Rough Surfaces Simulation and Its Contact Characteristic Parameters Based on Ubiquitiform Theory

Ubiquitiform is a new theory of finite-order self-similar physical structure and it is more reasonable to describe real engineering surfaces by ubiquitiform rather than fractal. In this paper, by introducing the frequency truncation criterion, a new analytical expression of the two-dimensional W–M function based on the ubiquitiform theory is firstly derived and constructed and the two-dimensional ubiquitiformal curve characterization under different contact characteristic parameters is achieved. On this basis, the anisotropic three-dimensional surface W–M function with ubiquitiformal features is constructed, and the evolution law of the anisotropic three-dimensional surface morphology under the regulation of the ubiquitiformal complexity is investigated. Then, an improved adaptive box counting algorithm is proposed, and the lower limit of the metric scale in the self-similarity region of the asperities on the rough surface is determined and then the computation method of the ubiquitiformal complexity is established. At last, the validity and accuracy of the method are confirmed by the Koch curves. Key findings include: (1) higher ubiquitiformal complexity D corresponds to increased surface irregularity and complexity; (2) the characteristic scale factor G affects surface height only; (3) reducing the lower limit of metric scale δmin increases surface undulation frequency, revealing finer details. This research provides a rationale and quantitative guidance for the matching design of critical joint interfaces in modern precision machinery.