Abstract
Abstract Laser peen forming (LPF) is a flexible forming process that brings many challenges for complex shaping. This study aims to develop an effective optimization method to complete efficient process planning of LPF to generate the desired geometry shape. The eigen-moment is proposed as a new intermediate variable to describe the bending deformation to relate the LPF process parameters and the geometry shape. The governing equation of eigen-moment is derived to characterize the bending deflection with a PDE equation. The numerical computation method is developed by the PDE weak form and finite element method to predict the bending shape. To achieve process planning of complex shaping, the distributed eigen-moment on both plate surfaces is prescribed, and a PDE-constrained optimization is utilized to define the process planning problem of LPF. Then, the eigen-moment field is optimized by adopting the interior-point algorithm to obtain the desired shape. The proposed eigen-moment is verified to be an intrinsic physical quantity to describe the bending behavior of LPF. A complex shape with saddle geometry is used as a typical case to demonstrate the process planning method. The experiments conducted with the planned LPF process parameters are validated to produce a shape consistent with the designed geometry.
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