Improving Laser Cutting Quality for Two-dimensional Contoured Paths via Model-based Optimisation

Quality improvements in laser cutting of mild steel have been achieved. by a newly developed model-based optimisation strategy. The specific aims of such efforts are to assure quality of cut when cornering. Such routines encompass a large proportion of all features processed on laser curting systems, and therefore their successful production is paramount. Associated with cornering is the elevation of workpiece temperature in the vicinity of the cut. This is because of the increased beam exposure time due to reduced cutting speeds associated there. Comer meltoff is therefore common. In order to focus on the development of such optimisation, constant thermo-physical properties and rwo-dimensional transient heat conduction are simply assumed. The model is therefore valid for the thin plate laser curting case, where temperatures are approximately homogeneous with workpiece depth. Nonlinear power adaption profiles are generated via the optimisation strategy in order to stabilise cutting front temperatures. Uniform temperatures produce better quality by reducing i) kerf widening effects, ii) heataffected zone extents, and iii) workpiece selfburning effects. At the very least, uniform curting front temperatures reduce the variability in cut quality which increases the odds that the fmal workpiece will reach acceptability standards. Currently, extensive trial-and-error based experimentation is needed in order to improve quality for these routines. Thus model-based optimisation has the added benefit of reducing this timeexhaustive step whilst leading to an optimal 100 solution. Experimental results are presented, and it is demonstrated that such process manipulation can produce significant quality improvements. INTRODUCTION Today, laser cutting of highly complex and intricate workpieces is a reality. Of concern though, is the effect of part geometry on the quality achievable. Such part programs typically contain many pre-cut sections and boundaries, and because of the obvious size of such workpieces, heat accumulation is often severe. This can result in poor curting quality in the form of widespread burning, increased dross, increased surface roughness, increased heat-affected zone, and kerf widening being common amongst other problems. The appearance of even one of these anornalities can render the complete job useless. In cases where heat fluxes are· strong enough to melt the material as in laser cutting, the problem becomes complex due to the moving solid-liquid interface. Efficient curting occurs when the beam rides ahead on the unmolten material and therefore little energy falls through the generated cut. When the curting front speed increases due to heat accumulation, or when curting at slow processing speeds, the beam tends to lag behind the front. As a result, much more laser beam energy passes through the cut with little or no heating effect. Such characteristics of the process alter the amount of energy input into the interaction zone, and therefore cutting front temperatures are expected to change. Consequently, such temperature deviations are attributable to the generation of inconsistent cut quality. There have been many models developed over the years to describe the laser cutting process. A comprehensive review of these is given elsewhere by the authors Di Pietro 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. This fraction was determined using a moving point source model. The model was used to determine the interrelationship between cutting speed, cut width and power required for efficient laser cutting. Powell (1993) devised cutting experiments to investigate the transmission and reflection losses occurring in the cutting process based on previous work done by Miyamoto et al. ( 1984, 1986). It was shown that the amount of reflected/transmitted light reduced as sample thickness was increased. Schreiner-Mohr et al. (1991) also conducted experimental work which showed that at maximum cutting speeds, the beam centre can precede the front location. At slow cutting speeds the beam centre was shown to lag behind the cutting front. A finite difference model for laser cutting thin metallic glasses was also conducted (Glass et al., 1989). It accounted for proper material removal by including the energy lost through the kerf by removing those nodes above the melting temperature. A mono-dimensional finite difference model was proposed by Yuan et al. (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, and the formation of striations on the kerf walls could be explained well by the relative movement between the front and the laser beam. Previous attempts at characterising the process have often assumed infmite workpiece length or they have prescribed fixed boundary temperatures. But in laser cutting of intricate parts, this assumption leads to low heat accumulation estimates. Such simplifications allow the general heat conduction equation to revert to the case of steady multi-dimensional conduction. A transient model was therefore 101 developed to account for workpiece geometry and the presence of a kerf is considered, with nodal points within it becoming part of the convective environment. Thin plate laser cutting is considered, so that the model can assume the two-dimensional heat conduction form in order to reduce the complexity of the optimisation tasks. Inherent problems associated with a moving cutting front and temporal variations of the energy input per unit time are resolved. These issues require a numerical approach, which would otherwise be impossible to address analytically. BACKGROUND Simple observation of laser-cut comers show that in most cases, comer tip melt-off is common. This is due to the increased time the laser beam is in this area due to the deceleration of one axis, and then acceleration of the other to perform the desired task with adequate positional control. Many systems now allow the adaption of laser power when cornering to compensate for the reduced cutting speeds associated there (Leece, 19 84, Delle Piane, 1985, VanderWert, 1985, Steen and Li, 1988, and Powell, 1993). This was possible through advances made in controller design. Such adaption ensures that the rate of energy input into the interaction zone and the rate of melt ejection from the kerf is kept somewhat balanced. This technique can be used either under continuous wave (CW) or pulsed mode operation. The determination of this power-feed ratio currently relies on extensive experimentation. One method of achieving this control feature is by varying the pulse frequency and/or pulse length propottionally to the feedrate (Moriyasu et al., 1986, Schuocker and Steen, 1986, Borgstrom, 1988, and Schwarzenbach and Hunziker, 1988). Such duty cycle modulation produces very accurate control of the laser output by altering the precentage of beam 'ontime' to suit the feedrate. If the system can respond quickly to power commands from the controller, then the input current to the laser can be manipulated for an effective power-feed strategy. Another approach is termed channel switching (Henzel, 1987), whereby various power levels can be accessed via control functions in the part program generated. Multi-channel capabilities are therefore required so that each channel can be preset with a different power level. It is suggested that the controller needs to be able to effectively switch channels without significant delay in order to assure that no irregularities appear on the cut edge. MODEL-BASED OPTIMISATION A complete description of the mathematical formulation has been presented elsewhere by the authors, Di Pietro and Yao (1995a). Additionally, model-based optimisation for laser cutting when encroaching upon a boundary has been studied previously in order to assure cut quality right up to pre-cut sections (Di Pietro et a!., 1995b). Results showed that process manipulation can lead to · significant quality improvements. The work is therefore extended to examine the geometric case of cornering. A brief summary is given below. The Japanese corporation Mitsubishi (Moriyasu e.t a!., 1986), and other research groups realised early on that adaptive control of laser parameters was a real possibility with conventional CNC (computer numeric control) systems. By adapting parameters such as laser power levels, switching between continuous wave (CW) and pulsed mode, and effecting cutting speed changes, vast quality improvements were obtainable. Such techniques are trial-and-error based, and therefore are time consuming, whereby the optimal set of parameters may still not be reached. It was recognised by Biermann and Geiger ( 1991) that simulation of the laser process under the effects of the motion system can lead to improved results for laser processing. An optimisation strategy is therefore proposed in which it forces the cutting front temperature to remain uniform, even when laser cutting conditions are unsteady. The problem of minimising the deviation from steady state results in a non-linear power profile, .as the inter-relationships between laser parameters are complicated by the mobility exhibited by the cutting front. Uniform cutting front temperatures affect quality in various ways. They produce better quality by reducing i) kerf widening effects, ii) heat102 affected zones, and iii) wide spread selfburning. At the very least, uniform cutting front temperatures reduce the variability in progressive cut quality. The strategy developed is iterative by nature (see Fig. 1 ). The model proceeds forward in time by the accumulation of the timestep D.t of integration. By monitoring the status of the front temperature at every instance, a steady state value can be established.