Richard Leach - Fundamental prinsiples of engineering nanometrology (778895), страница 53
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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). 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].
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