一、额定数据及主要尺寸
1.输出功率 P 2 =7.5kW
2.电源电压 U 1 =380V(△联结)
3.功电流 =6.58A
4.效率 η ′=0.904
5.功率因数 cos φ ′=0.84
6.极对数 p =2
7.定、转子槽数 Q 1 =36 Q 2 =28
8.定、转子每极槽数 Q p1 = =9 Q p2 = =7
9.定、转子冲片尺寸(见图2-24,单位:mm)
图2-24 定、转子冲片尺寸
定子槽形(圆底槽): b 01 =0.3 b s1 =0.74 b s2 =1.00 R =0.5 h s0 =0.08 h s1 =0.127 h s2 =1.363
转子槽形(圆底槽): b 02 =0.10 b r1 =0.9 r =0.165 h r0 =0.05 h r1 =0.187 h r2 =2.253
10.极距 τ p = =10.68cm
11.定子齿距 t 1 = =1.186cm
12.转子齿距 t 2 = =1.516cm
13.节距 y =9(1~9,2~10,11~18)
14.转子斜槽宽 b sk = t 1 =1.186cm
15.每槽导体数 N s1 =34
16.每相串联导体数 N Φ1 = =408
17.绕组线规 N 1 =2 N 2 =1
d 1 / d i1 =0.9/0.96 d 2 / d i2 =1.12/1.185(参照书末附录表A-1)
18.槽满率
槽面积 1.515cm 2
式中 = h s1 + h s2 =(0.127+1.363)cm=1.49cm;
h =0.2cm(见图2-21)。
槽绝缘占面积 S i = =0.025×(2×1.49+3.14×0.5)cm 2 =0.114cm 2
槽有效面积 S e = S s -S i =(1.515-0.114)cm 2 =1.401cm 2
槽满率
19.铁心长 l =18.5cm
气隙长度 δ =( D i1 -D 2 )/2=(13.6-13.52)cm/2=0.04cm
铁心有效长 l eff = l +2 δ =(18.5+0.08)cm=18.58cm
净铁心长 l Fe = K Fe l =0.97×18.5cm=17.945cm
20.绕组系数 K dp1 = K d1 K p1 =0.9598
(1)分布系数
式中, =20°。
(2)短距系数 K p1 =sin( β ×90°)=sin(1×90°)=1
式中, =1
21.每相有效串联导体数 N Φ1 K dp1 =408×0.9598=391.6
二、磁路计算
22.每极磁通 =8.095×10 -3 Wb
式中, E 1 = =0.926×380V=351.88V(假设 =0.926)
23.齿部截面积 定子 S t1 = b t1 l Fe Q p1 =0.468×17.945×9cm 2 =75.58cm 2
转子 S t2 = b t2 l Fe Q p2 =0.585×17.945×7cm 2 =73.48cm 2
式中
24.轭部截面积 定子 S j1 = =1.797×17.945cm 2 =32.25cm 2
式中, =1.797cm
h s = h s0 + h s1 + h s2 + R =(0.08+0.127+1.363+0.5)cm=2.07cm
转子 S j2 = =1.76×17.945cm 2 =31.58cm 2
式中, =1.76cm
h r = h r0 + h r1 + h r2 + r =(0.05+0.133+2.307+0.165)cm=2.655cm
25.气隙面积 S δ = τ p l eff =10.68×18.58cm 2 =198.43cm 2
26.波幅系数 F S =1.428(假设 =1.373,由本章附录图2C-1中查取)
27.定子齿磁通密度
28.转子齿磁通密度
29.定子轭磁通密度
30.转子轭磁通密度
31.气隙磁通密度
32.50WW270硅钢片直流磁化曲线,查书末附录图C-13得: H t1 =16.65A/cm, H t2 =24.28A/cm, H j1 =1.685A/cm, H j2 =1.868A/cm。
33.齿部磁路计算长度 定子
转子
34.轭部磁路计算长度 定子
转子
35.有效气隙长度 δ e = δK δ1 K δ2 =0.04cm×1.2334×1.027=0.051cm
式中, =1.2334
36.齿部磁压降 定子 =16.65×1.657A=27.59A
转子 F t2 = =24.28×2.495A=60.58A
37.轭部磁压降 定子 F j1 = =0.572×1.685×7.537A=7.264A
转子 F j2 = =0.408×1.868×2.575A=1.963A
式中 C 1 =0.572, C 2 =0.408(根据 B j1 =1.255T, B j2 =1.282T, =0.168, = =0.165,查本章附录图2C-3得到。)
38.气隙磁压降 F δ =0.8 B δ δ e ×10 4 =0.8×0.583×0.051A×10 4 =237.86A
39.饱和系数 =1.371
此值与26项假定值基本相符,(1.371-1.373)/1.373=-0.15%。
