State space modeling of variation propagation in multistage machining systems with generalized fixture layouts: A case study from an engine manufacturing enterprise
Fangrui Li, Shichang Du, Chen Zhao
Abstract
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.