(完整版)三相异步电动机电磁计算

三相电机
额定电压U=380V，f=50HZ,机座号Y132，输出P2=8KW， p=4极
1.型号：Y132M
2.输出功率：P N=8KW
3.相数：m1=3
4.接法：
5.相电压：Uφ=380V
6.功电流：I w=P2×103
m1UΦ=8×103
3×380
=7.018A
7.极对数：p=2
8.定子槽数：Z1=36
9.转子槽数：Z2=32
10.定子每极每相槽数：Q
p1=Z1
2pm1
=36
2×2×3
=3
11.定子外径：D1=21cm
定子内径：D i1=13.6cm
气隙长度：δ=0.4mm
转子外径：D2=13.52cm 13.6-0.04*2=13.52cm
转子内径：D i2=4.8cm
定子槽型：半闭口圆底槽
定子槽尺寸：b o1=0.35cm b1=0.67cm h o1=0.08cm R1=0.44cm h12=1.45cm
转子槽形：梯形槽
转子槽尺寸：b o2=0.1cm b r1=0.55cm b r2=0.3cm h o2=0.05cm h r12=2.3cm
12.极距：τ=πD i1
2p =3.1415×13.6
4
=10.681cm
13.定子齿距：t1=πD i1
Z1=3.1415×13.6
36
=1.187cm
14.转子齿距：t2=πD2
Z2=3.1415×13.52
32
=1.327cm
15.气隙长度：δ=0.04cm
16.转子斜槽距：b sk=t1=1.187cm
17.铁芯长度：l=16cm
18.铁芯有效长度：无径向通风道：l ef=l+2δ=16.08cm
19.净铁芯长：无径向通风道：l Fe=K Fe l=0.95*16=15.2cm
K Fe=0.95（不涂漆）
20.绕组型式：单层交叉式
21.并联支路数：a1=1
22.节距：1-9,2-10,11-18
23.每槽导线数：由后面计算的数据根据公式计算为：
每极磁通φ1=0.00784wb
波幅系数：K A=1.46
绕组系数：K dp1=0.96
每相串联有效导线数：Nφ1K dp1=K z′U1×10−2
K Aφ1×50
f1
=
1.21×380×10−2 1.46×0.00784×50
50
=401.70 K’z取1.21
每相串联导线数：Nφ1=Nφ1K dp1
K dp1=401.70
0.96
=418
每槽导线数：N1‘=418
12
=34.83取整数：N1=35
24.线规：导线并饶根数与截面积之积（式中的值由其后的公
式算得）：
N1’A1′=I1
a1J1=9.1627
1×5.19
=1.7655mm2
由此可通过查表知线规为：2-1.06（N-φ）
25.每根导线截面积：A cl=0.00882cm2
26.槽有效面积：A e=A s-A i=1.1444cm2
A s=2R+b s1
2×(h s′−h)+πR2
2
A i=C i(2h s12+πR)
C i-绝缘厚度 h-槽楔厚度 C i=0.08mm
27.槽满率：k s=N s1N cl d2
A e ×100%=2×35×0.013
1.1444
=79.5%
d-绝缘导线外径 d=1.14mm
28. 每相串联导线数：N φ1=Z 1N s1ma 1
=
35×363
=420
29. 绕组分布系数：K d1=sin (α
2q 1)
q 1sin (α
2)
=0.96
q 1=Z 12pm
=
364×3
=3
α=
2pπZ 1
=
2×2×180
°
36
=20°
30. 绕组短距系数：K p1=sin (β×90°
)=1 β=
y mq 1
31. 绕组系数：K dp1=K d1K p1=0.96
二．磁路计算
32. 每极磁通：∅1=
K E U ∅2.22fN ∅1K dp1
=0.00784Wb =
380×0.923
2.22×50×420×0.96
K E =0.923 K E 范围0.85-0.95 33. 定子齿截面积:A t1=
