CAPÍTULO 3. RESULTADOS DE LA APLICACIÓN DE LA HERRAMIENTA
3.1 Presentación de la herramienta informática
The challenge of adequately verifying proper operation is greatly eased by the use of small modules that are used sequentially.
Running many trials of basic stylus shapes over simple surfaces, including single or clustered delta functions, rapidly identifies major bugs and increases confidence that no subtle errors remain. Just one example is given here, Figure 5.2. The pattern of a flat scanning across a noise-free sinusoidal prism is readily recognizable.
Figure 5.2 Scanning across a noise-free sinusoidal surface
It is also intuitively obvious that the contact pattern on the stylus has a low, uniform count (matching the flat regions on the modified surface) but there are higher values at the leading and trailing corner points (flank contact) and occasional multi-point contacts.
5.3. Kinematic and Threshold Models
Figure 5.3a shows a small map (128 by 128 points on a 0.2 µm sample grid) taken by atomic force microscopy from a typical ground steel surface. The fine detail has both sharply varying and plateau-like regions. For clarity of illustration, Figure 3b shows the severe effect of applying a ~2 µm square flat stylus (11 by 11 points) under kinematic conditions. The serious distortion is no surprise, with high-points being converted to plateaus, but, even so, the general structure is preserved: e.g., peak-to-valley amplitude has reduced merely from 758 nm to 746 nm.
A typical profilometer set up to measure finish ground surfaces might have an effective noise floor of the order of 10 nm to 20 nm peak. Its digitized resolution might typically be 1 nm to 10 nm.
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Figure 5.3: Modification of a surface detail by a 2 mm flat: (a) AFM image; (b) simulation
Alternatively, noise-related issues could be handled in terms of a fraction, say 0.5% to 0.1%, of full range (maybe a few tens of micrometres, typically). Hence, thresholds from 5 nm to 50 nm (for deliberate over-emphasis) seem relevant for study here. The simplest form of thresholding is roughly equivalent to ideally pressing the probe into the surface. For the illustrations used here the modified surfaces are largely unchanged other than a slight vertical offset. Interest lies in how the shift interacts with additional surface features to alter the probe contact patterns.
As an elementary illustration, Figure 5.4 shows the effects on the position of contacts on the probe when adding a 50 nm threshold to the case shown in Figure 5.3b.
For clarity, the maps show simply the presence or absence of contact at each point. Within the bounds of this flat probe, the actual area detected as ‘in contact’ is then highly analogous to the operation of the well-known bearing area. Note, though, that the pattern varies as the probe scans over the whole surface and more complex patterns will arise with more realistic probe shapes.
Centring the probe at (61, 66) – using ordinates, not dimensions, for simulations – puts it on a steep flank and kinematic contact is at one corner. Even 50 nm threshold causes only slight growth in the primary contact and the first signs of a second one nearby.
By contrast, (61, 66) and (109, 120) are in plateau regions, they show large contact growth, dominated by a single region and occasional secondaries.
In both cases, the kinematic contact is far from the centre of the region. Even at this small scale, growing the region develops a shape that correlates with the surface lay.
In all three cases, the ‘true’ contact is significantly displaced laterally from the nominal line of action of the probe, a result also seen elsewhere (Dowidar and
Figure 5.4: Positions of kinematic and 50 nm threshold contacts on a flat probe for three selected places from Figure 5.3b
Chetwynd, 2002) that has implications for measurement uncertainty of all topographic parameters except the simplest amplitude measures.
Although Figure 5.4 shows only the regions of contact, the intensity of contact at each point is of physical interest. One simple indication (not shown here) of this is to plot the probe maps in terms of how far each point on the probe would have encroached into the original surface to settle at the specified height relative to the kinematic condition. This gives, for example, a crude indication of the stress intensities associated with each contact, and so of its likely practical significance in defining the reported surface height of a real instrument.
As a further experiment, figure 5.5 shows an ideal conical stylus and a map indicating its contact against an ideal flat. The initial geometric contact is a single point.
With a threshold, all surface points sufficiently close to the tip are considered to be in contact: a large value generates a symmetrical patch of contact. Here, we get effectively the same image as from an ideal indenter into a plastic material.
Figure 5.7 shows just the tip of the 10X10 µm conical stylus and contact with a flat using a much smaller threshold. The basic behavior is the same, but resolution limits within the geometry become apparent.
Figure 5.7: (a) Conical shape Stylus 10x10 µm (b) Map of contact points with 23nm threshold
Figure 5.8 shows a 20x20 µm small map (64 by 64 points on a 0.2 µm sample grid) taken by atomic force microscopy (AFM) from a typical ground steel surface. The fine detail has both sharply varying and plateau-like regions.
Figure 5.9 shows the stylus in (figure 5.7a) contacting local features of ground surface figure 5.8. Again using heavy threshold for clarity, key observations (fig 5.9b) are that the initial contact is not central and the patch grows asymmetrically, eventually picking out the major structures of the surface.
The total local height variation over this 10 µm by 10 µm is about 1000 nm, so thresholding to a few percent of height suggests real working simulations should be perhaps 10-20 nm.
To measure such a surface we might expect to use an instrument range of perhaps 5000 nm, with inherent noise of up to 1% full scale. Thus thresholding to a few tens of nanometers is also appropriate for modeling noise sensitivity.
For the particular condition illustrated, the map remains essentially the single point (in blue at Figure 5.9b) for thresholds as high as 40 nm; there is a single, real peak
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Figure 5.9: 3D ground surface 10x10 µm (b) Map of contact with 149 nm threshold (c) with 40 nm threshold
that is likely to dominate local contact behavior at the scale of this tip. Figure 5.9c shows the threshold up to 40 nm leaves single point, which is the first contact. Comparing figure 5.9, and figure 5.10 (after moving the surface across and putting the tip in the middle), by applying heavy threshold, the pattern is very heavy threshold, and the pattern is very similar. It can be concluded that here is only dominant peak and it is not noise sensitive. In figure 5.9, the lateral error is about 1.5 um. It also showed that here (tip radius fairly large) little change in reported contact under local movements. (i.e. not much different to flat stylus in actual behavior).
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Figure 5.10: 3D Ground surface 8X8µm with tip at the centre. (b) Map of contact with149 nm threshold.