A 50 hp, 1760 r/min, 440 V, 3-phase induction motor drives a load having a total moment of inertia of 25 kgm² . The dc resistance between two stator terminals is 0.32 Ω , and the rated motor current is 62 A. We want to stop the motor by connecting a 24 V battery across the terminals.

Calculate

a. The dc current in the stator
b. The energy dissipated in the rotor
c. The average braking torque if the stopping time is 4 min

Question

A 50 hp, 1760 r/min, 440 V, 3-phase induction motor drives a load having a total moment of inertia of 25 kgm² . The dc resistance between two stator terminals is 0.32 Ω , and the rated motor current is 62 A. We want to stop the motor by connecting a 24 V battery across the terminals.

Calculate

a. The dc current in the stator
b. The energy dissipated in the rotor
c. The average braking torque if the stopping time is 4 min

Calculate

a. The dc current in the stator
b. The energy dissipated in the rotor
c. The average braking torque if the stopping time is 4 min

Accepted Answer

a. The dc current is

[latex]I=E / R=24 / 0.32=75 A[/latex]

This current is slightly higher than the rated current of the motor. However, the stator will not overheat, because the braking time is short.

b. The kinetic energy in the rotor and load at 1760 r/min is

[latex]\begin{aligned}E_{ k } &=5.48 imes 10^{-3} J n^{2} \&=5.48 imes 10^{-3} imes 25 imes 1760^{2} \&=424 kJ\end{aligned}[/latex]

Consequently, the rotor absorbs 424 kJ during the braking period.

c. The average braking torque T can be calculated from the equation

[latex]\begin{aligned}\Delta n &=9.55 T \Delta t / J \1760 &=9.55 T imes(4 imes 60) / 25 \T &=19.2 N \cdot m\end{aligned}[/latex]

Question 14.5: A 50 hp, 1760 r/min, 440 V, 3-phase induction motor drives a...

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