交流电机电枢绕组的电动势和磁动势

1、交流电机电枢绕组交流电机电枢绕组The WINDINGS of AC ELECTRICAL MACHINE 的电动势与磁通势的电动势与磁通势交流电机的工作原理交流电机的工作原理Basic principles of AC electrical machine n共同点n同步synchronousn异步Asynchronous 当定子绕组通上当定子绕组通上三相交流电，产生的三相交流电，产生的旋转磁场切割转子导旋转磁场切割转子导体产生感应电动势和体产生感应电动势和感应电流感应电流,在旋转磁场在旋转磁场的作用下产生电磁转的作用下产生电磁转矩矩,使转子转动使转子转动. 右图是一台三相鼠笼型异步右图是一

2、台三相鼠笼型异步电动机的外形图。电动机的外形图。下面是它主要部件的拆分图。下面是它主要部件的拆分图。nAn AC motor is an electric motor that is driven by an alternating current. nAn AC motor consists of two basic parts:nAn outside stationary stator having coils supplied with AC current to produce a rotating magnetic field;nAn inside rotor attached to

3、 the output shaft that is given a torque by the rotating field. nThere are two types of AC motors, depending on the type of rotor used:nThe synchronous motor, which rotates exactly at the supply frequency or a submultiple of the supply frequency. The magnetic field on the rotor is either due to curr

4、ent transported with slip rings or a permanent magnet.nThe induction motor, which turns slightly slower than the supply frequency. The magnetic field on the rotor of this motor is created by an induced current. 旋转磁场的产生旋转磁场的产生rotating magnetic fieldAYCBZ异步机中异步机中,旋转磁场代替了旋转磁极旋转磁场代替了旋转磁极AiBiCimIt0n()电流出

5、电流出( )电流入电流入X240sin120sinsintIitIitIimCmBmAAXYCBZ0tAiBiCimItBiAXBYCZAiCi合成磁场方向：合成磁场方向：向下向下NS180tXBZ0nAYC 60tAXYCBZSN0n60A120tXYCBZ0n同理分析，可得同理分析，可得其它电流角度下其它电流角度下的磁场方向：的磁场方向：AiBiCitmINNnThrough electromagnetic induction, the time changing and reversing (alternating in direction polyphase currents) rot

6、ating magnetic field induces a time changing and reversing (alternating in direction)current in the conductors in the rotor.nT h i s s e t s u p a t i m e c h a n g i n g a n d counterbalancing moving electromagnetic field that causes the rotor to turn in the direction the field is rotating. nThe ro

7、tor always moves (rotates) slightly behind the phase peak of the primary magnetic field of the stator and is thus always moving slower than the rotating magnetic field produced by the polyphase electrical supply. 旋转方向旋转方向：取决于三相电流的相序。：取决于三相电流的相序。0n0n改变电机的旋转方向：换接其中两相。改变电机的旋转方向：换接其中两相。AiBiCimItAiCiBimI

8、t旋转磁场的旋转方向旋转磁场的旋转方向旋转磁场的旋转磁场的转速转速大小大小 一个电流周期，旋转磁场（即定子磁场）在空间一个电流周期，旋转磁场（即定子磁场）在空间转过转过360。则同步转速（即旋转磁场的速度）为：。则同步转速（即旋转磁场的速度）为：AXYCBZNSAXYCBZSN0n60AXYCBZNSAiBiCimIt分）转 /( 600fn电动机转速和旋转磁场同步转速的关系电动机转速和旋转磁场同步转速的关系电动机转速（即转子转速）电动机转速（即转子转速）:n电机转子转动方向与磁场旋转的方向一致，电机转子转动方向与磁场旋转的方向一致， 但但 异步异步电动机电动机0nn无转距无转距转子与旋转磁场

9、间没有相对运动转子与旋转磁场间没有相对运动无转子电动势（转子导体不切割磁力线）无转子电动势（转子导体不切割磁力线）无转子电流无转子电流提示提示：如果如果0nn nWhere a polyphase electrical supply is available, the three-phase (or polyphase) AC induction motor is commonly used, especially for higher-powered motors. nThe phase differences between the three phases of the polyphas

10、e electrical supply create a rotating electromagnetic field in the motor. Applicationn25W small motors from CD player, toy and CD/DVD drive reader n250W motor from a washing machine A 3-phase generators stator has three identical windings. The three windings are placed at 120to each other . When the

11、 magnet is rotated at constant speed, the voltages induced in the three windings have the same effective values, but the peaks occur at different times. () Operating principle of 3-phase synchronous motor() Operating principle of 3-phase asynchronous motornIf we connected a 3-phase source to the sta

