1 Introduction

Projection welding of crossed bars (i.e. cross-wire welding) is not a simple process as regards the shape of the parts to be welded. An important problem is the initially very small contact area of parts to be welded and, consequently, high contact resistance [1, 2]. Cross-wire welding is characterised by much higher initial resistance than, for example, spot welding [3, 4]. The cross-wire welding of bars as such is a demanding process. The author of publication [5] describes the process as solid-state bonding involving just the melting of the surface and the squeeze-out of the melted phase. In turn, the author of the work [6] presents the process as (primarily) solid-state bonding and local melting.

However, the projection welding of crossed bars continues to evolve and the authors of the study indicate a number of factors affecting the welding process and the quality of the welded joint. These factors include (i) compression of the materials to be welded prior to the flow of welding current (cold compression) [5], (ii) need to ensure the repeatability of welding cycle parameters [7] for a constant bar penetration value [8] and (iii) power (energy) of the welding process [9]. Other authors point out other aspects, such as an electrode clamping system [10,11,12], the special shape of electrodes [13], the intensive cooling of both electrodes and parts to be welded [14] and welding sequence [15], aimed to limit welding deformations. The adjustment of overly low electrode force could result in excessive interface heating and in an insufficient contact (bonding) area (leading to potential expulsion). In turn, the adjustment of excessively high electrode force could result in cold welding [16].

It should be noted that the range of welding parameters is very narrow. In addition, some authors claim that cross-wire welding cannot take place without expulsion [17]. Expulsion is an unfavourable phenomenon as it could lead to the formation of sharp edges, which are both unaesthetic and could result in injuries. The authors of publications [10,11,12] pointed out in previous works the possibility of optimising the process of cross-wire welding using a servomotor system for exerting the pressure by welding machine electrodes and applying a special algorithm for controlling the displacement of electrodes (and not the force exerted by the electrodes). Such a solution enables process stabilisation, lower energy consumption, higher process repeatability and improved joint quality. The authors [18] investigating the cross-wire welding process found further research gaps in several areas and proposed an in-depth numerical analysis of the phenomenon as well as research on controlling the welding up-slope time. The authors also performed an analysis concerning the influence of the thickness of protective coatings (e.g. zinc) on the welding process as well as took up the challenge of analysing the two-pulse cross-wire welding technology. The research was concerned with an inverter welding machine with a 1 kHz DC current source (allowing the welding current to be changed every 1 ms). The results obtained in the research were subsequently compared with those obtained using a 50 Hz AC welder.

Quality is particularly important in Industry 4.0 [19,20,21]. Because of its relatively vast applications in various industrial sectors, welding is a preferable process when it comes to the implementation of Industry 4.0. Particular attention is paid to the online monitoring of weld quality and checks for defects (if any) [22, 23]. The analysis of joint quality is supported by numerical analyses aimed to optimise the welding process. The aim is, amongst other things, to predict the formation of potential defects resulting from the use of specific technological parameters. Currently, there are a number of process optimisation methods, including soft computing (providing approximate solutions to insoluble high-level problems in computer science). However, traditional hard-computing algorithms, such as FEM, are still in use [24, 25].

2 Numerical model

The optimisation of the welding process, including the identification of the influence of the welding current waveform and value as well as other technological parameters on the quality of welded joints made of steel bars required the development of appropriate numerical models and the performance of related calculations. Numerical models were developed for two variants of calculations, i.e. 1) for bars without protective coatings (Fig. 1 and Fig. 2) for bars with protective coatings (Fig. 2).

Fig. 1
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Three-dimensional model of the cross-wire welding of bars without protective coatings

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Fig. 2
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Three-dimensional model of the cross-wire welding of bars provided with protective coatings

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Numerical (FEM-based) calculations were performed using a SORPAS 3D software model [26]. The software allows the performance of related analyses, including combined electrical, thermal, mechanical and metallurgical analyses. The finite element mesh (Fig. 1 and Fig. 2) was concentrated in critical areas, i.e. where mechanical and thermal issues were highly dynamic. The model included the geometry of the bars (subjected to joining), the electrodes and the zinc (Zn) protective coatings. The parameters used in the numerical simulations are shown in Table 1, whereas the welding process parameters used in the FEM model are presented in Table 2.

