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 cutting speed for the minimum cost criteria of machining process is

• A. 87.5 m/min
• B. 64.3 m/min
• C. 31.7 m/min
• D. 17.5 m/min

Answer 1

The correct option is C 31.7 m/min

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

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

$L_m=0.20$

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