Принципы нанометрологии (1027623), страница 55
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The heightsare taken from the reference plane.8.3.6.4.3 Inverse areal material ratio of the scale-limited surface,Sdc(mr)The inverse areal material ratio is the height, c, at which a given arealmaterial ratio, mr, is satisfied, taken from the reference plane (seeFigure 8.16).239240C H A P T ER 8 : Surface topography characterizationFIGURE 8.15 Areal material ratio curve.8.3.6.4.4 Areal parameters for stratified functional surfaces ofscale-limited surfacesParameters (Sk, Spk, Svk, Smr1, Smr2, Svq and Smq) for stratified functionalsurfaces are defined according to the specification standards for stratifiedsurfaces [22,23].FIGURE 8.16 Inverse areal material ratio curve.Areal surface texture characterization8.3.6.4.5 Void volume, Vv(mr)The volume of voids per unit area for a given material ratio is calculated fromthe material ratio curve,ð 100 %KVvðmrÞ ¼½SdcðmrÞ SdcðqÞdq(8.20)100 % mrwhere K is a constant to convert to millimetres per metre squared. The dalevolume at p material ratio is given byVvv ¼ VvðpÞ(8.21)and the core void volume (the difference in void volume between p and qmaterial ratio) is given byVvc ¼ VvðpÞ VvðqÞ(8.22)where the default values for p (also for Vvv) and q are 10 % and 80 %respectively [26].8.3.6.4.6 Material volume, Vm(mr)The material volume is the volume of material per unit area at a givenmaterial ratio calculated from the areal material ratio curve,ð mrKVmðmrÞ ¼½SdcðqÞ SdcðmrÞdq(8.23)100 % 0where K is defined as in equation (8.20).
The peak material volume at p isgiven byVmp ¼ VmðpÞ(8.24)and the core material volume (or the difference in material volume between pand q material ratio, is given byVmc ¼ VmðqÞ VmðqÞ(8.25)where default values for p (also for Vmp) and q are 10 % and 80 % respectively[26].Figure 8.17 shows the parts of the material ratio curve that are represented byVvv, Vvc, Vmp and Vmc.8.3.6.4.7 Peak extreme height, SxpThe peak extreme height is the difference in height between p and q material ratio,Sxp ¼ SmrðpÞ SmrðqÞ(8.26)where the default values for p and q are 97.5 % and 50 % respectively [26].241242C H A P T ER 8 : Surface topography characterizationFIGURE 8.17 Void volume and material volume parameters.8.3.6.4.8 Gradient density functionThe gradient density function is calculated from the scale-limited surfaceand shows the relative spatial frequencies against the angle of the steepestgradient, a(x, y), and the direction of the steepest gradient, b(x, y), anticlockwise from the x axis, thussffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffivz2 vz2þ(8.27)aðx; yÞ ¼ tan1vyvxand2 3vz6vy 77bðx; yÞ ¼ tan1 6(8.28)4vz5:vx8.3.6.5 Miscellaneous parameters8.3.6.5.1 Texture direction of the scale-limited surface, StdThe texture direction parameter, Std, is the angle, with respect to a specifieddirection, q, of the absolute maximum value of the angular power spectrum.The angular power spectrum for an areal surface would be displayed as a 3Dplot in which the x and y axes represent the various spatial frequencies fora given direction.
The amplitude of the angular power spectrum (displayed onthe z axis) represents the amplitude of the sine wave at a particular spatialAreal surface texture characterizationfrequency direction. The angular power spectrum is found by integrating theamplitudes of each component sine wave as a function of angle.Std is useful in determining the lay direction of a surface relative toa datum by positioning the part in the measuring instrument in a knownorientation. In some applications such as sealing, a subtle change in thesurface texture direction may lead to adverse conditions. Std may also be usedto detect the presence of a preliminary surface modification process (forexample turning), which is to be removed by a subsequent operation (forexample grinding).8.3.7 Feature characterizationTraditional surface texture parameters, i.e. the profile parameters and theareal field parameters, use a statistical basis to characterize the cloud ofmeasured points.
