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。

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【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

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Step03 Set Default Units 设置默认单位

– Select the menu item Modeler -> Units

• Set units to cm (centimeters) and press OK

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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

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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

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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

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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

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阻抗矩阵

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RL矩阵

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Flux Linkage 磁链

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Inductive Coupling Coefficient:电感耦合系数

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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

   

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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

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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

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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

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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

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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

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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。

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