Принципы нанометрологии (1027623), страница 38
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They have an irregular profile in thedirection of the traverse (similar to a ground profile) that repeats in thelongitudinal direction after some number (usually five) of the samplinglengths (see section 8.2.3) for which it is designed. The profile shape isconstant normal to the measuring direction of the artefact.Type E – used to verify the form measuring capability of the instrument orthe straightness of the reference datum slideway (or its equivalent for anoptical instrument).
They come in two sub-groups: type E1 – a sphericaldome-shaped artefact that is characterized by its radius and Pt (see section8.2.6.5), and type E2 – a precision prism characterized by the angles betweenthe surfaces and Pt on each surface.6.10.3 Calibration of areal surface texture measuringinstrumentsISO/FDIS 25178 part 701 [123] describes six types of artefacts that are usedto calibrate all the characteristics of areal surface measuring stylus instruments. Optical instruments will be covered in future ISO specificationstandards, but for now the artefacts described in [123] should be adaptedwhere possible.
Researchers [124,125] have developed a range of prototypeartefacts for calibrating both contact and non-contact areal surface measuringinstruments, and more artefacts are discussed in [114].The six types of artefacts described in ISO/FDIS 25178 part 701 are:Type ER – measurement standards with two or more triangular grooves,which are used to calibrate the horizontal and vertical amplification coefficients of the instrument.
Type ER standards are characterized by depth, d,angle between flanks, a, and the intersection line between their flanks. TypeER artefacts come in three variations:-Type ER1 – two parallel grooves (see Figure 6.29) where themeasurands are the groove spacing, l, and d.-Type ER2 – rectangular grooves (see Figure 6.30) where themeasurands are the spacing between the grooves, l1 and l2, d and theangle between the grooves, q.-Type ER3 – circular grooves (see Figure 6.31) where the measurands arethe diameter of the groove, Df, and d.Type ES – sphere/plane measurement standards (see Figure 6.32) are usedfor calibrating the horizontal and vertical amplification factors, the xy159160C H A P T ER 6 : Surface topography measurement instrumentationFIGURE 6.29 Type ER1 – two parallel groove standard.FIGURE 6.30Type ER2 – rectangulargroove standard.perpendicularity, the response curve of the probing system and the geometryof the stylus.
The measurands are the largest distance of a point of the sphereto the plane P, d, the radius of the sphere, Sr, and the diameter of the circleobtained by the intersection between the sphere and the plane P, Di, given byqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(6.7)Di ¼ 2 Sr2 ðSr dÞ2Calibration of surface topography measuring instrumentsFIGURE 6.31 Type ER3 – circular groove standard.Type CS – contour measurement standards (see Figure 6.33) are usedfor the overall calibration along one horizontal axis of the instrument.The measurands are the radius, R, of the arcs of circle, the distances, l1.ln,between the centres of the circles and/or the summits of the triangles withrespect to the reference plane, and the heights, h1.hn, between the centres ofthe circles and/or the intersections of the flanks of the triangles.Type CG – cross grating standards, which are characterized by the averagepitches in the x and y axes, and the angle between the x and y axes.
Type CGstandards come in two variations:Type CG1 – X/Y crossed gratings (see Figure 6.35), which are used forcalibrating the horizontal amplification coefficients and the xy perpendicularity of the instrument. The measurands are the average pitches in the x andy axes, lx and ly, and the average angle between the x and y axes.Type CG2 – X/Y/Z crossed gratings (see Figure 6.35), which are used forcalibrating the horizontal and vertical amplification coefficients and the xyperpendicularity of the instrument. The measurands are the same as the typeCG1 standards but include the average depth of the flat-bottomed pits, d.Type DT – random topography standards that are composed of a series ofunit sampling areas with pseudo-random surface topography. Type DTmeasurement standards are used for the overall calibration of the measuringinstrument as with the type D profile standards.