Table 1 Simulation parameters
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Table 2 Pariants of FEM calculations, welding cycle and technological parameters in relation to bars made of steel AISI1005 (ϕ = 4.2 mm)
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This paper presents the analysis of significant welding process variables in relation to bars provided with protective zinc coatings (of various thicknesses) as well as those without such coatings. Welding cycle parameters subjected to analysis included the value of welding current and the time of its flow, electrode force and current up-slope time. The modelling process was based on welding cycle process parameters used by the manufacturer of fence mesh (panels). The analysis was performed for the one-pulse and multi-pulse welding technology.

The designations used in relation to computational and experimental designations were as follows:

  • “F” (FEM) – numerical calculations,

  • “E”- experiment performed using an inverter welding machine.

The tests involved the performance of six computational series concerning bars made of steel AISI 1005 [27] and having a diameter of 4.2 mm (Table 2):

  • no. 1: without protective coatings,

  • no. 2: with a protective coating (Zn) having a thickness of 10 µm, up-slope = 10 ms,

  • no. 3: with a protective coating (Zn) having a thickness of 10 µm, up-slope = variable,

  • no. 4: with a protective coating (Zn), up-slope = 10 ms, zinc layer thickness gZn = variable,

  • no. 5: with a protective coating (Zn) having a thickness of 10 µm, 2-pulse technology,

  • no. 6: with a protective coating (Zn), zinc layer thickness gZn = variable, 1-pulse technology.

2.1 Results of numerical calculations (series no. 1: bars without protective coatings)

Table 3 and Fig. 3 contain results (FEM) for variants F1 – F7 (Table 2). The numerical calculations included the analysis of the following parameters:

  • volume of weld nugget molten metal,

  • weld nugget type (full/ring-shaped),

  • welding energy,

  • maximum temperature in the welding area,

  • penetration of bars (displacement of electrodes),

  • weld nugget cross-sectional area.

Table 3 Welding cycle preset parameters and characteristic parameters of cross-wire welding (ϕ = 4.2 mm, without the zinc protective coating, FEM)
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Fig. 3
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Images presenting the distribution of temperature fields in relation to various values of welding current and current flow time (ϕ = 4.2 mm, without the protective coating, FEM)

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The images presented in Fig. 4 represent the fragment of the welding area constituting the area of direct contact between the elements subjected to welding (as presented in Fig. 1 and Fig. 2).

Fig. 4
figure 4

Images presenting the distribution of temperature in relation to various values of welding current and electrode force for selected values current flow time (ϕ = 4.2 mm, zinc protective coating gZn = 10 µm, FEM)

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2.2 Results of numerical calculations (series no. 2: bars with protective coatings)

Table 4 and Fig. 4 present results (FEM) for variants F8 – F16 (Table 2) in relation to a zinc protective layer thickness of 10 µm. The numerical calculations also included the analysis of energy supplied to the weld and the expulsion of liquid metal from the weld nugget.

Table 4 Welding cycle preset parameters and characteristic parameters of cross-wire welding (AISI 1005 [12]) ϕ = 4.2 mm) provided with the protective zinc coating having thickness gZn = 10 µm (FEM)
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Variants F8, F11, F12 and F14-F16 (Table 4) were characterised by the phenomenon of expulsion triggered by an excessively long welding time. The fields of temperature presented in Fig. 4 do not reveal the effect of expulsion as they show the distribution of temperature shortly before the above-named phenomenon, i.e. at the end of current flow.

