Carbon to cast iron electrical contact resistance constitutive model for finite element analysis

Numerical study of anodic voltage drop in the Hall-Héroult cells by finite element method = Étude numérique de la chute de voltage anodique dans les cuves Hall-Héroult par la méthode des éléments finis /

“…A non-uniform contact at the interface can cause a different current density profile and different temperature distribution throughout the anode assembly, particularly in the stub hole area. Figure 1.7 illustrates how thermal, electrical and mechanical phenomena are coupled, as shown by Richetrd et al [7]. Apart from expansion, a change in TEM properties can change the behavior of the system e.g.…”

“…Cooper-Mikic-Yovanovitch model (CMY model), published in 1969 [15], is considered by several publications [7,16] where A r is the real contact area, in other words, the total area of the microscopic asperities actually in contact; A a represents the apparent contact area, the area which seems to be in contact together; k s is the harmonic mean thermal conductivity, calculated with the root mean square (rms) method; the contact spot density is represented by the symbol n; and finally, symbol a is the mean circular contact radius. where a represents the root mean square (rms) surface asperities height of the equivalent surface; m, the harmonic mean slope of the same equivalent surface, p e the harmonic mean electrical resistivity of the connecting materials, P the contact pressure and H c , the microhardness of the softest surface, as presented in the CMY mode.…”

“…The Majumdar and Tien fractal model was introduced in 1991 [24] and is based on a fractal representation of the surfaces, obtained from a Weierstrass-Mandelbrot generating function whose parameters are calibrated by comparing its power spectrum to that of the real surface's pro filo metric data. The fractal model is built on a better surface representation, which allows an objective characterization of the contact surfaces; nevertheless, since both models rely on the same mechanical assumptions, the fractal model eventually takes on the same form as the CMY model [25].The CMY and the fractal model are based on the following key variables:…”

“…This was repeated at five temperatures from ambient to around 1000 °C. Contact resistance was calculated by extrapolating the electrical potential from both sides of the interface [25].…”

“…Moreover, as discussed by Beck [29], this method of calculating contact resistance by extrapolation of the potential to the interface is prone to error. Indeed, it assumes a linear behavior of the potential, which might not be a good approximation when the location of the measuring probes is far from the contact surfaces, since thermal conductivity and electrical resistivity are temperature dependent and are different for carbon and cast iron [25]. shows the general expression of the contact resistance suggested by Richard such that:…”