Distortion and Residual Stress Reduction Using Asynchronous Heating Sources for Multi-Robot Coordinated Wire-Arc Directed Energy Deposition

Abstract

Multi-robot coordinated wire-arc directed energy deposition (MRC-WA-DED) has proliferated in recent decades, employing asynchronous independent heating sources to deposit material simultaneously. Beyond enhancing efficiency, MRC-WA-DED introduces a synergic effect between the heating sources, resulting in a controllable thermal field on the deposit component. This research aims to investigate if the synergic effect is beneficial for residual stress and distortion reduction and how it can be applied to enhance the quality of MRC-WA-DEDed parts. A finite element model was developed to compare the thermodynamic response of WA-DED when both coordinated heating sources (CHSs) and a single heating source (SHS) are applied. Simulation and deposition experiments were carried out to clarify the influence of different coordination strategies on the fabricated component’s thermal behavior, stress distribution, and distortion conditions. The results indicate that the synergic effect of CHSs leads to a smoother temperature gradient than that accomplished by a SHS, reducing the maximum distortion of a single layer by 49.1%. As validated by actual depositions, the residual stress, maximum distortion, and hardness of a ten-layer component were reduced by 6.5%, 11.2%, and 18.6%, respectively.

1. Introduction

1.1. Background and Motivation

Additive manufacturing (AM) fabricates solid parts directly from CAD models by gradually melting, fusing, sintering, or extruding raw materials layer by layer [1]. A heating source with high energy density is normally employed to melt and solidify raw materials in the form of wire, powder, or sheet to fabricate metallic parts. Common heating sources include lasers, arcs, electronic beams, and plasma. Wire-arc directed energy deposition (WA-DED) is a typical metal AM technology characterized by its cost-competitiveness and time efficiency. WA-DED has been extensively utilized for manufacturing large-scale metallic parts [2,3]. Reported instances include propellers [4], turbine blades [5], vertebrae [6], and multi-directional pipe joints [7].

During the WA-DED process, the deposited component is repetitively heated by a power source with a relatively high heat input, resulting in a large temperature gradient and complex thermal cycles [8,9]. The cumulative effect of heat input and non-equilibrium solidification is to generate significant residual stress and distortions on the deposited component, which reduces the forming accuracy of the component, influences the stability of the deposition process, and produces crack defects [10]. For this reason, residual stress and distortion are widely recognized as major issues in WA-DED [11].

Since a meter-scale part usually takes weeks or longer to be fabricated, the concept of multi-robot coordinated (MRC-) WA-DED has gained significant attention in recent decades, introducing asynchronous independent heating sources to deposit material simultaneously [12]. Beyond improving efficiency, MRC-WA-DED creates a synergic effect between the heating sources, resulting in the coordination of asynchronous thermal fields on the deposited component. However, it is still unclear whether the synergic effect benefits the deposit and how it can be applied to enhance the quality of WA-DEDed parts. In addition, the concept of MRC-WA-DED introduces more concerns than classical WA-DED regarding the work amount, deposition position, and work time of individual robots. Process planning and optimization become a complex issue. There is a lack of theoretical fundamentals that underpin the process optimization from the perspective of coordinated heating sources (CHSs).

The above-mentioned facts stimulated the research work of this paper. Specifically, this paper focuses on the synergic effect of CHSs on the residual stress and distortion behavior of deposited components. Both simulation and deposition experiments were carried out to clarify the influence of different coordination time intervals on the distortion conditions and stress distribution of the fabricated component. The findings form a basis for optimizing the deposition process of MRC-WA-DED.

1.2. Literature Study

Much research attention has been paid to investigating the residual stress and distortion behaviors of the WA-DEDed parts using the finite element method (FEM). Recent studies have shown that the residual stress in the longitudinal direction within a WA-DED component surpasses that in other directions [13,14]. The distribution of residual stress in the build direction is also heterogeneous. Since the lowermost layer on the substrate experiences faster heat dissipation than the layers above, the stress along the deposition direction exhibits a sequential pattern of ‘tensile–compressive–tensile’ when the height of the component exceeds a certain value [15]. Before clamps are released, the longitudinal stress along the deposition direction in both the deposit and substrate exhibits a relatively uniform distribution. This uniformity acts as tensile residual stress in the deposit and compressive residual stress in the substrate. However, after clamps are released, the distribution of residual stress changes, resulting in a zero-bending moment. Consequently, the component warps at both ends along the depositing direction.

