As for author's succesive studies, the number of all asperities on the solid surface exhibiting one of the sample space and the probability density functions (
p.
d.
f.) with reference to the number of contact spots and the real contact area at the lst process in the analysis of contact phenomena are determined, because it is clear that the nature of the contact problems is resulted from the stochastic phenomena, and then the basic quantities about the state of the contact phenomena, for example the number of contact spots and the real contact area, are gained by them according to the probability theory.
Moreover, the method of analysis for the dynamic cantact phenomena caused by the relative motion is developed from the above method of analysis for the statical contact phenomena.
These evaluation method applied for the contact phenomena are proved by some experiments and the Monte-Carlo method simulation.
So, in this paper, as the lst report, the method of determining the number of surface asperities as the size of the statistic set, and the
p.
d.
f. as the probability expressions on the 3 dimensional characteristics of the solid surface are mainly discribed.
In this case, making use of the probability properties basic on the roughness curve signified as one of the cross section on the solid surface, the density of the surface asperities and the
p.
d.
f. as the basic expression for the analysis of the contact phenomena are determined by the two roughness curve perpendicular each other.
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