Effects of multiscale surface topography on assembly accuracy: A precision mirror case

Surface topography critically affects assembly accuracy, yet conventional studies rarely capture its multiscale nature or provide observational evidence, consequently restricting predictive confidence and physical understanding. Accordingly, this paper presents a novel multiscale analysis framework integrating surface decomposition with finite element simulation to bridge this gap, as verified and validated in a precision mirror case study. An improved Bidimensional Empirical Mode Decomposition (BEMD) method is developed to effectively separate simulated and measured surfaces into form, waviness, and roughness components, enabling a quantitative investigation into the contribution of each surface component to the mirror's surface-figure error. The results indicate that waviness contributes more to the RMS than form (44.34% vs. 30.18%) in ground surfaces, despite its smaller flatness error (6.40 μm vs. 12.65 μm), while form dominates in milled surfaces. This counterintuitive phenomenon reveals the fact that waviness induces greater non-uniformity in contact stress distribution. By clarifying scale-specific effects, this work not only underscores the importance of multiscale analysis in precision assembly but also establishes a rational link between manufacturing processes and final assembly performance.