The literature has presented many strategies to govern residual stress and mitigate distortions, including mechanical methods and thermal field manipulation [16,17]. Concerning mechanical methods, Hönnige et al. [18] applied cold rolling to control the distortion of WA-DEDed aluminum components. Sun et al. [19] applied laser shock peening as a post-processing technique that can convert tensile residual stress to compressive residual stress. However, mechanical methods require additional devices, which increases system complexity and the preparation time before manufacturing. On the other hand, Wen et al. [20] investigated the residual stress and distortion of Ti6Al4V walls using a modified inherent strain method. The work revealed that reducing the inter-pass temperature can alleviate heat accumulation and reduce the thermal gradient, decreasing the inherent strains by up to 50%. Abusalma et al. [21] found that an appropriate elongation of interlayer idle time can reduce the residual stress of thin-walled components in both the longitudinal and build directions. Lu et al. [22] implemented a compulsory cooling system to improve the heat exchange within built components during WA-DED, resulting in less stress and distortion than under natural cooling conditions. Wu et al. [23] developed a rapid cooling approach to reduce the height error of thin-wall structures.

Substrate preheating is another strategy for managing the thermal field of WA-DEDed components. This strategy can reduce the temperature distinction between the component and the substrate, reducing the defect formation probability. However, the microstructure and properties of the component are significantly affected due to the additional heat input [24]. For instance, Wang et al. [25] found that substrate preheating can reduce the speed of heat dissipation, leading to unexpected heat accumulation and microstructure conditions. Moreover, post-processing heat treatment is also an effective solution for reducing residual stress. Goviazin et al. [26] executed heat treatment on a 316 stainless steel cylinder in a vacuum at 600 °C, yielding negligible residual stresses.

It can be seen from the literature that the main approach for controlling stress and distortion by thermal field manipulation is to manage thermal conditions and reduce heat accumulation. While these methods offer an innovative solution to enhance WA-DED forming quality, certain limitations persist. Some methods require additional preparations, while others incur high implementation costs. In the context of MRC-WA-DED, the synergic effect of CHSs provides an opportunity to govern thermal conditions, based on enabling control over residual stress and distortion [27,28]. This principle has been proven effective in welding, such as the double-sided arc welding (DSAW) approach for thick high-strength steel plates [29]. Like DSAW, laser–arc hybrid welding has been proven effective in reducing tensile residual stresses in T-joints by up to 42% [30]. In such cases, every SHS acts as a pre-heating or post-heating source for other sources.

Many pioneering studies on AM using asynchronous heating sources have been reported. For instance, Evans et al. [31] developed a heat transfer model for investigating the thermal behavior of multi-laser-beam powder bed fusion (LPBF). The study utilized a second laser to trace the path of a preceding laser. The result showed that the multi-beam process facilitates slower cooling rates and lower temperature gradients, thereby diminishing residual stresses within the part. Wu et al. [32] designed a numerical model of a WA-DED process with two parallel arcs. It was found that maintaining the arcs in parallel with a certain time interval resulted in a substantial reduction in residual stresses. This reduction is attributed to the diminished temperature gradient during cooling. He et al. [33] implemented a WA-DED system with five weld guns. The fabricated components revealed property enhancement in strength, elongation, and impact energy absorption compared to those achieved by an SHS. The introduction of asynchronous heating sources significantly reduced the size of pearlitic and ferrite grains.

In previous research on the MRC-WA-DED process, it has been demonstrated that simultaneous deposition using parallel heating sources can reduce residual stresses compared with repetitive deposition using SHS. This research pays more attention to the synergic effect of multiple heating sources. Therefore, the arrangement strategy of coordinated heating sources (CHSs) are arranged in several groups for both simulation and experiments. The most intuitive manifestation is the change in time interval between CHSs, which has been marked with t, as shown in Figure 1.

It can be concluded from the literature that utilizing asynchronous heating sources for metal AM has shown considerable superiority regarding both residual stress and distortion control and mechanical property enhancement. However, the existing research focuses on a fixed spatial relationship between the heating sources, while the synergic effect is not sufficiently revealed. Since MRC-WA-DED employs independent heating sources that robots can control, the increased system flexibility provides an opportunity for further optimizing the relationship of asynchronous heating sources, giving rise to the concept of coordinated heating sources (CHSs).

1.3. Objective and Content

This paper aims to investigate the synergic effect of CHSs by strategically arranging the sources to reduce residual stress and distortion. The scientific contribution is to provide an optimization principle for MRC-WA-DED process management. The content of this paper is organized as follows: Section 2 introduces the experimental setup of both numerical modeling and practical experiments. Section 3 presents the results of the simulation and their implications. Actual depositions were also conducted to validate the findings from the simulation research. Conclusions are drawn in Section 4.

