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3D S Parameters - Height (Amplitude) Parameters

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.

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.