(EE problem solving) motor problem solving on squirrel cage?

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 frequency is 60 Hz. (EE problem solving) motor problem solving on squirrel cage?
I realize this is a homework problem, but it sounds like you need some help setting up the formulas...





First, note that the rated mechanical output power, Pout = 22 kW.


The AC windings are rated 440V line-to-line.


Since you are given efficiency and power factor, we can calculate the electrical input power, and thus input current.





Input real power, Pin = Pout * (1/efficiency), in kW


Input apparent power, S = Pin * (1/power factor), in kVA





Given S and V, it is easy to calculate current, I


S = sqrt(3) * V * I , in kVA where V is the line-line rms voltage


I = S / (sqrt(3) * V)





Next, to calculate motor speed at full load:


Identify the synchronous speed of the system, which corresponds to slip = 0.


synch speed = 60 Hz * (60 rpm / Hz) * (2/number of poles)


So, a 2-pole machine would have a synchronous speed of 3600 rpm.


But, our 6-pole machine has a synch speed of 1200 rpm.





At synchronous speed, an induction machine (either squirrel cage or wound rotor) cannot produce any torque, and thus it cannot produce any output power. There must be non-zero slip to induce current flow in the rotor, which then results in torque %26amp; power production.





Rated speed, s = synch speed * (1 - rated slip).


So, s = 1200 rpm * (1 - 0.02) = 1200 rpm * 0.98 = 1176 rpm.





Now that we have speed, it is possible to calculate torque.


The equation is: Pout = T * w, where w 'omega' is the speed in radians per second.





So, we have to convert rpm to rad/s.


w = rpm * (1/60 ) * 2pi = 123.15 rad/s





T = 22000 Watts / 123.15 rad/s = 178.64 N-m