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.
–渦流求解器
•解決頻域中正弦變化的磁場。僅解決3D中的襯里材料。它是一個全波求解器，因此考慮位移電流。還考慮了感應場，例如趨膚和鄰近效應。
【仿真介紹】
• 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.
本仿真通過一個簡單的線圈上帶有一個磁盤（disk）的簡單模型，介紹渦流解算器的使用。該計算器可以計算在特定頻率正弦信號下的磁場。線性和非線性（飽和效應）的磁性材料均可以使用。此外，還考慮渦流，趨膚效應和鄰近效應。
• 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幾何：
螺旋線圈上方的鐵盤–正弦500 Hz電流將分配給鑄鐵盤下面的八匝螺旋線圈。線圈在板中感應出渦流和損耗。如下所示，將使用2D RZ軸對稱求解器建立2D模型。
【建模分析】
Step01 Create Design 創建設計文件
– Select the menu item Project -> Insert Maxwell 2D Design
Step02 Set Solution Type 設置解算器類型
– 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
如下圖
Step03 Set Default Units 設置默認單位
– Select the menu item Modeler -> Units
• Set units to cm (centimeters) and press OK
Step04 Create Coil 創建線圈
大小為一個2*2cm的矩形，對角線坐標為(17,0,-1)和(19,0,1),顏色設置為黃色，材料設置為銅
– 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
根據模型可知，需要8個相同的矩形模型，所以接下來將對該Coil進行復制操作，方法如下，每個矩形的中心距為3.1
共需要8個
Duplicate Coil
– Select the sheet Coil from history tree
– Select the menu item Edit-> Duplicate -> Along Line 線性排列
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 創建 plate
Plate的大小為41*1，頂點坐標為(0,0,1.5)和(41,0,2.5)材料為cast_iron鑄鐵，顏色為橘黃色
– 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 創建解算區域
– 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 創建激勵
• 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：選擇"Solid "指定將考慮線圈中的渦流效應。另一方面，如果選擇"Stranded "，則僅會計算出直流電阻，而不會考慮線圈中的交流電影響。當趨膚深度比絞合導體的厚度大得多時，例如使用利茲線時，絞合是合適的。注意，在兩種情況下，都將計算板中的渦流效應。
Step08 Assign Boundary and Parameters 創建邊界和參數
• 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：在對稱軸上，將自動跳過"氣球邊界"分配，這也可以通過選擇不在對稱軸上的區域的邊緣來實現。
• 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 結果數據
• 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:收斂性
阻抗矩陣
RL矩陣
Flux Linkage 磁鏈
Inductive Coupling Coefficient:電感耦合系數
Step11 Compute Power Loss 計算功率損耗
• 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上的損耗大約是260W
Step12 Create Field Plots 創建場圖
• 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，由於磁力線是磁性的，因此磁力線被吸引到平板上。而且，由於板上有渦電流流動，因此在板上存在集膚效應。由圖可以看出，極板上的磁力線分布不均勻，存在集膚效應
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 將解算頻率設置為1e-6Hz仿真DC情況下的情況
磁力線：
由圖可以看出，在DC情況下，導體中的磁力線分布均勻，基本不存在集膚效應。
