GATE 2026 ME – Question 64
A drill bit during its lifetime can produce 150 through holes in a plate at a drill-speed of 200 RPM. If the drill-speed increases to 300 RPM, then it can produce 60 through holes in the same plate before the drill bit fails. Assume all other parameters remain constant. The value of the exponent in Taylor's tool life equation is ________ (*rounded off to 2 decimal places*).
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Correct answer: 0.43 to 0.45
Explanation
Taylor's equation is $VT^n = C$. The tool life is proportional to the number of holes, so $200 \times 150^n = 300 \times 60^n$. This gives $\left(\frac{150}{60}\right)^n = \frac{300}{200} = 1.5$, so $n = \frac{\ln 1.5}{\ln 2.5} = \frac{0.4055}{0.9163} = 0.44$.