Question

The tool life equation for HSS tools is $V{T}^{0.14}{f}^{0.7}{d}^{0.4}$ = Constant. The total life (T) of 30 min is obtained using the following cutting conditions:
V = 45 m/min, f = 0.35 mm, d = 2.0 mm
If speed (V), feed (f) and depth of cut (d) are increased individually by 25%, the tool life (in min) is

• A. 0.15
• B. 1.06
• C. 22.50
• D. 30.0

Answer 1

The correct option is B 1.06

Given Tool life equation:
$V{T}^{0.14}{f}^{0.7}{d}^{0.4}$ = Constant.

$45000\times {30}^{0.14}\times {0.35}^{0.7}\times 2^{0.4}=K$

$K=45,842.58$

If speed (V), feed (f) and depth of cut (d) are increased individually by 25%, the tool life (in min) is

$\Rightarrow T^{0.14}=\frac{K}{\left(1.25V\right){\left(1.25f\right)}^{0.7}{(1.25\times d)}^{0.4}}$

$\Rightarrow T^{0.14}=\frac{K}{(1.25\times 45000){(1.25\times 0.35)}^{0.7}{(1.25\times 2)}^{0.4}}$

$\Rightarrow T=1.06min$