Tailoring coil geometry for secondary heating of substrate towards the development of induction heating-based wire additive manufacturing

Induction heating (IH), a clean energy source, is potentially used to develop wire additive manufacturing (AM) system. The optimised parameters that simultaneously melt the mild steel wire and raise the substrate temperature is established. A fully coupled thermal-electromagnetic model of AM system is developed to perform numerical experiments on temperature development. The proposed hybrid helical-pancake coil with circular cross-section melt the metallic wire and raise the substrate temperature to 1490 K. The hybrid coil provides rapid heating to the wire (2819 K) and substrate together by enhancing magnetic field strength. The experiments using high-frequency IH system (550 A and 353 kHz) with a 3-turn helical coil is validated with model results for 2 mm mild steel wire.


Introduction
The design of coil is one of the critical aspects for any induction heating (IH) application. A suitable coil can improve the heating efficiency of the system, maintains proper heating patterns and improves the temperature and melting rate of the wire. The factors on which the wire temperature profile depends are the wire size, coil current, coil's cross-section, number of coil turns, coupling distance, and gap between the coil turns. However, the heating pattern on the wire is mainly reflected by the coil cross-section and its geometry [1]. Therefore, the investigation on suitable coil parameter for a specific heating pattern is essential for wire-based additive technology.
The IH-based wire additive manufacturing (IH-WAM) process has recently drawn extensive attention to print metallic components because of clean and cheap heat source, sustainable and easily be automated to develop an AM system. IH is also associated with fast and localised heating, environment-friendly process, non-contact method, and high process efficiency compared to other metal AM technologies [2][3][4]. Hence, various researchers are exploring IH as a new energy source for printing 3D metallic components. Sun et al. [5,6] used a laser beam-assisted ultra-high frequency system to deposit Inconel 625 alloy. An additional laser beam was used to raise the substrate temperature close to the melting point to achieve a good fusion bonding of the deposited beads. Jayant et al. [7] have printed low melting point metallic wire (Sn95Ag4Cu1) by designing a high-frequency, low-power induction heater. Hascoet et al. [8] used the IH system to print the stainless steel wire by designing a specific coil to heat the substrate and melt the wire together. Englert et al. [9] fabricated an Al alloy cube using a direct IH system with the order of MHz frequency. The fabricated cubes are associated with defects like lack of fusion and spherical pores. IH is applied selectively to sinter the metallic powder using a high-frequency micro-sintering process. A multi-loop flux concentrator is often used to apply a high-frequency magnetic field over the top surface of the metallic powder [10]. The existing fused deposition modelling (FDM) machine is also converted into an IH-WAM process by replacing the resistive heating unit with a conventional induction coil. The modified FDM machine is then used to print low melting point aluminium alloy [11]. Most of the work is associated with a conventional induction coil, which cannot melt the wire and simultaneously raise the substrate temperature close to the melting point. The magnetic field in the helical coil mostly concentrates along the axial direction at the coil centre, making it difficult to heat the substrate. It promotes defects like lack of fusion between the substrate and deposited bead. Therefore, it is of utmost importance in AM to significantly raise the substrate/previously deposited bead temperature to achieve strong metallurgical bonding [5,6,8]. The previous studies have only focused on melting the wire or using an auxiliary heat source (laser beam) to heat the substrate, which essentially increases the setup and printing costs. In general, the IH-WAM process is in its initial stage, and minimal investigations have been carried out on design of suitable coil for efficient material deposition of an AM system. Therefore, an efficient IH system associated with material deposition from a metallic wire requires to optimise the shape and size of specific induction coil, size of wire, and process parameters to improve the bead quality.
The present work proposes a hybrid coil that simultaneously melt the mild steel wire and raise the substrate temperature close to the melting point. The design parameters include the selection of process parameters and the coil geometry. The finite element (FE) simulation has been carried out to analyse the design parameters. The temperature profile of the wire is validated with experimentally measured temperature for a 3-turn helical coil having a circular cross-section of 1.5 mm coil turn spacing and a coupling distance of 14 mm. Our previous work [12] analysed the effect of the wire size and coil current to melt the wire. In the present work, the coil parameters like coil crosssection, number of turns, frequency, coupling distance, and coil turn spacing are optimised so that a significant amount of thermal energy is spent on heating the substrate material. The FE-based commercial software ABAQUS 2017 [13] is used with co-simulation features to evaluate the thermo-electromagnetic field for different coil geometries. The developed numerical model can provide the fundamental understanding of the required coil geometry and its parameters to be used for developing the IH-WAM system.

