Robert Ducharme

The laser welding of thin metal sheets: an integrated keyhole and weld pool model with supporting experiments

An integrated mathematical model for laser welding of thin metal sheets under a variety of laser material processing conditions has been developed and tested against the results of experiments. Full account is taken in the model of the interaction of the laser-generated keyhole with the weld pool. Results calculated from the model are found to agree well with experiment for appropriate values of the keyhole radius. The analysis yields values for power absorption in the metal. In a complementary calculation the total absorption of the laser energy is determined from detailed consideration of the inverse Bremsstrahlung absorption in the plasma and Fresnel absorption at the keyhole walls. To test these results, experiments were performed on 1 mm mild steel using a high-speed video camera, which measured the surface dimensions of the melt pool. Processing parameters were varied to study the effect on the melt pool; parameters considered included traverse speed, laser power and shroud gas species. The general shape of the weld pool was found to depend on whether penetration was full, partial or blind; only the results for full penetration were compared with the theory, which is for complete penetration only.

A mathematical model of the arc in electric arc welding including shielding gas flow and cathode spot location

A mathematical model of a free-burning TIG electric arc with non-consumable electrodes using a flat anode and argon shielding gas is presented. Differential equations describing the conservation of mass, momentum and energy are solved together with Maxwells equations describing the electromagnetic field. The dependence of transport coefficients on temperature is taken into account. The gas flow is assumed to be laminar and the partially ionized plasma is assumed to be in local thermodynamic equilibrium. The mathematical model can cope with a broad range of operating conditions. The model is used to demonstrate the strong influence that the velocity and temperature of the flow of gas entering the top of the electric arc in the region of the cathode can have on the arc column. In particular, it is shown that cathode flows of strength sufficient to produce a significant constriction of the electric arc need to be assumed in order to account for experimentally measured electric fields in the arc column as well as the total voltage drop for 10 mm arcs. The use of this model also shows the part played by the cathode spot and its location in the nature of the electric arc column. In particular, two complementary techniques for studying the arc column are highlighted. In the first, a strictly stable static arc is needed in order to employ the spectroscopic technique of temperature measurement. In contrast, when the position of the arc is less stable, a rapid measurement with an electric probe is indicated in order to measure the electric field. The arc model described by Ducharme et al (1993) will then yield the temperature field. The model presented here produces the results for the temperature distribution and for the electric field based on the use of appropriate boundary conditions.

A mathematical model of glass flow and heat transfer in a platinum downspout

Abstract The possibility of using a heat exchanger system to control the flow of glass through a platinum downspout is investigated. Downspouts are used in place of refractory throats since they avoid some of the problems associated with throats. It is assumed that the flow is predominantly axial and an integral expression for the flow field is obtained. The temperature distribution in the glass is calculated using the finite difference method. The formulation of the heat transfer problem includes a detailed analysis of the anisotropic radiation field in the glass.

A MATHEMATICAL MODEL OF THE FLOW OF BLOOD CELLS IN FINE CAPILLARIES

A description of the flow of blood cells in the capillary blood vessels is presented. The model employs the lubrication theory approach first suggested by Lighthill (J. Fluid Mech. 34, 113-143, 1968). The work of previous investigators is extended by taking into account a wider range of the elastic deformations which affect the cell.

A mathematical model of TIG electric arcs operating in the hyperbaric range

In a recent paper Ducharme et al presented a model for a free-burning tungsten inert gas (TIG) electric arc with non-consumable electrodes using a flat anode and argon shielding gas. The model evaluates the laminar gas flow, temperature distribution and electric field in the arc column by treating the current carrying region of the arc as a partially ionized plasma in local thermodynamic equilibrium. The dependence of transport coefficients on temperature is taken into account, as is the entrained shielding gas flow entering the arc from around the cathode. This model is extended here to investigate both 5 mm long 200 A and 10 mm long 100 A electric arcs at elevated pressures in the ranges 1 - 5 and 1 - 14.8 bar respectively. The results of the electric arc model are found to be in satisfactory agreement with a range of experimental data including spectroscopic temperature maps, electric field distributions, voltage drops, arc radii and total radiative emissions. It has been shown by Allum et al that short arcs length < 4 mm) become unstable once a critical Reynolds number has been reached, signifying the onset of turbulence for the flow emerging from the arc nozzle. This analysis, however, does not explain the inherent instability of longer arcs, which may be present even in a still argon atmosphere. It is proposed here that these are caused by the onset of turbulence in the entrained shielding gas. Two seperate Reynolds numbers, therefore, come into play in the physics of the TIG arc in connection with instabilities and these are estimated in the paper.

