工程电磁场数值分析试题.docx

工程电磁场数值分析试题

一、 一同轴电缆，内导体（铜）外半径为0.01m，外导体（铜）内半径为0.03m，外导体厚度为0.003m，内外导体间有两层电介质，一层电介质为聚乙烯()，
另外一层电介质为聚氯乙烯()，两层电介质厚度均为0.01m，内导体电位为5kV，外导体电位为0V。
（1）试用有限元法求内外导体间的电位和电场强度分布，
（2）求此电缆中最大场强的位置和最大值，能否击穿电介质或发生局部击穿，（3）在不击穿的前提下，此电缆能承载的最大电压为多少？

分析：
参数设置：铜相对介电常数ε=1，电阻率ρ=1e-7Ω/m
聚乙烯相对介电常数ε=3，电阻率ρ=1e+13Ω/m
聚氯乙烯相对介电常数ε=6，电阻率ρ=1e+14Ω/m

（1） 其中电位分布及场强分布如下：

通过定义路径（-0.033,0）到（0.033,0）分析其场强分布如下图：

电压分布如下图：

（2）从图中可以看出其场强最大值位于内导体外半径附近处取得距离内导体圆心0.0132m处取最大值422728V/m。聚乙烯击穿场强为35-50MV/m，聚氯乙烯击穿场强为20-35MV/m，计算可知无法击穿电介质。
（3）聚乙烯击穿场强为35-50MV/m，聚氯乙烯击穿场强为20-35MV/m，按最小值计算理论上0.01m距离上其耐压分别为350kv和200kv，所以电介质不会被击穿。如不击穿理论上应能够承压200kv。

二、一同轴电缆，内导体（铜）外半径为0.01m，外导体（铜）内半径为0.03m，外导体厚度为0.003m，内外导体间有一层电介质，电介质为聚氯乙烯()，电介质厚度均为0.02m，内导体电位为5kV，外导体电位为0V。
（1）试用有限元法求内外导体间的电位和电场强度分布，
（2）求此电缆中最大场强的位置和最大值，能否击穿电介质或发生局部击穿，（3）在不击穿的前提下，此电缆能承载的最大电压为多少？
（4）通过一题和二题的对比，说明同轴电缆的内外导体间用一层还是二层电介质比较好，为什么？

分析：
参数设置：铜相对介电常数ε=1，电阻率ρ=1e-7Ω/m
聚氯乙烯相对介电常数ε=6，电阻率ρ=1e+14Ω/m

（1）其中电位分布及场强分布如下：

通过定义路径（-0.033,0）到（0.033,0）分析其场强分布如下图：

电压分布如下图：

（2）从图中可以看出其场强最大值位于内导体外半径附近处取得距离内导体圆心0.0132m处，最大值343991.6V/m。聚氯乙烯击穿场强为20-35MV/m，计算可知无法击穿电介质。
（3）聚氯乙烯击穿场强为20-35MV/m，按最小值计算理论上0.01m距离上其耐压分别200kv，所以电介质被击穿。即能够承压200kv。
（4）通过一、二两题的对比，可知同轴电缆的内外导体间用两层电介质比较好，使用一层电介质时场强的峰值要小于使用两层电介质，但使用两层电介质时场强下降更为迅速，到达外层时场强也相对更低，则发生击穿的可能性相对更低，所以使用两层电介质使同轴电缆工作性能更强。

三、一同轴电缆，内导体（铜）外半径为0.01m，外导体（铜）内半径为0.03m，外导体厚度为0.003m，内外导体间有两层电介质，一层电介质为聚乙烯()，
另外一层电介质为聚氯乙烯()，两层电介质厚度均为0.01m，若内导体通电流密度J1=500A/m2，外导体通电流密度为J2=-500A/m2，求内外导体间的磁场分布，画出一路经找出最大磁场和最小磁场位置。
分析：
参数设置:铜相对磁导率μ=1，电阻率ρ=1e-7Ω/m
聚乙烯相对磁导率μ=1，电阻率ρ=1e+13Ω/m
聚氯乙烯相对磁导率μ=1，电阻率ρ=1e+14Ω/m

