Sa and Sq

Sa and Sq  are the average roughness and root mean square (rms) roughness evaluated over the complete 3D surface respectively. Mathematically, the Sa and Sq are evaluated as follows:

Application

The Sa and Sq parameters represent an overall measure of the texture comprising the surface. Sa and Sq are insensitive in differentiating peaks, valleys and the spacing of the various texture features. The figure above demonstrates two very different surfaces with identical Sa and Sq values, indicating the insensitivity of the Sa and Sq parameters. Nonetheless, once a surface type has been established, the Sa and Sq parameters may be used to indicate significant deviations in the texture characteristics.  Sq is typically used to specify optical surfaces and Sa is used for machined surfaces.

Ssk, and Sku

Ssk and Sku are the Skewness and Kurtosis of the 3D surface texture respectively. Figuratively, a histogram of the heights of all measured points is established and the symmetry and deviation from an ideal Normal (i.e. bell curve) distribution is represented by Ssk and Sku.  Mathematically, the Ssk and Sku are evaluated as follows:

Application

Ssk represents the degree of symmetry of the surface heights about the mean plane. The sign of Ssk indicates the preponderance of peaks (i.e. Ssk>0) or valley structures (Ssk<0) comprising the surface. Sku indicates the presence of inordinately high peaks/ deep valleys (Sku>3.00) or lack thereof (Sku<3.00) making up the texture.   If the surface heights are Normally distributed (i.e. bell curve) then Ssk is 0.00 and Sku is 3.00. Surfaces described as gradually varying, free of extreme peaks or valley features, will tend to have Sku <3.00.  Ssk is useful in specifying honed surfaces and monitoring for different types of wear conditions. Sku is useful for indicating the presence of either peak or valley defects which may occur on a surface.

Sz

Sz is the Ten Point Height over the complete 3D surface and represents the average difference between the 5 highest peaks and 5 lowest valleys. A peak  is defined as any point, above all 8 nearest neighbors.  A valley  is any point, which is below all 8 nearest neighbors. Peaks and valleys are constrained so they will be separated by at least 1% of the minimum “X” or “Y” dimension comprising the 3D measurement area.

Application

Sz is useful in characterizing the “envelope” that contains most of the surface heights, particularly when Sa or Sq is dominated by general texture features. The texture of sheet steel is typically specified with Sz as well as shaft surfaces when considering sealing applications. Sz may demonstrate a change sooner than Sa or Sq as a surface is modified such as when studying a wear mechanism.

Introduction:
Autocorrelation Function (ACF)

The development of the spatial parameters involves the use of the mathematical technique of the Autocorrelation Function (ACF).  This section will review the basic concepts behind the ACF, necessary to understand the various spatial parameters.

The ACF is found by taking a duplicate surface (Z(x-Dx,y-Dy)) of the measured surface ((Z (x, y)) and mathematically multiplying the two surfaces together, with a relative lateral displacement (Dx,Dy) between the two surfaces. Once multiplied together, the resulting function is integrated and normalized to Sq, to yield a measure of the area of overlap between the two functions. If the shifted version of the surface is identical to the original surface then the ACF is 1.00. If the shifted surface is such that all peaks align with corresponding valleys then the ACF will approach –1.00. Thus the ACF is a measure of how similar the texture is at a given distance from the original location. If the ACF stays near 1.00 for a given amount of shift, we conclude that the texture is similar along that direction. If the ACF falls rapidly to zero along a given direction, then we conclude that the surface is different and thus “uncorrelated” with the original measurement location.

Sds

Sds, the Summit Density is the number of summits per unit area making up the surface. Summits are derived from peaks. A peak is defined as any point, above all 8 nearest neighbors. Peaks are constrained to being separated by at least 1% of the minimum “X” or “Y” dimension comprising the 3D measurement area. Additionally, summits are only found above a threshold that is 5% of Sz above the mean plane.

Application

Sds is a key parameter when considering surfaces used in applications such as bearings, seals and electronic contacts. The manner in which the summits elastically and plastically deform under load is related to the Sds parameter. Depending on the application, a low Sds may result in high-localized contact stresses resulting in possible pitting and debris generation. In applications involving sliding components, a number of summits are needed to prevent optical contacting while maintaining a reasonable load distribution. Summit density may also be related to the cosmetic appearance of a surface once painted.

Str and Sal

Str, the texture aspect ratio, is a measure of the spatial isotropy or directionality of the surface texture. For a surface with a dominant lay, the Str parameter will tend towards 0.00, whereas a spatially isotropic texture will result in an Str of 1.00.  Sal, the auto-correlation length, is a measure of the distance over the surface in an optimum direction such that the new location will have minimal correlation with the original location.