2.3 Results of numerical calculations (series no. 3: various up-slope times)

Another aspect of numerical analysis was the current up-slope time. The results in the form of (cycle) preset parameters and characteristic parameters of cross-wire welding (ϕ = 4.2 mm, AISI 1005 [27], gZn = 10 µm) are presented in Table 5 and Fig. 5 The analysis involved the same preset and characteristic parameters as those specified in Table 3.

Table 5 Welding cycle preset parameters and characteristic parameters of cross-wire welding (AISI 1005 [2]) ϕ = 4.2 mm), protective zinc coating thickness gZn = 10 µm, up-slope = variable (FEM)
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Fig. 5
figure 5

Images presenting the distribution of temperature in relation to various values of welding current up-slope time (ϕ = 4.2 mm, gZn = 10 µm, up-slope = variable, FEM)

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Figure 5 contains results in the form of temperature distribution in the welding area in relation to selected values of welding current flow time.

2.4 Results of numerical calculations (series no. 4: various values of zinc protective coating thickness)

Table 6 and Fig. 6 present the results of numerical modelling in relation to various values of zinc protective coating thickness.

Table 6 Welding cycle preset parameters and characteristic parameters in relation to the thickness of the zinc protective coating (ϕ = 4.2 mm, up-slope = 10 ms, protective zinc coating thickness gZn = variable, FEM)
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Fig. 6
figure 6

Images presenting the distribution of temperature field in relation to various values of the zinc protective coating (ϕ = 4.2 mm, up-slope = 10 ms, zinc coating thickness gZn = variable, FEM)

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2.5 Results of numerical calculations (series no. 5: two-impulse welding cycle)

The numerical analysis also included FEM-based calculations in relation to the two-impulse welding cycle. The value of current from the range of higher values (as for the 1-impulse technology) was selected as the value of the first impulse. Afterwards, the value of current for the second impulse was reduced in relation to the reference variant (F9, Table 1, line 9).

The tests also involved a two-impulse cycle with a break (pause) between individual current impulses, yet without any positive effects.

The calculations were performed until the moment when the phenomenon of expulsion took place.

2.6 Results of numerical calculations (series no. 6: technological parameters used in production)

Table 8 contains the results of numerical calculations for various zinc layer thicknesses including welding cycle parameters as those present under actual welding conditions, i.e. welding current and electrode force. The authors also made an attempt at optimising the process within various current up-slope times and various zinc coating thicknesses.

It should be noted that the values of current in relation to variants F26–F34 were lower than in the cases of previous variants (F1–F25). The assumption of the FEM calculations included the detailed analysis of the welding process as well as the obtainment of knowledge concerning phenomena taking place during welding, which was possible when observing the formation of the weld nugget as the molten material of the elements subjected to welding. Under production conditions, for obvious reasons, such as energy savings, heat input reduction or the reduction of welding deformations (distortions), the welding process is performed using lower energy-related parameters (lower welding current and shorter current flow time) and the welded joint is the one in the solid state. Column “J” of Table 8 contains the diameter of the weld and not that of the molten metal nugget, as was the case in the previous tables containing FEM calculation results.

3 Analysis of numerical calculation results

The analysis of results for each series is as follows:

  • Series no. 1, i.e. without the zinc protective coating (Table 3), was made as a reference series in order to obtain thorough knowledge concerning the course of the welding process, i.e. the heating of materials (subjected to welding) in the welding area as well as the formation of the liquid metal nugget and the squeezing of the molten metal outside the welding area.

  • Series no. 2, i.e. with the zinc protective layer (gZn =10 μm), contained variants F8 through F16 (Table 4 and Fig. 4). Because of the lack of expulsion, the obtainment of the full weld nugget and the largest diameter of (molten) weld nugget material (Table 4, line 2, column J), variant F9 was found to be the most favourable.

