第九节正弦电流时交流绕组的磁势_2016

1、123456i ic c。i ic ci ic cicic闭合回路包围的电流的总和7xFcFc整距线圈icNc /28。ccc2sin22ccN iFN IttItIimcc sinsin2 00,90 ?ttxFcFcicNc /29xFcFcx101( )212sin( )2cc cccfN i p xNItp x 2; 10; 1)(xxxp2411sin(sinsin3sin5 )235cccfN ItxxxxFcFcfc112411sin(sinsin3sin5 )235cccfN Itxxx4 211sinsinsinsin3sinsin5235ccN Itxtxtx xtFxtF

2、xtFccc5sinsin3sinsinsinsin531 14 20.92cccccFN IN I1331ccFF 11ccvFvF AXAXNcIm/2Fc1Fc3Fc518003600 /3 xtFxtFxtFfcccc5sinsin3sinsinsinsin531 vv vPPv /513xtFfccsinsin11 10.9cccFN I幅值AXANcIm/2Fc118003600 14xxtFfccsinsin11 sin t15u 极对数为极对数为p p，基波磁势沿气隙圆周有，基波磁势沿气隙圆周有p p个完整的个完整的正弦波。正弦波。例如例如: :2 2个整距线圈。个整距线圈。p

3、=p=2 2164 4极电机单层绕组（极电机单层绕组（q q=1=1）的脉振磁势）的脉振磁势xx1718xxxxxx矩形波叠加成阶梯波形20 21 xtFxtFxtFfqqqq5sinsin3sinsinsinsin531 R0Fc1Fc1Fq1 qR 11110.9qqccqcFqk FN qk I221sinsin qkqq 0.9cqvqvqvcvcN kFqk FqIv22sinsin vvqqvqk 23u A A相通交流电流相通交流电流i ic c后，产生后，产生一个一个2 2极磁场。极磁场。2425双层绕组的磁势双层绕组的磁势26u 两个阶梯波合成即得相绕组磁势仍为阶梯波。两个阶

4、梯波合成即得相绕组磁势仍为阶梯波。29 00180180y01111112sin9022 0.9mqqycyqcyFFF KqN K K I3022 0.9WvmvqvyvcqNKFF KIv xtFxtFfmmm3sinsinsinsin31 135110.9(2)sinsinsin3sin535ccwwwqNIt KxKxKx xtFxtFxtFfqqqq5sinsin3sinsinsinsin531 110.9qcqcFqN k I1112 0.9mcyqcFqN K K I31IcI/cPqNaN2/cPqNaN xtFxtFfmmm3sinsinsinsin31 1112 0.9mc

5、yqcFqN K K I111qyWKKK xtFxtFxtFfqqqq5sinsin3sinsinsinsin531 110.9qcqcFqN k I11qWKK 135110.9sinsinsin3sin5. .35WWWNFIt KxKxKxP1110.9sinsinsinsinWmNkfItxFtxP0.9sinsinsinsinWvvmvNkftvxFtxvP135110.9(2)sinsinsin3sin535mccwwwfqNIt KxKxKx135110.9sinsinsin3sin535qccwwwfqN It KxKxKx33p=p=2 2的磁场的磁场34xtFfmsins

6、in11 110.9WmNKFIPvxtFfmvvsinsin 0.9WvmvNKFIvP35x110.9WmNKFIP36u 相绕组磁势为脉振磁势。相绕组磁势为脉振磁势。37xtFfccsinsin11 11110.9qqccqcFqk FN qk I14 20.92cccccFN IN I1111122 0.9mqycyqcFF KqN K K I1110.9sinsinsinsinWmNKfItxPFtxxtFfmsinsin11 一相绕组基波磁势：一相绕组基波磁势：xtFfmsinsin11 110.9WmNkFIPx39xtFxtFxtFmmmcoscossinsin1211211)

7、cos(2111xtFFm 一、一、xFFtmcos21; 011 (1)(2)2cos(21;211xFFtm (3)cos(2111xFFtm ，(4)23sin(21;2311xFFtm 40f1)cos(2111xtFFm xFFtmcos21; 011 (1)(1)(2)(2)2cos(21;211xFFtm (3)(3)cos(2111xFFtm ，(4)(4)11313;cos()222mtFFx(5)(5)2cos(21211xFFtm ，x2/23/20 x2/23/20f1x2/23/20f12/23/20f12/23/20f1o 41随着随着 t t的增加，可看成整个波形

