Calculate cutting velocity in turning from diameter and spindle speed

Machining, Numerical

Question: What is the cutting velocity in m/sec, for turning a work piece of diameter 100 mm at the spindle speed of 480 RPM? [IAS‐1998]

Solution: In straight turning operation the cylindrical workpiece is rotated about a fixed axis at a fixed rpm (revolution per minute) while the cutting tool is fed parallel to the job axis after providing necessary depth of cut in transverse (radial to the workpiece) direction. The rotation speed of the workpiece is termed as spindle speed (N) and is commonly expressed in rpm. The tangential velocity at the point of cut is called cutting velocity (Vc) and is normally expressed in m/min.

The cutting velocity (Vc) is one important parameter in machining. This can be expressed in terms of the spindle speed (N) and diameter of the workpiece (D), as given below. It is to be mentioned that the following expression is based on the conventional units of measurement of the corresponding parameters. Here, cutting velocity is measured in m/min, the spindle sped is measured in rpm, and the workpiece diameter is measured in mm. Thus proper care should be taken on units; however if necessary, unit conversion can be performed through multiplicative conversion factors.

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

Relation between cutting velocity and spindle speed in straight turning

Calculation of cutting velocity in m/sec

Given, work piece diameter (D) = 100mm

Spindle speed (N) = 480RPM

So, cutting velocity can be calculated as follows:

\({V_C} = \frac{{\pi DN}}{{1000}} = \frac{{\pi  \times 100 \times 480}}{{1000}} = 150.79 m/\min \)

∴ VC = 2.51m/s

Thus cutting velocity for the given case is 2.51m/s.

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