A 3-phase, 8-pole induction motor driving a compressor runs at 873 r/min immediately after it is connected to a fixed 460 V, 60 Hz line. The initial cold rotor temperature is 23°C. The speed drops to 864 r/min after the machine has run for several hours.

Question

Calculate

a. The hot rotor resistance in terms of the cold resistance
b. The approximate hot temperature of the rotor bars, knowing they are made of copper

Accepted Answer

a. The synchronous speed is

[latex]n_{ s }=120 f / p =120 imes 60 / 8=900 r / min[/latex]

The initial and final slips are

[latex]\begin{aligned}&s_{ n }=(900-873) / 900=0.03 \&s_{ x }=(900-864) / 900=0.04\end{aligned}[/latex]

The voltage and torque are fixed; consequently, the speed change is entirely due to the change in rotor resistance. We can therefore write

[latex]\begin{aligned}s_{ x } &=s_{ n }\left(R_{ x } / R_{ n } ight) \0.04 &=0.03\left(R_{ x } / R_{ n } ight) \R_{ x } &=1.33 R_{ n }\end{aligned}[/latex]

The hot rotor resistance is 33% greater than the cold rotor resistance.

b. The hot rotor temperature is

[latex]\begin{aligned}t_{2} &=\frac{R_{2}}{R_{1}}\left(234+T_{1} ight)-234 \&=1.33(234+23)-234 \&=108^{\circ} C\end{aligned}[/latex]

Question 14.2: A 3-phase, 8-pole induction motor driving a compressor runs ...

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