Q $1.$

A deep drawing operation is performed on a sheet$-$metal blank that is $0\mathrm{.}125$ mm thick. The height of the cup $=155mm$ and its diameter $=100mm($both inside dimensions$).($a$)$ Assuming the punch radius $=0,$ compute the starting diameter of the blank to complete the operation with no material left in the flange. $($b$)$ Is the operation feasible $($ignoring the fact that the punch radius is too small$)?($c$)$ how many drawing operations are required to make the cup. Assume a reduction of $40\%$ for first draw, $30\%$ for second draw and $20\%$ for third draw.

$($d$)$ find the height of the shell after each draw

$($e$)$ Find the drawing force and holding force assuming die radius $4$ mm and Tensile strength $=400$ MPa and yield strength $=180$MPa for this sheet metal.