Correct Answer - Option 3 : 1
Concept:
Punching:
in sheet metal operation, punching operation the process in which sheared part is considered as scrap and the remaining part is desired part.
For punching opreration,
⇒ Punch tool size = Hole size = d
The maximum crushing stress induced in the punching tool,
\( ⇒ {{\bf{\sigma }}_{{\bf{cmax}}}} = \frac{{4{\bf{F}}}}{{{\bf{\pi }}{{\bf{d}}^2}}}\;\;\;\;\; \ldots \left( 1 \right)\;\)
The maximum allowable shearing stress,
\( ⇒ {{\bf{\tau }}_{{\bf{smax}}}} = \frac{{\bf{F}}}{{{\bf{\pi dt}}}}\;\;\;\;\;\; \ldots \left( 2 \right)\;\)
where, F = Punching force, d = diameter of the hole (punching tool diameter), t = thickness of the metal sheet
Calculation:
Given:
σcmax = 4τsmax
\( ⇒ \frac{{4{\bf{F}}}}{{{\bf{\pi }}{{\bf{d}}^2}}} = 4 \times \frac{{\bf{F}}}{{{\bf{\pi dt}}}}\;\)
⇒ d = t
⇒ The ratio of the diameter of the hole to plate thickness = 1