  • The analysis of results obtained in series no. 3 and concerning various values of welding current up-slope time (Table 5, Fig. 5) revealed that the extension of current flow time within the main interval (Table 5, column E) did not directly translate into an increase in the weld nugget diameter (weld area). An additional welding time (welding current up-slope time) resulted in the obtainment of larger weld nugget area (considered to be a favourable effect). The most favourable up-slope time = 40 ms (Table 5, line 4, variant F19) enabled the obtainment of the largest weld nugget area, where the main welding interval amounted to a mere 31 ms (Table 5, line 4, column E). The parameters of variant F19 were found to be the most favourable (best) welding conditions (BWC) for series no. 3, where analysis was concerned with the variability of welding current up-slope time.

  • When analysing the remaining results concerning the above-named series (Table 5, variants F9, F17 and F18), it should be noted that up-slope times shorter than those used in variant F19 (up-slope = 40 ms) translated into smaller areas of “molten” material (constituting the weld nugget). A similar effect could be observed in relation to longer up-slope times (Table 5, variant F20) if compared with the value used in most favourable variant F19. Variant F19 should be treated as the most favourable one in relation to the remaining welding cycle parameters, i.e. I = 4.5 kA, F = 1.0 kN, gZn = 10 µm. The analysis of the results revealed the maximum (of the function), in relation to which the largest weld nugget area and relatively low welding energy were obtained. As can be seen, current up-slope time had a significant effect on the welding process and the formation of the weld nugget.

  • Series no. 4 was concerned with tests involving various thicknesses of the zinc protective layer. The analysis of the results revealed that, in comparison with a zinc layer thickness of 10 µm (Table 6, Fig. 6, reference variant F9), the thinner, i.e. 5 µm thick zinc layer (Table 6, Fig. 6, variant F21) enabled the obtainment of the greater area and volume of the weld nugget using relatively low welding energy. In turn, when compared with that of 10 µm (Table 6, Fig. 6, reference variant F9), the greater thickness of the zinc layer amounting to 30 µm (Table 6, Fig. 6, variant F22) proved less favourable as it precluded the melting of the steel core in the central part of the weld. The unfavourable effect of the greater thickness of the zinc protective layer resulted from the fact that the elements subjected to welding were joined as a consequence of the melting of the zinc protective layer. The melting of the thicker zinc layer led to an unfavourable increase in the area of contact between the materials subjected to welding, which, in turn, was responsible for an inconvenient decrease in welding current density.

  • Series no. 5 showed results concerning the use of the two-impulse technology. The first impulse was tasked with the dynamic heating of the area of contact between the materials (bars) subjected to welding as well as the fast melting of the zinc layer and squeezing molten zinc outside the welding area. In turn, the second impulse was tasked with the primary heating (i.e. the melting) of the steel material of bar cores.

  • Because of inconveniently short times of welding current flow (Table 7, variants F24 and F25), entailing (in the above-named case) the significant dynamics of electrode (pressure) force systems, the above-presented solutions were recognised as unfavourable. The distribution of temperature in the welding area is presented in Fig. 7. The images of temperature distribution present the manner of the melting of the zinc layer and that of the bar core steel material. The application of the variants characterised by short welding times (variants F24 and F25) was connected with the risk concerning the exertion of improper electrode force, potentially resulting in the undesirable phenomenon of expulsion. Such an effect was observed in variant F25 (Table 7, line 3, column N). Amongst all the variants subjected to analysis, the most favourable was variant F23, the parameters of which could be recognised as the most favourable (best) welding conditions with respect to the two-impulse technology (Table 7).

  • However, in relation to reference variant F9 (Table 4), the use of the two-impulse technology led to an undesirable increase in the extension of welding time (from 60ms to 115ms, i.e. by 83%) and an unfavourable increase in welding energy (from 314 J to 374 J, i.e. by 19%).

  • The tests also included the analysis of the two-impulse technology with a break (pause) between the impulses. In authors’ opinion, the process was so dynamic that the extension of welding time by adding breaks (pauses) between welding current impulses did not produce any desirable and positive results.

