Peening pattern optimization with integer eigen-moment density for laser peen forming of complex shape

Laser peen forming (LPF) is a novel flexible forming technology facing challenges in process planning to obtain the designed shape. This paper proposes an optimization framework to determine the peening patterns with consistent process conditions for complex shaping based on topology optimization. The eigen-moment is used as the intermediate variable between process conditions and deformed geometry. The interpolation schemes of eigen-moment are conceived according to the Solid Isotropic Material with Penalization model, and the eigen-moment density is specified as the design variable. The process planning method is developed to minimize the deviation between the planned and target surface. The optimality criteria (OC) method and the improved gradient descent (IGD) method are designed to solve the proposed model. Besides, an intermediate element suppression technique is applied to lead the eigen-moment density to integer values in the IGD method. The LPF experiment is designed regarding a saddle surface as the target and conducted based on the optimized peening patterns. The planning results show that the IGD method can present a more accurate planning surface than the OC method, and the assessment of the formed plate validates the effectiveness of the proposed process planning method. The process planning of the cylinder and wave surfaces also validates the proposed method and demonstrates the high forming flexibility of LPF.