Analytical prediction of Joule heat losses in electromagnetic forming coils

Coils in electromagnetic forming operations are exposed to mechanical as well as thermal loads. Especially in case of high volume production the thermal loading due to Joule heat losses needs to be considered in the coil and process design to prevent thermal overstressing. For this purpose an analytical approach to calculate the Joule heat losses in a one-turn coil with rectangular cross section is presented. It takes the geometrical and physical properties of coil and workpiece as well as the amplitude, frequency, and damping behavior of the discharge current into account. While a simplified approach assumes a constant electrical conductivity of the coil, the enhanced approach considers the temperature-dependent course of the electrical conductivity. Verification of the analytical model is realized using a combination of experimental and numerical investigations. Fiber-optical measurements of the coil temperature are used to verify the simulation. The Joule heat loss per unit length determined with the verified numerical model is then used to evaluate the prediction quality of the analytical approach. Different conductor materials (CuCr1Zr, Cu-ETP, and EN AW-1050A), conductor geometries, and discharge energies are analyzed in this verification procedure. Compared to the numerical Joule heat prediction an average deviation of 13.1% and 9.0% is determined for the simplified and the enhanced analytical model, respectively. Especially in case of higher discharge energies the enhanced model shows an improved accuracy and should be preferred over the simplified approach. Considering complexity and accuracy, the analytical approach is a proper instrument for the thermal coil and process design in electromagnetic forming operations.