How to Couple Electrostatic and Heat Transfer Analyses for Joule Heating

The ability to predict how electrical current will affect temperature distribution is useful when analyzing spot welding, circuit breakers or other systems involving Joule heating, where materials heat up due to their resistance to a current passed through them. Engineers can determine what applied voltages are necessary to generate the required heat in the material while maximizing electrode life.

You can model Joule heating effects as follows:

First, run an electrostatic current and voltage analysis on the model. This involves specifying the electrical conductivity of the material (the inverse of its resistivity) and applying voltages. The resulting current distribution will be used as a load in a subsequent heat transfer analysis.

For illustration, consider a spot welding system in which two relatively thin metal plates are permanently bonded together by passing an electrical current through them (Figure 1). For the electrostatic current and voltage analysis, copper electrodes on either side of the steel plates are loaded with applied voltages (+12 volts on the positive electrode and -12 volts on the negative electrode).

Figure 1: An electrostatic current and voltage analysis of the spot welding model produced this current distribution.

Next, change the analysis type to either steady-state or transient heat transfer.

Note: Alternately, you can save the FEA model as a new filename. If you use separate models, the electrostatic model must be identical in geometry to the heat transfer model.

For each part where you want to apply Joule heating, specify a value of "1" for the "Internal Heat Generation" option on the "Loading" tab of the "Element Definition" screen (Figure 2). This will act as a flag telling the processor to use the heat generation values calculated from the electrostatic analysis on this part.

Figure 2: On the "Loading" tab of the "Element Definition" screen, specify a value of "1" in the "Internal Heat Generation" field. Do this for each part that will undergo Joule heating.

For the spot welding model, a steady-state heat transfer analysis was specified with internal heat generation, convection and 100°C fixed nodal temperatures on the ends of the electrodes for loading.

On the "Analysis Parameters" screen (Figure 3), access the "Multi-Physics" tab and click on the checkbox to use electrostatic results to calculate Joule effects. Use the "Browse..." button to specify the location of the electrostatic results file (.efo extension).

Figure 3: On the "Multi-Physics" tab of the "Analysis Parameters" screen, activate the "Use electrostatic results to calculate Joule Effects" option and specify the location of the electrostatic model.

On the "Multipliers" tab of the "Analysis Parameters" screen, assign a value to the "Heat generation multiplier" field. This value will be used to scale the heat generation effects due to the current. For the spot welding model, a value of "1" was used.

Run a heat transfer analysis on the model. The temperature distribution obtained will include Joule heating effects as shown in Figure 4.

Figure 4: A steady-state heat transfer analysis produced this temperature distribution for the spot welding model, which simulates internal heat generation based on current distribution from the electrostatic current and voltage analysis.

In the spot welding model, the metal undergoes Joule heating based on its resistivity to the current. The plates are heated until they begin to melt and flow together, forming a weld "nugget" at the intersection of the two plates. The current is then removed and the material is allowed to cool to form the bond.

Knowledge of the temperature distribution in the plates and the electrodes is important not only for weld size and quality but also to maximize the life of the electrodes. If too much current is applied, then excessive heat will be generated that will result in a "melt through" of the plates and a significant decrease in electrode life. If insufficient current is applied, then the heat produced will be inadequate to provide an appropriate "melt" region, resulting in a weak bond between the plates.

Thus, coupled electrostatic current and voltage and heat transfer analyses can account for heat generated in a model due to Joule heating.

For more information about the Joule heating capability, see the ALGOR User's Guide.