Question

Bars of $250mm$ length and $25mm$ diameter are to be turned on a lathe with a feed of $0.2mm/rev$. Each regrinding of the tool costs is Rs.20.The time required for each tool chnage is 1 min. Tool life equation is given as $V{T}^{02}=24$ (where cutting speed $V$ is in /(m/min\) and tool life $T$ is in $min$). The optimum tool cost per piece for maximum production rate is $Rs$
(round off to $2$ decimal places).

Answer 1

$\text{Given L}=250mm,D=25mm$,

$\text{Feed, f}=0.2mm/rev,\text{Tool change time}=1min$

$\text{Optimum tool life}\left(T_0\right)=\frac{T_c(1-n)}{n}=\frac{1(1-0.2)}{0.2}=4min$


$V_0{T}_0^n=Cor{V}_o=\frac{C}{T_o^n}=\frac{24}{4^{0.2}}$

$=18.19m/min$

$V=\pi DN$

$\Rightarrow 18.19=\pi \times 0.025\times N$

$\Rightarrow N=231.6rpm$

Machining time per piece

$\left(T_m\right)=\frac{L}{fN}=\frac{250}{0.2\times 23.16}=5.397min$

Number of tool needed per piece work

$=\frac{5.397}{4}$ piece
$\therefore$ The optimum tool cost per piece

$=\frac{5.397}{4}\times 20=26.935$