  • Series no. 6 concerned results related to technological welding tests performed using the target welding station for the fabrication of fence mesh/panels. The analysis of the results revealed that the most favourable welding conditions were those of variant F29 (Table 8). The aforesaid variant included all the most favourable aspects analysed in the previous computational series.

Table 7 Welding cycle preset parameters and characteristic parameters in relation to the two-impulse cross-wire welding cycle (AISI 1005 [2], ϕ = 4.2 mm, gZn = 10 µm, FEM)
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Fig. 7
figure 7

Images presenting the distribution of temperature field in relation to various values of the two-impulse welding cycle (ϕ = 4.2 mm, gZn = 10 µm, FEM)

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Table 8 Welding cycle preset parameters and characteristic parameters (ϕ = 4.2 mm, FEM)
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4 Experimental tests

The experimental verification of the above-presented numerical calculations involved the performance of welding tests using a Dalex MPS 14-6MF medium-frequency (1kHz) spot-projection inverter welding machine featuring a pneumatic electrode force system. The welding machine was also provided with a GENIUSHWI 424W PRO-EA IQR PQS AMC controller (Harms & Wende). The maximum welding current amounted to 60 kA, whereas the maximum electrode force was 12 kN. The welding machine was equipped with a proportional valve, enabling the repeatable setting of electrode force and its changes within one welding technology. The welding machine used in the tests is presented in Fig 8.

Fig. 8
figure 8

Dalex MPS 14-6MF medium-frequency (1kHz) spot-projection inverter welding machine

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The above-presented numerical calculations were verified by performing technological welding tests (Fig. 8) and metallographic tests (involving selected joints). The results of the technological welding tests (shear strength, expulsion) along with welding cycle parameters are presented in Table 9.

Table 9 Welding cycle preset parameters and characteristic parameters (shear strength, expulsion—(ϕ = 4.2 mm, experiment)
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Strength tests were performed for all the variants subjected to analysis. The results are shown in Table 9 (column F). The tests revealed different types of welds, i.e. (1) lack of weld, (2) ring-shaped weld nugget and 3) full weld nugget. The remaining results are presented in Table 10. In order to better reveal the type of weld obtained, the joints were subjected to destructive (peel) tests. The welded joint contained areas where it was clearly visible that the material was not molten (Table 10, line 1), areas where the material had melted and areas where welding took place in the solid state (Table 10, line 2 and 3).

Table 10 View of different types of weld after the peel test
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Metallographic tests were performed for variants E1 and E12 (Table 9). Variant E1, characterised by a relatively low current of 3.5 kA and a minimum up-slope time of 3 ms, triggered expulsion (Table 9, Fig. 9). Variant E12 characterised by a (higher) current of 4.1 kA and an up-slope time of 40 ms, did not lead to expulsion (Table 9, Fig. 10) and enabled the obtainment of the highest strength of the weld.

Fig. 9
figure 9

Microstructure of joint no. E1

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Fig. 10
figure 10

Microstructure of joint no. E12

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5 Verification of numerical calculations

Microstructural Figs. 9 through 13 revealed that welding proceeded in the solid state. The layer of zinc was melted and squeezed out of the welding area. It was possible to notice one-sided flash from the steel core material squeezed out of the welding area (variant E1, Fig. 9) and smaller two-sided flash from the welded joint (variant E12, Fig. 10). The base material of the bars subjected to welding is presented in Fig. 11, whereas the heat affected zone (HAZ) is presented in Fig. 12.

Fig. 11
figure 11

Base material

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Fig. 12
figure 12

Heat affected zone – joint E12

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It was not possible to notice the easily visible zone of incomplete fusion (adhesive–diffusive joint) or the molten weld nugget, which indicated that the joint was formed in the solid state. The lack of the fusion zone was confirmed by related metallographic tests (see Fig. 12).

The experimental tests were performed for the bars provided with a 10 µm thick zinc protective layer. The assumed criterion accompanying the analysis of experimental test results was the highest strength of the weld obtained using relatively low energy parameters. The above-named criterion was satisfied by variant E12. The Authors made an additional attempt involving the performance of the welding process using lower current values (variants E13 – E16), yet without increasing the strength of welded joints.

