Numerical investigation of a double frequency approach for longitudinal HF welding of cladded pipes

This article contains findings of simulation research on longitudinal induction welding of cladded pipes with use of simultaneous double frequency. Solutions are proposed to reach the required temperature distribution at the welding edge for the cladding composite of S355 and Alloy 625 with single and simultaneous double frequency. An advanced consideration of magnetic and other material properties was performed to simulate the dominating physical effects of high frequency (HF) welding. The background of use and advantages of simultaneous double frequency are presented. In the context of the research, a correlation for welding speed, frequency and temperature distribution with industrial relevance was found for the cladded pipe welding.


Introduction
Today, cladded pipes are used in niche applications in natural gas transportation systems, power plants and the chemical industry. The combination of two different metals within one pipe offers high corrosion and abrasion resistance in an economical way. Until today the cladded pipes are manufactured by discontinuous arc welding, weld cladding or mechanical bracing with comparatively low production rates. Bended cladded sheet material, which is metallurgically bonded by explosive cladding, cold roll or hot roll bonding, serves as the feedstock for the welding process. Induction heating is a state of the art process in longitudinal seam welding of single material pipes. It is widely used in the almost all industries. Despite its very high productivity (feed speed of up to 200 m/min [2]) and energy efficiency, inductive longitudinal seam welding is not applied in the manufacturing of cladded pipes. With less than 5 m/min [3], [4] arc welding as the conventional joining process is far less productive. In this paper, a 2D model of pipe welding is used to examine the dominating process parameters for a common material combination of the fine-grained ferritic carbon steel S355 and the nickel base Alloy 625. S355 exhibits a good weldability and is applied as an outer carrier material. The inner layer of Alloy 625 is characterised by a great resistivity against all kinds of corrosion.

Solution Approach
In this work, a 2D dynamic model is created to determine the influence of the main pipe welding parameters, such as feed rate, Vee angle, distance of inductor to the welding point, geometry of cross sections and the electrical parameters. The dynamic model is able to represent the 3D induction welding as shown in [5]. This can be done, as due to proximity effect, where the inductor have only a localized effect on current distribution, but a weak effect on the welding edge current.  The basic geometries of the inductive welding is shown in Fig. 3 a, the model geometry and considered parameters for the numerical research in Fig. 1 b, c. The solution was calculated by a weak electromagnetic -thermal coupling algorithm in the commercial FEM software ANSYS ® Mechanical as shown in [6]. After each time step the results were transferred between the electromagnetic and thermal solutions. The electromagnetic solution was calculated in several iterations to adapt the magnetic permeability according to magnetic field strength.

Material Properties and Influence
Electro-and thermo-physical properties of the cladded pipe materials are pivotal to reproduce the physical effects in the simulation. Due to the non-linearity of the material parameters for the alloys used, the process behaviour is highly sensitive to the change of any input properties. To obtain precise results, physical properties of used material need to be considered and determined from ambient temperature to the melting (or liquefaction) point. In this context, the specific electrical resistance and the thermal conductivity are considered as shown in Fig. 2 The liquefaction temperatures of the alloys used are given as (S355) = 1471°C [7] and (Alloy 625) = 1340°C [8]. The function for the temperature dependent specific heat capacity for each alloy [9], [10] is complemented by the enthalpy of the fusion distribution function ℎ( ), which integral equalizes the enthalpy of fusion value . The heat of fusion is calculated by the pure element enthalpy of fusion and the mass proportion of each element in the alloy. For the S355, the heat of fusion is determined as , 355 = 266 / which is close to reference value , 355, = 268 / [11]. For the nickel-based Alloy 625, the enthalpy of fusion is calculated as , .625 = 338.4 / . In the context of material precision, a particular look on the relative magnetic permeability of the backing steel S355 and the ferrite material of the impeder is made. Except the consideration of temperature depending change up to the Curie temperature, magnetic field dependence must also be taken into account. Equation (1) is an approximation function for the real part of magnetic permeability µ ′ , introduced by Fisher [12, pp. 286-299] and transferred from the magnetic flux B(H) to the relative magnetic permeability µ r (H) relation. By choosing a F = 390 and b F = 0.697 [13, p. 67] as coefficients for the soft magnetic material S355 [14], the magnetic field dependency of material S355 is taken into account. For the impeder an adapted magnetic saturation function, with a starting pitch is used as shown in Fig. 3 b.
For the temperature-field dependence of the magnetic permeability, equation (2) is used, with a function φ(T) representing the temperature dependence of the permeability. This function is taken from [15, p. 76] and redrawn in (Fig.  3 c).
(H, T) = φ(T) * (µ r ( ) − 1) + 1 The saturation effect is correlated with the welding current and can be indirectly used for the process control by two input parameters. The change of current frequency influences the electromagnetic skin depth and therefore the required welding current. The second influence on the saturation is the welding rate, which is also positively correlated to the required current. Due to the complexity of the process, both input parameters have side effects. For example, a lower feed rate increases the effect of the divergent heat conductivity of materials by extending the process time. The 2D dynamic model has some limitations in the representation of the process: For example the longitudinal heat transfer and effect of adverse current circuit on the pipe inside cannot be displayed. Despite this the model represents the main physical effects of welding in the cross section and can be used for the task of finding matching process parameters.

