Jacobian Torsor Model for Statistical Synthesis of Three-Dimensional Tolerances in Mechanical Assemblies

In industrial sectors like aerospace, precision and cost are tightly intertwined factors concerning tolerances. Tight tolerances necessitate the use of sophisticated materials and processes, resulting in increased costs. Conversely, looser tolerances are more economical as they facilitate easier production with minimal material investment. As a result, the analysis and the synthesis of tolerances emerge as critical topics in industries, particularly in precision-driven sectors such as aerospace. Balancing precision with cost-effectiveness is imperative for maintaining competitiveness and ensuring quality in industrial operations. This study introduces a statistical approach for redefining tolerances in aerospace engineering applications by integrating the Jacobian torsor model with Monte Carlo simulation. This method offers a practical solution for scenarios where traditional methods struggle to establish accurate statistical models. In the context of aerospace engineering, precise tolerance management is crucial for ensuring the reliability and the performance of complex assemblies. By identifying the functional requirements of the assembly and its constituent functional elements, the Jacobian torsor model is utilized to describe their functional relationship. Then Monte Carlo simulation is employed to convert the deterministic model into a statistical one, enabling the generation of simulated data to determine statistical boundaries. Through redistributing tolerances based on the percentage contribution of each functional element to the overall requirement, critical tolerances are redefined to meet the specified functional requirement. Illustrated with a practical case study, the effectiveness of the proposed technique is demonstrated, highlighting its relevance and applicability in aerospace engineering contexts.