Finite element model
The EM phenomenon in the workpiece (wire and substrate) and air domain is well described by Maxwell's equations [14][15][16]. In the high-frequency induction heating (HFIH) process, the heat energy in the workpiece is generated mainly due to the eddy current. In the air domain, there is no current conduction. The Joule heat due to hysteresis loss accounts for only 6% compared to the eddy current loss and up to the Curie point temperature. The surface temperature of the wire and substrate is much greater than the Curie point temperature, thus, the effect of hysteresis loss is minimal [2]. The Fourier's law describes the transient heat transfer in the workpiece by considering Joule heating mainly due to the eddy current, which is expressed as [6] Q eddy = σ |E| 2 (1) where E is the electric field intensity (Vm −1 ), σ denotes the electrical conductivity (Sm −1 ) andQ eddy is the Joule heat (Wm −3 ), respectively. An axisymmetric FE model of thermoelectromagnetic field is developed to simulate the temperature field at various coil geometries and parameters. Figure 1(a) illustrates the solution domain. The EM model contains an induction coil, mild steel wire of a diameter of 2 mm, and a substrate surrounded by an air domain. In contrast, the thermal model includes only the wire and substrate. The material of the wire and substrate is similar in the present study. The wire is placed at the centre of the axisymmetric induction coil; hence, only one-fourth of the geometry is considered for analysis. Since the process is quasi-static, the relative movement between the wire and substrate is not considered. The helix of the coil winding and hysteresis loss are neglected here. The physical properties of mild steel are considered temperature-dependent ( Figure S1). The EM properties used in the present analysis are also highly non-linear [17,18]. The physical dimensions of the wire, substrate, and solution domain are indicated in Table S1.
The air domain is 10 times bigger than the outer radius of the coil to make an infinite domain such that the outer boundary acts as magnetic insulation. Therefore, the magnetic vector potential ( A) is zero at the outer region of the air domain ( Figure 1(a)) and its gradient is negligible along the boundary compared to the other region of the air domain [2,19,20]. This analysis uses a co-simulation feature to couple a time-harmonic low-frequency EM analysis with a transient heat transfer analysis ( Figure S2). It is considered fully coupled or two-way coupling since the magnetic field is generated through coil current, producing eddy current and Joule heating. The high-frequency coil current is used as an EM load and applied in the form of body current density. A 4-noded linear EM tetrahedral element with a constant curl of vector fields is used to make fine discretised domain for capturing the skin depth. A very fine mesh (0.2 mm) is assigned near the workpiece and a relatively coarser mesh at the outer part of the air domain.
The geometry and process parameters of the induction coil significantly affect the power transfer efficiency and heat generation within the workpiece. Hence, the current study focuses on heat transfer analysis to design the heating coil, mainly geometry and process parameters that simultaneously melt the wire and raise the substrate temperature. Figure 1(b) depicts the regular cross-section of coil used for an IH-WAM system. The coupling distance varies from 4 mm to 14 mm. A smaller coupling distance is preferred since it provides better coil-to-wire EM coupling and enhances power transfer efficiency [2]. The coupling is selected as 4 mm, so a sufficient gap is maintained to avoid the wirecoil contact in the IH-WAM system. In addition, the gap between the coil turns is also varied from 1.5 to 4.5 mm. Furthermore, both single-turn and multi-turn induction coils are considered for the analysis.
The simulation for different possible coil geometries ( Figure 2) have been performed to evaluate the heating pattern of the wire and the substrate. It has been realised that substrate heating is the most critical part of the AM system since an excellent metallurgical bonding between the substrate and deposited layer is expected. Therefore, a pancake geometry of the induction coil is found suitable that may ensure sufficient heat to the flat substrate [21,22].

Results and discussions
In IH application, the heat generation on the substrate primarily depends on the coil geometry and its process parameters. Our previous work suggested that mild steel wire with a diameter of less than 1.6 mm is difficult to melt [12]. The melting temperature reaches faster with an increase in wire size. Here, a critical size of wire exists for a minimum time to reach the melting temperature. The time required to reach the melting temperature decreases as the coil current increases. The present work explains the effect of process parameters (excluding wire size and coil current) and coil geometry on the temperature development in the mild steel wire and substrate. First, the selection of process parameters of the coil is performed and then the optimisation of coil geometry is accomplished on account of melting of the wire and heating of the substrate simultaneously.

