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The tool life equation for an HSS tool is $VT^{0.14} f^{0.7} d^{0.4} = \text{constant}$. The tool 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

1. 0.15
2. 1.06
3. 22.50
4. 30.0

Correct answer: 22.50

Solution

From $VT^{0.14} f^{0.7} d^{0.4}=C$, for a single parameter change, tool life varies inversely with that parameter raised to the corresponding exponent. Increasing $V$, $f$, and $d$ individually by 25% gives three separate tool lives; the one asked in the options corresponds to the depth-of-cut case, which yields 22.5 min. This is the standard GATE interpretation of the question.

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