Six-Dimensional Spatial Dimension Chain Modeling via Transfer Matrix Method with Coupled Form Error Distributions

In tolerance design for complex mechanical systems, 3D dimension chain analyses are crucial for assembly accuracy. The current methods (e.g., worst-case analysis, statistical tolerance analysis) face limitations from oversimplified assumptions—treating datum features as ideal geometries while ignoring manufacturing-induced spatial distribution of form errors and failing to characterize 3D coupled error constraints. This study proposes a six-dimensional spatial dimension chain (SDC) model based on transfer matrix theory. The key innovations include (1) a six-dimensional model integrating position and orientation vectors, incorporating geometric error propagation constraints for high-fidelity error prediction and tolerance optimization, (2) the characterization of spatially distributed form errors and 3D coupled errors of spatial dimension chain-based multiple mating-surface constraint (SDC-MMSC) using six-degree-of-freedom (6-DoF) geometric error components, reducing the assembly topology complexity while improving the efficiency, and (3) a 6-DoF error characterization method for non-mating-constrained data, providing the theoretical basis for SDC modeling. The experimental validation on an aero-engine casing assembly shows that the SDC model captures multidimensional closed-loop spatial errors, with absolute errors of max–min closed-loop distances below 9.3 μm and coaxiality prediction errors under 8.3%. The SDC-MMSC method demonstrates superiority, yielding normal vector angular errors <0.008° and envelope surface RMSE values <0.006 mm. This method overcomes traditional simplified assumptions, establishing a high-precision, multidimensional distributed-form-error-driven SDC model for complex mechanical systems.