12、tor winding, alternating currents will flow in the windings. The current will have the same value but will be displaced in time by an angle of 120. nThese currents produce a rotating field. nAccording to Faradays Law and Lorenz force (左右手定左右手定则则)on a conductor, a voltage will be induced in the rotor

13、 winding. The induced voltage immediately produces a current. Because the current-carrying conductor lies in the rotating field, it experiences a mechanical force. The force always acts in a direction to drag the conductor along with the rotating field.() Operating principle of 3-phase asynchronous

14、motornIf the rotor were to move at the same speed as the rotating field, the induced voltage and current would become zero. Under this condition the force acting on the rotor bars would also become zero, which would cause the rotor to slow down. p空间电角度空间电角度机械角度机械角度电机整个转子表面所占的空间几何角度电机整个转子表面所占的空间几何角度3

15、60度，叫度，叫机械角度机械角度。一对主磁极表面所占的空间距离用空间角度表示，并定为一对主磁极表面所占的空间距离用空间角度表示，并定为360度，叫度，叫空间电角度空间电角度。交流电机电枢绕组交流电机电枢绕组基本概念基本概念 Basic conceptions of AC windings 1 电角度和机械角度：电角度和机械角度： Electric angle and mechanical angle Electric angle= mechanical anglepoles2 极距和槽距角极距和槽距角Pole pitch and coil pitch anglenThe distance be

16、tween adjacent poles is called the pole pitch. It uses the number of slots to express.nThe width of each coil is called the coil pitch. It also uses the number of slots to expressnThe coil pitch is usually made less than the pole pitch in order to save copper and to improve the flux distribution in

17、the air gap. Q/2pnSlot pinch angle p360 / Q3 极相组The number of phase groups slotsnA lap winding consists of a set of phase groups evenly distributed around the stator circumference. The number of groups is given by the equationnGroups= polesphases qQ/(2pm) 60pnf 导体的基波电动势频率导体的基波电动势频率（每秒基波电动势变化的周数）：（每秒

18、基波电动势变化的周数）：由于转子有由于转子有p对极，电机转子每转一圈，导体中的基波电对极，电机转子每转一圈，导体中的基波电动势变化了动势变化了p周，而电机每秒转了周，而电机每秒转了n/60转。转。2260pnwf用用f表示转子的电角速度：表示转子的电角速度：交流电枢绕组的电动势交流电枢绕组的电动势The INDUCED ELECTROMOTIVE FORCE IN AC WINDINGS sinbBeb lv260nwpwt设电机的基波气隙磁密：设电机的基波气隙磁密：导体产生的电动势：导体产生的电动势：转子旋转的电角速度：转子旋转的电角速度：时间过时间过t秒，导体移到：秒，导体移到：6.1.1

19、 导体电动势导体电动势The fundamental electromotive force in conductor sinsinbBBwtsinsin2sinmeb lvB lvwtEwtEwt导体感应的基波电动势瞬时值：该处的气隙磁密：导体中感应基波电动势的最大值：2() (2)222260mavavavEB lvBlffB lfBBB lnvpf 其中为气隙磁密平均值为气隙磁密平均值为气隙每极基波磁通量为气隙每极基波磁通量为线速度为线速度112.2222mEEff 导体基波电动势：TAXeeeTAXEEE22 2.224.44TAEEff6.1.2 整距线匝电动势整距线匝电动势The

20、fundamental electromotive force in coil 线匝基波电动势：相量表示：有整距线匝电动势：4.44yyEfN6.1.3 整距线圈电动势2sin24.44sin24.44yAyypEEyfNyfN k6.1.4 短距线圈电动势0yAXAXEEEEEy 短距线圈基波电动势相量：短距线圈基波电动势：例6-2 如果把相距150度空间电角度的A、X两根导体组成线匝，每根导体电动势为10V，求该线匝的基波电动势。6.1.5 整距分布线圈组的电动势整距分布线圈组的电动势The fundamental electromotive force in coils 6.1.5 整距

21、分布线圈组的电动势123qyyyEEEE2 sin22 sin2yqERERq2 sin22sin2qyRqEqEqR基波电动势相量一个线圈和线圈组的电动势有6.1.5 整距分布线圈组的电动势2 sin22sin2qyRqEqEqRsin2sin2qyydqEqEqE kq4.44qydEfqN k4.444.44qy dpy dpEfqN k kfqN k例6-3 一台电机的定子槽里放了4个分布着的整距线圈，相邻线圈的槽距角为15度空间电角度，每个线圈的基波电动势为30 V。现将这些空间分布着的整距线圈按头尾相连构成线圈组，求该线圈组的基波电动势。6.2 交流电机电枢绕组6.2.1 三相单层

