Problem

Rectangular slabs cast from $1020$ annealed steel are heated and flat$-$rolled to improve their metallurgical structure and reduce their thickness. The slabs are $1\mathrm{.}5m9m18cm$ with a density of $7590k\frac{g}{m^3}.$ After passing through a $5-$stand roughing mill, the rolled product will have a thickness of $3mm.$ Vertical rolls are used to prevent widening of the slabs so the width of the finished product does not change; however, the density of the finished product increases by $0\mathrm{.}1\%.$

a$)$ What is the length of the final rolled product?

We want the first stand in the $5-$stand roughing mill to reduce the thickness of the slab from $18cm$ to $16cm.$ The roll's diameter is $600mm$ and it rotates at $75rpm.$ The motor driving the roll has $8,000kW$ of power with an efficiency of $75\%.$ For $1020$ annealed steel, $K=745$MPa and $n=0\mathrm{.}20.$

b$)$ Will you be able to perform this rolling job in one pass $($i$.$e$.,$ reduce from $18cm$ to $16cm$ in one pass through the rolls$)?$

c$)$ Will you be able to perform this rolling job in two passes $($with equal reduction in every pass$)?$

Justify your answer with calculations.

Submission Instructions

Submit one PDF file

Clearly state your name and student ID on the first page of your submission

Submission is through Blackboard in the Assignments Content Area

Late submissions will be penalized $(10\%$ for each day of delay$)$

Final answers are not accepted $-$ show the steps of your work