40.总磁压降 F = F t1 + F t2 + F j1 + F j2 + F δ =(27.59+60.58+7.264+1.963+237.86)A=335.26A
41.满载励磁电流 =2.534A(线电流: =4.39A)
42.满载励磁电流标幺值 =0.3851
43.励磁电抗 =2.597
三、参数计算
44.线圈平均半匝长 l Z = l d + K s τ y =(21.5+1.2×10.59)cm=34.21cm
式中, l d = l +2 d =(18.5+2×1.5)cm=21.5cm
45. =0.85
单层线圈此项不计算
46.单层线圈端部平均长 l s =2 d + K s τ y =(2×1.5+1.2×10.59)cm=15.71cm
47.漏抗系数 =0.04865
48.定子槽单位漏磁导 λ s1 = K U1 λ U1 + K L1 λ L1 =1×0.511+1×0.774=1.285
式中, K U1 =1、 K L1 =1(查本章附录图2C-10或附录表2A-3)
查附录图2B-1得 =0.511
λ L1 =0.774(根据 =1.363和 =0.74查本章附录图2C-6得到)
49.定子槽漏抗 =0.0225
50.定子谐波漏抗 ×0.04865=0.0317
式中,∑ S =0.0129(根据 q 1 =3, β =1查本章附录表2A-4或查本章附录图2C-11得到)
51.定子端部漏抗 ×0.04865=0.017
52.定子漏抗 =0.0225+0.0317+0.017=0.0712
53.转子槽单位漏磁导 λ s2 = λ U2 + λ L2 =0.5+1.187=1.687
式中, =0.5
查本章附录图2B-4得 +0.813=1.187
λ L =0.813(根据 =6.827和 =2.727,查本章附录图2C-6得到。)
54.转子槽漏抗 ×0.04865=0.0350
55.转子谐波漏抗 ×0.04865=0.0384
式中,∑ R =0.017(根据 =7,查本章附录表2A-5或本章附录图2C-14得到。)
56.转子端部漏抗 ×0.04865=0.005
(铸铝转子 l B = l ,端环平均直径 D R =10.27cm。)
57.转子斜槽漏抗 ×0.0384=0.012
58.转子漏抗 =0.0350+0.0384+0.005+0.012=0.0904
59.总漏抗 =0.0675+0.0904=0.1579
60.定子相电阻 =1.523Ω
式中 ρ = ρ 20℃ [1+ α ( t -20)]=0.0178×[1+0.004×(95-20)]Ω·mm 2 /m=0.0231Ω·mm 2 /m
61.定子相电阻标么值 =0.0264
62.有效材料
每台定子导线重 G Cu = Cl Z N s1 Q 1 S 1 ×8.9×10 -5 =1.05×36.45×34×36×2.256×8.9×10 -5 kg=9.41kg
每台硅钢片重 G Fe = K Fe l ( D 1 + Δ ) 2 ×7.8×10 -3 =0.97×18.5×(21+0.5) 2 ×7.8×10 -3 kg=64.70kg
式中,冲剪余量 Δ =0.5cm
63.转子电阻
导条电阻 =0.959Ω
式中, =46.01
端环电阻
式中, ρ R = ρ B =0.0463Ω·mm 2 /m S R =2.97cm 2
导条电阻标幺值 =0.0166
端环电阻标幺值 =0.00507
转子电阻标幺值 =0.0166+0.00507=0.0217
64.满载电流有功部分 =1.106
65.满载电抗电流
式中, K m = =1+0.3851×0.0675=1.026
66.满载电流无功部分 =0.3851+0.205=0.5901
67.满载电动势系数 1 -ε L =1- =1-(1.106×0.0264+0.5901×0.0675)=0.931
此值与22项假定值基本相符,(0.931-0.926)/0.926=0.5%。
68.空载电动势系数
69.空载定子齿磁通密度
70.空载转子齿磁通密度
71.空载定子轭磁通密度
72.空载转子轭磁通密度
73.空载气隙磁通密度
74.空载定子齿磁压降 =30.28×1.657A=50.17A
式中, H t10 =30.28A/cm(50WW270硅钢片直流磁化曲线,根据 B t10 =1.60T查书末附录图C-13得到。)
75.空载转子齿磁压降 F t20 = =44.45×2.495A=110.90A
式中, H t20 =44.45A/cm(50WW270硅钢片直流磁化曲线,根据 B t20 =1.644T查书末附录图C-13得到。)
76.空载定子轭磁压降 F j10 = =0.535×2.325×7.537A=9.38A
式中, H j10 =2.325A/cm(50WW270硅钢片直流磁化曲线,根据 B j10 =1.31T查书末附录图C-13得到。)
77.空载转子轭磁压降 F j20 = =0.366×2.874×2.575A=2.71A
式中, H j20 =2.874A/cm(50WW270硅钢片直流磁化曲线,根据 B j10 =1.34T查书末附录图C-13得到。)
