A 15 hp, 240 V, 1780 r/min dc series motor has a full-load rated current of 54 A. Its operating characteristics are given by the per-unit curves of Fig. 11.

Calculate

a. The current and speed when the load torque is 24 N·m
b. The efficiency under these conditions

Question

A 15 hp, 240 V, 1780 r/min dc series motor has a full-load rated current of 54 A. Its operating characteristics are given by the per-unit curves of Fig. 11.

Calculate

a. The current and speed when the load torque is 24 N·m
b. The efficiency under these conditions

Accepted Answer

a. We first establish the base power, base speed, and base current of the motor. They correspond to the full-load ratings as follows:

[latex]a\begin{aligned}P_{ B } &=15 hp =15 imes 746=11190 W \n_{ B } &=1780 r / min \I_{ B } &=54 A\end{aligned}[/latex]

The base torque is, therefore,

[latex]\begin{aligned}T_{ B } &=\frac{9.55 P_{ B }}{n_{ B }}=9.55 imes 11190 / 1780 \&=60 N \cdot m\end{aligned}[/latex]

A load torque of 24 N·m corresponds to a perunit torque of

[latex]T( pu )=24 / 60=0.4[/latex]

Referring to Fig. 11, a torque of 0.4 pu is attained at a speed of 1.4 pu. Thus, the speed is

[latex]\begin{aligned}n &=n( pu ) imes n_{ B }=1.4 imes 1780 \&=2492 r / min\end{aligned}[/latex]

From the T vs I curve, a torque of 0.4 pu requires a current of 0.6 pu. Consequently, the load current is

[latex]I=I( pu ) imes I_{ B }=0.6 imes 54=32.4 A[/latex]

b. To calculate the efficiency, we have to know [latex]P_{ o }[/latex] and [latex]P_{ i }[/latex]

[latex]\begin{aligned}P_{ i } &=E I=240 imes 32.4=7776 W \P_{ o } &=n T / 9.55=2492 imes 24 / 9.55 \&=6263 W \\eta &=P_{ o } / P_{ i }=6263 / 7776=0.805 ext { or } 80.5 \%\end{aligned}[/latex]

Question 5.5: A 15 hp, 240 V, 1780 r/min dc series motor has a full-load r...

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