b t1l Fe Z 1
2p =76.05cm 2 34. 转子齿截面积：A t2=b t2l Fe Z 2
2p
=75.95cm 2
b t1,b t2-定，转子齿宽
35. 定子轭部截面积：A j1=h j ′
l Fe =1.877×15.2=28.53cm 2 h j ′
=D 1
−D i1
2
−h s +13
R =3.7−(0.08+1.45+0.44)+
0.443
=
1.877
36. 转子轭部截面积：A j2=h j2′
l Fe =30.65cm 2 h j2′
=
D 2−D i2
2
−h R −2
3
d k =2.016
因无通风孔d k =0
37. 空气隙面积：A δ=τl ef =10.681×16.08=171.8cm 2 38. 波幅系数：K A =1.46 K S =1.276
K A 由饱和系数K S 查得，开始计算时先假定K S
39. 定子齿磁密：B t1=K A
∅1A t1×104
=1.46×
0.0078476.05
×104
=
1.505T
40. 转子齿磁密：B t2=K A
∅1A t2×104
=1.46×
0.0078475.95
×104
=
1.507T
41. 定子轭磁密：B j1=12×∅1A j1×104
=12×0.0078428.53×104
=1.37T 42. 转子轭磁密：B j2=12
×∅1A j2
×104
=12
×
0.0078430.65
×104
=1.28T
43. 气隙磁密：B δ=K A
∅1A δ
×104
=1.46×
0.00784171.8
×104=0.666T
44. 定子齿磁场强度：H T1=20.58A/cm （查表硅钢片磁化曲线） 45. 转子齿磁场强度：H t2=20.79A/cm （查表硅钢片磁化曲线） 46. 定子轭磁场强度：H j1=11.44A/cm （查表硅钢片磁化曲线） 47. 转子轭磁场强度：H j2=8.43A/cm （查表硅钢片磁化曲线） 48. 定子齿磁路计算长度：h T1′=h s1+h s2+R
3
=1.597cm
49. 转子齿磁路计算长度：h T2′
=h R1+h R2=2.3cm 50. 定子轭磁路计算长度：l j1′
=π(D i1−h j1′
)
4p
=7.51cm 51.
转子轭部磁路计算长度：l j2
′
=
π(D i2+h j2′)
4p
=2.67cm
52. 气隙磁路计算长度：δe =δK c1K c2=0.4×1.308×1.031÷10=0.05393cm
K c1=t1
t1−r1δK c2=t2
t2−r2δ
t-齿距 b0-槽口宽
53.定子齿磁位降：F t1=H t1×h t1′=32.86A
54.转子齿磁位降：F t2=H t2×h t2′=47.81A
55.定子轭部磁位降：F j1=C1H j1l j1′=43.31A
C1=0.504 定子轭部磁路校正系数
56.转子轭部磁位降：F j2=C2H j2l j2′=9.23A
C2=0.41 转子轭部磁路校正系数
57.气隙磁位降：Fδ=0.8Bδδe×104=0.8×0.666×
0.05393×104=287.34A
58.饱和系数：K s=F t1+F t2+Fδ
Fδ=32.86+47.81+287.34
287.34
=1.28
与38项比对
59.总磁位降：F=F t1+F t2+F j1+F j2+Fδ=32.86+
47.81+43.31+9.23+287.34=420.55A
60.励磁电流：I m=4.44pF
mN∅1K dp1=4.44×2×420.55
3×420×0.96
=3.087A
61.励磁电流标幺值：I m∗=I m
I w =3.087
7.018
=0.4399
62.励磁电抗标幺值：X m∗=1
I m∗=1
0.4399
=2.2732
三．参数计算
63.线圈平均半匝长度：l c1=l e+2(d+l E′)=31.22cm
