外文翻译--激光切割陶瓷砖的速度：理论和经验值的比较

外文翻译--激光切割陶瓷砖的速度：理论和经验值的比较内容摘要：

ent of the above, Chryssolouris presents a general model [7] based principally on a heat balance at the erosion front and a temperature calculation inside a material from heat conduction equations. In order to give a quantitative understanding of the effect of the different process parameters on the cutting process, an infinitesimal control surface on the erosion front surface is shown in Fig. 4. The control surface is inclined at an angle y with respect to the Xaxis and at an angle  with respect to the Yaxis, and is subjected to a laser beam of intensity J(x, y). The Cartesian coordinate system (x, y, z) is moving with the laser beam which has intensity profile J(x, y) projected onto the control surface. The heat balance at the control surface is In order to derive simple analytical relations, simplifications need to be made. For instance, although heat is conducted threedimensionally near the erosion front due to the presence of a bottom surface in cutting, which behaves as an adiabatic boundary, the heat conduction occurs twodimensionally (downward conduction is negligible pared with conduction in other directions). Thus, in cutting it is assumed that heat is conducted twodimensionally into the solid, so that the conduction term in Eq. (16) can be simplified as which gives the heat balance condition at the cutting front. The temperature gradient at the erosion front, assuming that the conduction area and direction do not change, can be determined by solving the following 1D heat conduction equation From Eq. (18) the temperature distribution inside the solid can be determined and differentiation of this gives the following temperature gradient at the erosion front By substituting the temperature gradient into the heat balance, an equation for the erosion front slope (. tan  ) in the cutting direction can be obtained. This slope is said to have an infinitesimal depth which forms an integral which, upon integration, gives an expression for the depth of cut By setting d= s and the melt temperature at the top surface along the centre line of the cut, TS  1327 C , a value of V opt can be calculated for a specific type and thickness of tile, where (again) P  450 W, r  3380 kg/m3 , D = 2R =  10 3 m， L  103 J/kg ， C  800 J/kg K ， T0 =18 C and A = 1.. Therefore, Eq. (20) can be arranged to give which, again, is similar to the formula derived from Steen and Powell39。 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, V opt  1/s. This is what would be expected in practice. The differences between the individual theoretical predictions of V opt can be ascribed to the different analytical approaches taken in formulating a suitable cutting model. However, probably the most significant factor in the difference between predicted and experimental values of V opt is the variation in thermal and material proper。