A mathematical model for the penetration depth in welding with continuous CO₂ lasers Available to Purchase

Continuous CO₂ lasers have been used successfully for many years to weld a variety of materials. An interesting problem has, however, emerged. This is the question of the value of the penetration depth of continuous CO₂ laser light in mild steel. Experimental measurements of the penetration depths of continuous CO₂ laser light in mild steel specimens have been made for a variety of translation speeds and incident laser powers. The results indicate that the ratio of the keyhole radius at the top of the work piece is almost exactly three times the radius at the bottom in the case of maximum penetration. This ratio is independent of all operational parameters apart from the f-number of the laser’s optical system; in particular, it does not depend on the translation speed or the power of the laser. This in turn determines the radius of the keyhole at the top, although it should be noted that this is not the focal spot radius because of the defocusing effect of the plasma emerging from the keyhole. The present paper uses a simple model of Fresnel absorption to investigate the consequences of this relation and confirms that the depths predicted by the model agree very closely indeed with the results of experiment. The integrated keyhole and weld pool model can be employed to obtain more accurate values, but the model confirms the principle. The optics of the laser light in the keyhole is investigated and this, together with the nature of the simple model, confirms that the process of welding at the maximum possible thickness for the given values of the other operational parameters is dominated by the processes of Fresnel absorption and reflection at the keyhole walls.