22、绕组三相单层绕组 3-phase single-layer winding1 三相单层集中整距绕组单层绕组：定子的每个槽里能放一个圈边，两个槽中的相距一定距离的两个圈边形成一个绕组元件。 In a single-layer winding the stator has as many half slots as it has coils. chain single-layer windingTo get an overall picture of a chain single-layer winding, let us suppose a 24-slot stator is laid out

23、flat.3602 3603024pZ2 三相单层分布绕组1）定子相邻两槽间的槽距角2）画基波电动势相量图1 calculating 、q2 drawing a star graph of voltage3 splitting phase4 drawing expansion graph例：三相电机定子总槽数例：三相电机定子总槽数Z=24，极对数，极对数p=2，连接成三相单层分布绕组。连接成三相单层分布绕组。注意：每个相量代表一个导体的电动势，相差180度的两个导体形成整距线圈电动势。6.2 交流电机电枢绕组24222 3 2Zqmp 3）按60度相带法分相每极每相槽数相带：把基波电动势星形相

24、量图分成六等份，每份为60度空间电角度，槽在定子表面所占的地带。6.2 交流电机电枢绕组4）画绕组连接图6.2 交流电机电枢绕组11224.44A XA XydydEEqE kfqN k14.444.444.44ydyddyEfqN kpapqNfkafN kpqNNa5）确定绕组并联的路数a6）计算相电动势每对极下属于一相的线圈组的基波电动势大小相等，其值为P对极下属于一相的线圈组的基波电动势大小相等，其值为6.2.2 三相双层绕组 3-phase double-layer winding 双层绕组：定子的每个槽里能放两个圈边，每个圈边为一层。电机线圈总是与定子总槽数相等。优点：线圈能任意短

25、距，对改善电动势波形有好处。36023602036pZ1）定子相邻两槽间的槽距角2）画基波电动势相量图注意：每个相量代表一个短距线圈的电动势，而不是导体电动势。例：三相电机定子总槽数例：三相电机定子总槽数Z=36，极对数，极对数p=2，节距，节距y1=7个槽，并联支路数个槽，并联支路数a=1，连接成三相双层短距，连接成三相双层短距分布绕组。分布绕组。3）按60度相带法分相每极每相槽数36322 3 2Zqmp 6.2 交流电机电枢绕组4）画绕组连接图6.2 交流电机电枢绕组5）确定绕组并联的路数6）计算相电动势4.444.444.44yypqydpdpEfN kEfqN k kEfNk2ypq

26、NNa短距线圈基波电动势极相组基波电动势相绕组基波电动势每相串联匝数n例6-4 一台三相异步电动机，定子采用双层短距分布绕组。已知定子总槽数为36，极对数为3，线圈的第一节距为5槽，每个线圈串联的匝数为20，并联支路数为1，频率为50，基波每极磁通量为0.00398。求：（1）导体基波电动势（2）线匝基波电动势（3）线圈基波电动势（4）极相组基波电动势（5）相绕组基波电动势6.2.3 绕组的谐波电动势绕组的谐波电动势sin2pkysin2sin2dqkq谐波短距系数：谐波绕组系数：谐波分布系数：dpdpkk k6.3 交流电机电枢单相绕组产生的磁通势交流电机电枢单相绕组产生的磁通势The MA

27、GNETOMOTIVE FORCES of AC WINDINGS 1 整距线圈整距线圈（单层分布）（单层分布）的的磁通势磁通势The fundamental magnetomotive force in coils 交流电机电枢单相绕组产生的磁通势2 cosiIwt112cos22yyyfiNINwt112cos22yyyfiNINwt 22322线圈流过电流展开后，矩形分布的展开后，矩形分布的脉振脉振磁通势磁通势交流电机电枢单相绕组产生的磁通势135( ,)coscos3cos5cos4 11sin22yyfwtCCCCCiN2 磁通势展开用傅立叶级数展开1354 14 11( ,)2co

28、scos2coscos32234 112coscos525yyyyyyyfwtINwtINwtINwtfff2 cosiIwt代入有1142coscos2coscosyyyfINwtFwt33421coscos323coscos3yyyfINwtFwt 55421coscos525coscos5yyyfINwtFwt5115yyFF3113yyFF11yyFf有幅值：有谐波极对数：1pp磁通势幅值都随时间按coswt变化，即在时间上都为脉振波。整距线圈产生的磁通势中，基波是最主要的，其最大幅值是：422yIN2coscoscos()cos()1111111cos()cos()22yyyyyfF

29、wtFwtff3 基波脉振磁通势由三角公式：整距线圈的基波磁通势1142coscos2coscosyyyfINwtFwt3 基波脉振磁通势 一个脉振磁通势波可以分为两个波长与脉振波完全一样，分别朝相反方向旋转的旋转波，旋转波的幅值是原脉振波最大振幅的一半； 当脉振波振幅为最大时，两个旋转波正好重叠在一起。6.3.2 短距线圈（双层分布）的磁通势The fundamental magnetomotive force in short coils 单相双层短距绕组相串联6.3.2 短距线圈的磁通势41sin241yypCiNyiNk135( ,)coscos3cos5cosfwtCCCC双4 12

