Analytical model for weld penetration prediction in finite plates with time-varying heat sources

The dynamic behavior evolution of the welding molten pool presents challenges due to their invisibility and difficulty of quantification. In engineering applications, the perception of weld penetration depth and width faces limited generalization, making it difficult to meet the demands of complex time-varying welding conditions in scenarios not covered by historical data. This study proposes a new analytical solution for the double-ellipsoidal heat source, extending its application scope to finite plate and time-varying heat input. Utilizing the boundary thermal effect mirroring principle and a more concise parametric equations for mirror coordinate mapping, we rederived an analytical formula for the time-varying double-ellipsoidal heat source model. High resolution accuracy and strong generalization capability of the model were validated using finite element analysis and real-world complex welding experiments, with width and depth errors under 1.0 mm. The study addresses the quantitative characterization of liquid molten pool geometric parameters (weld width and penetration depth) in complex welding scenarios, providing a scientific methodology and technical pathway for self-learning intelligent welding models and adaptive control in complex, time-varying welding conditions.