## Relationship to manufacturing processes

In any machining process, the tolerance that can be achieved will depend upon two things. Firstly, the variability caused by the vagaries within a manufacturing process such as vibrations, discontinuities, inconsistencies, etc. These will produce a deviation about some mean value. Secondly, there is the variation that occurs when the tool wears. This will be progressive. Thus, in any accuracy graph or table, there will be two factors: an increasing trend with wear and variability scattered around this trend. This is shown in the graph in Figure 5.2. The nominal diameter was 10mm and the manufacturing process was gun-drilling. The graph shows that there is a general trend produced by wear and variability given by the 'error' bars essentially equi-spaced about the mean. In this case the variability about the mean value represents the out-of-roundness. This

 - - c T3 C 3 - / / J" > y' n— 1 Nominal dian 1 leter =10mm Drilled Length (m) Figure 5.2 Gun-drill wear against hole diameter showing wear trend and out-of-roundness Drilled Length (m) Figure 5.2 Gun-drill wear against hole diameter showing wear trend and out-of-roundness is the deviation of the hole from a perfectly circular hole. The out-of-roundness refers to random as well as systematic errors. An example of a systematic error is shown in the picture in Figure 5.3. This is a photograph of a 6mm-diameter hole in a 3mm thick aluminium sheet. The hole is clearly of a triangular form. The 'halo' round the edge of the hole is where it has been chamfered to remove the burr. The reason the hole is triangular is because of a lack of stability of the drill caused mainly by the fact that the tip breaks through the thin sheet before the outer edges are engaged in cut. The ensuing vibrations have caused the drill to both rotate and oscillate. It is significant that a 2-point measurement using, say, a digital calliper produces an almost constant diameter of 6,5mm whereas in fact the circumscribed circle diameter is some 15% larger than the inscribed circle diameter. This difference would be seen if a 3-leg internal micrometer were used to measure the hole. 6mm diameter hole in 13mm thick aluminium sheet Figure 5.3 A 6mm-diameter hole drilled in a thin aluminium sheet using a twist drill