City Guilds Model Questions Vol1 2024 Engineering Question 43

An engineering turning operation is to reduce a steel rod from an initial diameter of 55 mm to a final diameter of 50 mm over its full length of 200 mm. The recommended cutting speed for the steel is 80 m min$^{-1}$. The cutting speed $V$ (m min$^{-1}$) is related to spindle speed $N$ (rpm) and diameter $D$ (mm) by $V = \frac{\pi D N}{1000}$.\ \(a\) Determine the spindle speed $N$ (rpm) that should be set when the diameter is at its final value.\ \(b\) Using a feed rate of 0.2 mm rev$^{-1}$, calculate the material removal rate (MRR) in mm$^{3}$ min$^{-1}$ at this spindle speed. Use the average diameter during cutting $D_{\text{avg}} = \frac{55+50}{2}$ mm and the formula $\text{MRR} = \pi D_{\text{avg}} L f N$, where $L = 200$ mm and $f = 0.2$ mm rev$^{-1}$.\ \(c\) The tool life follows Taylor's equation $V T^{n} = C$ with $n = 0.25$ and $C = 200$. Compute the tool life $T$ (minutes) at the cutting speed used in part (a).\ Give your answers for (a), (b) and (c) rounded to the nearest whole number.