Statistical Criteria of Amplitude.

It is possible to calculate amplitude parameters of roughness common to all surfaces when numerical data z(x,y) or z(x) of the surface are available.

Rt for total roughness defined by zmax – zmin. Rt represents the total width of the heights distribution function.

Ra for the average arithmetic deviation, defined by
Rq for the standard deviation (s), defined by :
Sk for the third order moment, agreed upon by :

This criteria shows the dissymmetry of the surface, agreed upon for Rq.

Ek for the fourth order moment agreed upon by the value of the Rq parameter to the fourth power, defined by :

This criteria shows the flattening of the distribution in case the of a Gaussien distribution Ek=3.

Heights Distribution and Abbott Curves.

Rough surfaces can be characterized by picturing them through the use of a random stationary periodic function of which the probability density must be determined. This heights distribution can then be compared to a Gaussien distribution which has a standard deviation s. This distribution is defined by :

The surface can also be characterized by calculating its contact area in function of the depth defined by :

This function, expressed in %, is called Abbott’s curve.