Mathematical approach to the validation of field surface texture parameter software

Abstract

Abstract A new method for performance validation of surface texture parameter calculation software is introduced, focussing on field surface texture parameters. Surface height functions are defined mathematically, either using Fourier series or polynomials, and are then input into the surface texture parameter definitions to obtain mathematical parameter values. A series of user-adjustable parametric surface functions are defined that correspond to each surface texture parameter, enabling users to create a variety of surfaces to assess their software whilst still retaining mathematical traceability. This method is expanded to include complex surface textures. Chebyshev polynomials are used to perform numerical calculations of surface texture parameters for a selection of polynomial surface functions. Mathematical reference parameter values are calculated for a series of fifteen predefined surfaces and ten parametric surfaces to assess the performance of the software under test for a given dataset resolution. Assessment of the number of significant figures of the software-obtained values that agree with the reference values is used as a performance metric that enables comparison between different third-party software applications for a given dataset resolution. An assessment of the sampling methods used to create discrete datasets of a mathematical surface function for use with numerical third-party software is performed. Two implementations of surface height sampling are used to create datasets that are input into four third-party surface texture parameter calculation software packages, and the results compared, showing a significant variation in the performance metric values for different sampling methods.