Establishing functional correlations between multiscale areal curvatures and coefficients of friction for machined surfaces
Journal article, 2018

The objective of this research is to determine the strengths of correlation, and their variation with scale, between friction coefficients and topographic characterization parameters, calculated using statistical representations of multiscale areal curvatures. The surfaces are created by milling and manual polishing. Coefficients of friction were measured during bending under tension tests. Surfaces were measured with a white light interferometer. Curvature tensors were calculated using a normal based method adapted for multiscale analysis. Three different regions were analyzed from each of eight samples. Curvature tensor parameters: principal, mean, and Gaussian curvatures were calculated for scales between 0.78 and 47.08 mu m. These statistical measures of the curvatures were regressed against the coefficient of friction. Three different analyses were performed, taking into account entire curvature distributions, only negative or positive values and curvatures of top heights. Strong correlations (R-2 > 0.85 for many and as large as 0.96) were found for the standard deviations for all four curvature measures when entire distributions were considered. These results suggest that the frictional responses of surfaces could be related to the variance of their topographic curvatures. Average curvature parameters correlate strongly with coefficients of friction for negative values. Curvatures calculated from top regions present strong correlations for both mean and standard deviation of maximal, mean and Gaussian curvatures. This supports the use of multiscale curvature tensor methods for characterizing interactions between surface topography and tribological performance.




curvature tensor


T. Bartkowiak

Poznan University of Technology

Johan C Berglund

Chalmers, Industrial and Materials Science, Product Development

Swerea IVF AB

C. A. Brown

Worcester Polytechnic Institute

Surface Topography: Metrology and Properties

2051-672X (eISSN)

Vol. 6 3 034002

Subject Categories

Manufacturing, Surface and Joining Technology

Other Physics Topics

Probability Theory and Statistics



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