Multi-Scale Digital Modeling of Precision Assembly Interfaces for Tolerance Analysis Using a Fractal-Wavelet Approach

The assembly interface topography of precision machinery exhibits complex multi-scale geometric features, including roughness, waviness, and form error, which critically influence assembly accuracy and tolerance analysis. To address the lack of adaptivity in existing separation criteria, this paper proposes a multi-scale digital modeling approach oriented toward tolerance analysis of precision assembly interfaces, based on a fractal-wavelet framework. Firstly, multiple Weierstrass–Mandelbrot functions with independent fractal dimensions are superposed to construct a multi-fractal topography model with controllable multi-scale characteristics, grounded in the power spectral density energy additivity property. Subsequently, wavelet functions are employed to hierarchically decompose the topography height field information. The effects of the compact support length and vanishing moments of the wavelet functions on the decomposition performance are analyzed to establish a clear basis for their selection. Finally, an adaptive multi-scale separation criterion based on wavelet energy K-means clustering is then proposed, with the optimal number of scale classes determined by maximizing the silhouette coefficient, eliminating reliance on empirical thresholds. Case study results show that the fused waviness-and-form-error model retains 94.8% of the original energy while reducing convex peak count by over 90%, significantly simplifying the interface microstructure for downstream tolerance computation. The proposed method provides a high-fidelity, adaptive digital foundation for assembly accuracy prediction of precision interfaces.