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Question 10.49: A punching press is required to punch 30 mm dia holes in a p...

A punching press is required to punch 30 mm dia holes in a plate of 20 mm thickness at the rate of 20 holes per minute. It requires 6 N m of energy per mm² of sheared area. If punching takes place 1/10th of a second and the speed of the flywheel varies from 160 to 140 rpm, determine the mass of the flywheel having radius of gyration of 1 m.

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\text { Work required per punch, } E_{1}=\pi \times 30 \times 20 \times 6=11309.7 Nm .

\text { Time required to punch a hole }=60 / 20=3 s .

Energy required for punching per second=11309.7/3=3769.91 N m/s.

\text { Energy supplied by motor in } 1 / 10 \text { th second }, E_{2}=3769.91 / 10=376.991 N m .

E_{f}=E_{1}-E_{2}=11309.7-376.991=10932.71 Nm .

=0.5 \times M K^{2} \times(2 \pi / 60)^{2}\left(N_{1}^{2}-N_{2}^{2}\right) .

=0.5 \times M K^{2} \times(2 \pi / 60)^{2}\left(N_{1}^{2}-N_{2}^{2}\right) .

=0.5 M \times 1 \times(2 \pi / 60)^{2}\left(160^{2}-140^{2}\right) .

M=332.3 kg.

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