Process planning for laser peen forming of complex geometry: An analytical-based inverse study

Laser peen forming (LPF) is a promising process for the flexible manufacturing of complex thin-walled structures. However, process planning for LPF remains challenging due to the deformed geometry relying on the cumulative effect of thousands of laser shocks without dies. The optimization-based planning method is adaptable but easily gets trapped in local optima, leading to insufficient robustness and efficiency. To overcome these limitations, this study introduces an analytical-based inverse study to complement the optimization-based method. Firstly, an inherent and straightforward analytical model between eigen-moment and surface curvature is proposed, enabling a direct inverse determination of the eigen-moment field from the desired geometry shape. Subsequently, a clustering method is employed to achieve aggregation control over the analytically determined eigenmoment field, avoiding extensive optimization iterations. Moreover, a physical-based surface decomposition method is devised to formulate double-side LPF strategies for surfaces with negative or zero Gaussian curvature. To validate the proposed analytical-based process planning method, an elliptic paraboloid-like surface and a hyperbolic paraboloid surface are selected as the objectives. Experimental results show high conformity between the deformed and objective surfaces, validating the proposed method. The analytical-based planning method facilitates the efficient and robust determination of forming strategies, complementing the optimization-based method and providing a comprehensive solution for LPF process planning under small deformations.