At present, it is considered that the value of the ion fraction of the current in the welding arcs is approximately β ≈ 0.5. Assuming that the value of β does not depend on the value of the welding current (I), we determine the number of ions transferring the ion current in the cathode region (Ni) at different currents by the formula
Ni = Ii/е = βI/е,
where e — the electron charge, Кл, and the corresponding number of atoms evaporated from the cathode spot (Nп), according to the formula Nп = Gп/ mFe, where mFe — the mass of the iron atom, equal to 9,26*10–26 kg.
Ni ≈ Nп and with increasing current, the Ni/Nп ratio increases, and the total number of evaporated Ni + Nп atoms also increases. The mechanism of this process can be described as follows. The atoms evaporated from the cathode spot fall into the ionization part of the cathode zone, where the part of them (Ni) is ionized and returns to the cathode as an ion current, and the part (Nп) leaves the cathode zone and enters the arc column, partially displacing from the cathode zone the atoms of the protective gas.
Now consider the concentration of cathode atoms in the cathode zone, in this case iron atoms (nFe). From the surface of the cathode spot Ni + Nп of iron atoms is evaporated per unit time. In one second these atoms propagate in a volume equal to W = Sкп *Vа, where Sкп — the area of the cathode spot, m2, and Vа — the velocity of the thermal motion of the atom at the cathode spot temperature equal to the boiling point of iron Тк = 3160 К. The value of Vа is determined by the formula Va = √2kT/m, where k — the Boltzmann constant, J/K; T — the temperature of the evaporating atoms, K;
m = mFe. Substituting Т = Тк, we obtain Vа = 9,58*102 m/s. The value of Sкп can be determined from the formula Sкп = I/j, where j — the current density in the cathode spot for the iron electrode, which is ∼ 2*107 А/m2. According to what has been said, the concentration of iron atoms is determined by the formula
nFe = (Ni + Nп)/W = (Ni + Nп)j/(I √2kT /mFe).
nFe increases somewhat with increasing current and is about an order of magnitude smaller than the concentration of atoms at atmospheric pressure and the average arc temperature in СО2 equal to T = 7000 K, determined by the formula
n = p/(kT) = 1,04 ・ 1024 1/m3, где р = 105 N/m2 — the magnitude of atmospheric pressure. However, it must be taken into account that at the boundary of the cathode zone with the arc column, the gas flow rate (iron vapor) should decrease to the gas flow rate in the arc column. This speed is determined depending on the magnitude of the current and is ((0,68…1,09)*102m/s. Therefore, the velocity of the flux of evaporated atoms decreases at the boundary of the cathode spot, i.e. In the ionization space, about 9,58 /(0,68…1,09) = 14,1…8,79 times, i.e. About the order of magnitude, which in the same way causes an increase in the concentration of iron atoms in this part of the cathode zone.
