Question

During a turning operation, the following equation is given for tool life $V{T}^{0.13}{f}^{0.77}{d}^{0.37}=C$
A 60 minutes tool life was obtained while cutting at V = 30 m/min, f = 0.3 mm/rev and d = 2.5 mm. If the cutting speed, feed and depth of cut are increased together by 20% then the new tool life is

• A. 14.75 min
• B. 8.26 mm
• C. 2.98 min
• D. 5.22 min

Answer 1

The correct option is C 2.98 min

$V^{\prime }=30\times 1.2=36$

$f^{\prime }=0.3\times 1.2=0.36\times T=2.98min$

$d^{\prime }=2.5\times 1.2=3mm$

So, $V{T}^{0.13}{f}^{0.77}{d}^{0.37}=V^{\prime }{{(}^{\prime }{T}^{\prime })}^{0.13}{\left(d^{\prime }\right)}^{0.37}$

$\Rightarrow {\left(\frac{T^{\prime }}{T}\right)}^{0.13}=\frac{V}{V^{\prime }}\times {\left(\frac{f}{f^{\prime }}\right)}^{0.77}\times {\left(\frac{2.5}{3}\right)}^{0.37}=0.6769$

$\therefore$ $T^{\prime }={\left(0.6769\right)}^{1/0.13}\times T=2.98min$