8、在右方前进。在圆的增加，可看成整个波形在右方前进。在圆周内即为旋转波周内即为旋转波二、)cos(2112 xtFFm42)cos(2112 xtFFm1110;cos()2mtFFx(1)(2)111;cos()222mtFFx(3)111cos2mtFFx，(4)1131;cos()222mtFFx(5)1112cos()2mtFFx，x2/23/202/23/20 x2/23/20f2f2f22/23/20 x2/23/20f2f2fxt=02/23/20f1x2/23/20 x2/23/20fx2/23/202/23/202/23/20fx2/23/20 x2/23/20 x2/23/2

9、0t=/2t=f1f1f2f2f2fx2/23/20fx2/23/20t=3/2t=22/23/202/23/20 x2/23/20 x2/23/20f1f1f2f2)cos(2112 xtFFmxtFfmsinsin11 )cos(2111xtFFm fxt=02/23/20f1x2/23/20 x2/23/20fx2/23/202/23/202/23/20fx2/23/20 x2/23/20 x2/23/20t=/2t=f1f1f2f2f2fx2/23/20fx2/23/20t=3/2t=22/23/202/23/20 x2/23/20 x2/23/20f1f1f2f2x=0 x= )co

10、s(2112 xtFFm1112sinsinmfFtxFF)cos(2111xtFFm 0t111cos2mFFxx2/23/20f10 x 12mFF+（F1）460t21111cos()cos22mmFFxFx xx2/23/20f212mFx=0 x= F-（F2）F+（F1）F F1 1与与F F2 2为非静止为非静止量，那么旋转速度为多少？量，那么旋转速度为多少？在在 ，0t120FF47f1x2/23/202/23/20 x2/23/20f1f12/23/20 x2/23/20f1f1用幅值点的前用幅值点的前进速度来代替整个波形的进速度来代替整个波形的前进速度。前进速度。)cos(

11、2111xtFFm 0tx幅值总是发生在幅值总是发生在 处。处。dxvdt)cos(2112 xtFFm48 t tFF+F-x=0 x= x=0 x= F-（F2）F+（F1）0t 0t 2x49AXA A相轴线相轴线B B相轴线相轴线BYCZC C相轴线相轴线A A、B B、C C三相对称绕组三相对称绕组 tAIBICI三相电流对称电流三相电流对称电流50一、三相绕组的基波合成磁势一、三相绕组的基波合成磁势)240sin(2)120sin(2sin2CBAtIitIitIi51xtFfmAsinsin11 02 sin(t 75 )AiI1Af11,?BCff5211( , )sin(12

12、0 )sin(120 )Bmfx tFtx1( , )sin(240 )sin(240 )Cmfx tFtxB相电流建立的磁场的磁极与对称轴iB iB 相磁势空间分布波形53t=90)120sin()120sin(0011 xtFfmB )120sin()120sin(0011 xtFfmC xtFfmAsinsin11 54)cos(21)cos(21111xtFxtFfmmA )240cos(21)cos(210111 xtFxtFfmmB )240cos(21)cos(210111 xtFxtFfmmC )cos(23,11xtFtxfm )120sin()120sin(0011 xtF

13、fmB )120sin()120sin(0011 xtFfmC xtFfmAsinsin11 55AZBXCYAAf1(x,t)BC )cos(23,11xtFtxfm 56 )cos(23,11xtFtxfm AZBXCYAAf1(x,t)BCAZBXCYAf1(x,t)ABCAZBXCYAf1(x,t)ABC11m131.352WNKIFFp57 )cos(23,11xtFtxfm tx)240sin(2)120sin(2sin2CBAtIitIitIi090t0210t0330t58AXA A相轴线相轴线BYCZC C相轴线相轴线A A、B B、C C三相对称绕组三相对称绕组090t09

14、0 x 0001800210t0210 x 012003000330t0330 x 02400060360 )cos(23,11xtFtxfm B B相轴线相轴线A A相轴线相轴线59ABC2 sin2 sin(240 )2 sin(120 )iItiItiItAXA A相轴线相轴线B B相轴线相轴线BYCZC C相轴线相轴线A A、B B、C C三相对称绕组三相对称绕组0001800120030002400060360A A相轴线相轴线C C相轴线相轴线B B相轴线相轴线60)/(2dd1秒秒电弧度电弧度ftx min)/ r (6026011pfpnxtx )cos(23,11xtFtxf

