The resistance of a clean, ideal contact, where any influence due to oxide films is neglected and where it is assumed that a perfect point of contact is made at a spot of radius (r), is given by the following equation:
R = Contact resistance
p = Resistivity of contact material
r = Radius of contact spot
However, in actual practice, this is not the case and the real area of contact is never as simple as it has been assumed above. It should be recognized that no matter how carefully the contact surfaces are prepared, the microscopic interface between two separable contacts invariably will be a highly rough surface, having a physical contact area that is limited to only a few extremely small spots.
Furthermore, whenever two surfaces touch they will do so at two micro points where, due to their small size, even the lightest contact pressure will cause them to undergo a plastic deformation that consequently changes the characteristics of the original contact point.
It is clear then that contact force and actual contact area are two important parameters that greatly influence the value of contact resistance. Another variable that also must be taken into consideration is the effects of thin films, mainly oxides that are deposited along the contact surfaces.
The following relationship between the voltage drop measured across the contact and its temperature can be established. It is based on the analogy that exists between the electric and the thermal fields and on the assumption that in the close proximity of a contact there is no heat loss by radiation.
T = Temperature
h = Thermal conductivity of contact material
p = Electric resistivity of contact material
Vc = Voltage drop across contact
This equation however is valid only within a certain limited range of temperatures. At higher temperatures the materials at the contact interfaces will begin to soften and thus can undergo a plastic deformation. At even higher temperatures the melting point of the material will be reached. In Table below the softening and the melting temperatures together with their corresponding voltage drop are tabulated.
The significance of the above is that now we can determine for a specific material the maximum currents at which either softening or melting of the contacts would occur, and consequently the proper design to avoid the melting and welding of the contacts can be made.
The equations for the maximum softening and melting currents are:
The maximum softening and melting currents as defined by the above equations are applicable to the point of contact and are useful primarily for determining the contact pressure needs. However when dealing with the condition where the contacts are required to carry a large current for a short period of time it is useful to define a relationship between time, current and temperature for different materials.
Below is given a general derivation for a general expression that can be used for determining the temperature rise in a contact.
First, it will be assumed that for very short times all the heat produced by the current is stored in the contact and is therefore effective in producing a rise in temperature.
Then the heat generated by the current i flowing into a contact of R ohms during a dt interval is: