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It is usually greater than the evaluation length due to theneed to allow a short over-travel at the start and end of the measurement toallow mechanical and electrical transients to be excluded from themeasurement and to allow for the effects of edges on the filters.8.2.3 Profile filteringFiltering plays a fundamental role in surface texture analysis. In this context,it is any means (usually electronic or computational, but sometimesmechanical) for selecting for analysis a range of structure in the total profilethat is judged to be that of significance to a particular situation.
Alternatively,it may be thought of as a means of rejecting information considered irrelevant, including, for example, attempts to reduce the effect of instrumentnoise and imperfections. Filters select (or reject) structure according to itsscale in the x axis, that is in terms of wavelengths or spatial frequencies. Afilter that rejects short wavelengths while retaining longer ones is calleda low-pass filter since it preserves (or lets pass) the low frequencies. A highpass filter preserves the shorter-wavelength features while rejecting longerones. The combination of a low-pass and a high-pass filter to selecta restricted range of wavelengths with both high regions and low regionsrejected is called a band-pass filter. The attenuation (rejection) of a filtershould not be too sudden else we might get very different results from213214C H A P T ER 8 : Surface topography characterizationsurfaces that are almost identical apart from a slight shift in the wavelengthof a strong feature.
The wavelength at which the transmission (and so alsothe rejection) is 50 % is called the cut-off of that filter (note that this definition is specific to the field of surface texture).The transmission characteristics of a filter are determined by its weightingfunction. The weighting function, standardized in ISO 11562 [7,10], in theform of a Gaussian probability function is described mathematically by x 21expsðxÞ ¼(8.1)alalwhere a is a constant designed to provide 50% transmission at a cut-offwavelength of l, and is equal torffiffiffiffiffiffiffiffiln2z 0:4687:(8.2)pThe filter effect of the weighting function, s(x), is exclusively determinedby the constant a.
Filtering produces a filter mean line which results from theconvolution of the measured profile with the weighting.A surface profile filter separates the profile into long wave and short wavecomponents (see Figure 8.1). There are three filters used by instruments formeasuring roughness, waviness and primary profiles:ls profile filter. This is the filter that defines where the intersectionoccurs between the roughness (see section 8.2.3.2) and shorter-wavelength components present in a surface;lc profile filter. This is the filter that defines where the intersection occursbetween the roughness and waviness (see section 8.2.3.3) components;lf profile filter. This is the filter that defines where the intersectionoccurs between the waviness and longer wavelength components presentin a surface.FIGURE 8.1 Separation of surface texture into roughness, waviness and profile.Surface profile characterizationAlmost all modern instruments and software packages now employa Gaussian filter according to [10].
However, older instruments may employother forms of filter, for example the 2RC filter [7,11]. It is important to beaware of the type of filter used by an instrument and care should be takenwhen comparing data from such instruments to those from moderninstruments.8.2.3.1 Primary profileThe primary profile is defined as the total profile after application of the shortwavelength (low-pass) filter, with cut-off, ls, but including the effect of thestandardized probe (see section 6.6.1).
Ultimately the finite size of the styluslimits the rejection of very short wavelengths and in practice this mechanicalfiltering effect is often used by default for the ls filter (similar arguments canbe used throughout this chapter for optical instruments; for example, theequivalent to a finite stylus radius for an optical instrument will be eitherthe spot size, diffraction limit or pixel spacing). Since styli vary and since theinstrument will introduce vibration and other noise into the profile signalthat has equivalent wavelengths shorter than the stylus dimensions, the bestpractice is always to apply ls filtration upon the total profile.
Figure 8.2relates the primary to the roughness and waviness profiles.8.2.3.2 Roughness profileThe roughness profile is defined as the profile derived from the primaryprofile by suppressing the long-wave component using a long-wavelength(high-pass) filter, with cut-off, lc. The roughness profile is the basis for theevaluation of the roughness profile parameters.
