City Guilds Model Questions Vol1 2023 Engineering Question 30

A turning operation on a steel workpiece containing \(0.45\%\) carbon requires a surface finish of \(R_a = 0.8\ \mu\text{m}\). The recommended cutting speed for this material is given by \(V = \frac{C}{0.2}\) m min\(^{-1}\), where \(C\) is the carbon percentage. The workpiece is to be machined with a tool of diameter \(50\ \text{mm}\), and the machine spindle can rotate at a maximum of \(1500\ \text{rev min}^{-1}\). Determine (a) whether the recommended cutting speed can be attained, (b) the maximum cutting speed that can be achieved at the spindle limit, and (c) the feed per revolution required to obtain a material removal rate of \(120\ \text{cm}^{3}\text{min}^{-1}\). Give the feed to two decimal places in mm rev\(^{-1}\).