On the approximating criteria of parabolic asperities for measured surface profiles

Surface description is fundamental in mechanical contact analysis. In this paper, some of the most common approaches for roughness description are first briefly described. Some models for approximating a real rough profile with parabolas that guarantee the preservation of some specific characteristics are presented. The specimens of aluminum alloy with different surface roughnesses are prepared and measured. A data analysis program is developed to identify the measured profile with quadratic functions for different approximating criteria. Based on this, the effect of the approximating criterion and the sampling interval on the surface roughness parameters and the mechanical parameters is then presented and compared. The results show that the surface roughness Ra, asperity height H, and peak radii R increase with increasing surface roughnesses for different approximating criteria. The same root mean square approximating criterion is more suitable for calculating the surface roughness Ra. The asperity height H and peak radii R increase with increasing sampling intervals for all roughnesses, while the trend is opposite for the surface roughness Ra. The sampling interval has little effect on these parameters, especially for smoother surfaces.