Revision: Published Date: January ; Status: Superseded By: Superseded By : ASME B; Document Language: Published By: ASME International (ASME). ASME B Surface Texture (Surface Roughness, Waviness, and Lay) By: ASME International (ASME); Page Count: ; ANSI Approved: Yes; DoD. ASME B Ssk. Surface Skewness. ISO /1. ASME B ISO/DIS 2. ASME B Sku. Surface Kurtosis. ANSI B ASME B ISO/DIS.
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Valley Fluid Retention Index.
Dominant Radial Wave Length. The table lists the roughness parameters by their symbol, name, corresponding 2D standard and unit. Before the asne of the roughness parameters we recommend carrying out a slope correction by a 2 nd or 3 rd order polynomial plane fit. Note, also that roughness values depends strongly on measurement conditions especially scan range asje sample density.
It is therefore important to include the measurement conditions when reporting roughness data.
Some of the parameters depend on the definition of a local minimum and a local maximum. Here, a local minimum is defined as a pixel where all eight neighboring pixels are higher and a local maximum as a pixel where all eight neighboring pixels are lower.
As there are no pixels outside the borders of the b4 there are no local minimums or local maximums on the borders. The amplitude properties are described by six parameters, which give information about the statistical average properties, the shape of the height distribution histogram and about extreme properties.
All the parameters are based on two-dimensional standards that are xnsi to three dimensions. The Roughness Average, S ais defined as:.
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Note, that azme SPIP version 4. The Surface Skewness, S skdescribes the asymmetry of the height distribution histogram, and is defined as:. Values numerically greater than 1. The advantage of this is that deviations from the bearing plane can be quantified better when setting the bearing plane to zero see how this is done in the Plane Correction Dialog section.
For Gaussian height distributions S ku approaches 3. Smaller values indicate broader height distributions and visa versa for values greater than 3. They are defined as the height difference between the highest and lowest pixel in the image.
The Ten Point Height, S10 zis defined as the average as,e of the five highest local maximums plus the average height of the five lowest local minimums:. When there are less than aeme valid maximums or five valid minimums, the parameter is as,e defined. Maximum Valley Depth Sv: Maximum Peak Height Sp: Mean HeightS mean is the mathematical mean height of all pixels. There are three hybrid parameters. These parameters reflect slope gradients and their calculations are based on local z-slopes.
The Mean Summit Curvature, S scis the average of the principal curvature of the local maximums on the surface, and is defined as:. The Area Root Mean Square Slope, S dq6is similar to the Sdq but includes more neighbor pixels in the calculation of the slope for each pixel.
The Surfaces Area Ratio, S drexpresses the increment of the interfacial surface area relative to the area of the projected flat x,y plane:. The Projected Area, S2Aexpresses the area of the flat x,y plane as given in the denominator of R The Surface Area, S3Aexpresses the area of the surface area taking the z height into account as given in the numerator of R The functional parameters for characterizing bearing and fluid retention properties are described by six parameters.
All six parameters are defined from the surface bearing area ratio curve shown in the figures below. The surface bearing area ratio curve, which is also called the Abbott curve, is calculated by accumulation of the height distribution histogram and subsequent inversion. The hybrid parameters can be described graphically by the above figure. These lines are marked Z 0. Three parameters are calculated based on this figure. The Surface Bearing Index, S biis defined as:.
For a Gaussian height distribution S bi approaches 0. Large S bi indicates a good bearing property. Note,that negative peak artifacts may cause this parameter to be underestimated and in such cases it might be appropriate to perform some noise filtering. For a Gaussian height distribution S ci approaches 1. Large values of S ci indicate ase the void volume in the core zone is large.
For all surfaces S ci is between 0 and 0. For a Gaussian height distribution S vi approaches 0. Large values of S vi indicate large void volumes in the valley zone.