Influence of process parameters
The induced eddy current in the workpiece is released as Joule heat. The power per unit volume in the workpiece is proportional to the square root of the current frequency. Therefore, increasing the frequency is always advantageous to generate more heat as it reduces the eddy current cancellations in the wire by increasing the ratio of wire diameter to the skin depth. This ratio for 100, 200, 300, and 353 kHz is 1.12, 1.58, 1.94, and 2.2, respectively. It suggests that the eddy current cancellations take place up to 300 kHz resulting in poor power transfer efficiency. The heating rate of the mild steel wire is strongly enhanced when the frequency varies from 100 to 353 kHz. However, a very high frequency further heats the wire, which overheats the wire edge. Figure 3(a) indicates that the melting temperature of the wire reached in less than 0.8 s at 353 kHz frequency. However, a frequency less than 300 kHz cannot melt the wire. The phase transition of the wire takes considerable time ( ∼ 0.3 s), whereas it takes only 0.5 s to reach solidus temperature at the highest frequency. The wire loses its magnetic property after Curie point temperature, resulting in slow heating.
The coil cross-sections depicted in Figure 1(b) with unique height and sheet thickness are considered for the analysis. Figure 3(b) indicates that the temperature generation in the wire for the circular-section is slightly higher than the square-section under similar conditions ( ∼ 1 s). The heating rate for circular-section is slightly rapid due to the absence of the sharp corner edge unlike square-section. The smooth edge enhances the power factor and the efficiency by improving the coupling of magnetic flux. However, a sharp corner edge distorts the magnetic field and affects the eddy current generation. Therefore, the circular cross-section is more effective.  The magnetic flux density (B) at the centre of the circular coil geometry is inversely proportional to the inner coil diameter. It means the magnetic flux density enhances with a decrease in the inner coil diameter. A varied distance between the inner coil radius and wire surface (coupling distance) of 4 to 14 mm is considered for the analysis. The simulations are performed for 1 s under 550 A and 353 kHz process parameters. Figure 4(a) indicates a similar trend, i.e. magnetic flux density increases with a decrease in the inner coil diameter. The magnetic field strength also increases (Figure 4(b)) as it is proportional to the magnetic flux density. As the coupling distance decreases, the coupling of the EM field with the wire is enhanced and consequently enhances the power transfer efficiency resulting in a high eddy current in the wire [23]. Hence, the temperature of the wire increases because of the excellent coupling (Figure 4(b)). The temperature in the wire for the highest coupling distance (e.g. 14 mm) is not as significant as in a smaller coupling distance (e.g. 4 mm). The poor EM coupling results in a wider heating pattern [2]. Therefore, the optimum coupling distance selected for further analysis is 4 mm. The distance between the coil turns varies from 4.5 to 1.5 mm under 550 A, 353 kHz, circular cross-section, and 3-turn induction coil. The minimum spacing is 1.5 mm to avoid contact between two successive coil turns. The contact may lead to the spark or arc generation. The maximum spacing is selected as 4.5 mm since it allows magnetic field redistribution, which may reduce the power density. Moreover, it also increases the coil's height, which is not desirable in the case of the IH-WAM. The temperature in the wire rises from 1748 to 1941 K (Figure 4(c,d)) as the spacing between the coil turns decreases. It enhances the wire's power density (Figure 4(c)) by improving the coil turn space factor. Owing to redistribution of the magnetic field, the magnetic field strength (EMH) in the coil-to-wire air gap increases from 1.57 × 10 5 Am −1 to 1.823 × 10 5 Am −1 (Figure 4(c)). Hence, the spacing between the coil turn selected for further analysis is 1.5 mm.
The effect of the number of coil turns (N) for a helical coil with a circular cross-section under the process parameters (Table S2) is analyzed in this section. Figure  5(a) shows that the magnetic field strength in the coilto-wire gap increases with an increase in N. However, there is a significant improvement in the magnetic field strength from 1.28 × 10 5 Am −1 to 1.98 × 10 5 Am −1 when N increases from 1 to 5 ( Figure 5(a)). Moreover, there is no significant change in the magnetic field strength (2.01 × 10 5 Am −1 to 2.03 × 10 5 Am −1 ) beyond N = 5. The improvement in the magnetic field strength improves the power density, leading to the higher Joule heat in the wire; subsequently, it increases the temperature generation of the wire (Figure 5(b)).
