State space modeling of variation propagation in multistage machining systems with generalized fixture layouts: A case study from an engine manufacturing enterprise

In multistage machining systems (MMSs), dimensional variation propagates across stages due to fixture and datum deviations, compounded by process-induced deformation. Accurate modeling of this propagation remains challenging, as each stage may adopt distinct fixture layouts with different kinematic constraints. The lack of a unified mathematical representation further complicates variation propagation analysis under diverse fixture layouts. This paper presents a generalized Stream-of-Variation (SoV) model formulated within a unified state-space framework to overcome these limitations. The model accommodates generalized six-point fixture layouts by employing a locator matrix representation. Unlike conventional models that separately treat fixture and datum errors, the proposed model integrates them into a unified part-level differential motion vector (DMV), enhancing structural coherence and facilitating variation propagation analysis. A unified part-level differential motion vector (DMV) is explored by integrating fixture and datum errors into SoV model, enhancing structural coherence and facilitating variation propagation analysis. A six-stage engine block machining case study validates the model’s effectiveness. Experimental results show that the proposed model significantly outperforms classical and modified SoV models, with an average 22.78% reduction in prediction error. These improvements are particularly notable under generalized locating conditions where conventional models fail. The proposed model offers a scalable, physically grounded tool for variation analysis, with potential applications in adaptive control, online diagnostics, and quality assurance.