Advanced Computational Tolerance Engineering: Unified Jacobian-Torsor Modeling, Uncertainty Quantification, and Optimization

This book presents an advanced framework for the specification, analysis, and optimization of geometrical and dimensional tolerances in precision manufacturing. It addresses the growing accuracy demands of modern manufacturing by developing predictive methodologies that improve assembly quality, functional performance, and manufacturing robustness. The proposed framework is based on the Unified Jacobian-Torsor Model for three-dimensional tolerance analysis and uncertainty propagation. A hybrid methodology combining the Unified Jacobian-Torsor Model, Monte Carlo simulation, and the Bootstrap statistical technique is introduced to quantify tolerance variability and estimate confidence intervals. The approach is applied to the analysis and optimization of cam-clamping systems and integrates Computer-Aided Tolerancing (CAT) to predict and compensate for manufacturing deviations during the design stage. Validated through numerical and experimental investigations, this book provides researchers and engineers with advanced methodologies for computational tolerance engineering and precision manufacturing.