C 1 =0.535, C 2 =0.366(根据 B j10 =1.31T, B j20 =1.34T, =0.168, =0.165,查本章附录图2C-3得到。)
78.空载空气隙磁压降 F δ0 =0.8 B δ0 δ e =0.8×0.61×0.051×10 4 A=248.88A
79.空载总磁压降 F 0 = F t10 + F t20 + F j10 + F j20 + F δ0 =(50.17+110.90+9.38+2.71+248.88)A=422.04A
80.空载励磁电流 =3.19A(线电流: =5.53A)
四、性能计算
81.定子电流
82.定子电流密度 =3.65A/mm 2
83.线负荷 =235.89A/cm
84.转子电流 导条电流 =1.125
端环电流 =692.40A
85.转子电流密度 导条电流密度 =2.03A/mm 2
端环电流密度 =2.33A/mm 2
86.定子铜损耗 =1.25 2 ×0.0247=0.0386
87.转子铜损耗 =1.125 2 ×0.0217=0.0275
88.杂散损耗 =0.02
89.机械损耗 =43.76W
90.铁耗
(1)定子齿重量 G t1 = ×7.8×10 -3 =2×2×75.58×1.657×7.8×10 -3 kg=3.91kg
(2)定子轭重量 G j1 = ×7.8×10 -3 =4×2×32.25×7.537×7.8×10 -3 kg=15.17kg
(3)单位铁耗 p t1 、 p j1 根据 B t10 =1.60T、 B j10 =1.313T,50WW270硅钢片铁损耗曲线(50Hz),查书末附录图C-15得: p t1 =2.76W/kg, p j1 =1.68W/kg
(4)定子齿损耗 P t1 = p t1 G t1 =2.76×3.91W=10.79W
(5)定子轭损耗 P j1 = p j1 G j1 =1.68×15.17W=25.49W
(6)总铁耗 P Fe = k 1 P t1 + k 2 P j1 =(2.5×10.79+2×25.49)W=78.0W
91.总损耗 P * = =0.0386+0.0275+0.0104+0.02+0.0058=0.102
92.输入功率 =1+ P * =1+0.102=1.102
93.效率 =0.907
此值与64项假定值基本相符,(0.907-0.904)/0.904=0.33%。
94.功率因数
95.转差率
式中 ——旋转铁耗, =0.0104-(0.001439+0.003399)=0.005562
96.转速 =1461r/min
97.最大转矩倍数 =2.58
五、起动计算
98.起动电流开始假定值 =3.5×2.58×6.58A=59.42A
99.起动时漏磁路饱和引起漏抗变化的系数 K Z 查本章附录图2C-15得 K Z =0.42
100.齿顶漏磁饱和引起定子齿顶宽度的减少
C s1 =( t 1 -b s0 )(1 -K Z )=(1.186-0.3)×(1-0.42)cm=0.5139cm
101.齿顶漏磁饱和引起转子齿顶宽度的减少
C s2 =( t 2 -b r0 )(1 -K Z )=(1.516-0.10)×(1-0.42)=0.8213
102.起动时定子槽单位漏磁导
λ s1(st) = K U1 ( λ U1 -Δ λ U1 )+ K L1 λ L1 =1×(0.511-0.2731)+1×0.774=1.012
式中,按槽形查本章附录图2B-1:
103.起动时定子槽漏抗 =0.0177
104.起动时定子谐波漏抗 =0.42×0.0317=0.0133
105.定子起动漏抗 =0.0177+0.0133+0.017=0.048
106.考虑到趋肤效应的转子导条相对高度 =0.1987×2.44× =1.593cm
式中, h B = h r1 + h r2 =0.187+2.253=2.44cm, =1。
107.转子趋肤效应系数 =1.335, =0.866(根据 查本章附录图2C-17得到)。
108.起动时转子槽单位漏磁导 λ s2(st) = λ U2(st) + λ L2(st) =0.054+1.028=1.082式中, λ U2(st) = λ U2 -Δ λ U2 =0.5-0.446=0.054
查本章附录图2B-4得 =0.446
109.起动时转子槽漏抗 =0.0224
110.起动时转子谐波漏抗 =0.42×0.0384=0.0161
111.起动时转子斜槽漏抗 =0.42×0.012=0.00504
112.转子起动漏抗 =0.0224+0.0161+0.005+0.00504=0.0485
113.起动总漏抗 =0.048+0.0485=0.0965
114.转子起动电阻 =(1.335×1+0)×0.0166+0.00507=0.0272
115.起动总电阻 =0.0247+0.0272=0.0519
116.起动总阻抗 =0.11
117.起动电流 =59.82A(线电流: =103.61A)
此值与98项假定值基本相符,(59.82-59.42)/59.42=0.7%。
118.起动转矩倍数
注:本电磁计算方案非最佳设计,仅供计算时参考。