Answer Posted / daneshwar sahu

Calculation table for slip ring induction motor used for crane hoisting application
Calculation table for slip ring induction motor used for crane hoisting application


Result contain approximate values for cross-checking only
INPUTS
Power Rating
P2
100
HP
Speed
N
980
RPM
Stator Voltage
E1
415
V
Stator Current
Is
138
A
Rotor Voltage
E2
380
V
Rotor Current
I2
124
A
Synchronous Speed
Ns
1000
RPM
Frequency
f
50
Hz
No.of Steps in Speed Control
n
5
OUTPUTS
Slip
S=(Ns-N)/Ns
0.02
Rotor Frequency
f'=Sf
1
Hz
I2= (SE2)/(√(R22 (SX2)2)
For maximum starting torque application S=(R2/X2)= 0.02
Then R2= 0.02 X2 (Approx.)
From above two Equations we get

Rotor Reactance
X2
2.166940136
Ohm
Rotor Resistance
R2
0.043338803
Ohm

Starting Rotor Current I2s=(E2)/(√(R22 X22)


Starting Power Factor COSØ2s=(R2)/(√(R22 X22)

Power Factor (FL) COSØ2s=(SR2)/(√(R22 (SX2)2)




Starting Rotor Current














I2s














175.3274198














A
Starting Power Factor
COSØ2s
0.019996001
Power Factor (FL)
COSØ2
0.707106781

T= (60P2)/(2лNs)
T=(KSR2E22)/ (√(R22 (SX2)2)
Smax= (R2/X2)
Tm=(KE22)/ (2X2)
Tstm=(KE22)/ (2R2)



Torque (FL)
T
42747.13376
N-m
Torque constant
K
1.282970635
Maximum Slip
Smax
0.02
Maximum Torque
Tm
42747.13376
N-m
Maximum Starting Torque
Tstm
2137356.688
N-m

Pm=(1-S)P2
Pcu=SP2
Tsh=(60P2)/ (2лN)




Mechanical Power
Pm
73.0786
kW
Cu loss
Pcu
1.4914
kW
Shaft Torque
Tsh
42747.13376
N-m

R1’,R2’,R3’,R4’,R5’- Total resistance per phase in the rotor circuit on the 1st, 2nd, 3rd, 4th, 5th Stud respectively
r1’,r2’,r3’,r4’,r5’- Total resistance of the different steps

R1’=(R2/Smax)
k=(Smax)1/n-1
R2’=kR1’
R3’=kR2’=k2R1’
R4’=kR3’=k3R1’
R5’=kR4’=k4R1’






R1'
2.166940136
Ohm
k
0.376060309
R2'
0.814900178
Ohm
R3'
0.306451613
Ohm
R4'
0.115244288
Ohm
R5'
0.043338803
Ohm
r1’=R1’-R2’=(1-k)R1’
r2’=R2’-R3’=(k-k2)R1’=kr1’
r3’=k2r1’
r4’=k3r1’
r5’=k4r1’





Resistance 1st Step










r1'










1.352039958










Ohm
Resistance 2nd Step
r2'
0.508448565
Ohm
Resistance 3rd Step
r3'
0.191207325
Ohm
Resistance 4th Step
r4'
0.071905486
Ohm

S1=1
S2=k
S3=K2
S4=K3
S5=Smax


Slip 1st Step
S1
1
Slip 2nd Step
S2
0.376060309
Slip 3rd Step
S3
0.141421356
Slip 4th Step
S4
0.053182959
Slip 5th Step
S5
0.02

N1=0
N2=(1-S2)Ns
N3=(1-S3)Ns
N4=(1-S4)Ns
N5=N

Speed 1st Step
N1
0
RPM
Speed 2nd Step
N2
623.9396907
RPM
Speed 3rd Step
N3
858.5786438
RPM
Speed 4th Step
N4
946.817041
RPM
Speed 5th Step
N5
980
RPM

T=(KSR2E22)/ (√(R22 (SX2)2)


Torque 1st Step




T1




1709.20167




N-m
Torque 2nd Step
T2
4534.013993
N-m
Torque 3rd Step
T3
11853.64241
N-m
Torque 4th Step
T4
28167.51282
N-m
Torque 5th Step
T5
42747.13376
N-m

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