Squirrel cage motor problem solving!!?

Can you help me out with this?





A 22KW, three phase, 440v squirrel cage motor operates at full load with efficiency of 0.90, a power factor of 0.90 and slip of 0.02. Calculate the torque, speed, speed and current drawn by this motor at full load. If number of poles is six (6) and power supply frequency6 is 60 Hz.





I need it for my take home exam. Thank You!Squirrel cage motor problem solving!!?
22kW motor power rating is output power not input!





Sync RPM = 120f/p = 1200 RPM (p=poles)


Slip = Sync RPM X slip = 1200 X .02 = 24 RPM


FL RPM = Sync RPM - slip = 1176 RPM





Input kW = Output kW/eff = 22/.9 = 24.44 kW


Input kW = V x I x sqrt3 x pf / 1000


Input current I = Input kWx1000 / (Vxsqrt3xpf) = 35.6A





Output kW = Torque X RPM / 9549


Torque = 22 X 9549 / 1176 = 178.6 N-m


Squirrel cage motor problem solving!!?
Calculate the synchronous speed Syn = F/P f= frequency p = pole pairs


Syn = 60/3 = 20 Hz convert to RPM = 20 x 60 = 1200 RPM


Motor speed = Syn - slip = 100% - 2% = 98 % of Syn = 1200 x 0.98 = 1176 Rpm


Motor power = max power x efficiency = 22kW x 0.9 = 19.8kW or 19800W


Torque = Power/speed in Rad/sec


There is a constant to change RPM to rad/sec = 0.1047 which is 2pi/60


Speed = RPM x 2pi/60 Rad/sec = 1176 x (6.28/60) = 123.48 Rad/sec


Torque = Power/Speed = 19800/123.48 = 160.35 NM


Power = Sqroot 3 x VL x IL x PF


19800 = 1.7321 x 440 x IL x 0.9 rearrange for IL


IL = 19800/(1.7321 x 440 x 0.9) = 19800/685.9 = 28.87 Amps per phase