QUESTION ONE

A cup$-$drawing operation is performed in which the cup's inside diameter is $80$ mm and its height is $50$ mm $.$ The stock thickness is $3\mathrm{.}0$ mm $,$ and the blank diameter is $150$ mm $.$ The punch and die radii are $4$ mm $.$ The sheet material is an aluminium alloy with a tensile strength of $400$ MPa and a yield strength of $180$ MPa.

Given that $F_d=D_{p}t{}_{\text{u}\text{t}\text{s}}(\frac{D_b}{D_p}-0\mathrm{.}7)$ and $F_h=0\mathrm{.}015{}_y[D_b^2-(D_p+2\mathrm{.}2t+2R_d{)}^2]$ carry out the following:

$($i$)$ Determine the feasibility of the cup$-$drawing operation

$[4$ Marks $]$

$($ii$)$ Calculate the drawing force

$[2$ Marks $]$

$($iii$)$ Calculate the blankholder force

$[2$ Marks $]$

$($iv$)$ Determine the volumes of the blank and the drawn cup. What is the major reason for the difference, if any, in the two material volumes and how do you reduce this difference?

$[4$ Marks$]$