6 Summary and conclusions

The above-presented numerical calculations and their experimental verification concerning the cross-wire welding of steel bars (AISI 1005; ø 4.2 mm) justified the formulation of the following conclusions:

  1. 1.

    The numerical analysis with respect to welding current up-slope time revealed its very significant effect on the course of the welding process, including the manner of heating, melting and the shaping of the weld nugget liquid metal as well as the final result in the form of the welded joint (aesthetics, strength of welds). A clearly visible maximum (amongst others, from the point of view of weld strength) was observed for the up-slope time of 40 ms. This parameter enabled the obtainment of the largest melted area of contact, full weld nugget, relatively low welding energy and, last but not least, precluded expulsion. All the aforesaid factors were tantamount to an increase in the strength of the weld. The extension of up-slope time proved very beneficial.

    The above-presented analysis constitutes an entirely new approach to the optimization of the projection welding of bars. The optimization was enabled through the use of a DC 1 kHz inverter welding machine, allowing the current to be shaped every 1 ms.

  2. 2.

    The numerical modelling revealed that the thickness of the zinc protective layer (coating) had substantially affected the course of the welding process and the quality of welded joints. The thinner the zinc protective layer, the more favourable course of the welding process (demonstrated by the larger area of the weld and the greater volume of the bar core molten (steel) material. In turn, in relation to the greater thickness of the zinc layer, it was possible to observe the lack of the melting of the bar core material and the lack of liquid weld nugget formation. The above-presented situation resulted from the partial melting of zinc and the formation of the greater area of contact between the elements (bars) subjected to welding (particularly at the initial stage of the current flow), which directly led to an unfavourable decrease in welding current density and, consequently, to the reduced intensity of the heating (melting) of the bar core material. Greater thicknesses of the zinc protective layer required the use of different welding parameters, including higher welding current.

  3. 3.

    The experimental verification of the numerical test results confirmed that the extension of up-slope time positively affected the quality of welded joints. The extended welding current up-slope time was also demonstrated by the size of flash. The analysis of metallographic images related to the longer welding time (40 ms – DC welding machine), if compared with a very short up-slope time of 3 ms (AC welding machine), proved more favourable as it was responsible for the significantly smaller flash of liquid metal. An unquestionable advantage resulting from extended up-slope time was a significant welding energy decrease of approximately 43%. The use of the above-named welding parameters translated into an increase in the strength of the welded joint.

  4. 4.

    During the tests involving the use of the DC 1kHz inverter welding machine, it was possible to shape the current waveform every 1 ms as well as to adjust a very advantageous linearly increasing current time of 40ms (the so-called up-slope time). In turn, in relation to the AC 50 Hz welding machine, the up-slope time amounted to 3 ms and, according to the research results, proved overly short and unfavourable as it triggered expulsion. The above-presented comparison revealed that it was definitely more favourable to weld bars in the crosswise configuration using the DC inverter welding machine (1 kHz).

  5. 5.

    The metallographic test results concerning the most favourable welding conditions revealed that the joints were formed in the solid state (they did not have the clearly visible molten weld nugget).

  6. 6.

    The extension of up-slope time above the optimal value of 40 ms only resulted in the plasticization of the material, without melting the base material of the bar. An unfavourable increase in welding energy observed during the process did not trigger the desired melting of the base material of the bar. The aforementioned welding parameters (long up-slope) did not translate into favourable thermal conditions. The materials subjected to welding only underwent plasticization, which led to the formation of a large unfavourable contact area (between the bars), triggered a drop in current density and precluded the melting of the base material (core) of the bar.

  7. 7.

    The numerical analysis of the two-impulse technology revealed the unfavourable extension of welding time and an undesirable increase in welding energy. In addition, the extension of welding time by additional breaks (pauses) between welding current impulses did not produce any positive results either.