2. Materials and Methods

The presented work follows the methodology of simulation-based research. A test platform and an FE model were implemented to compare the simulation results and actual depositions. After confirming the accuracy of the FE model, the thermal behaviors of different CHSs were investigated. The residual stress and distortion were measured, and the optimal time interval was determined using simulations. The optimal time interval and findings were then validated using an actual deposition experiment. The residual stresses, microstructure, and properties of components deposited by both SHS and CHSs were compared to confirm the research findings. Detailed information on the experimental setup and simulation is presented below.

2.1. Experimental Setup

As shown in Figure 2, both forerunning and validation experiments were performed using an experimental testbed, which included two Yaskawa AR1730 robots from Shanghai, China, two Megmeet Artsen 500 gas metal arc (GMA) power supplies from Shenzhen, China, a linear structured-light visual sensor, and a computer. The substrate material was Q235 steel with dimensions of 300 mm × 200 mm × 10 mm, while the fed wire was ER50-6 low-carbon steel with a diameter of 1.2 mm. The robot execution program was implemented by offline programming software and delivered to the robot control cabinet via Ethernet communications. The visual sensor was used to measure the geometries of the deposited bead. The accuracy of the sensor was 0.05 mm.

A forerunning experiment was performed to provide a reference for the FEM, and the results of the simulation study were confirmed using a validation experiment. Parameters applied in both the forerunning and validation experiments are presented in

Table 1. Parameters applied in the forerunning and validation experiments.

Parameter	Value and Unit
Speed of deposition	6 mm/s
Voltage	21 V
Current	153 A
Nozzle-to-plate distance	12 mm
Wire feed speed	3.7 m/min
Bead width	7.5 mm
Bead height in the first layer	2.5 mm
Bead height in the other layers	2.0 mm
Step-over distance between beads	5.0 mm

. It is worth mentioning that the height of the bead in the first layer was 2.5 mm, while that in the other layers was 2.0 mm. The measured height of a ten-layer dual-bead component was 20.5 mm. To ensure consistency in comparison, these geometries were set for the FEM, and the details are given in the next section.

To obtain the temperature history of the deposit and substrate, the JK5000 multichannel thermocouple instrument from Jinke Co., Changzhou, China. was used. The blind-hole method was applied to measure the residual stress of the deposited component. The measuring device was a JH-30 residual stress tester from Juhang Co., Nanjing, China. Before checking the microstructure of the deposit, the samples were corroded by Nital reagent (10% nitric acid and 90% ethanol) for 60 s. The grain size of the WA-DEDed component was measured by CX200E metalloscopy from AOSVI Co., Shenzhen, China.

2.2. Finite Element Modeling

A three-dimensional thermo-mechanical model was built using the finite element method (FEM) to analyze the synergic effect of CHSs. The thermo-mechanical analysis included both the thermal and structural aspects. The following assumptions were made to simplify the temperature, stress, and distortion computation:

• The thermophysical properties of the material are isotropic and independent of temperature, including the density of the material, the coefficient of thermal expansion, specific heat at constant pressure, thermal conductivity, etc.;
• The material of the substrate remains stable during the AM process, ignoring the effect of solid-state phase changes;
• The heat source model maintains a consistent morphology during the AM process;
• The thermal convection effect of liquefaction in the molten pool is neglected. The size and retention time of the molten pool liquid phase are negligible compared to the overall component simulation.

The solution of the heat conduction equation fundamentally lies in solving the differential equation of heat conduction. The differential equation of heat conduction is derived based on the energy conservation law combined with Fourier’s law (law of heat conduction). According to Fourier’s law, heat conduction ensures that the quantity of heat traversing a specific cross-sectional area per unit of time correlates proportionally with the rate of temperature change perpendicular to the direction of that cross-section and the corresponding area of the cross-section.

As for MRC-WA-DED, this law captures the interactions among heat flow, temperature gradients, and spatial dimensions during heat transfer. The asynchronous heating sources model can be represented by

$${\mathit{q}}_{\mathit{i}}=-\lambda {𝛻T}_i=-\lambda \left(\mathit{j}{\displaystyle \frac{{\partial T}_i}{\partial x}}+\mathit{k}{\displaystyle \frac{{\partial T}_i}{\partial y}}+\mathit{l}{\displaystyle \frac{{\partial T}_i}{\partial z}}\right)$$

(1)

where $i$ refers to the heat source number, ${\mathit{q}}_i$ is the heat produced by the $i$^th heat source; $\lambda$ is the thermal conductivity of the material; and ${𝛻T}_i$ is the differential operator of temperature. The negative sign in the equation signifies that the energy is being transferred due to a decrease in temperature.

