Three-dimensional calculation of the distribution of eddy currents and the heating effect on slit tubes when welding longitudinal seams

A numerical model is presented for the process of the inductive longitudinal-seal welding of tubes. This model refers to a three-dimensional, quasi-stationary electromagnetic field and a three-dimensional temperature field. The characteristics of the material dependent on the field in both cases are taken into consideration in iterative ways in the form of local functions. The differential equations describing the electromagnetic field are integrated as an A-φ formulation into the method of finite elements. The discretization, adapted to suit the problem, leads to grid networks with up to 100.000 nodes. The results of the calculations shown permit the determination of optimum process parameters