Numerical modeling of electrical contacts

Goal of the project

Electronic assemblies influence our life more and more. Even in power plants and automobiles the portion of electric devices increases constantly. Therefore the business of engineers is to guarantee a smooth run of every process. Especially, when current flows between two or more components, to this day, it is a big challenge to design stable contacts. A numerical simulation tool can help to provide insights into the behavior of current flow at electrical devices. For the prediction of arising phenomena ,especially when contact occurs, good constitutive equations are needed.

Contact current flow

One effect at electrical contacts is the appearance of an additional resistance accompanied by an increasing temperature. Since contact takes place only at a few randomly distributed spots, the lines of current flow get closer to each other, leading to a stronger resistance for the charge in the body (Fig.~1)

Fig. 1: Contact spots and constriction of the current lines

In the modeling process, the constriction is described by cylindrical flux tubes, uniformly distributed over the contact surface. On the basis of the resistance of a single flux tube [1], Ohms law and the parallel connection of the resistivity, a new constitutive model for the current density between two boundaries is developed

This model depends on the mean electrical conductivity σ and Vickers hardness H_v of the two bodies, as well as on the apparent contact area A_a and the pressure t_N. Furthermore, the arising Joule heat follows by a multiplication of the current density with the contact voltage  φ² - φ¹.

Modeling of wear

For the estimation of the wear at contacts, there exist different types of formulas, where the famous ones are due to Holm [1] and Archard [2]. Obviously, there is a connection between the dissipation and the wear. Hence, we proposed a new relation, where the amount of wear depends directly on the dissipation

linked only by the latent heat of evaporation γ and a factor β indicating how many bonds of the molecules get lost.

Damage due to wear

Additionally, the change of the running track due to worn out particles influences the frictional behavior and thus also the dissipation and the wear, respectively. We describe this change of the surface by using a damage model, which is included in Coulomb law via a dependence of the coefficient of friction μ on the damage Φ

A damage function controls therein the change of the surface

The inner damage variable can be computed by an evolution equation for  the mechanical  and the electrical part displays the maximum value of the damage and
T_D determines how fast the maximum value of damage is reached.

Numerical investigations

All the constitutive models were implemented in the Finite Element code FEAP. Due to the pressure dependence of the current flow across the bodies and the arising Joule heat at the contact zone, mechanical, thermal and electrical fields have to be coupled.

Fig. 2: Contact between two copper bars: Resulting voltage and temperature

A comparison between the experimental data [1] and the numerical results shows a good accordance for the constriction resistance of two copper bars at different load levels.

Fig. 3: Contact between two copper bars: Comparison of experimental and numerical results

Also the computed amount of wear at a load of 16 kPa of a carbon brush on a copper track is in the range of measured values.

Fig. 4: Carbon brush on copper track: Comparison of experimental and numerical results

Following the wear amount at different load levels, the Joule heating is the dominating effect in wear site, if the pressure is low, whereas at higher pressures, the frictional dissipation provides the wear evolution.

Fig. 5: Carbon brush on copper track: Amount of wear at different load levels

References

[1] R. Holm: Electric contacts, Springer Verlag, 1979.
[2] J. F. Archard: Contact and rubbing of flat surfaces,  Journal of Applied Physics, 1953.