# Theoretical and experimental analysis of the remote welding process on thin, lap-joined AISI 304 sheets

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## Abstract

In this study, a theoretical approach of the remote welding process has been developed and discussed. The study obtains numerically the melting boundaries of different heat source angles, based on an analytical calculation of the keyhole depth. The approach considers the dominant process parameters of the laser power, the welding speed and the inclination of the laser beam on the workpiece surface. The geometrical particularities of the beam spot, due to the different inclination of the laser beam upon the processing plane, have also been considered in a previous study of the authors. The theoretical results present good agreement when compared with experimental data obtained from a remote welding system (RWS) on lap welding of AISI 304 stainless steel, thin sheets.

## Keywords

Remote welding Inclined laser welding Laser welding modelling Remote welding system RWS## Abbreviations

- RWS
remote welding system

- FEA
finite element analysis

## Nomenclature

## *Latin Symbols*

*A*the material’s absorptivity,

*b*the keyhole radius at direction vertical to the laser beam propagation direction (m),

*C*_{P}the material’s specific heat (J/kgK),

*C*_{Pair}the specific heat of air (J/kgK),

*d*the keyhole depth along the direction of the laser beam propagation (m),

- H
the material’s enthalpy (J/kg),

- \( \overline{h} _{{forced}} \)
the forced convection film coefficient for the upper surface of the upper sheet (W/m

^{2}K),- \( \overline{h} _{{free,LH}} \)
the free convection film coefficient for the lower, horizontal surfaces of the sheets (W/m

^{2}K),- \( \overline{h} _{{free,I}} \)
the free convection film coefficient for the interface surface between the sheets (W/m

^{2}K),- \( \overline{h} _{{free,UH}} \)
the free convection film coefficient for the upper, horizontal surface of the lower sheet (W/m

^{2}K),- \( \overline{h} _{{free,V}} \)
the free convection film coefficient for the vertical surfaces of the sheets (W/m

^{2}K),*k*the material’s thermal conductivity (W/mK),

*k*_{air}the thermal conductivity of air (W/mK),

*L*_{m}the material’s latent heat of melting (J/kg),

*L*_{v}the material’s latent heat of vaporisation (J/kg),

*n*the coordinate normal to an infinitesimal keyhole surface,

*P*the provided laser power (W),

*P*_{max}the maximum output laser power (W),

*Q*the applied volume heat load (W/m

^{3}),*Q′*the applied volume heat load (W/m

^{2}),- \( r_{f} \prime \prime {\left( {z_{r} \prime } \right)} \)
the laser beam radius as a function of distance, \( z_{r} \prime \) (m),

- \( r_{{f,\phi }} \prime \prime \)
the laser beam radius at distance \( z_{{r,\phi }} \) from the focal plane (m),

- \( r_{{f_{0} }} \)
the Gaussian laser beam radius at the focal plane (m),

- \( r_{{f_{0} }} \prime {\left( \phi \right)} \)
major semi-axis of the elliptic laser beam spot at zero focal depth (m),

*T*the temperature at any arbitrary point (K),

*T*_{0}the ambient temperature (K),

*T*_{m}the material’s melting temperature (K),

*T*_{v}the material’s vaporization temperature (K),

*u*the welding speed (m/s),

*u*_{air}the speed of the air jet (m/s),

*x, y, z*the Cartesian co-ordinates of the local co-ordinate system at the keyhole (m),

*x′, y′, z′*the Cartesian co-ordinates of a rotated coordinate system around axis

*y*about angle*φ*, of the local keyhole co-ordinate system (m),*x*_{E},*y*_{E}the Cartesian coordinates of an arbitrary point of the elliptical beam spot’s boundary (m),

- \( z_{r} \prime \)
the distance from the focal plane along the laser beam propagation (m),

- \( z_{{r,\phi }} \prime \)
the distance of the plane parallel to the focal plane that intersects with the laser beam’s waist at the surface of the workpiece for a given angle

*φ*(m),

## *Greek symbols*

- ε
the material’s emissivity,

*δ*_{f}the position of the focal plane in respect to the processing plane (m),

*λ*the wavelength of the laser (m),

- ν
_{air} the kinematic viscosity of air (m

^{2}/s),*ρ*the material’s density (kg/m

^{3}),*ρ*_{air}the density of air (kg/m

^{3}),*φ*the supplementary angle to the incidence angle (Degrees),

*φ*_{w}the weld angle (Degrees).

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## Notes

### Acknowledgement

The work reported, was partially supported by the EU funded project: G1RD-2000-00332, “Highly Efficient & Flexible Remote Welding Systems for Advanced Welded Structures-REMOWELD”.

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