A Multi-Vector-Loop Assembly Deviation Analysis Method for Modelling and Transforming Three-Dimension Macro-Micro Errors

The surface form errors and deformations of high-precision mechanical components significantly influence the final assembly deviations. However, existing analytical methods often fail to adequately account for the effects of surface morphology and deformation. This paper proposes a novel Multi-Vector-Loop method, which is based on the Skin Model Shapes and a multi-closed-loop structure, for three-dimension macro-micro assembly deviation analysis. The method is employed to establish a high-precision mathematical model that directly links surface morphology, deformation, and assembly concentricity deviations. The stop-bolt mechanism is used as the study object. Firstly, an approach is introduced to construct a Skin Model Shapes that represents non-ideal surfaces due to machining errors. Then, force-deformation relationships for various surface morphological characteristics are derived through finite element method and interpolation methods. Finally, the development of a steady assembly state search algorithm has been achieved to obtain the final assembly state, and the Multi-Vector-Loop deviations transfer model was utilized to predict concentricity deviations. The numerical calculations of concentricity deviation for the three cases showed errors of 13.90% (Case 1), 20.46% (Case 2), and 9.93% (Case 3) relative to the finite element calculations. The results confirm the effectiveness of the proposed high-precision error transfer model.