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Question 10.48: A machine is required to punch 4 holes of 40 mm diameter in ...

A machine is required to punch 4 holes of 40 mm diameter in a plate of 25 m thickness per minute. The work required is 6 N m per square mm of sheared area. The stroke of punch is 100 mm and maximum speed of flywheel at its radius of gyration is 30 m/s. Find the mass of the flywheel so that the speed does not fall below 27 m/s at the radius of gyration. Also determine the motor power required.

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\text { Work required per punch, } E=\pi \times 40 \times 25 \times 6=18849.6 Nm .

\text { Now }\left(\theta_{2}-\theta_{1}\right) / 2 \pi=t / 2 L=25 / 200=1 / 8 .

E_{f}=(1-t / 2 L) E=(1-1 / 8) \times 18849.6=16493.4 .

=0.5 M K^{2}\left(\omega_{1}^{2}-\omega_{2}^{2}\right) .

=0.5 M\left(K^{2} \omega_{1}^{2}-K^{2} \omega_{2}^{2}\right) .

=0.5 M\left(30^{2}-27^{2}\right) .

= 85.5 M.

M=192.9 kg.

\text { Energy supplied per minute }=18849.6 \times 4=75398.4 Nm .

\text { Motor power }=75398.4 /(60 \times 1000)=1.257 kW .

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