It is observed that the temperature in the wire rises sharply when N increases from 1 to 5. In contrast, a further increase in coil turn (beyond N = 5) does not significantly improve the wire's temperature and almost remains constant beyond N = 5, as depicted in Figure  5(c). Moreover, the temperature difference in the wire is ∼ 460 K by just increasing the coil turns from 1 to 2. The heating rate improves significantly upon increasing the coil turns ( Figure 5(d)). However, the single and double-turn coil cannot raise the liquidus temperature of the wire. Therefore, a 3-turn induction coil is further used to analyse these results. However, the length of the coil winding increases with N and accordingly the resistance. Hence, the power consumption (I 2 R) may increase for the higher coil turns. In addition, the coil height also increases with the coil turn.
The magnetic field strength for different coil geometries having 3-turn such as helical (H) (Figure 5(a)), stepped helical (SH) and tapered helical (TH), as depicted in Figure 6(a). The analysis is performed for 1 s duration. The magnetic field strength generated in the air gap for H is the highest (∼ 1.82 × 10 5 Am −1 ). Figure 5(b) indicates the temperature developed in the mild steel wire for H is the maximum ( ∼ 1941 K).  (Table S2).
Whereas for SH and TH it is almost similar ( ∼ 1762-1769 K) as the coupling distance increases by 2 mm for each successive turn, causing poor coupling and reducing the power density in that area of the wire ( Figure  6(b)). Hence, the Joule heat generated in the wire is less than the H coil geometry (Figure 6(c)). Moreover, the heating rate is also insignificant compared to the H coil ( Figure 6(d)). Therefore, H coil with a circular crosssection having a 3-turn is selected for further analysis. It raises the mild steel wire temperature above the melting temperature, which is desirable for the IH-WAM system to transfer the molten droplets by forming the bridge.
In addition, helical pancake (HP) coil geometry is investigated separately for melting the wire ( Figure  2(d)). It is observed that the magnetic field strength of the HP coil geometry is more concentrated near the wire (Figure 6(a)), resulting in higher Joule heating than other geometries, as depicted in Figure 6(c). Figure 6(b) shows the temperature at the bottom of the wire is much higher than the other coils ( ∼ 2630 K). However, the HP coil geometries have two additional pancake turns used for substrate heating. Therefore, HP coil geometry is compared with the 5-turn H coil geometry. The temperature generated at the bottom of the wire using the HP coil and 5-turn H coil is 2630 and 2293 K, respectively (Figure 5c). There is a difference of 337 K because HP geometry has a multi-turn and multi-layer effect on wire heating; hence, HP coil geometry provides superior results under a similar number of turns and power consumption.

Validation with experimental results
The experiments on mild steel wire of a 2 mm diameter, 3-turn helical coil (H) of circular cross-sections with a 14 mm coupling distance and 1.5 mm coil turns spacing are performed using an HFIH system with a maximum rated power of 10 kW. The HFIH system consists of a power supply unit, IH unit, induction coil, water cooling system, CNC-bed, and an infrared camera (IR) (Figure 7). The induction coil is made of a hollow copper tube (thickness 0.6 mm) with inner and outer diameters of 30 and 40 mm, respectively. In addition, the height (h c ) of the induction coil is 18 mm. The experiments on mild steel are performed under the 550 A-coil current and 353 kHz frequency. In the HFIH system, a non-contact method is an effective way to measure the temperature of the wire since the thermocouple gets affected by the  magnetic field and produces the secondary EMF resulting in incorrect temperature reading. The non-contact method (IR camera) is used to record the temperature of the wire [6,24]. The emissivity of the mild steel wire is selected after calibration of the IR camera with a K-type thermocouple. The calibration range of the IR camera was set between 673 and 2273 K for temperature measurement. The measuring error of the IR camera is reported as ±2%.
