Machining operations are utilized in view of the better surface finish that could be achieved by it compared to other manufacturing operations. Thus, it is important to know what would be the effective surface finish that can be achieved in a machining operation. The surface finish in a given machining operation is a resulting of two factors:

1. The ideal surface finish, a result of the geometry of the manufacturing process, which can be determined considering the geometry of the machining operation.

2. The natural component, a result of a number of the uncontrollable factors in machining, which is difficult to predict..

Ideal Surface Finish in Turning:

In Fig.1, the geometry of the surface produced in turning with a sharp-cornered tool is shown. The situation shown is only possible with no sharp tool, no BUE, no machine-tool chatter, and elimination of all possibilities machine- tool inaccuracies in movements.

Normally the surface finish is represented by any suitable index, such as arithmetic average, R_a, or centre linear average, R_eta. It is defined as “the arithmetic average value (AA) of the departure of the whole on the profile both above and below is centerline throughout the prescribed meter cut-off ” in a plane substantially normal to the surface.

Referring to Fig.1, the surface roughness value is given by,

$R_{e t a}=\frac{|A r e a \ a b c|+|A r e a \ c d e|}{f}$

Where f is the feed rate.

Since triangles abc and cde are equal,

$R_{e t a}=\frac{2(A r e a a b c)}{f}=\frac{R m a x}{4}$

From the geometry,

$R_{e t a}=\frac{f}{\cos \gamma+\cot \gamma}$

Substituting this in the above equation, we get

$R_{e t a}=\frac{f}{4(\cot \gamma+\cot \gamma)}$

However, the actual turning tool used would have a nose radius in place of the sharp tool point, which modifies the surface geometry as shown in Fig. 2a. If the feed rate is very small, as it normally happens in finish turning, the surface is produced by the nose radius alone as shown in Fig.2b

It can be shown that for Case(a), the surface roughness value is

$R_{\text {eta }}=R(1-\cos \gamma)+f \sin y \cos \gamma-\sqrt{2 f R \sin ^{3}-f^{2}} \sin ^{4}[y]$

It can be shown that for Case (b), the surface roughness value is

$R_{\text {eta }}=\frac{8 f^{2}}{18 \sqrt{3 R}}$

The above are essentially the geometric factors and the values represent an ideal situation. However, the actual surface finish obtained depends to a great extent upon a number of factors such as

1. Cutting process parameters, speed, feed and depth of cut

2. Geometry of the cutting tool

3. Application of cutting fluid

4. Work and tool-material characteristics

5. Rigidity of the machine tool and the consequent vibrations

The major influence on surface finish is exerted by the fee d rate and cutting speed. As the feed decreases, from the above equations, we can see that the roughness index decreases. Similarly, as the cutting speed increase, we have better surface finish. Thus, while making a choice of cutting-process parameters for finish, it is desirable to have high cutting speed and small feed rate.