肤效应
Step13 Create Field Plots (Contd…)
• Plot Current Density Scalar on Plate
– Select the sheet Plate from history tree
– Select the menu item Maxwell 2D Fields > Fields > J > JAtPhase
– In Create Field Plot window, Press Done
• Plot Current Density Scalar on Coils
– Press Ctrl and select all coils from history tree
– Select the menu item Maxwell 2D > Fields > Fields > J > JAtPhase
– In Create Field Plot window, Press Done
Step14 Plot Ohmic Loss Distribution
• Plot Ohmic Losses
– Press Ctrl and select all coils and Plate
– Select the menu item Maxwell 2D > Fields > Fields > Other > Ohmic_Loss
– In Create Field Plot window, Press Done
• Modify Plot Attributes
– Double click on the Legend to modify plot
– In the window,
• Scale tab
– Select Log
• Press Apply and Close
Step15 Plot Current Density Vectors
• Plot Current Density vectors
– Select the sheet Plate from history tree
– Select the menu item Maxwell 2D >Fields >Fields > J > J_Vector
– In Create Field Plot window, Press Done
– Double click on the Legend to modify plot
– In the window,
• Plots tab
– Plot: Change to J_Vector1
– Change Vector plot spacing
• Min: 0.5
• Max: 0.5
• Press Apply and Close
• Animate Plot
– Select the Vector plot from Project Manager tree, right click and select Animate
– In Setup Animation window,
• Press OK with default settings
– A window will appear to start, stop, pause or save the animation
Step16 将解算频率设置为1e-6Hz仿真DC情况下的情况
磁力线：
由图可以看出，在DC情况下，导体中的磁力线分布均匀，基本不存在集肤效应。
