Optimization of Partial Differential Equations for Minimizing the Roughness of Laser Cutting Surfaces

Possible explanations for different surface quality in laser cutting with 1 and 10 μm beams

“…Poprawe and co-workers mathematically analyzed the melt film stability. 6,7 They found a parameter that measures the degree of the stability. According to the parameter, the system is more stable as       sin sin   A becomes small.…”

“…Whereas wavelength dependence of the Fresnel absorption law has been related to difference in achievable thickness, 5 very few investigations have been made on the mechanism of the difference in the cut surface quality. Poprawe and co-workers observed ripple formations on the kerf front with a 1 m beam but not with a 10 m beam, 6,7 which they claim is the cause of the quality difference. This correlation between the ripples on the front and the striations on the sides is not so clear; striations appear even in the case of CO 2 laser cutting where the ripple formations were not observed.…”

Study on striation generation process during laser cutting of steel

“…Schulz et al [Schulz 1999] showed a more complete dynamical model of melting and melt ejection processes during laser cutting, although no concrete example of the simulation results was explained in this paper. Recently the stability of the system was analysed with a similar model [Vossen 2010, Poprawe 2010. It was concluded that this coupled system of a kerf front and a melt layer is inherently 40 unstable but the system is more stable as the following parameter c 0 becomes small.…”

“…The validity of this operation is not obvious. Poprawe and co-workers mathematically analyzed the melt film stability [Poprawe 2010, Vossen 2010]. They found the parameter c 0 that measures the degree of the stability (see eq.(3-4)).…”

“…et al[Schulz 1999] ont analysé un modèle dynamique plus complet des procédés de fusion et d'éjection du liquide. Ils ont finalement conclu que le front avant de la saignée et la couche liquide dans ce système couplé sont intrinsèquement instables et ont proposé un paramètre c 0 qui pilote le degré de cette instabilité [Poprawe 2010,Vossen 2010]. …”