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3D S Parameters - Height (Amplitude) Parameters

**Sa and Sq****Ssk and Sku****Sp, Sv, Sz**

For the discussions that follow, Z(x,y) is the function representing the height of the surface relative to the best fitting plane, cylinder, or sphere. Note that the "a" used in the following integral expressions implies that the integration is performed over the area of measurement and then normalized by the cross-sectional area "A" of the measurement.

Sa and Sq

**Sa** and **Sq** are
the Average Roughness and Root Mean Square Roughness are evaluated
over the complete 3D surface respectively. Mathematically, **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. Thus** Sa **or** Sq** may be
misleading in that many surfaces with grossly different spatial and height
symmetry features (e.g., milled vs. honed) may have the same **Sa or Sq**,
but function quite differently. 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 (Skewness) and Sku (Kurtosis)

**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 predominance 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. Since **Ssk** and **Sku** involve
the higher order powers of the surface heights, one must make enough measurements
to provide statistically significant values and/or properly select filtering
bandwidths to eliminate erroneous peaks or valleys.

Sp (Max Peak Height), Sv Max Valley Depth) and Sz (Max Height of Surface)

**Sp**, **Sv**,
and **Sz** are parameters evaluated from the absolute highest
and lowest points found on the surface. **Sp, **the Maximum
Peak Height**, **is the height of the highest point, **Sv**,
the Maximum Valley Depth, is the depth of
the lowest point (expressed as a negative number) and **Sz **the
Maximum Height of the Surface), is found from **Sz =** **Sp – Sv**.

Note: earlier
standards referred to **Rz** as a average of the 10 highest to 10 Lowest Points and other variations.
The ISO community agreed for the newer standard, ISO 25178-2 to establish
Sz as strictly the peak to valley height over a areal measurement.

Application

Since **Sp**, **Sv**,
and **Sz** are found from single points, they tend to result
in unrepeatable measurements. Thus when using these three parameters, one
must properly set spatial filtering bandwidths to eliminate erroneous peaks/valleys
and average multiple measurements at random locations along the sample,
to obtain a statistically significant result. Typical applications for **Sz** may
include sealing surfaces and coating applications. **Sp** may
find application when considering surfaces that will be used in a sliding
contact application. **Sv** may find application when
valley depths relating to fluid retention may be of concern such as for
lubrication and coating systems.