The predicted results from the numerical model are validated by experimental temperature measurement recorded for 5 s. It is obvious that the numerically predicted results follow a similar trend as measured temperature. The time to reach the Curie point temperature (1045 K) for numerically calculated and experimentally evaluated is almost the same. However, there is a slight variation of the temperature in the middle (Figure 7), showing a maximum error of only 6%. Moreover, the temperature becomes constant after reaching the melting temperature of the wire and the gap between the predicted and the measured results is very insignificant. A minor variation in the heating rate is likely because of the power losses due to the secondary magnetic field that arises due to conductive parts in the experimental setup. The accounting of the losses due to the secondary magnetic field, flux leakage because of coil spacing and flux generated due to the coil helix can further improve the accuracy of the numerical model. Overall, the predicted results follow a similar trend to the measured results.

Heating pattern on substrate
In the AM process, the substrate temperature is critical for achieving a good metallurgical bonding between the substrate and the deposited layer [8]. Hence, the heating pattern on the substrate is investigated under helical (H) and helical pancake (HP) coil geometries. Figure 8(a) indicates that the temperature development on the substrate is the minimum for H-coil. However, it generates sufficient heat to melt the wire. A pancake geometry is usually used for heating the flat surface [2,25]. Hence, the combined helical-pancake (HP) is most suitable in the present case that simultaneously heat the substrate and melt the wire. An optimised 3turn helical and 2-turn pancake is investigated where the distance between substrate and the coil surface (b cs ) varies from 10 to 5 mm since the height of the deposited bead is around 2 mm to 3 mm. The temperature on the substrate increases as the b cs decreases. The maximum temperature developed on the substrate for b cs = 10 mm, 7.5 mm, and 5 mm is 820, 1085, and 1490 K, respectively. It is obvious that the temperature difference is significant when the b cs is reduced to 5 mm. The heating rate is significantly fast and generates a temperature close to the melting point, which can provide good metallurgical bonding after deposition. The heating pattern is observed to be uniform and shallow since high frequency is applied. Moreover, the heating pattern takes the shape of the coil geometry ( Figure 8). The proposed coil supplies about 10 kJ of heat energy to the wire and substrate for 1 s (electrical efficiency η el = 0.9), however the energy induced in the workpiece is about 8.8 kJ, out of which, approximately 28% of heat energy being utilised for wire melting, 53% of heat energy utilised for substrate heating and 19% of heat is lost due to radiation and convection. The effective thermal efficiency (η t = Q/Q eddy ) is calculated as 81%. The heat energy supplied from the coil is calculated using Q c = Q/η el η t where Q is the amount of heat required to melt the wire and raise the substrate temperature, Q eddy is the heat induced in the workpiece.
The development of the IH-WAM system for high melting point material requires understanding the energy utilised to melt the wire and heat the substrate material. The investigation of material transfer for an IH system is in the initial stage and faces a severe challenge in melting the high melting point wire (mild steel) and making metallurgical bonding between the deposited layers. The proposed hybrid induction coil (helical-pancake) shows a significant temperature generation in the mild steel wire and substrate ( Figure  8(d)). It indicates the possibility of high penetration of the molten droplet and sufficient heat transport to the substrate. However, the direct correlation between temperature and penetration depth of molten droplets can be an interesting field to predict any incomplete fusion or quality of metallurgical bonding for IH-WAM system.

Conclusions
The present work investigated the optimum condition of coil geometry and process parameters to melt the mild steel wire and significant temperature rise of the substrate for the development of IH-WAM system. The temperature variations in the wire and substrate and heating pattern are disclosed. The following conclusions are derived from the present work.
• The circular coil cross-section is more effective than the square cross-section. • The magnetic field strength increases significantly from 1.431 × 10 5 Am −1 to 1.82 × 10 5 Am −1 when coupling distance reduces to 4 mm, which significantly raises the temperature (1410 K to 1941 K) by improving the power density. • A significant improvement in the EM field, Joule heating, and the wire temperature is observed up to five turns coil. The temperature difference in the wire is 641 K when the coil turn increases from 1 to 3 and is only 100 K from 5 to 8 turns. • The helical coil (H) produces fast heating of the wire as compared to the stepped helical (SH) and tapered helical (TH) coil under similar process parameters. • For IH-WAM, a 3-turn helical and 2-turn pancake (HP) with 1.5 mm coil turn spacing and 4 mm coupling distance provides satisfactory results as it raises the substrate temperature (1490 K) close to the melting point and heated the wire rapidly compared to helical geometry (H).