Note that such evaluationautomatically includes the use of the lf profile filter, since it derives from theprimary profile.FIGURE 8.2 Primary (top), waviness (middle) and roughness (bottom) profiles.215216C H A P T ER 8 : Surface topography characterization8.2.3.3 Waviness profileThe waviness profile is derived by the application of a band-pass filter to selectthe surface structure at rather longer wavelengths than the roughness. Filter lfsuppresses the long-wave component (profile component) and filter lcsuppresses the short-wave component (roughness component). The wavinessprofile is the basis for the evaluation of the waviness profile parameters.8.2.4 Default values for profile characterizationISO 4287 [9] and ISO 4288 [12] define a number of default values for variousparameters that are used for surface profile characterization.
Unless otherwise stated these default values apply. For example, unless otherwise stated,five sampling lengths are used to calculate the roughness parameters.Table 8.1 shows the relationship between cut-off wavelength, tip radius andmaximum sampling spacing.When a component is manufactured from a drawing the surface texturespecification will normally include the sampling length for measuring thesurface profile. The most commonly used sampling length is 0.8 mm. However,when no indication is given on the drawing the user will require a means ofselecting the most appropriate value for his or her particular application.
Thesampling length should only be selected after considering the nature of thesurface texture and which characteristics are required for the measurement.8.2.5 Profile characterization and parametersA surface texture parameter, be it profile or areal, is used to give the surfacetexture of a part a quantitative value.
Such a value may be used to simplifythe description of the surface texture, to allow comparisons with other parts(or areas of a part) and to form a suitable measure for a quality system.Surface texture parameters are also used on engineering drawings toTable 8.1Relationship between cut-off wavelength, tip radius (rtip)and maximum sampling spacing [12]lc (mm)ls (mm)Roughness cut-offwavelength ratio lc/lsrtip max (mm)Maximum samplingspacing (mm)0.080.250.82.582.52.52.5825301003003003002225100.50.50.51.55Surface profile characterizationformally specify a required surface texture for a manufactured part. Someparameters give purely statistical information about the surface texture andsome can describe how the surface may perform in use, that is to say, itsfunctionality.All the profile parameters described below (and the areal parameters – seesection 8.3.5) are calculated once the form has been removed from themeasurement data.
The ideas of ‘peaks’ and ‘valleys’ are important inunderstanding and evaluating surfaces. Unfortunately it is not always easy todecide what should be counted as a peak. To overcome the confusion causedby early non-coordinated attempts to produce parameters reflecting thisdifference, the modern standards introduce an important specific concept:the profile element consisting of a peak and a valley event.
Associated withthe element is a discrimination that prevents small, unreliable measurementfeatures from affecting the detection of elements.A profile element is a section of a profile from the point at which it crossesthe mean line to the point at which it next crosses the mean line in the samedirection (for example, from below to above the mean line). The part ofa profile element that is above the mean line, i.e. the profile from when itcrosses the mean line in the positive direction until it next crosses the meanline in the negative direction. It is possible that a profile could have a veryslight fluctuation that takes it across the mean line and almost immediatelyback again. This is not reasonably considered as a real profile peak or profilevalley.
To prevent automatic systems from counting such features, onlyfeatures larger than a specified height and width are counted. In the absenceof other specifications, the default levels are that the height of a profile peaks(valley) must exceed 10 % of the Rz, Wz or Pz parameter value and that thewidth of the profile peak (valley) must exceed 1 % of the sampling length.Both criteria must be met simultaneously.8.2.5.1 Profile parameter symbolsThe first capital letter in the parameter symbol designates the type of profileunder evaluation.
For example, Ra is calculated from the roughness profile, Wafrom the waviness profile and Pa from the primary profile. In the descriptiongiven below only the roughness profile parameters are described, but thesalient points apply also to the waviness and primary profile parameters.8.2.5.2 Profile parameter ambiguitiesThere are many inconsistencies in the parameter definitions in ISO 4287 [9].Some parameter definitions are mathematically ambiguous and thedescription of the W parameters is open to misinterpretation. Perhaps themost ambiguous parameter is RSm, where a different value for the parameter217218C H A P T ER 8 : Surface topography characterizationcan be obtained purely by reversing the direction of the profile. Theseambiguities are described elsewhere [13] and, in the case of RSm, a nonambiguous definition has been proposed [14].8.2.6 Amplitude profile parameters (peak to valley)8.2.6.1 Maximum profile peak height, RpThis parameter is defined as the largest profile peak height within thesampling length, i.e.
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