Question: Carbide tool is used to machine a 30mm diameter steel shaft at a spindle speed of 1000 revolutions per minute. What is the cutting velocity of the above turning operation?

Solution: In straight turning operation, the cylindrical workpiece is rotated at a fixed spindle speed (measured in rpm or revolution per minute); while, the single point turning tool is fed in longitudinal direction at a pre-defined feed rate (measured in mm/rev). Necessary depth of cut (measured in mm) is also provided in transverse direction prior to feeding the tool. Tangential velocity of the rotating workpiece at the point of cutting is termed as cutting velocity (measured in m/min). This cutting velocity (V_c) can be expressed in terms of spindle speed (N) and diameter of the cylindrical workpiece (D) at the point of cutting (remember initial diameter is considered for calculation).

Relation between spindle speed and cutting velocity in turning

\[{V_c} = \frac{{\pi DN}}{{1000}}\]

Please note that the above formula is based on the standard unit of measurement of the related quantities, as mentioned below. So attention must be given to the units before blindly applying the formula.

V_c = Cutting velocity (m/min)

N = Spindle speed or cutting speed (rpm)

D = Diameter of the workpiece (mm)

In this particular case as given in question

D = 30mm

N = 1000rpm

\[{V_c} = \frac{{\pi  \times 30 \times 1000}}{{1000}} = 94.25\]

Therefore, cutting velocity in turning as per the given conditions is 94.25m/min.