By combining the law of energy conservation with the Fourier’s law, a differential equation governing heat conduction in the Cartesian coordinate system can be derived:

$$\rho c{\displaystyle \frac{\partial T}{\partial t}}=\sum \lambda ∆T_i=\sum \left[{\displaystyle \frac{\partial }{\partial x}}\left(\lambda {\displaystyle \frac{{\partial T}_i}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(\lambda {\displaystyle \frac{{\partial T}_i}{\partial y}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(\lambda {\displaystyle \frac{{\partial T}_i}{\partial z}}\right)\right]$$

(2)

where, $\partial T/\partial t$ is transient temperature change at the given position; $\rho$ is density of the material; $c$ is heat capacity of material; $∆T_i$ is the Laplace operator of temperature produced by the $i$^th heat source.

The initial condition of the temperature field is noted as

$$T(x,y,z,t=0)=T_0(x,y,z)$$

(3)

Given the initial conditions of convective and radiative heat transfer, the thermal distribution in space and time can be calculated using the heat transfer equation. Subsequently, the result of temperature distributions can be calculated to conduct a steady-state structural analysis based on material properties.

To clarify the benefit of the synergic effect, an FE-based comparative study was carried out, in which the thermo-mechanical responses of SHS and CHSs were investigated using a mono-layer dual-bead model and a ten-layer dual-bead model. These two basic components were assumed to be deposited using either SHS-WA-DED or CHS-WA-DED. Figure 3 provides a schematic representation of the models. The thermo-mechanical calculations were executed using Simufact 2020^® software. The materials and geometries of the components were set according to the forerunning experiment, and the parameters are presented in

Table 2. Material parameters applied in FEM.

Parameter	Value and Unit
Melting point of substrate material	1520 °C
Density of substrate material (27 °C)	7850 kg/m3
Convective heat transfer coefficient (27 °C)	15 W/m2·°C
Substrate thermal conductivity (27 °C)	55 W/M·°C
Heat source input power	3197.7 J/cm
Radiation intensity	0.6
The initial temperature of the substrate and wire	27 °C

. Every bead in the components spanned a total length of 270 mm and featured a parabolic cross-sectional profile [34]. The model incorporates a transitional mesh near the components to facilitate computational accuracy and efficiency.

In the simulations of CHS-WA-DED, every bead in a layer was deposited using an independent heating source. Every moving source was represented by a standard double-ellipsoidal model to conform to the shape of the melt pool. After the first source started to deposit, the second heating source followed with designated time intervals, which were arranged as 0 s, 5 s, 10 s, 20 s, 30 s, and 40 s, respectively. This sequential operation emulates the thermodynamic influence of asynchronous heat treatments on the component. Birth–death elements of the beads were generated according to [35] to simulate the deposition process by arc. For SHS-WA-DED simulations, the second heating source started only after the first source was turned off, indicating that the two beads were deposited by a single source. Furthermore, for the components containing ten layers, an interlayer idle time of 20 s and a cooling time of 300 s at the end of deposition were applied. Therefore, a total number of 14 simulations were carried out for both the mono-layer and ten-layer components.

The simulative investigations commenced with an analysis of temperature, residual stress, and distortion distributions concerning the components. During simulations, temperature profiles at the midpoint of the beads were recorded because temperature is the primary cause of stress and distortion evolution. In addition, residual stresses in proximity to the interface between the substrate and deposit were monitored, as these are considered primary contributors to crack propagation and warpage in WA-DEDed components [36]. Moreover, the longitudinal stresses and distortion along the deposition direction, as represented by the A–A line in Figure 3, were compared among the simulations as they typically exhibit greater magnitudes than those along the other two directions.

3. Results

3.1. The CHSs Effect in a Layer

3.1.1. Model Validation

To validate the effectiveness of the FE model, a comparative study was carried out to contrast the thermal behaviors of both simulation and actual deposition. A mono-layer dual-bead component was deposited on a substrate. During the deposition, the CHSs in a layer were arranged at a time interval of 20 s. A K-type thermocouple at point P was used to record the thermal data. The temperature history results of both cases are presented in Figure 4.

A similar appearance between the simulation and actual deposition cases can be observed. Although there are discrepancies in absolute values, the designed FE model aligns well with the actual experimental results in the overall trend, offering an adequate reference for simulative investigations. The differences were caused by the FE simulation settings, such as heat source input efficiency, ambient convective heat transfer coefficient, and material properties. The research focused on the spatial thermal influence and unraveled the residual stress and strain distribution patterns within the components. To enhance experimental efficiency, this research took advantage of the validated model to investigate the thermodynamic influence of the CHSs for WA-DED.