d=1.5cm(直线部分伸出长) l E′=kτc
k对2,4极取0.58 τc-平均节距τc=10.54cm
64. 线圈端部平均长度：l E =2(l E ′
+d )=15.22cm 65. 线圈端部轴向投影长度：f d =l E ′
sin α=3.77cm 66. 阻抗折算系数：K z =
m 1(N ∅1K dp1)2m 2(N ∅2K dp2)
2
=15241
式中：对笼型转子m 2=Z 2，N ∅2=1，K dp2=1 67. 定子相电阻：R 1=ρ1N ∅1l
c1a 1N c1A c1
=1.61Ω ρ1-导线电阻率
标幺值：R 1∗=
R 1I w U ∅
=0.0297
68. 转子导条电阻：R B =K z
K B ρB l B A B
=1.1407Ω
式中：K B =1.04(对铸铝转子) ρB -导条电阻率 l B =16cm(转子导条长度) A B =0.965cm 2(每根导条截面积) 标幺值：R B ∗=R B ×
I 2U ∅
=1.1407×
7.018380
=0.0211
69. 转子端环电阻：R R =K z
ρR Z z D R
2πp 2A R =0.3467Ω
ρ
R
-端环电阻系数 D R-端环平均直径（10.7cm） A R-端环截面积（2.6cm2）
标幺值：R R∗=R R I w
U∅=0.3467×7.018
380
=0.006
70.转子电阻标幺值：R2∗=R B∗+R R∗=0.0211+0.006=
0.0271
71.漏抗系数：C x=0.4π2fl ef(N∅12
pq1)(I w
U∅
)×10−5=0.4×
3.14152×50×16.08×(4202
2×3)(7.018
380
)×10−8=0.01723
72.定子槽漏磁导：λs1=K U1λU1+K c1λc1=1.2431
K U1=1 K c1=1 λU1=0.4097 λc1=0.8334
73.定子槽漏抗：X s1∗=(lσ1
l ef )λc1C x=(16
16.08
)×0.8334×
0.01723=0.01429
lσ1=l1(对无径向通风道)
74.定子谐波漏磁导：λd1=0.0129
对60°相带整数槽绕组，且2
3
≤β≤1
λd1=π2
18×[
(5q12+1)−(1
4
c
q1
+2
3
c2−1
4
c3
q1
)
3q12
]−K dp12
式中:c-短距槽数，c=8q1(1-p)
75.定子谐波漏抗：x d1∗=m1q1τ
π2δef K s
λd1C x=1.8243×0.01723=
0.03143
76.定子端部漏磁导：λE1=0.67(l E-0.64τc)=5.6778
77.定子端部漏抗：X E1∗=(q1
l ef )λE1C x=(3
16.08
)×5.6778×
0.01723=0.01825
78. 定子漏抗标幺值：X 1∗=X s1∗+X d1∗+X E1∗
=0.01429+0.03142+0.01825=0.06397
79. 转子槽漏磁导：λs2=λU2+λc2=2.1754 λU2=
h R0b 02
=0.5(槽上部漏磁导)
λL2=1.6754(槽下部漏磁导)
80. 转子槽漏抗：X s2∗=(l
σ2
l ef
)K dp12(Z
1Z 2
)λs2C x =0.03862=
2.2413×0.01723 l σ2=l 2
81. 转子谐波漏磁导：对笼型转子：λd2=∑1
(k Z 2
p ±1)
2=0.013
K=1，2,3 82.
转子谐波漏抗：X d2
∗=
m 1q 1τK dp12
π2δef K s
λd2C x =1.6757×0.01723=
0.02887
83. 转子端部漏磁导：λE2=0.757(l B
−l 21.13
+
D R 2p
)=2.025(对笼型
转子)
84. 转子端部漏抗：X E2∗=q 1l ef
K dp12λE2C x =0.3478×0.01723=
0.00599 85.
