Development of an Offline Digital Twin Framework for Forging Dies Based on the Upper Bound Energy Method

The reliable prediction of forging load during the early stages of die design is critical for ensuring process feasibility, die durability, and press capacity selection, particularly in the forging of geometrically complex components such as gears. Conventional trial-and-error procedures and finite element simulations, although effective, may significantly increase development time and computational cost. In this study, an analytically driven offline digital twin framework is developed for gear forging die design by integrating an Upper Bound Energy Method-based analytical formulation with a structured parameter space architecture. The proposed framework enables rapid estimation of forging load as a function of key geometric, material, and process parameters without relying on real-time sensor data or computationally intensive simulations. A systematic dataset is generated through controlled variation of billet dimensions, gear geometry, friction conditions, and forming parameters within industrially relevant ranges. The predictive capability of the analytical core is validated using experimentally reported benchmark forging cases under fully filled die conditions. The results demonstrate that the proposed model preserves the overall trend of experimental measurements while providing conservative load estimates within acceptable engineering tolerance limits. The developed offline digital twin framework functions as a computationally efficient decision-support tool for early-stage die design and contributes to the integration of analytical modelling and digitalization strategies in metal forming engineering.