GATE 2024 ME – Question 60

Machining and Machine Tool Operations · Cutting tool materials, tool life and wear, economics of machining · 2 marks · Numerical answer

A cutting tool provides a tool life of 60 minutes while machining with the cutting speed of 60 m/min. When the same tool is used for machining the same material, it provides a tool life of 10 minutes for a cutting speed of 100 m/min. If the cutting speed is changed to 80 m/min for the same tool and work material combination, the tool life computed using Taylor's tool life model is ____________ minutes (*rounded off to 2 decimal places*).

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Correct answer: 21.76 to 21.98

Explanation

Taylor's model is $VT^n = C$. From the two tests, $60 \times 60^n = 100 \times 10^n$, so $6^n = \frac{100}{60}$ and $n = \frac{\ln(100/60)}{\ln 6} = 0.2851$. Then $T = 60\left(\frac{60}{80}\right)^{1/n} = 60 \times 0.75^{3.507} = 60 \times 0.3645 = 21.87$ minutes.