iYLH9周耀忠, 唐申生(Z+v,q430033)K1:将任意形状的通电线圈的磁场看作是多段通电直导线磁场之和,列出了一般和特殊情况下通电直导线磁场计算公式;将所有公式归结为两类积分,并编写了相关计算程序软件。实践证明,该方法计算量较小,精度高,适用性强,适用于具有复杂形式和结构的线圈磁场计算。1oM:载流导线;通电线圈;磁场计算ms|:TM 154.1DS:AcI|:1009-3486(2009)03-0071-04Calculation of magnetic field of current coils in arbitrary shapeZHO U Yao-zhong , TANG Shen-sheng(College of Electrical and Information Engineering , Naval Univ.of Engineering , Wuhan 430033, China)Abstract:T he m agnetic field of current coils in arbitrary shape w as regarded as the sum of the mag-netic field of many line current coils.The formulas w ere presented for calculating the m agnetic fieldsof line current coils under both com mon and special conditions.All the form ulas w ere reduced to tw okinds of integral used for programming .The experiment proves that the proposed method is so sim-ple , accurate and applicable that it is efficient for calculating the m agnetic field of current coils in com-plex shape .Key words:car rying-current conductor ;current coil;m agnetic field calculationhHL!9T,iYLH95。1pH,ZE9,|KLjKL,|BFbHLeKL5L。Se,9v。|iLrsLF,ibBLHT#+yf/eT,|H9TBs。9BLHH,I9s0#0,iV。Ll,ZE9,e。1 bWLH1.1LHilLLHVrLHF1 ,1s,Vr。yN,T%bWibLH95,*bWib、LLH957。2132009M6 海 军 工 程 大 学 学 报JOURNAL OF NAVAL UNIVERSITY OF ENGINEERING Vol.21No.3Jun.2009l:2008-09-15;:2008-10-26。Te:2(1954-),3,q,1Z_s/hH,E-mail:hanlu 77163.com。1.2LHm1U,!ABbWibBL(I=4A),Biot-Savar t,LbWBp(x0 ,y0 ,z0)3Hm1LFig .1Carrying-current conductorH(x,y,z)=dl rr3 =(y0 -y)k -(z0 -z)jr3 dx+(z0 -z)i -(x0 -x)kr3 dy +(x0 -x)j -(y0 -y)ir3 dz 。:(x ,y ,z)LdlUS;r =(x0 -x)2 +(y0 -y)2 +(z0 -z)21/2Ldlp。HTc3Hs,Hx =y2y1(z 0 -z)r3 dy -z2z1(y0 -y)r3 dz , (1)Hy =z2z1(x0 -x)r3 dz -x2x1 (z0 -z)r3 d x, (2)Hz =x2x1(y0 -y)r3 d x -y2y1(x0 -x)r3 dy。 (3)T:(x1 ,y1 ,z 1)(x2 ,y2 ,z2)LABUS。T(1)-(3)LbWibLH9T。2 +yf/H9Te5,XbWibLH9T,V9iLLH,tH9TVe,V7vvh9T。:LxyHH9TeHx =(z0 -z1)y2y11r3 dy, (4)Hy =-(z0 -z1)x2x11r3 dx, (5)Hz =x2x1(y0 -y)r3 dx -y2y1 (x0 -x)r3 dy 。 (6)LxH,Hx =0, (7)Hy =-(z0 -z1)x2x11r3 dx, (8)Hz =(y0 -y1)x2x11r3 d x。 (9)3 9qIVT(1)-(9)VA:bWibL3H9TVB/s:BJF1,H1 =x2x1f x +e(cx2 +bx +a)3/2 dx; (10)=JF2,H2 =x2x11(cx2 +bx +a)3/2 dx。 (11)72 海军工程大学学报21JF1s,w 2H 1 =x2x1fx +e(cx2 +bx +a)3/2d x =-2 2k +r(f x2 +e)fq(cx22 +bx2 +a)1/2 +2 2k +r(f x1 +e)fq(cx21 +bx1 +a)1/2 。 (12)T:k =a f 2 -b e f +c e2 ;r =b f -2c e;q =4a c -b2 ;f =-(y2 -y1)(x2 -x1);e =(y0 -y1) x2 -(y0 -y2)x1(x2 -x1) ;c=1 +f2 +g2 ;b=2(f e+g d -x0);a =d2 +e2 +x2 。:g =-(z2 -z1)(x2 -x1);d =(z 0 -z1)x2 -(z0 -z 2)x1(x2 -x1) 。T(12)9,1I0 3 :J1(x0 ,y0 ,z 0 ,x1 ,y1 ,z1 , x2 ,y2 ,z2 ,u)JF1(a,b,c,d ,e, f ,g ,k,r ,q)。, J1TGUS(x0 ,y0 ,z0)LUS(x1 ,y1 ,z1 ;x2 ,y2 ,z2)9JF1L(a,b,c,d ,e, f ,g ,k,r ,q);JF1T9s,L3HH 2 。i,0J1H,1-3LUS,4 -6LLAUS,7 -9LBUS,10Lu(x0 ,y0 ,z0|)VU$fs0,u=x0 ,y0 ,z 0 ,sYVU$fs0x0 -x,y0 -y,z0 -z 。N,sMGQx,yzH,LsY(x0 ,y0 ,z0 ,x1 ,y1 ,z1 ,x2 ,y2 ,z2 ,u),(y0 ,z0 ,x0 ,y1 ,z1 ,x1 ,y2 ,z2 ,x2 ,u)(z0 ,x0 ,y0 ,z1 ,x1 ,y1 ,z2 , x2 ,y2 ,u)。JF2s:H2 =x2x11(cx2 +bx +a)3/2 dx,9H2 =x2x11(cx2 +bx +a)3/2 dx =-2(2cx2 +b)q(cx22 +bx2 +a)1/2 +2(2cx1 +b)q(cx21 +bx1 +a)1/2 。 (13)T(13)9,1I0:VIB0J2(x0 ,y0 ,z0 , x1 ,y1 ,z1 , x2 ,y2 ,z2 ,u)JF2(a,b,c,q,x1 ,x2)。-9JF2L(a,b,c,q,x1 , x2),9sH 2 。4 iHYLHm2U,!HLNL,sYA,B ,C, 。xxi ,yyi ,zziVUm2