Принципы нанометрологии (1027623), страница 56
Текст из файла (страница 56)
By inverting the surface so that peaks become pits, a similarprocess will establish the connection between peaks, saddle points and thechange tree.There are three types of change tree:-the full change tree (see Figure 8.20), which represents therelationships between critical points in the hills and dales;-the dale change tree (see Figure 8.21), which represents therelationships between pits and saddle points;-the hill change tree (see Figure 8.22), which represents the relationshipbetween peaks and saddle points.The dale and hill change trees can be calculated from the full change tree.FIGURE 8.20 Full change tree for Figure 8.19.Areal surface texture characterizationFIGURE 8.21 Dale change tree for Figure 8.19.FIGURE 8.22 Hill change tree for Figure 8.19.247248C H A P T ER 8 : Surface topography characterizationIn practice change trees can be dominated by very short contour lines dueto noise and insignificant features on a surface (this is the reason thata simulated surface was used at the beginning of this section).
A mechanism isrequired to prune the change tree, reducing the noise but retaining significantfeatures. There are many methods for achieving this pruning operation thatare too complex to be presented here (see [43] for a thorough mathematicaltreatment).
It is expected that the software packages for feature characterization will include pruning techniques. One method stipulated in ISO 25178part 2 [25] is Wolf pruning and details of this methods can be found in [44].8.3.7.3 Step 3 – Significant featuresIt is important to determine the features on a surface that are functionallysignificant and those that are not. For each particular surface function thereneeds to be defined a segmentation function that identifies the significantand insignificant features defined by the segmentation. The set of significantfeatures is then used for characterization. Methods (segmentation functions)for determining significant features are given in Table 8.5. Once again, it isexpected that all these functions will be carried out by the software packagesused for feature characterization.
Various research groups are currentlydeveloping further methods for determining significant features.8.3.7.4 Step 4 – Selection of feature attributesOnce the set of significant features have been determined it is necessary todetermine suitable feature attributes for characterization. Most attributes area measure of the size of features, for example the length or volume ofa feature.
Some feature attributes are given in Table 8.6. Various researchgroups are currently developing further methods for selecting feature attributes and different forms of attribute.Table 8.5Methods for determining significant featuresClass of featureSegmentation functionsSymbolParameter unitsArealFeature is significant if not connected to the edgeat a given heightFeature is significant if not connected to the edgeat a given heightA peak is significant if it has one of the top N Wolfpeak heightsA pit is significant if it has one of the top N Wolf pitheightsClosedTopHeight is given as materialratioHeight is given as materialratioN is an integerBotN is an integerAll–PointAreal, line, pointOpenAreal surface texture characterizationTable 8.6Feature attributesFeature classFeature attributeSymbolArealLocal peak/pit heightVolume of areal featureArea of areal featureCircumference of areal featureLength of lineLocal peak/pit heightLocal curvature at critical pointAttribute takes value of oneLpvhVolSVolEAreaLenglpvhCurvatureCountLinePointAreal, line, point8.3.7.5 Step 5 – Quantification of feature attribute statisticsThe calculation of a suitable statistic of the attributes of the significantfeatures, a feature parameter, or alternatively a histogram of attribute values,is the final part of feature characterization.
