City Guilds Model Questions Vol1 2023 Engineering Question 34

A turning operation on a work‑piece of diameter \(100\ \text{mm}\) uses a carbide insert. The cutting speed is \(120\ \text{m/min}\) and the depth of cut is \(0.8\ \text{mm}\). The material removal rate (MRR) must be at least \(1500\ \text{mm}^{3}\!\!/\text{min}\). The MRR for turning is given by \(\text{MRR}=\pi D a f N\), where \(D\) is the work‑piece diameter, \(a\) the depth of cut, \(f\) the feed per revolution (mm/rev) and \(N\) the spindle speed (rev/min). The spindle speed relates to cutting speed by \(V=\pi D N/1000\). Determine the minimum feed \(f\) (to two decimal places) that satisfies the MRR requirement, and then compute the expected tool life using Taylor's equation \(V T^{0.25}=C\). The observed tool life at \(V=120\ \text{m/min}\) is \(45\ \text{min}\).