3.1.2. Temperature Evolution

To clarify the influence of CHSs, the temperature evolution was investigated using the FE model. The temperature fields of CHSs with different time intervals are presented in Figure 5. Sub-figures, from Figure 5a to Figure 5f, depict the temperature conditions of WA-DED components at time intervals of 0 s, 5 s, 10 s, 20 s, 30 s, and 40 s, respectively. The melt pool is demarcated by the liquid-phase temperature of H08Mn2Si, and highlighted in the figure.

It can be seen from the temperature distributions that the heat-affected zone (HAZ) of the subsequent heat source progressively diminishes as the time interval between CHSs increases, leading to a reduction in the size of the melt pool. This phenomenon highlights a pronounced preheating effect of the leading heating source on the subsequent heat source. The post-heating effect of the subsequent heating source on the leading source becomes more prominent when the time interval is smaller. In addition, the substrate temperature is influenced by the thermal impact of the CHSs, which diminishes as the time interval increases. The reduction of substrate temperature correlates with lower residual stresses due to the decrease in temperature gradient [18].

Figure 6 depicts the temperature profiles of Point M in the temperature evolution of mono-layer component with different time intervals. Point M is located at the midpoint of the beads, which can reflect the thermal effect of CHSs. The parallel deposition of adjacent beads results in significant heat accumulation, as evidenced by the temperature peak over 1800 °C, leading to a substantial temperature gradient. As the time interval between the two heating sources increases, the peak temperature at Point M gradually decreases. The demarcation between the thermal influence of the leading and subsequent heating source becomes clearer, resulting in a decreased thermal gradient. Consequently, the temperature gradient becomes less significant, leading to a slower cooling rate. However, it is interesting that when the time interval is greater than 20 s, the temperature profile is almost the same as that experienced using the SHS.

The implication is that when the time interval between the two heating sources is greater than 20 s, the influence of the leading source is minimal, and the synergic effect disappears. Therefore, it is anticipated that the coordination of asynchronous heating sources plays a pivotal role in shaping the thermal behaviors of CHSs. Accordingly, balancing heat accumulation and temperature gradient is important. The balance between temperature peak and cooling speed can be achieved by controlling the time interval between CHSs reflected in the temperature profiles.

3.1.3. Residual Stresses

The stress distribution of mono-layer dual-bead components deposited using both SHS and CHSs is presented in Figure 7. The time interval between CHSs was set to 5 s. Four clamps were employed to fix the substrate corners during the depositions, which were released after the components cooled to room temperature. The accumulation of stress can be seen from the sectional view of the component. During the cooling of the substrate under the constraints of the clamps, high tensile stresses were induced within the component. Although high tensile stresses persisted near the interface between the substrate and deposition when the clamps were released, stresses across the component decreased notably.

A consistent trend emerges when comparing the stress distributions of SHS and CHSs. The maximum stress point was observed at the beads overlapping center of the arc distinguishing point before releasing clams, but it shifted to the middle of the bead after cooling to room temperature and clamp release. Components fabricated by CHSs exhibit lower stresses than those made with SHS, both in terms of maximum stress and overall stress distribution. Consequently, the pre-heating and after-heating effects achieved by the CHSs effectively reduce thermal stresses and mitigate internal stresses within deposited components after cooling to room temperature.

The longitudinal stress distribution of the components along the deposition direction at the interface between the substrate and the component can be seen in Figure 8. After the components cooled to room temperature and before the release of the clamps, a minimum stress distribution can be observed in the 5 s case. In the region between the substrate edge and beads, the CHSs time interval exhibited little influence on the stress distribution. Since this region is far away from the HAZ, most stress can be released when the part cools down. Experimental results reveal that the coordination effect of asynchronous heating sources can reduce the maximum longitudinal stress if a certain time interval between the sources is maintained. When the time intervals between CHSs were set from 0 to 40 s, the average longitudinal stresses were 369.9 MPa, 358.5 MPa, 369.1 MPa, 384.6 MPa, 388.6 MPa, and 392.1 MPa, respectively. In contrast, the average longitudinal stress of SHS was 393.5 MPa. The optimal time interval was found at 5 s under the applied deposition parameters. In this case, the average longitudinal stress of the main body part (i.e., from 50 mm to 250 mm) was 358.5 MPa on average, which was superior to the SHS case by 8.9% and the 0 s case by 3.1%.

Since stress distribution is sensitive to the input power of the heating source, the research further investigated if the obtained time interval is effective when the input power varies. For this reason, additional simulation experiments were carried out in which different current and voltage values of the subsequent heating source were set at a time interval of 5 s. The maximum stresses were recorded upon completion of WA-DED and the subsequent cooling of the component to room temperature. Both simulation settings and results are presented in

Table 3. The maximum residual stress concerning different input powers of the subsequent heating sources.

