Improvement of numerical instabilities in process planning of laser peen forming based on perimeter constraint

Abstract

Laser peen forming (LPF) is a novel flexible forming process with remarkable advantages in complex shape forming. The distributed process planning model, which applies eigen-moment as the intermediate design variable, is an effective way to realize the process planning for complex shape forming. Due to the immaturity of the model, numerical instabilities such as checkerboards and intermediate densities commonly occurring in process planning. Therefore, it is difficult to apply the planning results as a forming scheme directly. This study utilizes the perimeter constraint method, re-drives the process planning model's mathematical expression to realize the aggregation control of the eigen-moment field. Effects of perimeter constraint and Tikhonov regularization term are verified and compared through the numerical method. Results show that perimeter constraint is more effective in preventing numerical instabilities. Then the improved model is applied to the LPF process planning of cylinder, saddle, and wave surface. LPF experiments are carried out based on the process planning results. Experimental surfaces are measured and compared with objective surfaces to verified the improved model. Because there still exists a specific error between the experimental surfaces and the objective surfaces. Reasons for the error are analyzed and discussed, and methods to improve the precision of LPF technology are further proposed.