Consider a lathe machine with a motor rated at $1$ horsepower $($hp$).$ Efficiency of this

machine was found to be about $75\%.(10$ pts each, $30$ pts in total$)$

$($a$)$ Determine what is the maximum material removal rate $($MRR$,$ in $i\frac{n^3}{m}in)$ that is

possible when turning a stainless steel shaft of $4"$ diameter. From orthogonal cutting

experiments, specific cutting energy $($or unit power$)$ of stainless steel is known to be

$1hp-mi\frac{n}{i}{n}^3.(10$ pts$)$

$($b$)$ If the spindle is set to rotate at $500$ rpm and depth of cut is chosen as ${0\mathrm{.}005}^{\text{'}\text{'}},$ what is

the maximum feed rate? $(10$ pts $)$

$($c$)$ When the machine is being operated at half the maximum capacity $(1$ hp$),$ what is the

expected primary cutting force acting on the tool? $(10$ pts$)$