City Guilds Model Questions Vol1 2025 Engineering Question 6

A cylindrical steel shaft of length 200 mm and diameter 50 mm is to be turned on a CNC lathe. The machine can deliver a maximum power of 7.5 kW. The cutting force can be approximated by \(F_c = K_c \times A\) where \(K_c = 1800 \text{ N/mm}^2\) for the steel and the cross‑sectional area of cut is \(A = d_{\text{cut}} \times a\) with depth of cut \(d_{\text{cut}} = 2 \text{ mm}\) and feed per revolution \(a\) (mm). The cutting speed is \(V = \pi D N / 1000\) (m min\(^{-1}\)) where \(D = 50 \text{ mm}\) and spindle speed \(N\) is limited to 1200 rpm. Determine the maximum allowable feed per revolution \(a\) so that the power does not exceed 7.5 kW. Then compute the material removal rate \(\text{MRR} = \pi D a d_{\text{cut}} N\) (mm\(^3\) min\(^{-1}\)) and state whether it meets a required production rate of \(1.5 \times 10^{6}\) mm\(^3\) min\(^{-1}\).