Application

Str is useful in determining the presence of lay in any direction. For applications where a surface is produced by multiple processes, Str may be used to detect the presence of underlying surface modifications.  Str may find application in finding subtle directionality on an otherwise isotropic texture. Sal is a quantitative measure as to the distance along the surface by which one would find a texture that is statistically different from the original location. Sal is useful in establishing the distance between multiple measurements made on the surface to adequately determine the general texture specification of the surface.

Introduction Spatial Parameters: 
Angular Power Spectral Density Function (APSDF)

The development of the spatial parameters involves the use of the advanced mathematical technique of the Angular Power Spectral Density Function (APSDF). This section will review the basic concepts behind the APSDF necessary to understand the Std spatial parameter power spectrum is a measure of the amplitude of each sine wave for a particular frequency, along a given direction. Thus for a 3D surface, the power spectrum would be displayed as a “3D” function in which the X and Y axes represent the various spatial frequencies for a given direction. The amplitude of the power spectrum (displayed on the Z axis) represents the amplitude of the sine wave at a particular spatial frequency direction. The angular power spectrum is found by integrating the amplitudes of each component sine wave as a function of angle. The figures to the left demonstrate a crosshatched surface, the power spectral density of the surface and the angular power spectral density function.

Based on Fourier analysis, we can consider the surface texture to be composed of a series of sine waves in all directions with different frequencies and amplitudes.  

Std

Std, the texture direction, is determined by the APSDF and is a measure of the angular direction of the dominant lay comprising a surface. Std is defined relative to the Y axis. Thus a surface with a lay along the Y axis will return a Std of 0 deg.

 Application

Std is useful in determining the lay direction of a surface relative to a datum by positioning the part in the instrument in a known orientation. In some applications such as sealing, a subtle change in the surface texture direction may lead to adverse conditions. Std may also be used to detect the presence of a preliminary surface modification process (e.g. turning), which is to be removed by a subsequent operation (e.g. grinding).

Hybrid Parameters

Sdq and Ssc

Sdq is the root mean square (rms) surface slope comprising the surface. Ssc is the Mean Summit Curvature comprising the summits found for the Sds calculations. Sdq and Ssc are given by the following:

Application

Sdq is a general measurement of the slopes, which comprise the surface and may be used to differentiate surface with similar average roughness, Sa as demonstrated above. Sdq may find application for sealing applications and surface cosmetic appearance. Ssc is useful in predicting the degree of elastic and plastic deformation of a surface under different loading conditions and thus may be used in predicting friction and wear characteristics of a system.

Sdr

Sdr, the Developed Interfacial Area Ratio is expressed as the percentage of additional surface area contributed by the texture as compared to an ideal plane the size of the measurement region.

Application

Sdr may further differentiate surfaces of similar amplitudes and average roughness. Typically Sdr will increase with the spatial intricacy of the texture whether or not Sa changes. Sdr is useful in applications involving surface coatings and adhesion. Sdr and may also find relevance when considering surfaces used with lubricants and other fluids. Sdr may be related to the surface slopes and thus may also find application related to the manner in which light is scattered from a surface.

Functional Volume Family

Sm, Sc, and Sv

The functional volume parameters represent the volume of material or space provided by the surface relative to the cross sectional area of the measurement and thus have units of mm3/mm2. The volume parameters are derived from the bearing area analysis of the complete 3D surface. The bearing area curve is formed by establishing the amount of material a plane would rest on relative to the complete cross section of the surface for each height from the highest to the lowest point of the surface.

Application

The Sm, Sc and Sv parameters are used in tribology applications. Sm may be related to the amount of material available for initial running in or supporting of a load. Sc relates to the lubricant carrying and supporting properties of the core surface under load. Sv may be related to the void volume available for lubricant retention and debris entrapment.

Functional Index Family

Sbi, Sci, and Svi

The functional index family parameters are all unitless parameters designed to allow comparisons between surfaces of different average roughness. The functional index parameters are derived from the bearing area analysis of the complete 3D surface. The bearing area curve is formed by establishing the amount of material a plane would rest on relative to the complete cross section of the surface for each height from the highest to the lowest point of the surface. Sbi, the Surface Bearing Index is a measure, relative to Sq, of the surface height at the 5% bearing area ratio. Sbi is typically 0 ~ 3 with a larger Sbi indicating a larger relative load bearing area. Sci, the Core Fluid Retention Index is a measure, relative to Sq, of the volume (e.g. of a fluid filling the core surface) the surface would support from 5%-80% of the bearing ratio.  Svi, the Valley Fluid Retention Index is a measure relative to Sq, of the volume (e.g. of a fluid filling the valleys) the surface would support from 80% to 100% of the bearing ratio.

Application

Sbi, Sci and Svi are used to compare the tribological properties of surface with different average roughness. Sbi is related to the material available for initial load support. Sci and Svi relate to the relative retention of fluid the core and deep valley structures provide.