Fluctuation scaling of colour variability in automotive metallic add-on parts

Colour matching between the car body and assembled add-on parts is a complex process that increases costs and time in automotive manufacturing. Spanish researchers have investigated the statistical properties of colour coordinates for colour matching in automotive metallic coatings.

Fluctuation scaling of colour variability in automotive metallic add-on parts. Source: pixabay.com/CCO -

CIELAB lightness L*, red-green a*, and blue-yellow b* coordinates were calculated by using multi-angle spectrophotometric reflectance measurements from a broad range of metallic coatings from different manufacturers.

Colour coordinates of finishes follow fluctuation scaling

The scientists found that trial-to-trial L* variations are related to a self-similar stochastic process. The sample variance and the sample mean value of L* calculated over different viewing angles are correlated across painted pieces. A power function model describes the data quite well. This power function corresponds to a wide spread phenomenon known as fluctuation scaling in many engineering process. They also found that the sample skewness and the sample kurtosis of L*, a*, and b* follow a U-shaped pattern and a generalised version of fluctuation scaling.

Better prediction of lightness flop variations

The exponent of fluctuation scaling in the skewness-kurtosis plane depends on the cardinal directions, L*, a*, and b*. This suggests that different flake-shaped pigments mediate trial-to-trial correlations of colour coordinates. The researchers conclude that fluctuation scaling provides a powerful approach for better prediction of lightness flop variations and for better colour quality control between car manufacturers and suppliers of add-on parts.

The study is published in: Progress in Organic Coatings, Volume 104, March 2017, Pages 118-124.

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