The Leading Heating Source	The Subsequent Heating Source			Maximum Residual Stress (MPa)
Input Power (J/cm)	Current (A)	Voltage (V)	Input Power (J/cm)
3197.7	173	22.1	3814.9	388.7
3197.7	163	21.5	3500.5	382.4
3197.7	153	20.9	3197.7	380.5
3197.7	143	20.3	2906.4	382.2
3197.7	133	19.4	2626.5	380.9

. It can be seen that when the input power of the subsequent heating source remained at 3197.7 J/cm, the residual stress of the component was minimal. The difference among residual stress values was small, indicating that heat input variations between CHSs had negligible effects on deposit distortion. Furthermore, different heat inputs of asynchronous sources may result in deviations of bead morphology, which is not desirable from the design point of view. Accordingly, it can be concluded that the power of the heat source is not a significant factor influencing the synergic effect of CHSs.

3.1.4. Distortion

The synergic effect of CHSs on deposit distortion was investigated. Figure 9 presents the distortion conditions of mono-layer dual-bead components deposited by both SHS and CHSs. The time interval between CHSs was set to 5 s. Before releasing the clamp, there is a significant increase in distortion in the substrate along the deposition direction. This was attributed to clamp constraints during WA-DED, which prevented the substrate and beads from retracting during cooling. The major factors that cause the distortions include (i) bulging at the interface between substrate and deposition, (ii) the influence of the thermal impact of the heat source, and (iii) the shrinkage at the center of the bead. After the clamps were loosened, the substrate and beads could deform freely. The substrate warped around the constrained positions. Consequently, the bending at the ends of the bead is slightly more significant than that observed in the SHS component, owing to increased heat input from the CHSs.

Figure 10 illustrates the distortion distribution at the interface between substrate and component (represented by the A–A′ line in Figure 8) along the deposition direction when different depositing time intervals between CHSs were applied. In all simulated cases, the distortion of the arc starting point is slightly smaller than that of the arc distinguishing point. This trend is opposite to what was observed in stress evolution. When the two heating sources move simultaneously (i.e., the 0 s line), the excessively concentrated heat input leads to substrate bulging near the arc starting point. As the time interval between the CHSs increases, substrate warpage gradually intensifies. The distortion value at the bead overlap center rises. The above trends gradually converge toward the distortion results of the SHS case.

The distortion values of the entire component are presented in

Table 4. The distortion conditions of CHSs at different time intervals.

	Max Distortion		Average Distortion
	Absolute Value/mm	Compared with SHS	Absolute Value/mm	Compared with SHS
SHS	0.173	-	0.114	-
0	0.090	52.0%	0.051	44.7%
5	0.097	56.1%	0.056	49.1%
10	0.122	70.5%	0.076	66.7%
20	0.148	85.5%	0.099	86.8%
30	0.155	89.6%	0.102	89.5%
40	0.172	99.4%	0.115	100.9%

. The optimal situation of the maximum distortion was found at 0 s, almost half of that in the SHS case, and the average distortion was approximately two-fifths. As the time interval between CHSs increases, the synergic effect gradually weakens. When the time interval reaches 40 s, the synergic effect between the two heating sources disappears. According to the results, repetitive heating is the cause of distortions. Introducing CHSs in WA-DED reduces the temperature gradient of the deposited material. When two parallel heating sources move simultaneously, the deposit and substrate do not experience repetitive heating. This is the reason why the distortion along the deposition direction can be minimal.

Based on the conducted research, it can be concluded that the synergic effect of CHSs is beneficial to the reduction of residual stress and distortion compared to those measured in the SHS case. In addition, the residual stress and distortion conditions change as the time interval between CHSs varies. An optimal arrangement of the CHSs time interval is needed. As suggested by the simulations, 5 s was the optimal time interval concerning the residual stress when the input power of the CHSs was 3197.7 J/cm. With regard to distortion, the best case was considered to be the one in which the CHSs move in parallel. When the time interval was set to 5 s, the distortion amount was almost the same as that in the parallel case. However, in the parallel case, the substrate near the arc starting point bulged due to huge instantaneous heat input and thermal gradient. The bulge phenomenon did not occur in the case of 5 s. The optimal time interval between CHSs was determined as 5 s for the above reasons. This optimization scheme was further validated in a ten-layer dual-bead component.

3.2. The Effect of CHSs in a Ten-Layer Component

3.2.1. Simulation Results of Stress and Distortion

As shown in Figure 3b, the FE model of a ten-layer dual-bead component was applied for simulative investigations. For comparison, the ten-layer dual-bead component was deposited using CHSs and SHS. The optimal time interval between CHSs was set to 5 s. In contrast, the SHS case assumed a sequential deposition of two beads in a layer by only one heating source. The rest of the deposition parameters of the two cases were the same. The deposition started from the same horizontal position and direction in the ten-layer component. The interlayer idle time was set to 5 s. The simulation recorded the internal stress and distortion until the components cooled down to room temperature. The stress distribution of deposited components by SHS and CHSs is presented in Figure 11.

