מכונות חשמליות

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iU = Im·cos(ωt)   |   iV = Im·cos(ωt − 120°)   |   iW = Im·cos(ωt + 120°)   |   iU + iV + iW = 0   |   F = 1.5·Im   |   ns = 120·fP   |   ωs = 2π·ns60
50 Hz
1 : 60
1500 rpm
157.08 rad/s
1.50 Im
0°
+1.00
−0.50
−0.50
0.00

ns = 120·fP
ns = 120·504 = 1500 rpm
ns = 120·304 = 900 rpm
9001500 = 3050 = 0.6
ωs = 2π·150060 = 157.08 rad/s

ns = 120·f1P  |  s = ns − nns  |  f2 = s·f1  |  ωs = 2π·ns60  |  Pgap = T·ωs  |  Pmech = (1 − s)·Pgap  |  Pcu2 = s·Pgap
1440 rpm
1500 rpm
1440 rpm
0.0400
2.00 Hz
7.13 A
29.15 N·m
4578 W
4395 W
183 W

ns = 120·f1P = 120·504 = 1500 rpm
s = ns − nns = 1500 − 14401500 = 0.04
f2 = s·f1 = 0.04·50 = 2 Hz
ωs = 2π·ns60 = 2π·150060 = 157.08 rad/s Pgap = T·ωs = 29.15·157.08 = 4578.2 W Pmech = (1 − s)·Pgap = 0.96·4578.2 = 4395.1 W Pcu2 = s·Pgap = 0.04·4578.2 = 183.1 W 4395.1 + 183.1 = 4578.2 W
n = ns : s = 0 , f2 = 0 , I2 = 0 , T = 0

s = ns − nns   |   R2's = R2' + R2'·(1 − s)s
Vth = V1·Xm√R1² + (X1 + Xm)²   |   Zth = j·Xm·(R1 + j·X1)R1 + j·(X1 + Xm)
T = 3 · Vth² · R2'sωs · [ (Rth + R2's)² + (Xth + X2')² ]
smax = R2'√Rth² + (Xth + X2')²   |   Tmax = 3 · Vth²2 · ωs · [ Rth + √Rth² + (Xth + X2')² ]
0.040
30 N·m
1440 rpm
30.0 Ω
7.13 A
29.15 N·m
2.00 Hz
4395 W
65.99 N·m
102.47 N·m
0.3271

V1 = 400√3 = 230.94 V  ·  ns = 120 · 504 = 1500 rpm  ·  ωs = 157.08 rad/s
Vth = 230.94 · 45√1² + 46.8² = 10392.346.811 = 222.01 V Rth = 0.9241 Ω  ·  Xth = 1.7505 Ω
R2's = 1.20.04 = 30.0 Ω
(Rth + 30)² + (Xth + X2')² = 30.924² + 3.551² = 956.30 + 12.61 = 968.91 T = 3 · 222.01² · 30157.08 · 968.91 = 4 435 830152 192 = 29.15 N·m
I2'(s=1) = 222.01√4.512 + 12.606 = 222.014.137 = 53.66 A I2'(s=0.04) = 222.0131.127 = 7.13 A  ·  53.667.13 = 7.52

ns = 120·fP  |  s = ns − nns  |  T = 3·Vth²·R2'sωs·[ (Rth + R2's)² + (Xth+X2')² ]  |  smax = R2'√Rth² + (Xth+X2')²  |  VY = VL√3  |  TY = TΔ3  |  IY = IΔ3
1.00
50 Hz
29.15 N·m
1500
0
1.000
53.66
65.99

VΔ = 400 V     VY = 400√3 = 230.94 V
Iph,Y = Iph,Δ√3
IY = IΔ√3 · √3 = IΔ3 = 53.663 = 17.887 A
TY = TΔ(√3)² = TΔ3 = 65.993 = 21.997 N·m
IY = 17.887 A    TY = 21.997 N·m

Ea = kΦ·n   |   V = Ea + Ia·Ra   |   n = V − Ia·RakΦ   |   T = kΦ·602π·Ia   |   Δn = n0 − nnnn·100 %
20 A
220 V
1.00
0 Ω
210.0 V
1200.0 rpm
33.42 N·m
20 A
0.1750
0

Ea = V − Ia·Ra = 220 − 20·0.5 = 210 V
kΦ = Ean = 2101200 = 0.175 V·min
T = kΦ·602π·Ia = 0.175·602π·20 = 33.42 N·m
Ea = 140 − 20·0.5 = 130 V
n = EakΦ = 1300.175 = 742.9 rpm

Ea = k′·Ia·n   |   n = V − Ia·(Ra+Rs)k′·Ia   |   T = k′·Ia²·602π   |   Vt = Ea − Ia·Ra   |   T = Ea·Iaω
20 A
0
0
0
0

Ea = V − Ia·(Ra+Rs) = 220 − 20 · 0.8 = 204 V
n = Eak′·Ia = 2040.0102 · 20 = 2040.204 = 1000 rpm
P = Ea·Ia = 204 · 20 = 4080 W ω = 2π·n60 = 2π · 100060 = 104.72 rad/s T = Pω = 4080104.72 = 38.96 N·m
Ea = 220 − 5 · 0.8 = 216 V n = 2160.0102 · 5 = 2160.051 = 4235.3 rpm

ns = 120·fp  |  s = ns − nns  |  smax = R2′|Zth + jX2′|  |  n = V − Ia·RakΦ
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