Принципы нанометрологии (1027623), страница 52
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Note that kurtosis cannot differentiate between a peak and a valley.8.2.8 Spacing parameters8.2.8.1 Mean width of the profile elements, RSmThe RSm parameter is the mean value of the profile element widths withina sampling length (see Figure 8.9). In other words, this parameter is theaverage value of the length of the mean line section containing a profile peakand adjacent valley. This parameter requires height and spacing discrimination. If these values are not specified then the default height discrimination used is 10 % of Rz. The default spacing discrimination is 1 % of thesampling length and both of these conditions must be met.8.2.9 Curves and related parametersThe profile parameters described so far have resulted in a single number(often with a unit) that describes some aspect of the surface.
Curves andrelated parameters give much more information about the surface fromwhich, often, functional information can be gained [7]. All curves and relatedparameters are defined over the evaluation length rather than the samplinglength.8.2.9.1 Material ratio of the profileThe material ratio of the profile is the ratio of the bearing length to theevaluation length. It is represented as a percentage.
The bearing length is theFIGURE 8.9 Width of profile elements.Surface profile characterizationsum of the section lengths obtained by cutting the profile with a line (slicelevel) drawn parallel to the mean line at a given level. The ratio is assumed tobe 0 % if the slice level is at the highest peak, and 100 % if it is at the deepestvalley. Parameter Rmr(c) determines the percentage of each bearing lengthratio of a single slice level or nineteen slice levels that are drawn at equalintervals within Rt respectively.8.2.9.2 Material ratio curveThe material ratio curve (formally known as the Abbot-Firestone or bearingratio curve) is the curve representing the material ratio of the profile asa function of level.
By plotting the bearing ratio at a range of depths in theprofile, the way in which the bearing ratio varies with depth can be easily seenand provides a means of distinguishing different shapes present on theprofile. The definition of the bearing area fraction is the sum of the lengths ofindividual plateaux at a particular height, normalized by the total assessmentlength, and is the parameter designated Rmr (see Figure 8.10). Values of Rmrare sometimes specified on drawings; however, such specifications can leadto large ambiguities if the bearing area curve is referred to the highest andlowest points on the profile.Many mating surfaces requiring tribological functions are usuallyproduced with a sequence of machining operations.
Usually the first operation establishes the general shape of the surface with a relatively coarsefinish, and further operations refine this finish to produce the propertiesrequired by the design. This sequence of operations will remove the peaks ofthe original process but the deep valleys will be left untouched.
This processleads to a type of surface texture that is referred to as a stratified surface. Theheight distributions will be negatively skewed, therefore making it difficultfor a single average parameter such as Ra to represent the surface effectivelyfor specification and quality-control purposes. A honed surface is a goodexample of a stratified surface.FIGURE 8.10 Material ratio curve.225226C H A P T ER 8 : Surface topography characterization8.2.9.3 Profile section height difference, RdcThe profile section height difference is the vertical distance between twosection levels of given material ratio.8.2.9.4 Relative material ratio, RmrThe relative material ratio is the material ratio determined at a profile sectionlevel Rdc, and related to a reference, C0, where C1 ¼ C0 Rdc and C0 ¼C(Rmr0).
Rmr refers to the bearing ratio at a specified height (seeFigure 8.11). A way of specifying the height is to move over a certainpercentage (the reference percentage) on the bearing ratio curve and then tomove down a certain depth (the slice depth). The bearing ratio at the resultingpoint is Rmr.
The purpose of the reference percentage is to eliminate spuriouspeaks from consideration – these peaks tend to wear off in early part use. Theslice depth then corresponds to an allowable roughness or to a reasonableamount of wear.8.2.9.5 Profile height amplitude curveThe profile height amplitude curve is defined as the sample probabilitydensity function of the ordinate, z(x), within the evaluation length. Theamplitude distribution curve is a probability function that gives the probability that a profile of the surface has a certain height, at a certain position.The curve has the characteristic bell shape like many probability distributions (see Figure 8.12).
The curve tells the user how much of the profile lies ata particular height, in a histogram sense.The profile height amplitude curve illustrates the relative total lengths overwhich the profile graph attains any selected range of heights above or below themean line. This is illustrated in Figure 8.13. The horizontal lengths of theFIGURE 8.11 Profile section level separation.Surface profile characterizationFIGURE 8.12 Profile height amplitude distribution curve.FIGURE 8.13 Amplitude distribution curve.profile included within the narrow band dz at a height z are a, b, c, d and e. Byexpressing the sum of these lengths as a percentage of the evaluation length,a measure of the relative amount of the profile at a height z can be obtained.Figure 8.13 is termed the amplitude distribution at height z.
By plotting densityagainst height the amplitude density distributed over the whole profile can beseen. This produces the amplitude density distribution curve.8.2.10 Profile specification standardsThere are nine ISO specification standards relating to the measurement andcharacterization of surface profile. These standards only cover the use of227228C H A P T ER 8 : Surface topography characterizationstylus instruments.
The details of the standards are presented in [8] and theircontent is briefly described in this section. It should be noted that the currentISO plan for surface texture is that the profile standards will become a sub-setof the areal standards (see section 8.3.4). Whilst the basic standards anddetails will probably not change significantly, the reader should keep abreastof the latest developments in standards.ISO 3274 [15] describes a typical stylus instrument and its metrologicalcharacteristics. ISO 4287 [9] presents the definitions of the surface profileparameters (i.e.
the P, W and R parameters – see section 8.2.3) and how tocalculate the parameters. ISO 4288 [12] describes the various default values,and basic rules and procedures for surface texture profile analysis. ISO 11562[10] describes the phase correct Gaussian filter that is applied for the variouscut-off filters used for surface profile analysis. ISO 12179 [16] presents themethods for calibrating contact stylus instruments for profile measurementand ISO 5436 part 1 [17] describes the artefacts that are used to calibratestylus instruments (see section 6.10.2). ISO 5436 part 2 [18] describes theconcepts and use of software measurement standards (see section 6.13). ISO1302 [19] presents the rules for the indication of surface texture in technicalproduct documentation such as drawings, specifications, contracts andreports.Note that there are no specification standards that relate to themeasurement of surface profile using optical instruments.
However, in manycases where a profile can be mathematically extracted from an areal opticalscan, the profile characterization and analysis standards can be applied. It isimportant, however, to understand how the surface data are filtered, especially when trying to compare contact stylus and optical results.There are no methods specified in ISO standards on how to remove formprior to surface texture analysis.
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