转子斜槽漏抗：X sk
∗=0.5(b sk t 2
)
2X d2
∗=0.5×(1.1871.327
)2×
0.02887=0.01155
86. 转子漏抗标幺值：X 2∗=X s2∗+X d2∗+X E2∗+X sk ∗=0.08503 87. 运行总漏抗：X ∗=X 1∗+X 2∗=0.06397+0.08503=0.149
四．运行性能计算
88.满载电流有功分量：I p∗=1
η=1
0.88
=1.136
设η=0.88 η−效率
89.满载电抗电流：I x∗=σ1X∗I p∗2[1+(σ1X∗I p∗)2]=1.0281×
0.149×1.1362×[1+(1.0281×0.149×1.136)2]=0.2037
式中：σ1=1+I m∗X1∗=1+0.4399×0.06397=1.0281 90.满载电流无功分量：I Q∗=I m∗+I x∗=0.4399+0.2037=
0.6436
91.满载电动势比值：K E=1−(I p∗R1∗+I Q∗X1∗)=1−
(1.136×0.0297+0.6436×0.06397)=0.925
与32项进行比对
92.定子电流：I1∗=√I p∗2+I Q∗2=√1.1362+0.64362=1.3056
I1=I1∗I w=1.3056×7.018=9.1627A
93.转子导条电流：I2∗=√I p∗2+I x∗2=√1.1362+0.20372=
1.154
I2=I2∗I w K1=1.154×7.018×37.8=306.13A
K1-电流折算系数
K1=m1N∅1K dp1
Z2=3×420×0.96
32
=37.8
94.转子端环电流：I R=Z2
2πp I2=32
2×3.1415×2
×306.13=779.58A
95.定子电密：J1=I1
a1N c1A c1×102=9.1627
1×1.76423
=5.19A/mm2
96.线负荷：A1=m1Z∅1I1
πD i1=3×420×9.1627
3.1415×13.6
=270.22A
cm
97.热负荷：AJ1=A1J1=1402.44
98.转子导条电密：J B=I2
A B×102=306.13
0.965×102
=3.17A/mm2
99.转子端环电密：J R=I R
A R×102=779.58
2.6×100
=2.998A/mm2
100.空载电动势比值：K E0=1−I m∗X1∗=1−0.4399×
0.06397=0.9719
101.空载定子齿磁密：B t10=K E0
K E B t1=0.9719
0.925
×1.505=1.5813T
102.空载定子轭磁密：B j10=K E0
K E B j1=0.9719
0.925
×1.37=1.4395T
103.定子齿单位铁损耗：p t1由B t10查表得44.02×10−3W/cm3 104.定子轭单位铁损耗：p j1由B j10查表的36.7×10−3W/cm3 105.定子齿体积：V t1=2pA t1h t1′=485.68cm3
106.定子轭体积：V j1=4pA j1l j1′=1713.73cm3
107.铁损耗：P Fe=k1p
t1V t1+k2p
j1
V j1
对半闭口槽：k1=2.5,k2=2
P Fe=(2.5×44.02×485.68+2×36.7×1713.73)×10−3= 179.24W
标幺值：P Fe∗=P Fe
P N×103
=0.0224
108.基本铁耗：
P Fe1∗=p
t1
V t1+p
j1
V j1 P N×103
=44.02×10−3×485.68+36.7×10−3×1713.73
8000
=0.01053
109.定子电阻损耗：P cu1∗=I1∗2R1∗=1.30562×0.0297=0.0506
P cu1=P cu1∗P N ×103
=0.0506×8000=404.8W
110. 转子电阻损耗：P cu2∗=I 2∗2R 2
∗=1.1542×0.0271=0.0361 P cu2=P cu2∗P N ×103
=288.8W 111. 风摩损耗：P fv *参考试验值确定为0.01 P fv =P fv ∗P N ×103
=0.01×8000=80W 112. 杂散损耗：P s *对铸铝转子可取0.02
P s =P s ∗P N ×103=0.02×8000=160W
113. 总损耗：∑P ∗=P cu1∗+P cu2∗+P Fe ∗+P fv ∗+P s ∗=0.0506+0.0361+0.0224+0.01+0.02=0.1391 114. 输入功率：P 1
∗=1+∑P ∗=1.1391 115. 满载效率：η=1−∑P ∗P 1
∗=1−
0.13911.1391
=0.878
η−η′η
=
0.878−0.880.878
=−0.0023>−0.005
与88项假定值比对
116. 功率因数：cos φ=1
I 1∗η=11.3056×0.878=0.872
117. 满载转差率：S N =
