Digitally characterising gear flank surface residuals

Accurate representation of gear flank surface deviations is increasingly important as digital workflows incorporate measured data into tooth contact analysis models and as optical measurement systems generate large scattered datasets. Traditional line-based measurements provide limited coverage of the working flank and no standardised methods exist for representing residual surface content. This work proposes a two-layer compactly supported radial basis function (CSRBF) model for characterising gear flank residuals following removal of nominal and form geometry. The method operates directly on structured tactile measurements and scattered optical datasets without requiring interpolation on a regular grid. The approach was validated using three datasets, including a UK master gear and production gear measurements obtained using tactile and optical systems. The CSRBF model reconstructs residual surfaces with sub-micron accuracy for low-noise datasets, with a 95% confidence interval below 0.2~ μm for the master gear and below 0.3~μm for a ground gear. The model captures surface content up to 30 orders matching the transmission characteristic of the standard ISO 1328-1:2013 line Gaussian filter. The combined two-layer model requires 6227 parameters to characterise the flank surface independent of input data density, achieving a compression ratio of approximately 3 for a standard 40-profile measurement. The CSRBF model provides a compact and data-agnostic representation of gear surface deviations while preserving spatial frequency content. By expressing surface features in terms of base pitch orders, the method links measured surface structure directly to gear meshing behaviour. This approach supports digital transfer of surface data between measurement systems and simulation tools, and provides guidance on sampling density requirements for areal gear surface measurement.