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Theoretical Considerations

Material Removal Rate

It is the volume of material removed per unit time. For each revolution of the workpiece, a ring-shaped layer of material is removed. The cross-sectional area of this ring is:

where,

Check again the schematic illustration of a turning operation.

The volume of this ring is the product of the cross-sectional area and the average circumference of the ring:

Average Circumference = ()(Davg)

where,

For light cuts, one can replace the average diameter by Do.

The rotational speed of the workpiece is N. Thus, the metal removal rate per revolution is:

MRR = Davg d f N

The tool travels at a feed rate of (f)(N). Thus, the cutting time for a workpiece of length l can be calculated:

This time does not include the time required for tool approach or retraction.

Forces in Turning

The three forces acting on a tool are shown below:

The cutting force, Fc, supplies the energy required for the cutting operation. This force can be calculated from the energy per unit volume, see table below.

The thrust force, Ft, also called feed force, acts longitudinally in the feed direction.

The radial force, Fr, is in the radial direction and tends to push the tool away from the workpiece.

Ft and Fr are difficult to calculate because of the many factors involved in the cutting process. They are determined experimentally. These forces are important in the design of machine tools as well as in the deflection of tools for precision machining operations.

Source: Kalpakjian, Manufacturing Processes for Engineering Materials.