Calculating maximum power dissipation based on contact area between two metal conductors

Question

I am trying to figure out how to properly calculate the minimum contact surface area based on the maximum required power dissipation. Let me explain..

I am creating a custom semi-circular metal tab that makes an electrical connection to a metal strip. The metal tab will be connected to a system that dissipates 7 watts. Assuming that I know that I need to support a maximum power current draw of ~.55A @ 12 V (this is where the ~7W power dissipation comes from), how can I best calculate the size of the contact surface area that the two metal contacts need to share in order to support the specified current dissipation. Please see the very crude drawing below. I am trying to determine the contact surface area highlighted in the blue circle.

Here are the givens...

1. I have control over the choice of metal for both the contact and strip

2. I can decide the thickness and size of both contacts.

3. A voltage drop of no more than .5 Volts may be tolerated

4. A temperature rise of no more than 10 C may be tolerated

5. The load has a current draw of ~.55 A @ 12 V (i.e. ~7W)

I am not looking for anyone to do the work for me, I am just looking for some help with the proper equations to use. Thanks.

Answer 1

You need to calculate contact resistances to find an answer to your question.

Contact resistance splits in two parts. Resistance coming from the small slot:

$$ \Lambda \approx\frac{3{,}7}{E^{*} \cdot \rho \cdot l} \cdot F_N $$

with Lambda being the conductivity in Siemens, E* the effective E-modulus of your materials, rho the specific resistance of the metal, and Fn the normal Force exhibited from the contact. l is the root mean square of surface height (aka roughness).

The effective E-modulus is approximated by

$$ E^* = \frac{E}{2\cdot(1-\nu^2)} $$

with nu beeing the Poisson's ratio.

You see, in this formula the area of contact doesn't show up. It is much more important to reach a sufficient contact force.

The other part is the resistance of surface layers, like oxides. If you resort to gold or palladium surfaces you can neglect it. Otherwise it is difficult or even impossible to calculate. If you have at least minimal movement between contact surfaces, oxide layers may be broken up. Other ways of getting rid of oxides is reaching the wetting current. AFAIK wetting currents are in the single mA range for many contacts. So this is perhaps no problem for you.

To get an idea how force and resistance are connected I recommend viewing a bunch of datasheets from manufactures of spring loaded contacts. Kitagawa has some with both values, and PTR gives maximum currents, too.

Sample contact data (PTR)

Kitagawa grounding contacts