A 746 kW, 8-pole, 3-phase, 50 Hz induction motor has a rotor resistance of 0.04 Ω per phase and standstill rotor reactance of 0.3 Ω per phase. Full load torque is obtained at 720 rpm. What is the ratio of maximum to full load torque?

Concept

The ratio of maximum to full load torque is given by:

\({T_{fl}\over T_{max}}={2S_{max}S_{fl}\over S^2_{max}+S^2_{fl}}\)

The maximum slip is given by:

\(S_{max}={R_2\over X_2}\)

where, S_max = Maximum slip

R₂ = Rotor resistance

X₂ = Rotor reactance

The full load slip is given by:

\(S_{fl}={N_S-N_R\over N_S}\)

S_fl = Full load slip

N_s = Synchronous speed

N_r = Rotor speed at full load

Calculation

Given, R2 = 0.04 Ω and X2 = 0.3 Ω

f = 50 Hz, P = 8

\(N_S={120f\over P}\)

\(N_S={120\times 50\over 8}=750\space rpm\)

\(S_{fl}={750-720\over 750}=0.04\)

\(S_{max}={0.04\over 0.3}=0.133\)

The ratio of maximum to full load torque is given by:

\({T_{fl}\over T_{max}}={2(0.133)(0.04)\over (0.133)^2+(0.04)^2}\)

\({T_{fl}\over T_{max}}=0.55\)

\({T_{max}\over T_{fl}}=1.8\)