GATE 2020 ME (ME2) – Question 55
Bars 250 mm long and 25 mm diameter are turned at feed 0.2 mm/rev. Each tool regrinding costs ₹20 and each tool change takes 1 minute. Tool life obeys $VT^{0.2}=24$, with V in m/min and T in min. Find optimum tool cost per piece for maximum production rate (rupees), to two decimals.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 26 to 28
Explanation
For maximum production rate, optimum tool life is $T=(1/n-1)t_c=(5-1)(1)=4$ min. Speed is V=24/4⁰·²=18.1886 m/min. Machining time isπ(0.025)(0.25)/(0.0002V)=5.39763 min. Tool cost allocated per piece is20(tm/T)=**₹26.99**. This is tool cost, not total machining cost.