A MATHEMATICAL INVESTIGATION OF THE PENETRATION DEPTH IN KEYHOLE WELDING WITH CONTINUOUS CO2-LASERS

Continuous CO2 lasers have been used for many years to weld a variety of materials. A problem of importance is the question of what is the t hickest work piece that can be reliably welded with complete penetrati on occurring at all times. Empirical results indicate that the size of the keyhole radius at the top of the work piece is almost exactly thr ee times the radius at the bottom in the case of maximum penetration. A mechanism based on the instability inherent in the variable absorpti on capabilities of the work piece when absorbing energy from a laser b eam with an interference pattern which is itself the result of reflect ion at the wall of the keyhole has been suggested and the implications investigated. A simple model has been studied in which the beam has a uniform intensity at any given cross section; an analysis in terms of geometrical optics and a parallel beam supports the empirical observa tion. The effect of the curvature of the keyhole wall was studied and found not to make a great difference to the results of the theory. The same techniques were used to investigate the effect of the convergenc e and subsequent divergence of the laser beam as it passes through the focal plane. The estimates provided by the theory have been compared with experimental results and shown to agree very well with them.