Such parameters, and in particular, profile parameters,were developed primarily to monitor the production process. But, how doesa human assess a surface? We do not usually see field parameter values butpatterns of features, such as hills and valleys, and the relationships betweenthem [5]. Pattern analysis assesses a surface in the same way. By detectingfeatures and the relationships between them it can characterize the patternsin surface texture. Parameters that characterize surface features and theirrelationships are termed feature parameters [42].
Much of the early researchwork on feature parameters stemmed from work in such areas as machinevision and cartography.Feature characterization does not have specific feature parameters definedbut has instead a toolbox of pattern-recognition techniques that can be usedto characterize specified features on a scale-limited surface. The featurecharacterization process defined in ISO 25178 part 2 [25] has five stageswhich are presented below.8.3.7.1 Step 1 – Texture feature selectionThe three main types of surface texture features are areal features, linefeatures and point features (see Table 8.3). It is important to select theappropriate type of surface texture feature to describe the function of thesurface that is being characterized.
The various types of feature will beexplained by example in the following sections.8.3.7.2 Step 2 – SegmentationSegmentation is used to determine regions of the scale-limited surface thatdefine the scale-limited features. The segmentation process consists of firstfinding the hills and dales on the scale-limited surface. This usually results in243244C H A P T ER 8 : Surface topography characterizationTable 8.3Types of scale-limited featuresClass of scale-limited featureType of scale-limited featureSymbolArealHillDaleCourse lineRidgePeakPitSaddle pointHDCRPVSLinePointover-estimation of the surface and so the smaller, or less significant,segments are pruned out to leave a suitable segmentation of the surface.Some criteria of size that can be used to define a threshold for small segmentsto prune out are given in Table 8.4.A surface can be divided into regions consisting of hills and regionsconsisting of dales.
Here a hill is defined as an area from which maximumuphill paths lead in to one particular peak, and a dale is defined as an areafrom which maximum downhill paths lead to one particular pit. By definitionthe boundaries between hills are course lines and the boundaries betweendales are ridge lines. Ridge and course lines are maximum uphill anddownhill paths respectively emanating from saddle points and terminating atpeaks and pits.ISO 25178 part 2 [25] defines a dale as consisting of a single dominant pitsurrounded by a ring of ridge lines connecting peaks and saddle points, anda hill as consisting of a single dominant peak surrounded by a ring of courselines connecting pits and saddle points.
Within a dale or hill there may beother pits or peaks, but they will be insignificant compared to the dominantpit or peak. Figure 8.18 shows a simulated surface and Figure 8.19 shows thecorresponding contour representation displaying all the features describedabove (a simulated surface has been used for reasons described in section8.3.7.2.1).Table 8.4Criteria of size for segmentationCriteria of sizeSymbolThresholdLocal peak/pit height (Wolf pruning – see sectionVolume of hill/dale (at height of connected saddle on change tree)Area of hill/daleCircumference of hill/daleWolfpruneVolSAreaCirc% of SzSpecified volume% of definition areaSpecified lengthAreal surface texture characterizationFIGURE 8.18 Example simulated surface.FIGURE 8.19 Contour map of Figure 8.18 showing critical lines and points.8.3.7.2.1 Change treeA useful way to organise the relationships between critical points in hills anddales, and still retain relevant information, is that of the change tree [36].The change tree represents the relationships between contour lines froma surface.
The vertical direction on the change tree represents the height. Ata given height all individual contour lines are represented by a point that is245246C H A P T ER 8 : Surface topography characterizationpart of a line representing that contour line continuously varying with height.Saddle points are represented by the merging of two or more of these linesinto one. Peaks and pits are represented by the termination of a line.Consider filling a dale gradually with water.
The point where the waterfirst flows out of the dale is a saddle point. The pit in the dale is connected tothis saddle point in the change tree. Continuing to fill the new lake, the nextpoint where the water flows out of the lake is also a saddle point. Again theline on the change tree, representing the contour of the lake shoreline, will beconnected to the saddle point in the change tree. This process can becontinued and establishes the connection between the pits, saddle points andthe change tree.
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