Isotropic and periodic surfacesare preferable and at least two by two unit measuring areas are needed. The unit161162C H A P T ER 6 : Surface topography measurement instrumentationFIGURE 6.32 Type ES – sphere/plane measurement standard.measuring area should be functionally closed so that the multiple samplingareas can be cyclic or periodic. The measurands are areal field parameters.6.11 Uncertainties in surface topography measurementThe calculation of uncertainties for surface texture measuring instruments isa very complex task that is often only carried out at the NMIs (see section6.10.1).
The biggest complication when calculating uncertainties in surfacetexture measurement is the contribution of the surface itself. Unlike lesscomplicated measurements, such as displacement, the surface beingUncertainties in surface topography measurementFIGURE 6.33Type CS – contourstandard.FIGURE 6.34 Type CG1 – X/Y crossed grating.measured can have a significant effect on the measurement, either by directlyaffecting the measuring probe, or because the surface texture is so variablethat repeat measurements in different locations on the surface give rise toa high degree of variability.
It is often possible to calculate the instrument163164C H A P T ER 6 : Surface topography measurement instrumentationFIGURE 6.35 Type CG2 – X/Y/Z grating standard.uncertainty, i.e. the uncertainty in measuring either (x, z) for profile or (x, y, z)for areal, but when the effect of the surface is taken into account thisuncertainty value may significantly increase, often in an unpredictablemanner. Where possible the guidelines in the GUM should be applied (seesection 2.9.3) to calculate instrument uncertainties and the effect of thesurface should be considered in as pragmatic a manner as possible. Examplesof methods to calculate the uncertainty in a profile measurement usinga stylus instrument are given in [116] and [117], but the methods are far frommathematically rigorous or applicable in all circumstances.
A rigorousuncertainty is calculated in [126], using the GUM approach, for the use ofa Gaussian profile filter but little work has been carried out for the uncertainty associated with areal parameters [127].When the instrument uncertainty has been calculated it is then oftennecessary to find the uncertainty in a parameter calculation. Once again thisis far from trivial and often the guidelines in the GUM cannot be easilyapplied. The problem is that for roughness parameters, some characteristicsof a roughness measuring instrument have an obvious influence ona roughness parameter, but for others this is highly unclear.
For example, foran Ra value it is obvious that an uncertainty of 1 % in the vertical axiscalibration results in a 1 % uncertainty in the Ra value, but it is far less clearwhat will be the effect if the probe diameter is 5 mm or 10 mm, instead of thestandard 2 mm, or what happens if the cut-off filter is not exactly Gaussian.For a spatial parameter such as RSm, the uncertainty in the vertical directionwill not be significantly relevant, but the x ordinate calibration is essential.Moreover, such effects are surface-dependent; a very fine surface will be moreComparisons of surface topography measuring instrumentssensitive to probe diameter deviations and deviations in the shortwavelength cut-off filter than a surface where most of the undulations arefar within the wavelength band.Experiments [112] and simulations [127–129] were carried out takinginto account the following effects: z axis calibration, x axis calibration, lc cutoff length, ls cut-off length, probe diameter, probe tip angle, probing force,straightness of reference and sampling density.
All these influencing factorshave different effects depending on the parameter and the surface measured.From a number of samples it became obvious that the precise definition of lcand the probe diameter can have larger effects than the z axis calibration, andof course for very smooth surfaces the reference guidance is a major factor.Some parameters such as RSm are very sensitive to many measurementconditions and can easily have a 20 % uncertainty for rough surfaces, whichis hidden when an instrument is only calibrated using sinusoidal artefacts(type C1, see section 6.10.2).So the conclusion of this section is that it is not straightforward tocalculate a rigorous uncertainty value for an instrument for all surfaces andfor all parameters.
Only a pragmatic approach can be applied for a givenmeasurement scenario. At the very least repeated measurements shouldalways be carried out and the standard deviation or the standard deviation ofthe mean quoted.6.12 Comparisons of surface topography measuringinstrumentsMany comparisons of surface topography measuring instruments have beenconducted over the years. The spreads in the results can be quite alarming,especially when comparing contact and non-contact instruments.
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