For all surfaces S vi is between 0 and 0. Parameters associated with the two-dimensional DIN standard are also calculated based on the bearing area ratio curve. The Reduced Summit Height, Spkis the height of the upper left anzi. The Core Roughness Depth, Skis the height difference between the intersection points of the found least mean square line. The spatial properties are described by five parameters. These parameters are the density of summits, the texture direction, the dominating wavelength and two index parameters.
The first parameter is calculated directly from the image, while the remaining are based on the Fourier spectrum. For these parameters we require the images to be quadratic. The Density of SummitsSdsis the number of local maximums per area:. The Texture DirectionStdis defined as the angle of the dominating texture in the image. For images consisting of ansk ridges, the texture direction is parallel to the direction of the ridges.
If asne angle aame the ridges is turned clockwise, the angle is positive and if the angle of the ridges is turned anti-clockwise, the angle becomes negative.
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This parameter is only meaningful if there is a dominating direction on the sample. We calculate Std from the Fourier spectrum. The relative amplitudes for the different angles are snsi by summation of the amplitudes along M equiangularly separated radial lines, as shown in the figure below.
The result is called the angular spectrum. The amplitude sum, A aat a line with the angle, ais defined as:. Fourier spectrum and the angular and radial spectra. The angular spectrum is calculated by the following formula:.
For non-integer values of andthe value of F u pv q is found by linear interpolation between the values of F u pv q in the 2×2 neighboring pixels. The line having the angle, awith the highest amplitude sum, Amaxis the dominating direction in the Fourier transformed image and is perpendicular to the texture direction on the image. The Texture Direction IndexStdiis a measure of how dominant the dominating direction is, and is defined as the average amplitude sum divided by the amplitude sum of the dominating direction:.
With this definition the Stdi value is always between 0 and 1. Surfaces with very dominant directions will have Stdi values close to zero and if the amplitude sum of all direction are similar, Stdi is close to 1. The Radial WavelengthSrwis the dominating wavelength found in the radial spectrum. The amplitude sum, b ralong a semicircle with the radius, ris. The radial spectrum is calculated by the following formula:.
The Dominating Radial Wavelength, Srwcorresponds to the semicircle with radius, r maxhaving the highest amplitude sum, b max: The Radial Wave IndexSrwiis a measure of how dominant the dominating radial wavelength is, and is defined as the average amplitude sum divided by the amplitude sum of the asms wavelength:.
With this definition Srwi is always between 0 and 1. If there is a very dominating wavelength, Srwi is close to 0, and if there is no dominating wavelength, it is close to 1.
The Mean Ajsi Wavelength, Shwis based on the integrated radial spectrum:. Shw corresponds to the radius r ansj. Having found r 0.
The Fractal Dimension, Sfd is calculated for the different angles by analyzing the Fourier amplitude spectrum; for different angles the amplitude Fourier profile is extracted and anis logarithm of the frequency and amplitude coordinates calculated. The fractal dimension, D, for each direction is then calculated as. The reported fractal dimension is the average for all directions.
The fractal dimension can also be evaluated from 2D Fourier spectra by application of the Log Log function. If the surface is fractal the Log Log graph should be highly linear, with at negative slope.
For an anisotropic surface the correlation length is in the direction perpendicular to the surface lay. The Texture Aspect Ratio Parameters, Str20 and Str37are used to identify texture strength uniformity of texture aspect.
In principle, the texture aspect ratio has a value between 0 and 1. For a surface with a dominant lay, the parameters will tend ansl 0. This may be the case for image containing well organized linear structures.
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Each point in the graph corresponds to the normalized power in a circle one frequency pixel wide in the squared FFT image the Power Spectrum Image. The calculated RMS roughness between cursors corresponds to the square root of the sum of all pixels in the 2D Power Spectrum Image between two concentric circles each with the radius of the inverse wavelength of the cursors in the IAPSD graph. The Cross Hatch AngleSch is the found angle of a cross hatch pattern typically created in seen in cylinder liners and created by a honing qsme used to ensure proper lubrication.
The angle measured, is the angle difference between the two most dominant angles found in the image by analyzing its autocorrelation function. Root Mean Square Gradient. Area Root Mean Square Slope.