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It has been easily extrapolatedfrom the linear profile Gaussian filter standard into the areal filter byinstrument manufacturers for at least a decade and allows users to separatewaviness and roughness in surface measurement.For surfaces produced using a range of manufacturing methods, theroughness data have differing degrees of precision that contains some verydifferent observations or outliers. In this case, a robust Gaussian filter (basedon the maximum likelihood estimation) can be used to suppress the influence of the outliers.
The robust Gaussian filter can also be found in mostinstrument software.It should be noted that the Gaussian filter is not applicable for all functional aspects of a surface, for example, in contact phenomena, where theupper envelope of the surface is more relevant. A standardized framework forfilters has been established, which gives a mathematical foundation for231232C H A P T ER 8 : Surface topography characterizationfiltration, together with a toolbox of different filters. Information concerningthese filters will soon be published as a series of technical specifications (ISO/TS 16610 series [27]), to allow metrologists to assess the utility of the recommended filters according to applications.
So far only Gaussian filters havebeen published, but the toolbox will contain the following classes of filters:Linear filters: the mean line filters (M-system) belong to this class andinclude the Gaussian filter, spline filter and the spline-wavelet filter;Morphological filters: the envelope filters (E-system) belong to this classand include closing and opening filters using either a disk or a horizontal line;Robust filters: filters that are robust with respect to specific profilephenomena such as spikes, scratches and steps. These filters include therobust Gaussian filter and the robust spline filter;Segmentation filters: filters that partition a profile into portionsaccording to specific rules. The motif approach belongs to this class and hasnow been put on a firm mathematical basis.Filtering is a complex subject that will probably warrant a book of its ownfollowing the introduction of the ISO/TS 16610 series [27] of specificationstandards.
The user should consider filtering options on a case-by-case basisbut the simple rule of thumb is that if you want to compare two surfacemeasurements, it is important that both sets use the same filtering methodsand nesting indexes (or that appropriate corrections are applied). Table 8.2presents the default nesting indices in ISO 25178 part 3 [26]. The usershould consult the latest version of ISO 25178 part 3 because at the time ofwriting there is still debate in the standards committees as to the values inTable 8.2.8.3.3 Areal specification standardsThe areal specification standards are at various stages of development. Theplan is to have the profile standards (see section 8.2.10) as a subset of theareal standards (with appropriate re-numbering).
Hence, the profile standards will be re-published after the areal standards (with some omissions,ambiguities and errors corrected) under a new numbering scheme that isconsistent with that of the areal standards. All the areal standards are part ofISO 25178, which will consist of at least the following parts, under thegeneral title Geometrical product specification (GPS) – Surface texture: Areal:-Part 1: Areal surface texture drawing indications-Part 2: Terms, definitions and surface texture parameters [25]Areal surface texture characterizationTable 8.2Relationships between nesting index value, S-filter nesting index,sampling distance and ball radiusNesting indexvalue(F-operator/L-filter) (mm)S-filter nestingindex (mm)Max. samplingdistance (mm)Max.
ballradius (mm).0.10.20.250.50.81.02.02.55.08.01020255080100..1.02.02.55.08.010202550801002002505008001000..0.30.60.81.52.53.06.08.01525306080150250300..0.81.52.04.06.08.01520406080150200400600800.-Part 3: Specification operators [26]-Part 4: Comparison rules-Part 5: Verification operators-Part 6: Classification of methods for measuring surface texture [28]-Part 70: Measurement standards for areal surface texturemeasurement instruments-Part 71: Software measurement standards [29]-Part 72: Software measurement standards – XML file format-Part 601: Nominal characteristics of contact (stylus) instruments [30]-Part 602: Nominal characteristics of non-contact (confocal chromaticprobe) instruments [31]233234C H A P T ER 8 : Surface topography characterization-Part 603: Nominal characteristics of non-contact (phase-shiftinginterferometric microscopy) instruments [32]-Part 604: Nominal characteristics of non-contact (coherence scanninginterferometry) instruments [33]-Part 605: Nominal characteristics of non-contact (point autofocus)instruments-Part 606: Nominal characteristics of non-contact (variable focus)instruments-Part 701: Calibration and measurement standards for contact (stylus)instruments [34]-Part 702: Calibration and measurement standards for non-contact(confocal chromatic probe) instruments-Part 703: Calibration and measurement standards for non-contact(phase-shifting interferometric microscopy) instruments-Part 704: Calibration and measurement standards for non-contact(coherence scanning interferometry) instruments-Part 705: Calibration and measurement standards for non-contact(point autofocus) instruments-Part 706: Calibration and measurement standards for non-contact(variable focus) instrumentsThe American National Standards Institute has also published specification standards [35] that include some areal analyses (mainly fractalbased).8.3.4 Unified coordinate system for surface texture and formSurface irregularities have traditionally been divided into three groupsloosely based on scale [36]: (i) roughness, generated by the materialremoval mechanism such as tool marks; (ii) waviness, produced byimperfect operation of a machine tool; and (iii) errors of form, generated byerrors of a machine tool, distortions such as gravity effects, thermal effects,set-up, etc.