After the SHS component cooled down to room temperature, there was an increase in maximum internal stress from 767.0 MPa to 820.9 MPa. The point with maximum internal stress shifted from the region between the first and second layers near the arc distinguishing point to the arc starting point. In addition, the CHSs component exhibited reductions in the internal stress by 4.1% and 6.2% at the end of deposition and the end of cooling, respectively. It can be seen that the application of CHSs facilitates the reduction in internal stress, which is in line with the phenomenon observed in the mono-layer case.

According to the literature, the longitudinal stress along the deposition direction is more significant than in other directions. Figure 12 provides a comparative result of the longitudinal stresses between SHS-WA-DED and CHS-WA-DED along the deposition direction (i.e., the A–A′ line in Figure 3). The results demonstrate that the residual stress of the CHSs component is superior to that of the SHS component at both the end of deposition and cooling. From the arc starting point to the arc distinguishing point, the residual stress in all cases performed the ‘tensile–compressive–tensile’ stress pattern. The residual stress distribution between the SHS and CHSs cases around the arc starting point is almost consistent. However, there was a significant difference among the four cases within the steady interval (i.e., from 75 to 225). In this section, the synergic effect of CHSs can alleviate the internal stress of the deposit. Compared to the SHS case, applying CHSs reduced internal stress by 17.7% on average. The synergic effect of CHSs presented better performance in controlling the residual stress of the ten-layer component.

The distortion distributions of the components deposited by CHSs and SHS are presented in Figure 13. The SHS component revealed 11.2% greater distortion in height. This observation aligns with the phenomenon observed in the mono-layer simulation. Additionally, the distribution of distortion revealed non-uniformity along the deposition direction. There was a difference in distortion between the arc starting point and the arc distinguishing point. Furthermore, as the layer number increased, the point where the maximum distortion happens shifted from the middle to the edge of the component. After the component cooled, the distortion value of the arc distinguishing point surpassed that of the arc starting point, and the difference increased as the number of layers grew.

The reason for the phenomenon can be explained as follows: During the cooling period of the component, residual stress is redistributed. The arc starting point initially experiences high residual stress due to rapid cooling. Then, the stress is transferred to the center of the component as it cools, leading to greater distortion at the arc distinguishing point. In addition, the solidification process of the molten pool contributes to the distortion pattern. The material near the arc starting point solidifies at the early stage of deposition, retaining residual stresses and distortion generated due to the high-temperature gradient. In contrast, the material at the arc distinguishing point solidifies at the final stage of deposition. Greater distortion is generated due to the influence of the distortion around the arc starting point. As the number of layers increases, heat dissipation worsens. The accumulated distortion from the previous layers affects the behavior of subsequent layers. This layer-to-layer distortion accumulation can amplify the difference between the arc starting and distinguishing points.

3.2.2. Experimentation in Practice

To validate the obtained knowledge, two ten-layer dual-bead components were deposited using SHS and CHSs, respectively. The experiment was conducted using the platform presented in Figure 2, and the deposition parameters were the same as those applied in the FE simulations. The deposited components are shown in Figure 14. After the components cooled down to room temperature, the residual stress of the components was measured and compared to validate the benefit of the CHSs.

The results are presented in Figure 15. The B–B′ line in Figure 15a is located at the upper surface of the substrate, and 15 mm parallel to the A–A′ line (i.e., the center of the bead joint). Five points that are uniformly distributed in the B–B′ line with an interval of 50 mm were selected for the measurement. It can be seen that the measured values aligned well with the FE values, which confirms the accuracy of the simulation results. The maximum principal stress distribution along the B–B′ line demonstrated noteworthy differences. In the component deposited by SHS-WA-DED, the average value of normal stress reached 206.5 MPa, while that in the component deposited by CHS WA-DED was 193.6 MPa. A reduction of 6.5% in the average residual stress was achieved by applying CHSs, while a reduction of maximum residual stress was realized from 247.9 MPa to 237.8 MPa. In addition, the residual stress around the arc starting point was lower than that around the arc distinguishing point. This difference is primarily attributed to the larger temperature gradient at the arc starting point, resulting in a faster cooling rate. More stress could be released, and less residual stress could remain after releasing the clamps.

