A punching press is required to punch 40 mm diameter holes in a plate of 15 mm thickness at a rate of 30 holes per minute. It requires 6 N m of energy per mm^2 of sheared area. Determine the moment of inertia of the flywheel if the punching takes one-tenth of a second and the speed of the flywheel

Question

A punching press is required to punch 40 mm diameter holes in a plate of 15 mm thickness at a rate of 30 holes per minute. It requires 6 N m of energy per mm² of sheared area. Determine the moment of inertia of the flywheel if the punching takes one-tenth of a second and the speed of the flywheel varies from 160 to 140 rpm.

Accepted Answer

Given: d=40 mm, t=15 mm
Energy supplied in punching a hole= π×40 ×15 × 6=11309.7 N m
Time taken for punching one hole=60/30=2 s.

[latex] ext { Power required }=11309.7 / 2=5654.87 N m / s ext { or } 5.655 kW [/latex].

[latex] C_{s}=\left(v_{\max }-v_{\min } ight) / v_{m}=(27.5-24.5) / 26=0.1154 [/latex].

Time to punch a hole in 15 mm thick plate=1/10 s.

[latex] ext { Energy supplied by motor in } 0.1 s=11309.7 imes 0.1 / 2=565.5 Nm [/latex].

[latex] ext { Energy supplied by flywheel, } E_{f}=11309.7-565.5=10744.2 Nm [/latex].

[latex] N_{m}=(160+140) / 2=150 rpm , C_{s}=20 / 150=2 / 15 [/latex].

[latex] W=900 gE /\left(\pi^{2} K^{2} N_{m}^{2} C_{s} ight) [/latex].

[latex] I=W K^{2} / g=900 imes 10744.2 imes 15 /\left[\pi^{2} imes(150)^{2} imes 2 ight]=326.6 kg m ^{2} [/latex].

Question 10.47: A punching press is required to punch 40 mm diameter holes i...

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