On the relation between fluid dynamic pressure and the formation of pores in laser keyhole welding

In the laser welding of metals with a continuous CO2 laser, a hole containing a partially ionized metal vapor is formed throughout the depth of the material. A full description of flow conditions inside this hole is needed for a complete understanding of the process, but much can be learned from a simpler analysis of this aspect of the problem. The balance of forces that keeps the keyhole open can be investigated in this way. Such a model shows that over most of the keyholes length, the dominant force keeping the keyhole open against surface tension is the fluid mechanical pressure in the plasma rather than the ablation pressure. This has a bearing on the problem of the formation of pores in the interior of the welded material. It is clearly observable on films made of the surface of the weld piece and of cross‐sections through it that the keyhole has some of the characteristics of instability. It is shown that under some circumstances the balance of pressure against the forces of surface tension can be ...

The induction melting of glass

The possibility of using coupled system of an induction coil and a metal susceptor for the purposes of melting glass is investigated. The magnetic field strength and the current density in the different regions of the furnace are calculated. Detailed consideration is then given to the influence of the glass on the electrical characteristics of the furnace and to the problem of magnetic forces on the susceptor.

A mathematical model for the penetration depth in welding with continuous CO2 lasers

Continuous CO2 lasers have been used successfully for many years to weld a variety of materials. An interesting problem has, however, emerged. This is the question of the value of the penetration depth of continuous CO2 laser light in mild steel. Experimental measurements of the penetration depths of continuous CO2 laser light in mild steel specimens have been made for a variety of translation speeds and incident laser powers. The results indicate that the ratio of the keyhole radius at the top of the work piece is almost exactly three times the radius at the bottom in the case of maximum penetration. This ratio is independent of all operational parameters apart from the f-number of the laser’s optical system; in particular, it does not depend on the translation speed or the power of the laser. This in turn determines the radius of the keyhole at the top, although it should be noted that this is not the focal spot radius because of the defocusing effect of the plasma emerging from the keyhole. The present paper uses a simple model of Fresnel absorption to investigate the consequences of this relation and confirms that the depths predicted by the model agree very closely indeed with the results of experiment. The integrated keyhole and weld pool model can be employed to obtain more accurate values, but the model confirms the principle. The optics of the laser light in the keyhole is investigated and this, together with the nature of the simple model, confirms that the process of welding at the maximum possible thickness for the given values of the other operational parameters is dominated by the processes of Fresnel absorption and reflection at the keyhole walls.Continuous CO2 lasers have been used successfully for many years to weld a variety of materials. An interesting problem has, however, emerged. This is the question of the value of the penetration depth of continuous CO2 laser light in mild steel. Experimental measurements of the penetration depths of continuous CO2 laser light in mild steel specimens have been made for a variety of translation speeds and incident laser powers. The results indicate that the ratio of the keyhole radius at the top of the work piece is almost exactly three times the radius at the bottom in the case of maximum penetration. This ratio is independent of all operational parameters apart from the f-number of the laser’s optical system; in particular, it does not depend on the translation speed or the power of the laser. This in turn determines the radius of the keyhole at the top, although it should be noted that this is not the focal spot radius because of the defocusing effect of the plasma emerging from the keyhole. The present...

The theory of radiative transfer in the plasma of the keyhole in penetration laser welding

