## Variation of features

No feature on a component can be perfect. No surface can be perfectly flat, no hole can be perfectly round, no two perpendicular surfaces can be at exactly 90°. The reason for this is that all manufacturing processes are variable to a greater or lesser degree and thus, all features have an inherent variability. During any type of manufacture of, say, a flat surface, there will be variability inherent within the manufacturing process caused by vibrations, inequalities, instabilities and wear. For a typically machined surface this is illustrated by the trace shown in Figure 4.11. This is from a single trace of a gun-drilled hole. The trace was taken using a diamond stylus having a tip radius of 2um. Because the tip radius is so small, not only does it record the surface waviness but it also records the surface roughness caused by the individual machining scratches.

The trace is some 10mm long and it shows that the surface is not a 10mm long ideal straight line. The deviation over this 10mm length from the highest peak to the lowest valley is 4,2 microns yet this is a surface produced by precision machining.

It is not only flat surfaces that are variable. Figure 4.12 shows roundness traces from three positions along a ground hole. The traces do not indicate the diameter of the holes, merely their variability. The fact that they are three concentric circles of varying

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Figure 4.11 Trace of a flat surface showing the deviations from the ideal straightness

Figure 4.12 Roundness traces of a ground hole showing deviations from an ideal circle

diameter is due to the fact that the instrument settings are varied so that the radii can be separated. Each trace thus represents the circular trace around the ground bore and displays the out-of-roundness, not the absolute diameter. Clearly, each trace is far from an ideal circle, showing that even a precision ground hole has some variability.

The above two figures have demonstrated that a hole can never be perfectly straight or round. The same will apply to other aspects of the hole like taper and perpendicularity. The variability will be different each time a surface is produced on the same machine and also between different machines and processes. The variability will be higher with rough-machined surfaces and lower with precision-machined surfaces. The table in Figure 4.13 shows the variability of some hole manufacturing processes. The data refers to processes used for producing holes 25mm in diameter. In the figure, the word 'taper' means the maximum inclination over a 40mm length. The word 'ovality' means the difference between the maximum and minimum diameters at perpendicular positions. The word 'roundness' means the deviation from a true circle. The words 'average roughness' (represented by 'Ra', see Chapter 6) mean the average deviation of the surface micro-roughness after waviness has been removed. The table shows that on average, the variability for rough-machining processes is in the order of tens of microns

 Data all for 25mm diameter holes Q Rough grinding Rough boring Reaming Fine grinding Honing Broaching Taper (um/40mm) 36 25 22 10 4 4 1 Ovality (um) 13 3 5 1 1 1 1 Roundness (um) - 5 9 3 6 0.5 2 Average roughness (um) Ra 14 4,3 3,4 5,2 0,2 1,1 0,5 Cost relative to drilling 1 9 5 3 30 10 3

Figure 4.13 Deviations, surface finishes and relative costs of 25mm diameter holes produced by a variety of manufacturing processes

Figure 4.13 Deviations, surface finishes and relative costs of 25mm diameter holes produced by a variety of manufacturing processes whereas the variability for precision-machined surfaces is in the order of microns. The table also shows the cost of producing the processes relative to drilling. In general, precision holes are more expensive to produce than rough-machined ones. One of the reasons for this is that higher quality machine tools are required to produce precision components. Typically, they would have more accurate bearings and have a more rigid and stable structure.

Figure 4.13 shows that holes can never be perfect cylinders. This then begs the question of what the real diameter of a hole is. The ovality shows that it varies in one direction in comparison to a perpendicular direction. The various drawings of components shown above (Figures 4.1, 4.2,4.3 and 4.6) are therefore ideal representations of components since in reality all the component outlines drawn should be wavy lines since in reality there is always some variability. The result is that if one considers a hole, for example, it is impossible to state a single value for the diameter. However, it is possible to state maximum and minimum values that cover the range of the variability. Thus, when dimensioning any feature, two things must be provided: the basic nominal dimension and the permitted variability. This will be the nominal dimension plus a tolerance.