Applicability and correction of temperature-voltage relation in the case of line contact

Contact temperature is one of the important factors in contact problems. The temperature-voltage relation is simple to use and applicable for temperature measurement in study, design, and use. In this relation, however, it is assumed that a contact has equivalent distributions between electric potential and temperature within it. If heat is transferred into the external atmosphere through the apparent contact surfaces and/or the contact faces, the relation may not be valid because of the disagreement between the two distributions. In this work, we take a line contact as an example and numerically analyze the effect of the heat transfer on the relation by using the finite difference method. The numerical computations are carried out using the values of electrical resistivity and thermal conductivity for Cu, which are assumed to be temperature-independent. The results show that the effect cannot be neglected under some conditions, We have also clarified the effect in terms of the correction factor, by which one cannot only establish the applicability of the relation, but also correct the theoretical values obtained from the relation. For this reason one can evaluate the effect without losing the simplicity and applicability of the relation.