Question

The following data are obtained during orthogonal machining with Merchants theory.

Ultimate shear strength of work material = 600 MPa,
Rake angle of the tool $=6^{\circ }$,
Coefficient of friction at chip tool interface $=0.2$,
Feed and depth of cut = 0.2 mm/rev and 3 mm respectively. Taylor's tool life equation is $V.T^{0.4}=100$.

What is the Optimum cutting velocity during machining if machine hour rate is Rs. 75 and cost of regrinding the tool one time is Rs. 15?

• A. 161.8 m/min
• B. 223.8 m/min
• C. 31.5 m/min
• D. 43.5 m/min

Answer 1

The correct option is C 31.5 m/min

$\mu =0.2,\alpha =6^{\circ },$

$n=0.4,C=100$

${\tau }_{\text{ultimate}}=600\text{MPa}$

$f=0.2\text{mm/rev}$

$d=3\text{mm}$

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

$=100{\left[\frac{0.4}{0.6}\frac{\frac{75}{60}}{15}\right]}^{0.4}$

$=31.46\text{m/min}=31.5\text{m/min}$