（1）其磁场分布如下图所示：

（2） 定义路径（-0.033，0）到（0.033，0）可得如下磁场分布图：

由图可知，最大磁场位于距离坐标原点距离为0.0099m的圆上，最小位置在坐标原点上。

四、设计一个煤气点火器。
分析：查阅资料得打火器利用尖端放电原理确定其参数放电间隙1mm，电压15000v建立相应模型。

仿真得其电场及电位分布图并通过定义路径（0，0.001）到（0，-0.001）得其路径上的场强分布如下：

此尖端放电模型可用于打火装置的设计，通过改变模型参数分析可得尖端间隙和尖端间电压对放电过程有影响。

五、 用Ansys分析220kV三相交流输电线路的电场分布和磁场分布，若为零序电流时再分析其电场和磁场分布。
（1）110kV三相交流输电线路的电场分布如下图所示：

（2）110kV三相交流输电线路的磁场分布如下图所示：

（3）零序电流时电场分布如下图所示：

（4）零序电流时磁场分布如下图所示：

六 如图1所示一个螺旋管线圈，图中1-12个点的坐标分别为：1（-0.05,0.2）,2(0.05,0.2),3(0.053,0.2),4(-0.053,0.2),5(-0.053,-0.2),6(0.053,-0.2),7(0.05,-0.2),8(-0.05,-0.2),9(0.058,-0.25),10(-0.058,-0.25),11(-0.058,0.25),12(0.058,0.25)，螺线管中的电流密度为和，（1）当螺旋管线圈中心为非铁磁性材料时，分析该螺线管线圈形成的磁场分布；（2）当螺旋管线圈中心为铁磁性材料且相对磁导率为3000时，分析该螺线管线圈形成的磁场分布；（3）比较（1）和（2）磁场的不同，说明原因。

