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