Electric arc welding processes are of utmost importance in various technological and manufacturing sectors, it is for this reason that understanding the complex phenomena present in these processes is fundamental for optimizing these. In this effort, the scientific community has generated and accumulated a large and varied amount of information about different operating conditions and processes related to electric arc welding. However, there are very few papers trying to summarize and condense this information simply and practically.
This paper aims to condense some of this information for electric arcs in GTAW welding processes. It shows the existence of a unique dimensionless form for welding arcs burning in typical operating conditions and burning in Ar, and He, providing simple and precise dimensionless algebraic equations of the main characteristics of the arc column, without the need to perform a complex numerical calculation or simulation.
A numerical model for electric arcs in GTAW welding processes from direct current DC to atmospheric pressure was implemented through a computer software CFD (Computational Fluid Dynamics) Phoenics 2017, based on the principles of mass conservation, amount of motion, energy, Maxwell laws and the law of Ohm, which describes the electrical properties of the arc column burning in Ar, and He, as magnetic field, flow patterns and temperature contours, which was developed and validated in a previous job. The most significant assumptions considered in this model are: (i) the arc is considered to be in the Local Thermodynamic Equilibrium (LTE), (ii) the current density in the cathode is assumed to be constant with a value of 6.5 107Am-2, iii) The anode surface is considered to be flat.
The universal form for arcs of Ar, and He is given through the radius of the arc (Ra), which coincides with the visible zone of the arc, which has enough electrical conductivity to maintain a continuous flow of electric current that is about 2850 S/m for arcs of Ar. This value of electrical conductivity is obtained at 10,000 and 14,900 K for arcs of Ar, and He respectively, and therefore the isotherms formed at these temperatures will determine the radius of the arc.
Shape of the arc
The universal shape of the arc can be obtained by graphing the radius of the arc Ra versus the axial distance Z dimensionally by dividing both numbers between the radius of the point on the cathode by which the current exits Rc. Additionally, these dimensionless coordinates are multiplied by the number of Prandtl evaluated at the temperature of the isotherm selected for each gas.
The universal shape of the arc can be easily adjusted through a simple algebraic equation given by:
R_a/R_c 〖Pr〗^0.85=ln(a+b(Z/R_c 〖Pr〗^0.85 )); R2 = 0.976 Eq. 1
Where, Ra, Rc and Z are in meters and “a” and “b” are constant.
Arc column characteristics
The characteristics of the arc column (magnetic field, speed and temperature) are also represented dimensionally by dividing them by their maximum value at any axial distance from the cathode, and by a dimensionless radial distance R/Ra *Prx.
The universal radial profiles in the arc column for the magnetic field, temperature and speed are computed respectively and it is clear the similar trend all cases present. These are independent of the used shielding gas (Ar, or He), the axial position (0.3 Z — 0.8 Z), the applied current (200 – 300 A) and the arc length (5 – 10 mm).
The magnetic field universal profile is:
B_Θ/(B_max°)=(a+b(R/R_a 〖Pr〗^(-0.5) )^0.5+c(R/R_a 〖Pr〗^(-0.5) ))/(1+d(R/R_a 〖Pr〗^(-0.5) )^0.5+e(R/R_a 〖Pr〗^(-0.5) ) ) Eq. 2
The arc temperature universal profile is:
T/(T_max°)=a+b(R/R_a 〖Pr〗^(-1) )+c(R/R_a 〖Pr〗^(-1) )^2+d(R/R_a 〖Pr〗^(-1) )^3+e(R/R_a 〖Pr〗^(-1) )^4+f(R/R_a 〖Pr〗^(-1) )^5+g(R/R_a 〖Pr〗^(-1) )^6 Eq. 3
The arc velocity universal profile is:
V_z/(V_max°)=(a+b(R/R_a 〖Pr〗^(-1) )+c(R/R_a 〖Pr〗^(-1) )^2)/(1+d(R/R_a 〖Pr〗^(-1) )+e(R/R_a 〖Pr〗^(-1) )^2 ) Eq. 4
Where R is the radial position (m), BΘ, Vz and T are the magnetic field (tesla), the axial arc velocity (m/s) and temperature (K) in the arc column respectively, while Bmax◦, Tmax◦ and Vmax◦ are maxima of the magnetic field, axial velocity, and temperature at each axial position.
The main characteristics of the electric arc column in GTAW welding processes burning in Ar, and He can be easily obtained through universal correlations formed by simple algebraic equations reported in this work.
By using the 10,000K isotherm in argon arcs and 14,900 K for He as a criterium to define the shape of the arc, a good result in selecting the boundary of the arcs burning in He was gotten, by taking the value of the electric conductivity at those temperatures for each gas (≈ 2850 S/m).
The proposed correlations involve the radial profiles at any axial distance of the following arc column characteristics: i) The shape of the arc (Eq. 1), magnetic field radial profiles (Eqs. 2), arc temperature fields (Eqs. 3), and arc velocity vector field (Eqs. 4).