【正文】 ting speeds. It should be noted that the cut zone referred to in Fig. 3 extends to an area corresponding to R = mm (. the beam radius). The curves in Fig. 3 show that by increasing V the peak temperature within the cut zone is reduced. They also show the optimum cutting speed that will cut the tiles, which occurs at the intersection with the line representing the representative melt temperature of ceramic tile, . TP =1327 C? (1600 K). Any cutting speed above this line should, in theory, produce FTC and any that fall below will not cut the tile. Note that thermal conductivity plays no part in Eqs. (7) and (8). In the calculation of V opt , Eqs. (7) and (8) are applied depending on whether the tile was considered to be thick or thin as defined by Eq. (6). To calculate V opt for a `thin39。 therefore R = r. However, in the case of the thicker tile Eq. (7) can be arranged to give where R = [( ? 10 3? )2 + s 2 ] 2/1 . For both cases the peak temperature is set to equal the melt temperature of the tile. . Calculating Vopt using heat balance models Powell [5] presents an analysis in which, during laser cutting, a dynamic equilibrium exists in the cut zone that balances the `ining39。 energy and material. Therefore a simple energy balance for laser cutting can be expressed as Energy supplied to cut zone= Energy used in generating a cut + Energy losses from the cut zone(by conduction, radiation, etc.) This can be expressed as the following formula If it is assumed that all of the laser power transmitted through the cut zone interacts with the cut front (P b =0), that all laser power is absorbed by the tile substrate (A = 1) and that the conductive, radiative and convective losses are negligible, then the above equation reduces to where w= 2r. Since the cut zone for good quality CW cuts rarely exceeds a few microns the previous assumptions are not unreasonable. Noting that for full through cutting, Vopt =l/t, rearranging the above formula gives Similarly, Steen [6] presents an analysis in which the cutting process can be approximately modelled by assuming all the energy enters the cut zone and is removed before significant conduction occurs (. no significant energy loss). The oute is a simple equation based on the heat balance for the material removed. If we assume that n31 when V = Vopt , then Eq. (14) reduces to which is the same as Eq. (13). This is to be expected since both Powell and Steen use basically the same energy balance approach. As an enhancement 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。 analysis does take this into account). (7) All of the laser power transmitted through the cut zone interacts with the cutting front. (8) There are negligible conductive, radiative and convective losses during cutting. (9) Powell39。s model assumes that the specific energy of cutting is taken to be constant. (11) Rosenthal39。 and `economy39。s contention that, at present, modelling the behavio