Question

Machining of a component is made under the following cutting conditions:
Cost of operating the machine = 20 paise per minute.
Cost of regrinding the tool one time = Rs. 8.
The cutting speed is 40 m/min when the tool life is 50 min for the depth of cut of 2 mm and feed rate of 0.3 mm.
Taylor's exponent is 0.2.
The time needed to change the tool one time is 3 min.

The optimum tool life for minimum cost criteria of machining is

• A. 3125 min
• B. 160 min
• C. 4.6 min
• D. 1 min

Answer 1

The correct option is B 160 min

$V_{opt}=C{\left[\frac{n}{1-n}\frac{L_m}{c_g}\right]}^n$

$C=V{T}^n=40\times (50{)}^{0.2}=87.46$

$L_m=0.20$

$V_{opt}=87.46{(\frac{0.2}{0.8}\times \frac{0.20}{8})}^{0.2}=31.69\text{m/min}$

$T_{opt}={\left(\frac{C}{V_{opt}}\right)}^{\frac{1}{n}}$

$={\left(\frac{87.46}{31.7}\right)}^{\frac{1}{0.2}}=159.86=160\text{min}$