Model-Based Process Planning for Laser Cutting Operations Under Unsteady-State Conditions

Boundary encroachment or cutting right up to pre-cut sections are examples of unsteadystate operations of the laser cutting process. Cornering and generating small diameter holes also fall into this category. Heat transferis often frustrated here, resulting in bulk heating of the workpiece. This in tum leads to a degradation of the cut quality.' Currently, trial-and-error based experimentation is needed in qrder to assure quality in these regions. Thus model-based process planning has the benefit of reducing this step whilst leading to an optimal solution. Numerical investigation of the laser-workpiece interaction zone quantifies significant effects of such transiency on cutting front mobility and beam coupling behavior. Non-linear power adaptation profiles are generated via the optimization strategy .in order to stabilize cutting front temperatures. Experimental results demonstrate such process planning can produce quality improvements. INTRODUCTION Laser cutting of complex and intricate workpieces has been common. Of concern though, is the effect of cut geometry on the quality achievable. Boundary encroachment, cornering and contouring often result in severe heat accumulation. This can result in poor quality in the form of widespread burning, increased surface roughness and heat affected zone, and kerf widening. A review of the efforts towards better understanding and quality improvement in the laser cutting process was given (DiPietro and Yao, 1994). In particular, Gonsalves and Duley (1972) first accounted for the fact that only part of the incident beam power is available for laser cutting sheet metals. Powell (1993) devised cutting experiments to investigate the transmission and reflection losses occurring in the cutting process based on previous work done by Miyamoto, Maruo and Arata (1984, 1986). Schreiner-Mohr, et al. (1991) also conducted experimental work which showed that at maximum cutting speeds, the beam center can precede the front location. At slow cutting speeds the beam center was shown to lag behind the cutting front. A monodimensional finite difference model was proposed by Yuan, Querry, and Bedrin (1988) which suggested that the cutting front could possess mobility when cutting at constant processing speeds. Arata et al. (1979) showed through high speed photography that the cutting front was indeed dynamic in nature. Laser cutting of curved trajectories has been studied by Sheng and Cai, 1994. It was shown that circular laser cutting produces larger kerf width, shifted centerline towards the center of rotation, and larger inner kerf wall taper. Systems which allow the adaptation of laser power when cornering to compensate for the reduced cutting speeds associated there have been available (e.g., Steen and Li, 1988, and Powell, 1993). One method of achieving this control feature is by varying the pulse frequency and/or duty cycle proportionally to the feedrate (e.g., Moriyasu et al., 1986, Schuocker and Steen, 1986). The determination of this power-feed ratio currently relies on experimentation. In order to obtain sharp edges on curved trajectories, pulsed mode operation is also commonly employed. The problem with this is that heat-affected zones are almost doubled in extent compared to using continuous wave power (Geiger et al., 1988). This is explained by the more gradual temperature gradients experienced when pulsing the laser beam. In this paper, a transient model is developed to investigate the effects of cut geometry (e.g., boundary encroachment, cornering or cutting small holes) on cutting front dynamic phenomena, especially cutting front speed, temperature and transmitted power fluctuations. Its effect on heat affected zone extent is also studied. Numerical solutions of the model are compared with experimental results. Finally, a power adaptation strategy is implemented to improve quality in these regions. MODELING STRATEGY A detailed description of the mathematical formulation has been presented elsewhere (Di Pietro and Yao, 1995a). A brief summary is given below for completeness. In order to focus on the development of optimization, constant thermo-physical properties and two-dimensional transient heat conduction are simply assumed. Realistic boundary conditions which allow convection and radiation to occur to the surroundings are considered. This results in the following equation: K (il 2 T il 2 T) ilT q ilT -++--(hf+h +2h)+-=pcv ax2 . ay2 PCvdZ n r PCv at (1) where K =thermal conductivity;·p =density, cv =heat capacity, forced convective heat transfer coefficient hr = Nuct KId and Nusselt number Nuct = 0.027 Recto.s Pr0-33 (J.tm I llw )0.14(White, 1988). At all points other than where the oxygen gas jet impinges, it is assumed that there is no farfield streaming and thus natural or free convection occurs. However underneath the cutting nozzle, forced convection is apparent and the resultant heat flux will generally be far greater than in the free convection case. Fully developed turbulent flow iri a smooth tube is assumed for the forced convection case. h, is the free convection contribution (relatively small), and h, the radiative heat transfer coefficient. The material removal process is in actual fact a rather complex interaction of the gas jet on the free surface of the melt, where shear stresses act on the cutting front and a boundary layer exists. It is assumed in our model that any area in the molten state is expelled out of the kerf immediately, by the force of the gas jet. The COzlaser source is assumed to be of Gaussian TEM00 mode. The energy produced by the exothermic reaction is considered. Assuming a pure oxygen supply for the assist gas, the following reaction occurs within the cutting kerf: Fe + 0.50z = FeO (Powell et al., 1992) and till= -257.58 kJimol, where till is the energy released during the reaction and the ignition point is 1473.15K (Geiger et al., 1988). If the mass removal rate of the melt out of the kerf is known or can be calculated, then the following relationship can be used to determine the energy obtained by reaction. P . (milH) exo = ratio amu (2) where amu = 1 mole FeO = 71.847 g/mol and ratio is the percentage of FeO:Fe ejected from the kerf. It has been assumed previously that the material removal rate m can be given approximately by the following equation (Schuocker, 1988): rh =phD~ where b =kerf width, D =workpiece thickness and Vb =velocity of laser beam. This is only true though when it is assumed that the processing speed equals the front speed as in steady state cutting. In reality though, the mass removal rate is more appropriately given as: