$20\mathrm{.}5($A$)($USCS units$)$ A turning operation is performed using a rake angle of $15.$ Cutting speed

$=200f\frac{t}{m}in,$ feed $=0\mathrm{.}012i\frac{n}{r}ev,$ and depth of cut $=0\mathrm{.}100in.$ The chip thickness ratio measured

after the cut $=0\mathrm{.}48.$ Determine $($a$)$ chip thickness after the cut, $($b$)$ shear angle, $($c$)$ friction angle,

$($d$)$ coefficient of friction, and $($e$)$ shear strain.

$20\mathrm{.}11($USCS units$)$ A turning operation is performed with a rake angle of $10,$ a feed of $0\mathrm{.}010$

$i\frac{n}{r}ev,$ and a depth of cut $=0\mathrm{.}100in.$ Shear strength of the work metal $=50,000l\frac{b}{i}{n}^2,$ and the chip

thickness ratio after the cut $=0\mathrm{.}40.$ Determine the cutting force and the feed force. Use the

orthogonal cutting model as an approximation of the turning process.

$20\mathrm{.}21($A$)($USCS units$)$ A cast iron workpiece is turned on a lathe whose mechanical efficiency $=$

$0\mathrm{.}87.$ Cutting speed $=400f\frac{t}{m}in,$ feed $=0\mathrm{.}011i\frac{n}{r}ev,$ and depth of cut $=0\mathrm{.}120in.$ Cutting force $=$

$250$ lb $.$ Determine $($a$)$ the horsepower consumed by the turning operation; $($b$)$ horsepower that must

be generated by the lathe; $($c$)$ unit horsepower and specific energy for the work material in this

operation.

$21\mathrm{.}3($USCS units$)$ A facing operation is performed on a cylindrical part with diameter $=6$ in and

length $=15in.$ The engine lathe spindle rotates at $200re\frac{v}{m}in.$ Depth of cut $=0\mathrm{.}110in,$ and feed $=$

$0\mathrm{.}008i\frac{n}{r}ev.$ Assuming the cutting tool moves from the outer diameter of the workpiece to exactly

the center at a constant velocity, determine $($a$)$ the velocity of the tool as it moves from the outer

diameter toward the center and $($b$)$ the cutting time.

$21\mathrm{.}10($USCS units$)$ A gun$-$drilling operation is used to drill a $9/64-$in diameter hole. It takes $2\mathrm{.}5$ min

to perform the operation using high pressure fluid delivery of coolant to the drill point. The current

spindle speed $=4000re\frac{v}{m}in,$ and feed $=0\mathrm{.}0017i\frac{n}{r}ev.$ In order to improve surface finish in the

hole, it has been decided to increase the speed by $20\%$ and decrease the feed by $25\%.$ How long will

it take to perform the operation at the new cutting conditions?

$21\mathrm{.}12($SI units$)$ A face milling operation removes $6\mathrm{.}0$ mm from the top surface of a rectangular piece

of aluminum that is $250$ mm long by $75$ mm wide by $50$ mm thick. Thickness after the cut $=44\mathrm{.}0$

mm $.$ The cutter follows a path that is centered over the workpiece. It has four teeth and an $85-mm$

diameter. Cutting speed $=2\mathrm{.}0\frac{m}{s},$ and chip load $=0\mathrm{.}18m\frac{m}{?}$ tooth. Determine $($a$)$ machining time

and $($b$)$ maximum metal removal rate during cutting.