15、m n n1 1=60=60f f/ /P Pxt62三相合成磁势三相合成磁势及其基波及其基波u 每相磁势是阶梯波；每相磁势是阶梯波； u 除基波外，有奇数次谐波。除基波外，有奇数次谐波。A A、B B、C C相绕组相绕组磁势及其基波磁势及其基波xx63IPWk.FWm39033xtFFmA3sinsin33 xtFxtFFmmB3sin)120sin(1203sin)120sin(030033 xtFxtFFmmC3sin)120sin(1203sin)120sin(030033 03333 CBAFFFfAXAXNcIm/2Fc1Fc3Fc518003600 /3 /564550.95Wm

16、NkFIPxtFFmA5sinsin55 )5cos(21)5cos(21555xtFxtFFmmA 00551205sin)120sin( xtFFmB )5cos(21)1205cos(211055xtFxtFFmmB 00551205sin)120sin( xtFFmC )5cos(21)1205cos(211055xtFxtFFmmC )5cos(2355xtFfm )cos(2311xtFFm 65)7cos(23)5cos(237m75m5xtFfxtFf )cos(2311xtFFm 66不对称不对称CBAIII ,tsinItsinItsinIiA 0222tsinI)tsin

17、(I)tsin(IiB 000212021202tsinI)tsin(I)tsin(IiC 000212021202)III(ICBAA231 )III(IBCAA231 )III(ICBAA310 CBAIIIICBAIIII0000CBAIIII6700000 CBAFFFFxsintsinFFmA 00)xsin(tsinFFmB000120 )xsin(tsinFFmC000120 68tsinItsinItsinIiA 0222tsinI)tsin(I)tsin(IiB 000212021202tsinI)tsin(I)tsin(IiC 000212021202111.35cos()

18、WmNKFItxPCBA69111.35cos()WmNkFItxPBCAtsinItsinItsinIiA 0222tsinI)tsin(I)tsin(IiB 000212021202tsinI)tsin(I)tsin(IiC 000212021202701111.35cos() 1.35cos()WWNkNkfItxItxPP t tYXmF1mF1mF1yxtcosFtcosFxmm 11tsinFtsinFymm 111)()(21122112 mmmmFFyFFx71mF1正正mF1反反合成的椭圆旋合成的椭圆旋转磁势转磁势tcosFFFFFmmmmm 22212121121tcos)

19、FF(tsin)FF(xytgmmmm 1111mF172mF1正正mF1反反合成的椭圆旋合成的椭圆旋转磁势转磁势 212121mmmFFFdtd mF1731111.35cos() 1.35cos()WWNWkNkfItxItxPPmF1正正mF1反反合成的椭圆旋合成的椭圆旋转磁势转磁势mF174四、圆形和椭圆形旋转磁势四、圆形和椭圆形旋转磁势 )xsin()xsin()x,( tFtFtf)cos(2311xtFFm 75)xsin()xsin()x,( tFtFtf76xtFFmsinsin xtFFmsincos cos()sin()mFFtx)cos(xtFFm )sin(xtFFm

20、 )xsin()xsin()x,( tFtFtf77xtFfccsinsin11 11110.9qqccqcFqk FN qk I14 20.92cccccFN IN I1111122 0.9mqycyqcFF KqN K K I1110.9sinsinsinsinWmNKfItxPFtxxtFfmsinsin11 78xtFfmsinsin11 110.9WmNkFIP79vxtFfmvmvsinsin 0.9WvmvNKFIvP80)cos(2311xtFFm 81习题解答n7-12 一台定子绕组三角形连接的电机，当绕组内有一相断线，所产生的磁动势是什么样的磁动势？当三相的进线断一相，又产

21、生什么样的磁动势iAiBicsin1sin2AmBCmiItiiIt如图1sinsinAmfFtx011sinsin1202BmfFtx011sinsin1202CmfFtx8211sinsin2ABCmfffFtx1sinsinAmfFtx011sinsin1202BmfFtx011sinsin1202CmfFtx11sinsin2BCmffFtx 83iAiBicsin1sin2AmBCmiItiiIt如图211()36AABCAIIIII211()36AACBAIIIII)III(ICBAA3101111.35cos() 1.35cos()WWNkNkfItxItxPP84iAiB85iAiB 01100110110011060cos21cos60cos60cos221coscos120cos21coscos21120sin120sinsinsin0120sinsin0 xtFxtFxtFxtFxtxtFxtxtFfffxtFf