Electrical and thermal contact.
Jang, Yong Hoon
1999
Abstract
The method of Greenwood and Williamson is extended to give a general solution for the coupled non-linear problem of steady-state electrical and thermal conduction across an interface between two conductors of dissimilar materials, for both of which the electrical resistivity and thermal conductivity are functions of temperature. The non-linear problem decouples into the solution of a pair of non-linear algebraic equations involving the boundary values and the material properties, followed by a linear mapping of the resulting one-dimensional solution into the actual conductor geometry. The method presented is sufficiently general to cover all combinations of conductor geometry, material properties and boundary values provided that (i) the current enters and leaves the conductor through two equipotential isothermal surfaces, (ii) the remaining boundaries of the conductor are thermally and electrically insulated and (iii) the interface(s) between different materials would be equipotential surfaces in the corresponding linear problem. In order to investigate the effect of microcontacts and clusters on electrical flow, a model for electric contacts is developed. A probabilistic analysis to determine the distribution of the actual diameter of contact spots from the distribution of line segments is introduced. A statistical version of Greenwood's approximation is developed to calculate current/resistance in microcontacts and clusters. An adaption of fractal description to contact process allows rigorous investigation of the effect of sampling interval on electrical flow where the electrical current density tend to a perfect contact value as additional microscales are added. A contact problem is considered in which an elastic half-plane is pressed against a rigid, fractally rough surface, whose profile is defined by a Weierstrass series. It is shown that no applied mean pressure is sufficiently large to ensure full contact and indeed there are not even any contact areas of finite dimension---the contact area consists of a set of fractal character for all values of the geometric and loading parameters. The contact area is found to decrease continuously with scale, <italic>n</italic>, tending to a power law behaviour at large <italic>n</italic> which corresponds to a limiting fractal dimension of (2 - <italic>D</italic>), where <italic>D</italic> is the fractal dimension of the surface profile. However, it is not a true fractal, since it deviates from the power law form at low <italic>n</italic>, at which there is also a dependence on the applied load. Contact segment lengths become smaller at small scales, but an appropriately normalized size distribution tends to a limiting function at large <italic>n</italic>. Measurements of contact resistance are made using bare and pretreated aluminum alloy. It is observed that the effect of sample-to-sample variation is more evident than that of variation within a sample. The pretreated. material exhibits a consistent behavior. The concept of receding contact is introduced to explain the anomalous contact resistance-force characteristic of bare aluminum in faying surface contact.Subjects
Conduction Contact Resistance Electrical Contact Thermal Contact
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