Comparison of Model Predictions of Current Density Variation across Simulated Contact Regions

The impact of spot size and location within a contact zone was evaluated using two different formulations provided by Greenwood and the present author respectively. It was seen that significant variation in current density across the contact region suggests, that as a contact degrades, there will be a non uniform degradation and failure of the contact spots as aging progresses. This is thought to produce a cascade effect where the spots with the highest current density fail initially, causing the remaining spots to carry greater current loads and subsequently age faster towards failure. In the present analysis, the first model is based on Greenwood´s work, using disc shaped contact spots. The second model was developed by the present author and is based on using hemispherical shapes for the contact spots. Both models allow for random variation of size and spacing across the interface. Both models are derived by solving the electrostatic problem of charged multiple conductors. Subsequently, the results are converted to the analogous steady current case that occurs in electrical contacts. The results from these models show very similar results and indicate spot shape is not as important as size and position in affecting the average current density through each spot. In addition, it was found that the variations of current density can be approximated using a simple relation that combines spot size and the spot position from the center of the contact region. It is believed this method allows a simpler analysis and clearer interpretation of the variation in current density across the contact region. Moreover, this method is used to demonstrate how a cascading failure mode can occur in the case of a circular shaped contact zone with multiple points of contact. This was done by assuming that as the current density of individual spots rise above a critical value, they become non conductive.