【正文】 isting laser machining database. Empirical models developed by the author are described which have been successfully used to predict cutting speeds for various thicknesses of ceramic tile. 1998 Elsevier Science Ltd. All rights reserved. Keywords: CO2 laser Ceramic materials Advanced cutting processes Laser modeling Cutting speeds 1. List of symbols A Absorptivity a Thermal (m2/s) C Specific heat (J/kg K) d Cutting depth (mm) Ecut Specific cutting energy (J/kg) k Thermal conductivity (W/m K) J Laser beam intensity (W/m2) L Latent heat of vaporisation (J/kg) l Length of cut (mm) n Coordinate normal to cutting front P Laser power (W) Pb Laser power not interacting with the cutting front (W) Q Heat input (J/s) R Radial distance (mm) r Beam radius (mm) s Substrate thickness (mm) Scrit Critical substrate thickness (mm) T Temperature ( C? ) T0 Ambient temperature ( C? ) TP Peak temperature ( C? ) TS Temperature at top surface ( C? ) t Time (s) V Cutting speed (mm/min) Vopt Optimum cutting speed (mm/min) w Kerf width (mm) X, Y, Z Coordinate location x, y, z Coordinate distance (mm) ? Conductive loss function ? Radiative loss function ? Convective loss function ? Angle between Zcoordinate and xcoordinate (rad) n Coordinate parallel to bottom surface ? Angle of inclination of control surface . Xaxis (rad) v Coupling coe?cient ? Translated coordinate distance (mm) ? Density (kg/m3 ) ? Angle of inclination of control surface . Yaxis (rad) 2. Introduction Laser cutting of a decorative ceramic tile has its own set of characteristic problems including burnout,striations, dross and outofflatness, which all affect the finish quality of a cut edge [13]. A typical cut may have some or all of these features depending on the type of ceramic tile being processed and on the setting of the various setup parameters. In a production environment, cutting speeds need to be optimised in order to reduce incut times without too much significant degradation of cutedge quality. An optimum cutting speed can be defined as that which will produce fullthroughcutting (FTC) with minimal microcracking both in the surface glaze and in the tile substrate. Therefore, it can be argued that the cutting speed necessary to raise approximately a cuboid of material of dimensions l, w and s to the materials39。s analysis. 4. Comparison with empirical models An empiricallyderived laser machining database for cutting ceramic tile has been piled from extensive (and ongoing) experimental work in the Department of Mechanical and Chemical Engineering at HeriotWatt University. The database contains specific information on cutting speeds associated with variation in such cutting parameters as shield gas type and pressure, nozzle size, focal point and, most importantly, surface finish quality. Table 1 below gives a parison between V opt from this database with the previously described theoretical approaches. Note that, where available, a range of values is given from the database since ceramic tile is a nonhomogeneous material and cutting conditions will vary markedly from one tile to another. Mean values of V were used to establish a best fit curve for the cutting data according to a method initially devised by Thomson [3], in which the empirical curve is plotted for the rated power of the laser cutter used and fitted to the following formulae where A, B, C and D are constants. This can be done in a variety of ways. The normal method to use is to take four points from the plotted graph and solve these simultaneously. The formula generated by fitting these coefficients back into Eq. (1) should then be checked to ensure that it follows the experimental curve and does not deviate beyond the upper and lower limits. If the first set of coefficients proves unsatisfactory, the process is repeated but different start points are chosen, or one or more of the coefficients A, C or D is set to zero. Cutting speeds at the machine limit should not be used when generating formulae for the curves, since the governing factor at these limits is no longer the process. For the given set of data for decorative ceramic tile, the following empirical equation was determined with C = D= 0. Livingstone and Black [1] developed an empirical equation describing the behaviour of V with s for the FTC of decorative ceramic tile which followed an exponential relationship of the form where ? and ? are constants determined by the leastsquares method. For the data presented in Table 1, an equation of the form resulted. The theoretical results predicted in Table 1 are represented graphically in Fig. 5, together with the empirical curves derived from the database results. 5. Concluding remarks Fig. 5 shows that the predictive models describe a decrease in Vopt with an increase in tile thickness, Vopt ? 1/s. This is what would be expected in pr