An optimization method for dimensioning hybrid passive–active die reinforcement systems in cold forging

Abstract Although cold forging enables the high-volume production of precision components, extrusion dies are exposed to severe cyclic loading. This promotes fatigue damage and dimensional scatter. Conventional shrink-fitted reinforcements increase tool life by prestressing the die in compression. However, they offer limited flexibility to compensate for variations in material and tribological conditions. Fully adaptive dies can tune external pressure during operation, yet they often require high actuation forces and highly loaded sliding interfaces. To leverage the key advantages of both reinforcement strategies, this paper introduces a hybrid passive–active die reinforcement concept. A passive shrink fit provides a robust baseline prestress, while an active stage superimposes an adjustable external preload. The actuation is realized by a wedge mechanism, so the actuator delivers only an incremental load relative to the passive baseline. A purely analytical dimensioning method is derived for this concept. It couples the wedge model with a Lamé-based compound-cylinder model of a double-ring reinforcement including interference-fit compatibility. The design is optimized across multiple load scenarios. The objectives are compressive die hoop stresses, a minimum characteristic safety factor, and maximum controllable bore diameter change. A deterministic grid search over the interference fits generates contour maps that highlight feasible regions and the trade-off between structural margin and adjustability. Representative design points are then evaluated by spot finite element simulations of a forward extrusion sequence. Die hoop stresses, ejector force, and final part diameter are used as evaluation metrics. The results provide a transparent and computationally efficient framework for selecting geometry, interference fits, and actuation settings. The procedure is transferable to industrial applications that require both structural safety and adjustable compliance.