Single Frequency Welding
The correct simulation of the welding of cladded pipes strongly relates to the material properties and their proportion to each other. The temperatures for the S355 and ( Fig. 1 b) for the Alloy 625 at both edges of the joint serve as the target variable (Fig. 1 b). The aim is to reach the liquefaction temperature of both alloys when the joining surfaces get in contact. Welding with single frequency (SF) is possible by adapting the frequency and the feed rate to the geometrical parameters. Therefore, a feed rate -frequency curve can be found for each material combination and geometrical setup. For a given setup (Fig. 4 a) a corresponding correlation of feed rate -welding velocity is presented in Fig. 4  As shown in Fig. 4 b, the frequency should match the chosen welding speed to melt both alloys at the desired position. Industrial welding generators usually do not offer the high enough flexibility to adapt the frequency in a wide range to the demanded feed rate in practical use. Therefore, the use of double frequency for the longitudinal welding of cladded pipe was investigated.

Simultaneous Double Frequency Welding
Welding with two simultaneous frequencies permits a higher flexibility for the operative adaptation of the welding process to industrial scale variations in pipe geometry and material. For a fixed geometrical and material setup, the usable range of feed speeds depends on the spread of the upper and lower frequency of the energy source. To lower the welding speed, it is necessary to increase the relative absorbed power in the ferritic steel layer in proportion to the austenitic alloy. This is necessary as the ferritic S355 offers a higher heat conductivity (Fig. 5 a). The examined frequencies for the research are = 220 for upper and = 10 for the lower frequency. From Fig. 4 it can be taken, that with the chosen frequencies the minimum and maximum welding velocities are = 10 / and = 68 / . For the welding velocity of = 40 / , the desired temperature distribution can be reached by setting a MF to HF current ratio of / = 4,06 (Fig. 5). Further suitable material combinations, such as S235 for the carrier material and X5CrNi18 or X2CrNiMo17 as cladding materials, can be found for the presented longitudinal seam welding approach.

Conclusion
By the use of FEM analysis, the theoretical capability of an inductive longitudinal seam welding process for cladded pipes can be demonstrated. Despite some simplification, the main dominating effects of the longitudinal seam welding were considered by the developed model. Industrial scale process windows for both, single frequency and simultaneous double frequency are presented in this work. The verification was performed on a cladding material combination of S355 and Alloy 625 with strongly divergent material properties, where several effects were used to reach the melting temperatures in the joint edges. The developed approach was also applied to other material combinations, which are not presented in this paper. Potentially, a wide range of metal combinations comprising ferritic alloys as carrier and austenitic alloys as cladding material can be welded by the presented approach. Therefore, a precise material properties determination needs to be existent. Future investigations will highlight the influence of inductor and the full 3D model. Also, thicker-walled cladded pipes are about to be examined for the inductive HF welding.