Physics-Informed Graph Neural Network for High-Precision Selective Assembly of Aero-Engine Bevel Gearboxes: A Mechanism-Data Fusion Approach

Abstract The assembly of aero-engine accessory gearboxes is a critical process governed by complex non-linear geometric error propagation. Achieving high-precision assembly is often hindered by the limitations of traditional analytical models in capturing contact deformations and the scarcity of labeled data for data-driven approaches. To address these challenges, this paper proposes a Physics-Informed Graph Neural Network for Selective Assembly (PI-GNN-SA). Moving beyond standard data-driven paradigms, our framework formally translates the classical Small Displacement Torsor (SDT) kinematic theory into a differentiable topological regularizer. This mechanism enforces rigorous geometric loop closure constraints, enabling the network to learn physically consistent representations within a highly sparse data manifold, effectively preventing the severe overfitting common in purely data-driven models. The trained PI-GNN serves as a high-fidelity surrogate model within a Non-dominated Sorting Genetic Algorithm II (NSGA-II) to optimize part matching. Experimental results based on real industrial data demonstrate that the proposed method reduces the root mean square error (RMSE) of backlash prediction by 43.5% compared to state-of-the-art graph networks. Furthermore, the optimized selective assembly strategy achieves a 96.5% one-pass qualification rate, significantly outperforming traditional methods. This work provides a robust, interpretable, and efficient solution for intelligent assembly in the aerospace industry.