In laser keyhole welding the laser beam generates a hole through the workpiece, and a plasma is formed in this hole. The role of this plasma is uncertain, but it seems probable that it assists in the transfer of energy from the laser beam itself to the molten material of the workpiece. This will be caused in part by thermal conduction in the plasma, but earlier investigations have ignored the effects of absorption, reradiation and scattering within the plasma itself. It is probable that in reality these effects are significant, as they are in, for example, energy transfer in glass furnaces, or in stellar structures. The processes involved in the keyhole are examined and assessed, and related to other phenomena known to be of importance, such as recombination at the boundary. From the point of view of incorporation into theoretical models of keyhole processes, the usual approximations to the theory of radiative transfer present problems near to the presence of boundaries, where there are substantial space gradients of the physical quantities. This problem of an appropriate mathematical representation is considered.In laser keyhole welding the laser beam generates a hole through the workpiece, and a plasma is formed in this hole. The role of this plasma is uncertain, but it seems probable that it assists in the transfer of energy from the laser beam itself to the molten material of the workpiece. This will be caused in part by thermal conduction in the plasma, but earlier investigations have ignored the effects of absorption, reradiation and scattering within the plasma itself. It is probable that in reality these effects are significant, as they are in, for example, energy transfer in glass furnaces, or in stellar structures. The processes involved in the keyhole are examined and assessed, and related to other phenomena known to be of importance, such as recombination at the boundary. From the point of view of incorporation into theoretical models of keyhole processes, the usual approximations to the theory of radiative transfer present problems near to the presence of boundaries, where there are substantial space ...

A mathematical model of ablation in the keyhole and droplet formation in the plume in deep penetration laser welding

CW CO2, CO and Nd:YAG lasers are well established as power sources for the welding of metals. The mechanisms for the coupling of energy from the beam to the weld specimen are important; one such mechanism is Fresnel absorption of laser light in the surface of the metal and another is inverse bremsstrahlung absorption in the plasma of the plume above the surface of the work piece, and in the keyhole produced by the process. For the inverse bremsstrahlung mechanism to work a plasma must be present. It probably forms as a result of ablation of gas from the walls of the keyhole that is then heated up under the action of the laser beam, forming a partially ionised plasma. This emits radiation and so its temperature drops. The radiative losses can be calculated but the process can be complicated by the line spectrum of radiation that is in general emitted. The radiative losses from argon plasmas have been studied in detail and if metallic plasmas have comparable radiative losses, their temperatures would remain high enough for the Saha equation to predict partially ionised plasmas under conditions of local thermodynamic equilibrium. For partially ionised metallic plasmas in electric arcs data exist that suggest a much higher level of radiation losses. This could lower the temperature of the plasma to a value at which ionisation in a state of local thermodynamic equilibrium could be too low to be of significance even for CW CO2 laser wavelengths. Levels of ionisation are lower for CW CO laser wavelengths and probably negligible for the Nd:YAG laser. Plasmas are nevertheless thought to occur when Nd:YAG lasers are used for laser welding. This suggests that some non-equilibrium mechanism is present in laser welding leading to plasma generation. Such a mechanism arises from spray formation at the walls of the keyhole when the temperature is at or slightly above the boiling point of the metal under laser action. Spray ejected from the keyhole walls is quickly vaporised in the beam path. Droplets of small radii experience high levels of surface tension that increase the internal pressure and hence their boiling point can be high enough to generate plasma. The lifetimes of droplets outside the path of the laser beam could be much larger than in the presence of the beam, resulting in condensation in a suitable region of the plume. Their presence could be detected by scattering of a low-power transversely directed laser beam; they have been observed by Matsunawa [1]. The formation of bubbles in the keyhole wall that gives rise to the spray is studied here. Droplet generation is considered under conditions of local thermodynamic equilibrium by kinetic rate processes in the environment of the keyhole; so too is their ablation to produce plasma. Condensation in the plume outside the path of the laser beam is analysed so a possible mechanism is described for plasma formation under the conditions of laser keyhole welding.CW CO2, CO and Nd:YAG lasers are well established as power sources for the welding of metals. The mechanisms for the coupling of energy from the beam to the weld specimen are important; one such mechanism is Fresnel absorption of laser light in the surface of the metal and another is inverse bremsstrahlung absorption in the plasma of the plume above the surface of the work piece, and in the keyhole produced by the process. For the inverse bremsstrahlung mechanism to work a plasma must be present. It probably forms as a result of ablation of gas from the walls of the keyhole that is then heated up under the action of the laser beam, forming a partially ionised plasma. This emits radiation and so its temperature drops. The radiative losses can be calculated but the process can be complicated by the line spectrum of radiation that is in general emitted. The radiative losses from argon plasmas have been studied in detail and if metallic plasmas have comparable radiative losses, their temperatures would remain...