The analyzed mathematical pattern is based on the transfer equation into a homogeneous thermic medium heated with a laser beam assisted by an active gas jet. In the determination of the temperature distribution one has to take into account the existent loss of energy through the electromagnetic radiation manufacturing could become very significant. The work is going to show a suitable methodology of determining the loss of energy through electromagnetic radiation in the case of manufacturing of a metal material by using laser beams containing CO2 while it is assisted by an active gas jet ( ), suitable for establishing the process parameters and for evaluating the thermic efficiency. 1. Introduction The way of manufacturing a material through laser beams consists in bringing the material given in vaporization and melting estate in the point of the interaction with the concentrating beam. The time evolution of the distribution of the temperature into a system is strictly related to the appearance of the heat flux from the hottest regions to the coldest ones. The three mechanisms which make the transfer of the heat, possible, are: the conduction, where the heat is transferred straight through the medium; the convection, where the transfer of the heat occurs at the some time with the movement of the fragments of medium; the radiation, where the heat has to be received as a form of transfer of the electromagnetic energy. When high temperatures occur at the surface in some practical cases, one must take into account the loss of the energy through radiation which could become significant. These losses will be taken into account under the conditions related to the surface. In order to determinate the loss of energy through electromagnetic radiation one must know the material surface temperature distribution, material which is manufactured by laser beam. By determining the shape of the domain, the initial temperature distribution and the limit conditions, the heat equation leads to the solution T(x, y, z, t) for an object characterized by the specific heat , massic density -- , and thermic conductivity - k For a "gaussian" distribution of the source of energy the solution of the heat equation is given by the relation : (1.1) where: is the maximum flux on the centre; d -- the ray concentrated laser beam; K - difusity of the medium; r - the radial coordinate; z - the axial coordinate. The destruction of the crystalline network of the material and bringing it in the vaporization estate along a pre-established curve is taking place because of the energy of the photons inside the material and because the jet of active, gas which contributes to the intensifying of the action of destroying the material extreme radiations it involves. In the concrete case of the complete source of temperature and on the condition that on the frontier of the semi-space considered (z 0), the intensity of the ray of photons and respectively the energy of oxidation should have "gaussian" distribution, for ( z = 0) one could obtain the radial distribution of the temperature: where: is the ambiental temperature; - the efficiency while oxidation; - - the energy of oxidation on the metal atom completely oxidated ; - the vaporization speed; M - the atomic mass; the specific heat of the metal; T(r, t) - the temperature of the surface of the material at t moment; the power of the laser beam. In order to evaluate the irradiative flux one can use Stefan-Boltzmann's law; thus resulting: (1.3) For the materials rich in Fe, the vaporization speed can be found out by a simplified relation based on the low of the energy conservation (the quantity of energy necessary to vaporization of the material in the inside of the hole which comes from the laser power absorbed by the material of this manufactured object and the power developed in the extreme, reaction of Fe atoms oxidation evaporated is given by the loss of power by thermic conduction and by the vaporization of the material in the considered time interval). Thus resulting: (1.4) where is the ray of the defocused laser beam (it is used to correct the flux of defocusing in calculation the evolution of the vaporization front to the inside of the material - the focusing occurring on the surface to be manufactured) and is calculated by the relation :
1.Draganescu, V., Velculescu, V., G., "Thermal Cutting With Laser Beams", Academy Publishing House, Bucharest, 1986; 2.Pearsica M., Constantinescu, C., "The Analytic Determination of the Radial Distribution of Temperature of the Metallic Materials Cutting Process with Laser Beam", XXVIII-th Scientific Communication Conference, Military Technical Academy, Bucharest, 1999.
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