(精品)《电机学》课后习题答案 下载本文

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首—首,尾—尾连接

4.16 已知Z=24,2p=4,a=1,试绘制三相单层同心式绕组展开图。

解:①画槽电动势星形图

?1?P?360Z?2?36024?30。 q?Z2mp?242?3?2?2 ??2Zp?244?6

槽电势星形图见4.15

4.17 一台三相同步发电机,f=50Hz,nN=1500r/min,定子采用双层短距分布绕组,q=3,y1/τ=8/9,每相串联匝数N=108,Y联接,每极磁通量Ф1=1.015×10-2Wb,Ф3=0.66×10-2Wb,Ф5=0.24×10-2Wb,Ф7=0.09×10-2Wb,试求: (1)电机的极数; (2)定子槽数;

(3)绕组系数kN1、kN3、、kN5、kN7;

(4)相电动势E1、E3、E5、E7及合成相电动势Eφ和线电动势El。

(1)

?P?60f60g50??2 nN1500?2P?4z2mp3g2g3?36 (2)?z?2mpq?2gQq?

8g90)?sin(g90)?0.9848?9q?3g20sin1sin2?2?0.9598kq1??20sinqsin13g22Pg3602g360?1???20?z36kN1?ky1gkq1?0.9452(3)ky1?sin(3y1g90?)?sin(3g80?)??0.86623q?1sin2?0.6667kq3?3qsin?12kN3?kq3ky3??0.667g0.866??0.5774ky3?sin(ky5?sin(5g80?)?0.64285g3g202?0.2176kq5? 5g203gsin2kN5?0.6428g0.2176?0.1399sin

y1ky7?sin(7g80?)??0.3427g3g202??0.1774 kq7?7g203gsin2kN7?(?0.342)g(?0.1174)?0.0607sin(4)E1?4.44fNkN1?1?4.44g50g108g0.9452g1.015g10?2?230.03(V)E3?4.44g3fNkN3?3?4.44g3g50g108g(?0.5774)g0.66g10?2?274.10(V)E5?4.44g5fNkN5?5?4.44g5g50g108g0.1399g0.24g10?2?40.25(V)E7?4.44g7fNkN7?7?9.17107E??E12?E32?E52?E72?...?360.19(V)EL?3E??405(V)4.18 一台汽轮发电机,2极,50Hz,定子54槽每槽内两根导体,a=1,y1=22槽,Y联接。已知空载线电压U0=6300V,求每极基波磁通量Ф1。

QV0?6300(V)?V?0?V06300??3637.41(V) 1.7323

E1?4.44fNkN1?N?2pq2g1g542g3aNc?g11g1?18 ky1y1?sin(?g90)?sin(2227g90)?0.9580sinq?1kq1?2??0.9555qsin12

q?z2mp?542g3g1?9?1g3601?4?166.7?kN1?ky1gkq1?0.9580g0.9555?0.9153??E1

1?4.44fNk?0.9945N1 4.19三相双层短距绕组,f=50Hz,2p=10,Z=180,y1=15,Nc=3,通φ1=0.113Wb,磁通密度B=(sinθ+0.3sin3θ+0.2sin5θ)T,试求: (1)导体电动势瞬时值表达式; (2)线圈电动势瞬时值表达式;

(3)绕组的相电动势和线电动势的有效值。

(1) q?z1802mp?2g3g5?6 ??z2p?18010?18 ?Pg3601?z?5g360180?10?N?2pqaNc?180 ky15y1?sin(1?g90)?sin(18g90)?0.9659

sinq?1sin6g10kq1?2?2?0.9561qsin?123gsin102kN1?ky1gkq1?0.9235导体电动势有效值

a=1,每极基波磁

最大值

Ec1?2.22f?1?2.22g50g0.113?12.543Ec1m?3Ec1?17.74(V)2

Q?1?Bav1?l??Bm1?l?3?Bav3?l??3??2?Bm3?l?3?1Bm1??3Bm3Bm30.0339g?1?3Bm13??3??5?Bm50.20.0226g?1?g0.113?5Bm155?Ec3?2.22f?3?2.22g50g0.0339?3.7629(V)Ec5?2.22f?5?2.22g50g0.0226?2.5086Ec3m?3Ec3?5.32(V)Ec5m?3Ec5?3.547(V)?el?el1?el3?el5?17.74sinwt?5.32sin3wt?3.547sin5wt(V) Qw?2?Pn160设t=0时??0,???wt

el?b(?)lv

(2)线圈电动势:

Ey1?4.44fNcky1?1?4.44g50g3g0.9659g0.113g50?72.69(V)Ey1m?2Ey1?1.414g72.69?102.8

ky3?sin(3g15g90)??0.707

?18Ey3?4.44fNcky3?3?4.44g50g3g(?0.707)g0.0339g50??15.96(V)3y1g90)?sin(Ey3m?2g15.96??22.57

ky5?sin(5y1?g90)?sin(5g75)?0.2588Ey3m?5.51(V)

?ey?102.8sinwt?22.57sin3wt?5.51sin5wt