This grouping gives the impression that surface texture shouldbe part of a coherent scheme with roughness at the smaller scale and errorsof form at the larger scale.The primary definition of surface texture has, until recently, been basedon the profile (ISO 4287 [9]). To ensure consistency of the irregularities in theAreal surface texture characterizationmeasured profile, the direction of that profile was specified to be orthogonalto the lay (the direction of the prominent pattern). This direction is notnecessarily related to the datum of the surface, whereas errors of form, suchas straightness, are always specified parallel to a datum of the surface [37].Hence, profile surface texture and profile errors of form usually have differentcoordinate systems and do not form a coherent specification.This situation has now changed since the draft standardization of arealsurface methods, in which the primary definition of surface texture ischanged from one being based on profiles to one based on areal surfaces.
Thismeans that there is no consistency requirement for the coordinate system tobe related to the lay. Therefore, a unified coordinate system has beenestablished for both surface texture and form measurement [26]. Surfacetexture is now truly part of a coherent scheme, with surface texture at thesmaller scale. The system is part of what is referred to as the geometricalproduct specification (GPS).8.3.5 Areal parametersThere are two main classes of areal parameters:-Field parameters – defined from all the points on a scale-limitedsurface;-Feature parameters – defined from a subset of predefined topologicalfeatures from the scale-limited surface.A further class of areal parameters are those based on fractal analysis.Fractal parameters are essentially field parameters but are given their ownsection in this book as they have certain distinguishing characteristics.Some examples of the use of areal parameters can be found in [38] for thetreatment of steel surfaces, [39] for the characterization of dental implants,[40] for the monitoring of milling tool wear and [41] for the analysis ofbiofilms.8.3.6 Field parametersThe field or S- and V-parameter set has been divided into height, spacing,hybrid, functions and related parameters, and one miscellaneous parameter.A great deal of the physical arguments discussed for the profile parametersalso apply to their areal equivalents, for example, Rsk and Ssk.
Therefore,when reading about the areal parameters for the first time, it would beprudent to become acquainted with the description of its profile equivalent(where one exists).235236C H A P T ER 8 : Surface topography characterization8.3.6.1 Areal height parameters8.3.6.1.1 The root mean square value of the ordinates, SqThe Sq parameter is defined as the root mean square value of the surfacedepartures, z(x, y), within the sampling area,vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu1ð ðuSq ¼ tz2 ðx; yÞdxdyA(8.11)Awhere A is the sampling area, xy. Note that equation (8.11) is for a continuous z(x, y) function and the same philosophy applies when converting toa sampled definition as in section 8.2.7.1.8.3.6.1.2 The arithmetic mean of the absolute height, SaThe Sa parameter is the arithmetic mean of the absolute value of the heightwithin a sampling area,ð1 dxdy:zðx;yÞ(8.12)Sa ¼AAThe Sa parameter is the closest relative to the Ra parameter; however,they are fundamentally different and caution must be exercised when theyare compared.
Areal, or S-parameters, use areal filters whereas profile, or Rparameters, use profile filters.8.3.6.1.3 Skewness of topography height distribution, SskSkewness is the ratio of the mean cube value of the height values and thecube of Sq within a sampling area, ðð1 13Ssk ¼z x; y dxdy :Sq3 A(8.13)A8.3.6.1.4 Kurtosis of topography height distribution, SkuThe Sku parameter is the ratio of the mean of the fourth power of the heightvalues and the fourth power of Sq within the sampling area, ðð1 14Sku ¼z ðx; yÞdxdy :Sq4 AA(8.14)Areal surface texture characterization8.3.6.1.5 The maximum surface peak height, SpThe Sp parameter is defined as the largest peak height value from the meanplane within the sampling area.8.3.6.1.6 The maximum pit height of the surface, SvThe Sv parameter is defined as the largest pit or valley depth from the meanplane within the sampling area.8.3.6.1.7 Maximum height of the surface, SzThe Sz parameter is defined as the sum of the largest peak height value andlargest pit or valley depth value within the sampling area.8.3.6.2 Areal spacing parametersThe spacing parameters describe the spatial properties of surfaces.
Theseparameters are designed to assess the peak density and texture strength.These parameters are particularly useful in distinguishing between highlytextured and random surface structures.8.3.6.2.1 The auto-correlation length, SalFor the Sal parameter it is first necessary to define the auto-correlationfunction (ACF) as the correlation between a surface and the same surfacetranslated by (tx, ty), given byÐÐzðx; yÞzðx tx; y tyÞdydyAÐÐACFðtx; tyÞ ¼:(8.15)zðx; yÞzðx; yÞdxdyAThe auto-correlation length, Sal, is then defined as the horizontaldistance of the ACF(tx, ty) which has the fastest decay to a specified value s,with 0 s < 1.
The Sal parameter is given byqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiSal ¼ min tx2 þ ty 2 :(8.16)For all practical applications involving relatively smooth surfaces, thevalue for s can be taken as 0.2 [26], although other values can be used and willbe subject to forthcoming areal specification standards. For an anisotropicsurface Sal is in the direction perpendicular to the surface lay. A large value ofSal denotes that that surface is dominated by low spatial frequency components, while a small value for Sal denotes the opposite case.The Sal parameter is a quantitative measure of the distance along thesurface by which one would find a texture that is statistically different fromthat at the original location.237238C H A P T ER 8 : Surface topography characterization8.3.6.2.2 Texture aspect ratio of the surface, StrThe texture aspect ratio, Str, is a parameter used to identify texture strength,i.e.
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