IEEE TRANSACTIONS ON MAGNETICS, VOL. 48, NO. 2, FEBRUARY 2012 483 A Translational Coupled Electromagnetic and Thermal Innovative Model for Induction Welding of Tubes Fabrizio Dughiero, Michele Forzan, Cristian Pozza, and Elisabetta Sieni Department of Electrical Engineering, University of Padova, 35131 via Gradenigo 6/a, Padova, Italy In the paper, a novel approach to numerical modeling of tube induction welding is proposed. The coupled electromagnetic and thermal model must take into account also the movement of the metal strip: in order to make possible this kind of simulation in reasonable computation time, a simplified approach to the modeling is presented and discussed. Index Terms—Coupled problem, finite-element field analysis, induction welding. I. INTRODUCTION T HE welding of tubes and pipes is usually achieved by high frequency induction heating. In recent years, solid state generators became available with rated power useful for this application, typically in the range 50–2000 kW, displacing the traditional vacuum tube oscillators. The solid state technology allows the possibility to choose the best frequency for the appli- cation, usually in the range 100–500 kHz. The better control of solid state inverters made the optimal design of welders crucial for the manufacturer [1]–[4]. Tubes are manufactured by bending steel strip and gradually approaching their edges until they join and form the tube as in Fig. 1. At the junction point the characteristic VEE is formed. During this process, an inductor generates a magnetic field that induces electrical currents on the tube. The particular tube ge- ometry concentrates the induced current density on the opening and in particular on the junction point causing the heating and, then, the melting of the metal that is going to form the welded seam. The welding device is composed mainly by the inductor, that generates the magnetic field, and a ferrite impeder, used to concentrate the field on the welding zone. Numerical modeling of induction welding process is required to achieve the best performance, but this kind of simulation can be very complicated because the coupled electromagnetic and thermal solution has to should take into account also the movement of the tube in a full 3D geometry [5]–[7]. Some ef- forts have been made in the past to simulate the tube welding process in order to evaluate the influence of different process variables. Some relevant studies are referred to 2D geometries to evaluate the effects on the welding temperature of the strip edges approaching [3], [8]. The numerical design of the tube heating using 3D models is an interesting problem because of the difficulty to take into account the movement and the geom- etry changes that occur when the strip edges join [1], [9] [10]. For instance, in [9] the electromagnetic problem of the induced current density computation on the metal strip has been solved using the impedance boundary condition on the tube surface, but in this case the tube is in a static position and any thermal effect is not considered. Then, the progressive heating of a point on the tube during its translational movement on the inductor and, Manuscript received July 07, 2011; revised October 10, 2011; accepted Oc- tober 29, 2011. Date of current version January 25, 2012. Corresponding author: F. Dughiero (e-mail: fabrizio.dughiero@unipd.it). Digital Object Identifier 10.1109/TMAG.2011.2174972 Fig. 1. From metal strip to tube: manufacturing problem. consequently, any variation of the material properties as a func- tion of the temperature is not considered. In this paper a new strategy for 3D simulation of the welding process that takes into account the movement and tube geom- etry change is proposed. In order to limit the complexity of the model, some simplifications are discussed and validated through simulations. II. COMPUTATION MODEL The sketch of Fig. 2(a) shows a simplified geometry of the tube welding systems. When the bended strip approaches to the welding point, W, it has a “V” shape, usually named VEE. During the welding process the tube moves forward with a ve- locity, , maintaining the welding point, W, at a fixed position with reference to the inductor one (Fig. 3). The solution of cou- pled magnetic and thermal problem is a challenging numerical problem because the model must be able to describe that the shape of the load does not change during the translation with reference to a fixed position, e.g. the inductor position, while the shape of tube varies with reference to the moving tube itself. The tube movement must be described in order to properly solve the thermal problem that obviously depends upon the mass trans- port due to the translation. This issue has been solved consid- ering the relative movement of the entire geometrical cylinder that represents the tube and the air gap before the welding as well as the formed tube after the welding, and applying mate- rial properties that varies as a function of the position inside the ‘welding region’. In particular, in the welding region , the electrical conductivity, the thermal conductivity and the specific heat are not described as time-dependent but as function of the position along the z-axis, using a step function : (1) 0018-9464/$31.00 © 2012 IEEE