The subject of this article is the forming process of closed die forging with flashes and the optimal design of the flash gutter dimensions. The goal is to conduct an in-depth theoretical analysis of the forming process of closed die forging with flash and to research the optimal design of the flash gutter dimension, aiming to improve the scientificity and efficiency of the forging process, guide the optimization of process parameters in actual production, extend the service life of dies, reduce material waste, and enhance product quality and production efficiency. The tasks were to establish an accurate mathematical model for closed die forging with flash to analyze metal plastic deformation and stress distribution, to conduct in-depth research on key factors such as stress distribution, position of the neutral plane, and flash gutter design during the forming process, and to validate the mathematical model through finite element simulation using DEFORM-2D software. The methods used include theoretical analysis, mathematical modeling, and finite element simulation validation. The theoretical analysis provides a foundation for understanding the forming process and stress distribution, whereas the mathematical model allows for quantitative analysis. Validation of the finite element simulation provides a means to test and refine the theoretical analysis and mathematical model. The following results were obtained: the existing mathematical model underestimates the height of the main deformation zone, which results in an unreasonable flash gutter design. After verification and correction, the error in the optimized mathematical model did not exceed 10 %, and the flash amount was significantly reduced. Additionally, a stress analysis of difficult-to-fill cavity positions revealed that the entrance radius of the cavity significantly affects the final filling. Conclusions. The scientific novelty of the results obtained is as follows: A mathematical model of closed die forging with flash was established to analyze the metal plastic deformation and stress distribution, providing theoretical support for die design optimization, forging quality improvement, cost reduction, and productivity improvement. Using the Deform-2D finite element simulation, the optimal design criterion for the flash was refined, resulting in a substantial reduction in the flash amount and material savings.
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