分析：
（1） 当螺旋管线圈中心为非铁磁性材料时，该螺线管线圈形成的磁场分布为：

（2） 当螺旋管线圈中心为铁磁性材料时，该螺线管线圈形成的磁场分布为：

（3）通过对（1）、（2）的比较可知，当使用铁磁性材料时，磁力线紧密的沿着螺旋线圈中心传导，从而使得漏磁更少。其原因是铁磁材料导磁能力更强，使得磁力线都更加紧密的沿着螺旋线圈指向。
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K,12,0.004,0.004,0,
K,13,0.001,0.004,0,
K,14,0.001,0.002,0,
LSTR, 1, 2
LSTR, 2, 3
LSTR, 3, 4
LSTR, 4, 5
LSTR, 5, 6
LSTR, 6, 7
LSTR, 7, 8
LSTR, 8, 9
LSTR, 9, 10
LSTR, 10, 11
LSTR, 11, 12
LSTR, 12, 13
LSTR, 13, 14
LSTR, 14, 1
FLST,2,14,3
FITEM,2,1
FITEM,2,2
FITEM,2,3
FITEM,2,4
FITEM,2,5
FITEM,2,6
FITEM,2,7
FITEM,2,8
FITEM,2,9
FITEM,2,10
FITEM,2,11
FITEM,2,12
FITEM,2,13
FITEM,2,14
A,P51X
CM,_Y,AREA
ASEL, , , , 1
CM,_Y1,AREA
CMSEL,S,_Y
!*
CMSEL,S,_Y1
AATT, 1, , 1, 0,
CMSEL,S,_Y
CMDELE,_Y
CMDELE,_Y1
!*
SMRT,6
SMRT,1
MSHAPE,0,2D
MSHKEY,0
!*
CM,_Y,AREA
ASEL, , , , 1
CM,_Y1,AREA
CHKMSH,'AREA'
CMSEL,S,_Y
!*
AMESH,_Y1
!*
CMDELE,_Y
CMDELE,_Y1
CMDELE,_Y2
!*
ALLSEL,ALL
FINISH
/SOL
!*
ANTYPE,0
FLST,2,6,4,ORDE,4
FITEM,2,1
FITEM,2,-3
FITEM,2,12
FITEM,2,-14
/GO
!*
DL,P51X, ,VOLT,15000
FLST,2,6,4,ORDE,2
FITEM,2,5
FITEM,2,-10
/GO
!*
DL,P51X, ,VOLT,0
/STATUS,SOLU
SOLVE
FINISH
/POST1
!*
/EFACET,1
PLNSOL, VOLT,, 0
!*
/VSCALE,1,1,0
!
!*
PLVECT,EF, , , ,VECT,ELEM,ON,0
PATH,1,2,30,20,
PPATH,1,0,0,0.001,0,0,
PPATH,2,0,0,-0.001,0,0,
/PBC,PATH,1
/REPLOT
/PBC,PATH,0
!*
!*
PDEF,V,VOLT, ,AVG
/PBC,PATH, ,0
!*
!*
PDEF,E,EF,SUM,AVG
/PBC,PATH, ,0
!*
PLPATH,V
PLPATH,V
PLPATH,E
FINISH
! /EXIT,ALL
第五题
/BATCH
/COM,ANSYS RELEASE 12.0.1 UP20090415 17:51:43 01/13/2017
/input,menust,tmp,'',,,,,,,,,,,,,,,,1
/GRA,POWER
/GST,ON
/PLO,INFO,3
/GRO,CURL,ON
/CPLANE,1
/REPLOT,RESIZE
WPSTYLE,,,,,,,,0
/FILNAME,Q5,0
!*
/NOPR
/PMETH,OFF,1
KEYW,PR_SET,1
KEYW,PR_STRUC,0
KEYW,PR_THERM,0
KEYW,PR_FLUID,0
KEYW,PR_ELMAG,1
KEYW,MAGNOD,0
KEYW,MAGEDG,0
KEYW,MAGHFE,0
KEYW,MAGELC,1
KEYW,PR_MULTI,0
KEYW,PR_CFD,0
/GO
!*
/COM,
/COM,Preferences for GUI filtering have been set to display:
/COM, Electric
!*
/PREP7
!*
ET,1,PLANE121
!*
!*
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,PERX,2,,1
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,RSVX,2,,1e-7
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,PERX,1,,1
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,RSVX,1,,1e-7
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDE,RSVX,2
MPDATA,RSVX,2,,1e+10
CYL4,0,0,0.1
CYL4,4,0,0.1
CYL4,-4,0,0.1
CYL4,0,0,4.5
FLST,2,4,5,ORDE,2
FITEM,2,1
FITEM,2,-4
AOVLAP,P51X
FLST,5,3,5,ORDE,2
FITEM,5,1
FITEM,5,-3
CM,_Y,AREA
ASEL, , , ,P51X
CM,_Y1,AREA
CMSEL,S,_Y
!*
CMSEL,S,_Y1
AATT, 1, , 1, 0,
CMSEL,S,_Y
CMDELE,_Y
CMDELE,_Y1
!*
CM,_Y,AREA
ASEL, , , , 5
CM,_Y1,AREA
CMSEL,S,_Y
!*
CMSEL,S,_Y1
AATT, 2, , 1, 0,
CMSEL,S,_Y
CMDELE,_Y
CMDELE,_Y1
!*
SMRT,6
SMRT,5
SMRT,4
SMRT,3
SMRT,2
SMRT,1
SMRT,1
MSHAPE,0,2D
MSHKEY,0
!*
FLST,5,4,5,ORDE,3
FITEM,5,1
FITEM,5,-3
FITEM,5,5
CM,_Y,AREA
ASEL, , , ,P51X
CM,_Y1,AREA
CHKMSH,'AREA'
CMSEL,S,_Y
!*
AMESH,_Y1
!*
CMDELE,_Y
CMDELE,_Y1
CMDELE,_Y2
!*
FINISH
/SOL
!*
ANTYPE,0
FLST,2,4,4,ORDE,2
FITEM,2,9
FITEM,2,-12
/GO
!*
DL,P51X, ,VOLT,220000
FLST,2,4,4,ORDE,2
FITEM,2,1
FITEM,2,-4
/GO
!*
DL,P51X, ,VOLT,-110000
FLST,2,4,4,ORDE,2
FITEM,2,5
FITEM,2,-8