30、coscos2yINwt142sincoscos242coscosyypINywtIN kwt单层整距线圈时，基波磁通势 fy1双层短距线圈时，基波磁通势 fy16.3.3 单层分布线圈组产生的磁通势qydFqF ksin2sin2dqkq1sin2sin2dqkq1111sin2sin2qyydqFqFqF kq整个单层分布线圈组的基波磁通势最大值整个单层分布线圈组的基波磁通势最大值其中谐波磁通势分布系数谐波磁通势最大幅值6.3.5 单相绕组磁通势135135421(,)(coscos 3231cos 5) cos5coscoscoscos 3coscos 5dpdpdpINfwtkkpkw

31、tFwtFwtFwt双层双层短距短距分布分布绕组的绕组的相相绕组磁通势绕组磁通势6.3.5 单相绕组磁通势11335542242 12342 125d pd pd pN kIFpN kIFpN kIFp2ypqNNa各磁通势分量的最大幅值分别为：其中每相绕组串联的匝数：6.4 三相电枢绕组产生的磁通势The fundamental magnetomotive forces of 3 -phase winding If we connected a 3 -phase source to the stator winding, alternating currents will flow in t

32、he windings. The current will have the same value but will be displaced in time by an angle of 120. 6.4 三相电枢绕组产生的磁通势2 cos2 cos(120 )2 cos(240 )ABCiIwtiIwtiIwt111111coscoscos(120 )cos(120 )cos(240 )cos(240 )ABCfFwtfFwtfFwt1 基波磁通势三相绕组流过电流：各相电流在电机气隙圆周方向产生的基波磁通势：滞后A相120度电角度的B相电流，流过位于A相前面120度空间电角度的B相绕组时，

33、产生的基波磁通势。11422dpNkIFp6.4 三相电枢绕组产生的磁通势11111111111cos()cos()2211cos()cos(240 )2211cos()cos(120 )22ABCfFwtFwtfFwtFwtfFwtFwt分解有6.4 三相电枢绕组产生的磁通势111111111111( ,)11cos()cos()2211cos()cos(240 )2211cos()cos(120 )223cos()2cos()ABCfwtfffFwtFwtFwtFwtFwtFwtFwtFwt111323 4222dpFFNkIp三相合成基波磁通势三相合成基波磁通势为一行波，或称旋转磁通势。

34、幅值为113 4222dpNkFIp三相合成基波磁通势的特点：1 幅值3 转速磁通势的转向决定于电流的相序，从领先相向滞后相旋转。旋转磁通势相对于定子绕组的转速为为同步转速n=60f/p r/min。2 转向4 瞬间位置瞬间位置当三相电流中的当三相电流中的某相电流值达正某相电流值达正最大值时，三相最大值时，三相合成基波旋转磁合成基波旋转磁通势的正幅值，通势的正幅值，正好位于该相绕正好位于该相绕组的轴线处。组的轴线处。These currents produce magnetomotive forces which, in turn, create a magnetic flux.When t=

35、0 , the current and combined magnetomotive forces are as shown in the Figure .When t=60 , the current and combined magnetomotive forces are as shown in the Figure .nThe rotation speed of the field depends upon the duration of one cycle, which in turn depends on the frequency of the source. It is giv

36、en by the expression: n=60f/p. because the speed of the rotating field is necessarily synchronized with the frequency of the source, it is called synchronous speed.nInterchanging any two lines of a 3-phase motor will, therefore, reverse fields direction of rotation. 6.4.2 三相的三次谐波磁通势33333333coscos3co

37、s(120 )cos3(120 )cos(120 )cos3cos(240 )cos3(240 )cos(240 )cos3ABCfFwtfFwtFwtfFwtFwt 3342 12 3dpNkIFp各相的三次谐波磁通势其中为三次谐波磁通势的最大值6.4.2 三相的三次谐波磁通势33333333( ,)coscos3cos(120 )cos3cos(240 )cos3cos3 coscos(120 ) cos(240 )0ABCfwtfffFwtFwtFwtFwtwtwt 三相合成的三次谐波磁通势三相的三次谐波磁通势为0。显然3n如九、十五等的合成也为0。n例6-5 已知三个匝数彼此相等的整距线圈AX、BY、CZ在定子的槽内集中地放在一起。若三个整距线圈里流过的电流分别为求产生的合成基波总磁通势。2 cosABCiiiIwtcoscoscos(120