The C–C′ line in Figure 15b was set to check the distribution of residual stress along the perpendicular direction of deposition. Three points were chosen for the measurement at distances of 10 mm, 20 mm, and 30 mm from the component edge. As shown, the maximum value of residual stress along the cross-sectional profile was found at the HAZ of deposition. In addition, reductions of 6.1% and 7.7% in the average and maximum residual stress were achieved by applying CHSs. The greatest difference was found in the deposited component.

3.2.3. Microstructure

According to the test results, CHSs facilitate a reduction in residual stress and distortion. However, simultaneous deposition of two heating sources increases the rate of thermal input. Variations in heat exchange and cooling rates contribute to significant differences in the microstructure of WA-DED components [37]. For this reason, the microstructure and properties of the deposited components were investigated. Figure 16 presents the microstructure of the components at different vertical positions. It can be seen that the grain size in the components deposited by CHSs is larger and more irregular compared to those in the SHS counterpart. Since the heat dissipation rate of the bottom layers is high, the temperature gradient is also high, resulting in a smaller gain size in this area. The effect of grain growth became obvious when a larger heat input was supplied by CHSs. Accordingly, a small temperature gradient and after-heating effect are conducive to forming larger grains. Meanwhile, incomplete fusion can be observed at the interface between substrate and deposition in the components deposited by SHS. This phenomenon arises due to the cold substrate and insufficient heat input during the experiment, leading to incomplete melting in the toe of the bead. Using SHS results in high internal stress within the component, consequently causing defects. Upon employing CHSs, the aforementioned issue is mitigated as residual stress is reduced.

In addition, CHS-WA-DED produced irregular grains. The slower temperature gradient introduced by the CHSs is a crucial factor influencing the grain size. A higher cooling temperature leads to a faster phase transition from the liquid to the solid state, accelerating grain formation speed. A quantitative analysis of grain size in the deposited components was conducted, and the results are shown in Figure 17. The average grain size of the CHS-WA-DED component increased by 28.1%, but homogeneity decreased by 44.2%. The increase in average grain size leads to a reduction in the strength and hardness of the component. The decrease in homogeneity may promote the initiation and propagation of fatigue cracks at grain boundaries, which reduces the fatigue life of the component.

The micro-hardness of the components was measured. Six points uniformly distributed along the deposition direction were selected, and the results are presented in

Table 5. A comparison of the hardness of the components deposited by SHS and CHSs.

	Hardness/HV						Average
	Point 1	Point 2	Point 3	Point 4	Point 5	Point 6
SHS	198.2	210.2	200.5	186.9	192.2	184.8	195.5
CHSs	162.6	163.7	158.9	156.2	158.1	155.9	159.2

. The hardness of the component fabricated by CHS-WA-DED is significantly lower than that of the SHS-WA-DED component, over 18.6%. Since hardness is attributed to the hindrance of dislocation propagation and crystal slip by grain boundaries, the CHSs can reduce the hardness of the material, enhancing formability and decreasing the brittleness of the deposited component.

4. Conclusions

This study presents a comprehensive analysis of the temperature field evolution and the thermodynamic response of wire-arc directed energy deposition (WA-DED) using coordinated heating sources (CHSs). A comparative research method was applied to investigate the synergic effect of CHSs and a single heating source (SHS) using finite element modeling and actual depositions. The findings from the work are beneficial to the path planning of multiple robots for coordinated additive manufacturing. The major conclusions are as follows:

(1)

CHS-WA-DED exhibits superior stress distribution when the time interval between CHSs is 5 s. This improvement is attributed to the preheating and remelting effects between the CHSs, resulting in a reduced cooling temperature gradient and more homogeneous temperature distribution;

(2)

The maximum distortion reduction condition is achieved when two parallel heating sources move simultaneously (i.e., time interval is 0 s). The high instantaneous heat input and thermal gradient cause significant bulging near the arc starting point. According to the simulation result, the optimal time interval between the CHSs is determined to be 5 s. The maximum and average distortions are 56.1% and 49.1% of those resulting from a SHS, respectively.

(3)

The obtained optimal scheme was validated by comparing ten-layer dual-bead components deposited by a SHS and CHSs. According to the results of the simulative study, the average residual stress of the CHSs component along the deposition direction was reduced by 4.1% and 6.2% at the end of deposition and the end of cooling, respectively, while the maximum distortion amount decreased by 11.2%.

(4)

As validated by experimental results, the synergic effect of CHSs reduced the average residual stress of the component along the deposition direction and the perpendicular direction by 6.5% and 6.1%, respectively. Although CHSs increased grain size and non-uniformity in the deposit, the synergic effect of CHSs is beneficial to stress and distortion reduction, which is the most crucial factor for fabricating large-scale parts by WA-DED and thereby preventing cracks during deposition.