Some attribute statistics are givenin Table 8.7. Various research groups are currently developing furthermethods for quantifying feature attribute statistics.8.3.7.6 Feature parametersTo record the results of feature characterization it is necessary to indicate theparticular tools that were used in each of the five steps. An example of how todo this that shows the convention isFC; D; Wolfprune : 5 %; Edge : 60 %; VolE; HistTable 8.7Attribute statisticsAttribute statisticSymbolThresholdArithmetic mean of attribute valueMaximum attribute valueMinimum attribute valueRMS attribute valuePercentage above a specified valueMeanMaxMinRMSPercHistogramSum of attribute valuesSum of all the attribute valuesdivided by the definition areaHistSumDensity––––Value of threshold in units ofattribute–––249250C H A P T ER 8 : Surface topography characterizationwhere FC denotes feature characterization and the next five symbols,delimited by semicolons, are the symbols from the five tables correspondingto the five steps.In sections 8.3.7.6.1 to 8.3.7.6.9 the default value for X is 5 % [26].8.3.7.6.1 Density of peaks, SpdThe density of peaks, Spd, is the number of peaks per unit area,Spd ¼ FC; H; Wolfprune : X %; All; Count; Density:(8.29)8.3.7.6.2 Arithmetic mean peak curvature, SpcThe Spc parameter is the arithmetic mean of the principle curvatures ofpeaks with a definition area,Spc ¼ FC; P; Wolfprune : X %; All; Curvature; Mean:(8.30)8.3.7.6.3 Ten point height of surface, S10zThe S10z parameter is the average of the heights of the five peaks with largestglobal peak height added to the average value of the heights of the five pitswith largest global pit height, within a definition area,S10z ¼ S5p þ S5v:(8.31)8.3.7.6.4 Five point peak height, S5pThe S5p parameter is the average of the heights of the five peaks with largestglobal peak height, within a definition area,S5p ¼ FC; H; Wolfprune : X %; Top : 5; lpvh; Mean:(8.32)8.3.7.6.5 Five point pit height, S5vThe S5v parameter is the average of the heights of the five pits with largestglobal pit height, within a definition area,S5v ¼ FC; D; Wolfprune : X %; Bot : 5; lpvh; Mean:(8.33)8.3.7.6.6 Closed dale area, Sda(c)The Sda(c) parameter is the average area of dales connected to the edge atheight c,SdcðcÞ ¼ FC; D; Wolfprune : X %; Open : c : Area; Mean:(8.34)Fractal methods8.3.7.6.7 Closed hill area, Sha(c)The Sha(c) parameter is the average area of hills connected to the edge atheight c,ShaðcÞ ¼ FC; D; Wolfprune : X %; Open : c; Area; Mean:(8.35)8.3.7.6.8 Closed dale volume, Sdc(c)The Sdc(c) parameter is the average volume of dales connected to the edge atheight c,SdcðcÞ ¼ FC; D; Wolfprune : X %; Open : c; VolE; Mean:(8.36)8.3.7.6.9 Closed hill volume, Shv(c)The Shv(c) parameter is the average of hills connected to the edge at height c,ShvðcÞ ¼ FC; H; Wolfprune : X %; Open : c; VolE; Mean:(8.37)8.4 Fractal methodsFractal methods have been shown to have a strong ability to discriminateprofiles measured from different surfaces and can be related to functionalmodels of interactions with surfaces.
There are many ways of analysingfractal profiles [45]. Fractal parameters utilize information about the heightand the spacing characteristics of the surface, making them hybridparameters. Fractal profiles and surfaces usually have the followingcharacteristics:-they are continuous but nowhere differentiable;-they are not made up of smooth curves, but rather maybe described asjagged or irregular;-they have features that repeat over multiple scales;-they have features that repeat in such a way that they are self-similarwith respect to scale over some range of scales.Many, if not most, measured profiles appear to have the above characteristics over some scale ranges; that is to say that many profiles and surfacesof practical interest may be by their geometric nature more easily describedby fractal geometry rather than by Euclidian geometry.Fractals have some interesting geometric properties.
Most interesting isthat fractal surfaces have geometric properties that change with scale. Peak251252C H A P T ER 8 : Surface topography characterizationand valley radii, inclination of the surface, profile length and surface area, forexample, all change with the scale of observation or calculation.
This meansthat a profile does not have a unique length. The length depends on the scaleof observation or calculation. This property in particular can be effectivelyexploited to provide characterization methods that can be used to modelphenomena that depend on roughness and to discriminate surfaces thatbehave differently or that were created differently. The lack of a unique lengthis the basis for length-scale analysis.Fractals are often characterized by a fractional, or fractal, dimension,which is essentially a measure of the complexity of the surface or profile. Thefractal dimension for a line will be equal to or greater than one and less thantwo. The fractal dimension for a surface will be equal to or greater than twoand less than three. For mathematical fractal constructs, this characterization by fractal dimension can be scale-insensitive [46].
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
