The form, waviness and roughness components of a measured profile are separated by means of digital filters. The aim of analysis was to develop an algorithm for one-dimensional filtering of profiles using approximation by means of B-splines. The theory of B-spline functions introduced by Schoenberg and extended by Unser et al. was used. Unlike the spline filter proposed by Krystek, which is described in ISO standards, the algorithm does not take into account the bending energy of a filtered profile in the functional whose minimization is the principle of the filter. Appropriate smoothness of a filtered profile is achieved by selecting an appropriate distance between nodes of the spline function. In this paper, we determine the Fourier transforms of the filter impulse response at different impulse positions, with respect to the nodes. We show that the filter cutoff length is equal to half of the node-to-node distance. The inclination of the filter frequency characteristic in the transition band can be adjusted by selecting an appropriate degree of the B-spline function. The paper includes examples of separation of 2D roughness, as well as separation of form and waviness of roundness profiles.

Surface roughness is an important indicator in the evaluation of machining and product quality, as well as a direct factor affecting the performance of components. A rapidly developing filtering technology has become the main means of extracting surface roughness. The International Organization for Standardization (ISO) is constantly updating and improving the standard system for filtering technology in order to meet the requirements of technological development. Based on the filters already accepted by the international standard ISO 16610, this study briefly introduces the filtering principle of each filter, reviews the development of each filter in the application of surface roughness, and compares the advantages and limitations of their individual performances. The application range of each filter is summarized and, finally, the future direction of the digital filtering used in surface roughness is extrapolated.