P cu2∗
P em
∗=
0.03611.07797
=0.0335
P em *-气隙电磁功率
P em ∗=P 1∗−P cu1∗−P Fe1∗
=1.07797
118. 额定转速：n N =60f (1−S N )
p
=
60×50×(1−0.0335)
2
=1449.75r/min
119. 最大转矩倍数： T max ∗=N
2×(R 1+√R 1+X ∗2)
=
2×(0.0297+√0.02972+0.1492)
=2.66
五．起动性能计算
I st =(2.5~3.5)T max ∗×I w =61.8A
120. 起动时槽磁动势： F st =0.707I st
N ∅1a 1
×(K V1+K dp1K d1Z
1Z
2
)√K E0=3071.09A
121. 虚拟磁密：B L =
F st ×10−41.6δβc
=5.0241T
βL =0.64+2.5√
δ
t 1+t 2
=0.955
122. 起动漏磁饱和系数：K as =0.418
123. 定子槽口宽增大：∆b 01=(t 1−b 01)(1−k as )=0.4874 124. 转子槽口宽增大：∆b 02=(t 2−b 02)(1−k as )=0.7141 125. 定子槽上部漏磁导减少：∆λU1=h r0−0.58h r1
b 01
(
∆b 01∆b 01+1.5b 01
)=
0.1836
126. 转子槽上部漏磁导减少：∆λU2=
h R0
b 02(
∆b 02
∆b 02+b 02
)=0.4397
127. 起动定子槽漏磁导：λs1st =K U1(λU1−∆λU1)+K c1λc1=1.0596 128. 起动定子槽漏抗标幺值：X s1st ∗=λs1st λs1
X s1∗=
1.05961.2431
×
0.01429=0.01218
129. 起动定子谐波漏抗标幺值：X d1st ∗=k as X d1∗=0.01218 130. 定子起动漏抗标幺值：X 1st ∗=X s1st ∗+X d1st ∗+X E1∗=0.01218+0.01313+0.01825=0.04356
131. 挤流转子导条相对高度：ε=2πh B √
b B
b s f
ρB ×109
=1.551
h B -转子导条高度（cm ） b R
b S
-转子导条宽与槽宽之比，对铸
铝转子为1
ρB -转子导条电阻率 h B =2.35cm 132. 导条电阻等效高度：h ρR =
h B φ(ε
)k a
=2.351.45
×1=1.621
133. 槽漏抗等效高度：h ρx =h B ψ(ε)k a =2.35×0.78×1=
1.833 134. 挤流电阻增大系数：K R =(1+a )φ2(ε)1+a [2φ(ε)−1]
=1.308
a =
b 1b 2
135. 挤流漏抗减少系数：K x =b 2(1+a )2ψ(ε)b px
(1+a ′)2(K r1
′
K r1)=0.888
a ′=
b 1b px
b px =b 1+(b 2⋯⋯b 1)ψ(ε)
136. 起动转子槽下部漏磁导：λL2st =K x λL2=K X ×2h 1b 0+b 1
+λL =
1.4875 λL =
4β
(1+α)2k τ1
137. 起动转子槽漏磁导：λs2(st )=(λU2−∆λU2)+λL2st =1.5478 138. 起动转子槽漏抗标幺值：X s2st ∗=
λs2st λs2
×X s2∗=0.0275
139. 起动转子谐波漏抗标幺值：X d2st ∗=k as X d2∗=0.01207 140. 起动转子斜槽漏抗标幺值：X skst ∗=k as X sk ∗=0.0048 141. 转子起动漏抗标幺值：X 2st ∗=X s2st ∗+X d2st ∗+X E2∗+X skst ∗=0.05036 142. 起动总漏抗标幺值：X st ∗=X 1st ∗+X 2st ∗
=0.04356+0.05036=0.09392
143. R Bst ∗=[k R
(l ef
−N V2b 02
l B
)+
l B −(l f −N V2b 02)
l B
]×R B ∗=0.0276
144. 转子起动电阻标幺值：R 2st ∗=R Bst ∗+R R ∗
=0.0276+0.006=0.0336 145. 起动总电阻标幺值：R st ∗=R 1∗+R 2st ∗
=0.0297+0.0336=0.0633 146. 起动总阻抗：Z st ∗=√R st ∗2+X st ∗2=0.1133
147. 起动电流：I st =I Kw
Z st
∗
=
7.0180.1133
=61.94A
61.94−61.861.94
=0.0023<0.005
148. 起动电流倍数：I st ∗=
61.949.1627=6.76 149. 起动转矩倍数：T st ∗=R 2(st )
∗
Z st ∗2(1−S N )=
0.03360.1133
2
×(1−
0.0335)=2.53。