Принципы нанометрологии (1027623), страница 54
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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.
uniformity of the texture aspect. The Str parameter can be defined as theratio of the fastest to slowest decay to correlation length, 0.2, of the surfaceACF and is given bypffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffimin tx2 þ ty 2pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi :Str ¼(8.17)max tx2 þ ty 2In principle, Str has a value between 0 and 1. Larger values, say Str > 0.5,indicate uniform texture in all directions, i.e. for no defined lay.
Smallervalues, say Str < 0.3, indicate an increasingly strong directional structure orlay. It is possible that the slowest decay ACF for some anisotropic surfacesnever reaches 0.2 within the sampling area. In this case, Str is invalid.The Str parameter is useful in determining the presence of degree of lay inany direction. For applications where a surface is produced by multipleprocesses, Str may be used to detect the presence of underlying surfacemodifications.8.3.6.3 Areal hybrid parametersThe hybrid parameters are parameters based upon both amplitude andspatial information.
They define numerically hybrid topography propertiessuch as the slope of the surface, the curvature of outliers and the interfacialarea. Any changes that occur in either amplitude or spacing may have aneffect on the hybrid property. The hybrid parameters have particular relevance to contact mechanics, for example, the friction and wear betweenbearing surfaces.8.3.6.3.1 Root mean square gradient of the scale-limitedsurface, SdqThe Sdq parameter is defined as the root mean square of the surface gradientwithin the definition area,vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu ð ð " #u1vzðx; yÞ 2vzðx; yÞ 2uSdq ¼ tþdxdy :Avxvy(8.18)AThe Sdq parameter characterizes the slopes on a surface and may be usedto differentiate surfaces with similar value of Sa.
The Sdq parameter is usefulfor assessing surfaces in sealing applications and for controlling surfacecosmetic appearance.Areal surface texture characterization8.3.6.3.2 Developed interfacial area ratio of the scale-limitedsurface, SdrThe Sdr parameter is the ratio of the increment of the interfacial area of thescale-limited surface within the definition area over the definition area and isgiven by0vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13"2 2 #ðð uu1vzðx; yÞvzðx; yÞSdr ¼ 4 @t 1 þþ 1Adxdy 5:Avxvy2(8.19)AThe Sdr parameter may further differentiate surfaces of similar amplitudes and average roughness.
Typically Sdr will increase with the spatialcomplexity of the surface texture independent of changes in Sa. The Sdrparameter is useful in applications involving surface coatings and adhesion,and may find relevance when considering surfaces used with lubricants andother fluids. The Sdr parameter may be related to the surface slopes and thusfinds application related to how light is scattered from a surface.8.3.6.4 Functions and related parametersThe functions and related parameters are an areal extension of the profilecurves and parameters described in section 8.2.9.8.3.6.4.1 Areal material ratio of the scale limited surfaceThis is a function representing the areal material ratio of the scale-limitedsurface as a function of height.
The related parameters are calculated byapproximating the areal material ratio curve by a set of straight lines. Theparameters are derived from three sections of the areal material ratio curve:the peaks above the mean plateau, the plateaux themselves and the valleysbetween plateaux.8.3.6.4.2 Areal material ratio of the scale-limited surface, Smc(c)The areal material ratio is the ratio of the material at a specified height, c, tothe evaluation area expressed as a percentage (see Figure 8.15).
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