. 
14 (+3) Parameters for 3D Surface
Roughness
This page includes fourteen parameters based on the project BRC No:
3374/1/0/170/90/2 and three new “volume” family parameters.
AMPLITUDE PARAMETERS Four parameters are used for characterizing the amplitude property of surfaces. They are classified into four categories, i.e. (i) dispersion, (ii) extreme, (iii) asymmetry of the height distribution and (iv) sharpness of the height distribution. (1). RootMeanSquare Deviation of the Surface Sq
( 1 ) where, M is a number of points of per profile, N is the number of profile. Sq is a very general and widely used parameter. In statistics, it is the sample standard deviation. (2) Ten Point Height of the Surface Sz
( 2 ) where and are the five highest surface summits and lowest surface valleys respectively, which rely on eight nearest neighbour summits. (3) Skewness of Topography Height Distribution Ssk
( 3 ) This parameter can effectively be used to describe the shape of the topography height distribution. For a Gaussian surface which has a symmetrical shape for the surface height distribution, the skewness is zero. For an asymmetric distribution of surface heights, the skewness may be negative if the distribution has a longer tail at the lower side of the mean plane or positive if the distribution has a longer tail at the upper side of the mean plane. This parameter can give some indication of the existence of "spiky" features. (4) Kurtosis of Topography Height Distribution Sku
( 4 ) This parameter characterizes the spread of the height distribution.
A Gaussian surface has a kurtosis value of 3. A centrally distributed
surface has a kurtosis value larger than 3 whereas the kurtosis of a well
spread distribution is smaller than 3. By a combination of the skewness
and the kurtosis, it may be possible to identify surfaces which have a
relatively flat top and deep valleys.
SPATIAL PARAMETERS Four parameters are used to characterize spatial properties, density of summits, texture aspect ratio, directionality of surface lay and Fastest decay autocorrelation length. (1). Density of Summits of the Surface Sds
( 5 ) (2). Texture Aspect Ratio of the Surface Str
( 6 ) where
In principle, the texture aspect ratio has a value between 0 and 1. Larger values, say Str>0.5, of the ratio indicates uniform texture in all directions i.e. no defined lay, Smaller values, say Str<0.3, indicates an increasingly strong directional structure or lay. Since the size of the sampling area is finite, it is possible that the slowest decay of the AACFs of some anisotropic surfaces never reaches 0.2 within the sampling area. In this case the longest distance of the AACF along the slowest decay direction can be used instead. (3). The Fastest Decay Autocorrelation Length Sal
( 7 ) For an anisotropic surface Sal is in a direction perpendicular to the surface lay. A large value of Sal denotes that the surface is dominated by low frequency (or long wavelength) components. While a small value of the Sal denotes the opposite situation. (4). Texture Direction of the Surface Std
( 8 ) where, is the position where the maximum value of the angular spectrum.
HYBRID PARAMETERS The hybrid property is a combination of both amplitude and spacing. Any changes that occur in either amplitude or spacing may have an effect on the hybrid property. Three hybrid parameters are calculated here. (1). RootMeanSquare Slope of the Surface
( 9 ) Where
(2). Arithmetic Mean Summit Curvature of the Surface Ssc
( 10 ) This parameter can only be calculated after the summits.
(3). Developed Interfacial Area Ratio Sdr
( 11 ) Where the interfacial area of the quadrilateral is
The developed interfacial area ratio reflects the hybrid property of
surfaces. A large value of the parameter indicates the significance of
either the amplitude or the spacing or both.
FUNCTIONAL PARAMETERS INDEX FAMILY
(1) Surface Bearing Index Sbi
( 12 )
where is normalised the surface height at 5% bearing area. A larger surface bearing index indicates a good bearing property. (2). Core Fluid Retention Index Sci
( 13 ) A larger Sci indicates a good fluid retention. For a Gaussian surface, this index is about 1.56. (3). Valley Fluid Retention Index Svi
( 14 ) Where
A larger Svi indicates a good fluid retention in the valley zone.
VOLUME FAMILY
(1). Materiel Volume of the Surface Sm
( 15 ) where
The material volume and the material volume ratio are not only geometrical descriptors of the surface, but also have significant functional implications. The material volume may reflect wear and the runningin properties. On the other hand, for a "flattopped" surface, such as a honed surface, the material volume ratio may increase quickly, whereas for a spiked surface, such as a bored surface, the function shows a slow increase with the truncation level. Thus functionally, the material volume reflects the resistance against wear and friction. Surfaces with a rapid increase in the material volume ratio show good runningin properties whereas those with a slow increase of the functions indicates that the top part of the material is easily worn. (2). Core Void Volume of the Surface Sc
( 16 ) (3). Valley Void Volume of the Surface Sv
( 17 ) The void volumes is proposed here to provide a direct inspection of
lubrication and fluid retention of surfaces. It represents the fluid
retention ability of a highly wear surface. For a flat topped surface,
such as a honed surface, the core void volume may decrease quickly with
the truncation level, whereas for a spiked surface, such as a bored surface,
the function shows a slow decrease. Thus functionally, the void volumes
reflect the fluid retention property.
Copyright/Source: Centre
for Ultra Precision Technologies

