GATE 2025 ME – Question 63
Cylindrical workpieces of diameter 60 mm and length 400 mm are machined on a lathe at a cutting speed of 25 m min$^{-1}$ and a feed of 0.2 mm rev$^{-1}$. The Taylor's tool life parameters $C$ and $n$ for this setup are 75 and 0.25, respectively. The tool changing time is 3 minutes. With a labor and overhead cost of ₹ 5 per minute, the tool changing cost per piece is ₹ ________ (rounded off to 2 decimal places).
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Correct answer: 2.78 to 2.80
Explanation
Taylor's equation $VT^n = C$ gives the tool life $T = \left(\frac{75}{25}\right)^{1/0.25} = 3^4 = 81$ min. The spindle speed is $N = \frac{1000 \times 25}{\pi \times 60} = 132.6$ rpm, so the machining time per piece is $\frac{400}{0.2 \times 132.6} = 15.08$ min. The number of tool changes per piece is $\frac{15.08}{81}$, and each costs $3 \times 5 = ₹15$. So the cost per piece is $15 \times \frac{15.08}{81} = ₹2.79$.