A mathematical analysis of heating effects and electrode erosion in conical electrical arc cathodes

Abstract

A spherical system of coordinates is used to solve the time-dependent heat-conduction equation for inside a conical cathode, whose surface is subjected, during arc welding processes, to complicated thermal heat-exchange effects. These arise from a variety of factors such as ion bombardment from the main body of the electrical arc, thermionic emission from the cathode's surface and Joule heating arising from the main current-carrying body of the cathode. The heat-conduction equation has a time-dependent source term arising from a combination of Joule heating and thermionic emission and is solved analytically using integral transform techniques. The solution is expressed in terms of integrals. These allow the response of the cathode for various currents and cathode geometries to be studied.

Thermal behaviour of the consumable electrode in the vacuum arc remelting process

“…Hence Lowke et al (1997) have built up a unified 2D model for a tungsten electrode and its plasma which allows the prediction of temperature field and arc voltage. The numerical model developed by Solana et al (1998) Nomenclature C P specific heat (J kg −1 K −1 ) g l fraction of liquid I electrical current of the arc (A) L latent heat of fusion (J kg −1 ) P(i) energy flux density transferred by the arc to the i cell (W m −2 ) P arc electrical power of the arc (W)…”

Heat transfer and modeling hollow cathode material structural state of vacuum plasmatron

“…On the one hand, the emission current density and erosion are determined by the temperature distribution along the working surface of the cathode, and on the other hand, the temperature stresses arising from the uneven heating of the electrode can lead to its destruction even before the contact surface with the arc melts. In addition, the mechanical destruction of the electrode can be facilitated by a change in its structure, for example, embrittlement as a result of metal recrystallization, which is important for hollow cathodes [3][4][5].…”

“…Based on the data of [11] for tungsten fiberboard, G = 10 15 exp (-753⋅10 3 /RT). The rate of nucleation in recrystallization in accordance with (5) has an activation mechanism in accordance with (5). Therefore, for calculation by analogy, one can use the formula for the growth of a new phase nucleus, suggesting that the latent heat of formation is equivalent in this case to the activation energy of primary recrystallization [12]: …”

Performance Evaluation of Arc-Electrodes Systems for High Temperature Materials Processing by Computational Simulation

“…[4][5][6][7][8][9] In the present study, the temperature and electric potential conditions are given only at the cooled surfaces of anode and cathode, represented as lines CЈDЈ, FA, in Fig. 1 without assuming the current density and temperature at the electrodes surface, represented as lines CD, FG, GB 11) and neglecting sheath boundary Vol.…”

“…Therefore, the numerical modeling is expected to be one of the effective approach to solve this problem. [4][5][6][7] In the present study the thermofluid analysis of free burning arc and tungsten cathode life evaluation 8,9) are conducted to provide the optimum operating conditions of an arc for the high energy efficiency and for a long life of electrode. In the thermofluid analysis, the electric field is solved in the total region including an arc flow zone and both cathode and anode regions by giving heat flux condition between arc and electrodes without assuming the distributions of temperature and electric current on the electrode surfaces.…”