Electron beam-directed energy deposition (EB-DED) has emerged as a promising wire-based metal additive manufacturing technique. However, the effects of EBs on pendant droplets at wire tips have not yet been determined. The aim of this study is to enhance the understanding of this action by analyzing the mechanism of droplet oscillation. The pendant droplet oscillation phenomenon hinders the stable transfer of droplets to the molten pool and limits the feasibility of manufacturing complex lattice structures by EB-DED. Hence, another aim of this study is to create an oscillation suppression method. An escalating asymmetric amplitude is the main characteristic of droplet oscillation. The primary oscillation-inducing force is the recoil force generated from the EB-acted local surface of the droplet. The physical mechanism of this force is the rapid increase and uneven distribution of the local surface temperature caused by the partial action of the EB. The prerequisites for droplet oscillation include vacuum conditions, high power densities, and bypass wire feeding processes. The proposed EB-dynamic surrounding melting (DSM) method can be applied to conveniently and effectively suppress oscillations, enable the accurate transfer of droplets to the molten pool, and achieve stable processes for preparing the strut elements of lattice structures. Lowering the temperature and improving the uniformity of its distribution are the mechanisms of oscillation suppression in EB-DSM. In this study, the physical basis for interpreting the mechanism by which EBs act on droplets and the technical basis for using EB-DED to prepare complex lattice structure parts are provided.
Zhiyue Liang, Zhenyu Liao, Haoyu Zhang, Zixiang Li, Li Wang, Baohua Chang, Dong Du.
Generation and Suppression of Pendant Droplet Oscillation in Electron Beam Directed Energy Deposition.
Engineering, 2024, 37 (6) : 215-229 DOI:10.1016/j.eng.2023.12.012
Additive manufacturing (AM) is a revolutionary manufacturing approach that employs a bottom-up approach, enabling innovative design and integrated manufacturing of end-use metal parts [1]. This method has garnered significant attention in various industries, including the aerospace, automotive, energy, and medical industries, because of its ability to fabricate high-performance and complex parts, offer customization, and shorten supply chains [2], [3], [4]. The extreme thermal conditions of AM, such as steep temperature gradients and high cooling rates, result in highly dynamic and nonequilibrium physical processes that differ from those of traditional manufacturing methods [5], [6]. The widespread application of AM has posed significant challenges to the consistency and repeatability of the deposition process, thereby impeding its development [7]. Consequently, there is an increasing demand for a comprehensive understanding of the underlying physical process of AM. In the realm of powder bed fusion (PBF) technology, the molten pool is a crucial physical process that demands attention [8]. Scholars have employed ultrahigh-speed X-ray imaging [9], [10] and simulation [11] to scrutinize the formation and conduction of keyhole pores in the molten pools. Conversely, wire-based directed energy deposition (DED) technology encompasses three primary physical processes: wire melting, molten pool formation, and droplet transfer [12]. Among these processes, the molten pool flow behavior [13], [14], [15] and droplet transfer behavior [16], [17], [18] have garnered the attention of scholars, while research on wire melting and droplet behavior is relatively scarce, particularly in the area of electron beam (EB)-DED.
EB-DED, also known as EB freeform fabrication (EBF3) and EBAM, is an AM technology that uses metal wire as the raw material and EB as the heat source. This technology has the advantages of high energy conversion efficiency, high energy utilization, high deposition rate, high material utilization, large part size, and high part density [19]. Since its introduction in the 1990s [20], the National Aeronautics and Space Administration (NASA) Langley Research Center [21], [22] and Sciaky, Inc. (USA) have vigorously promoted the development and application of EB-DED, which has become one of the fastest metal AM methods [23]. In recent years, this topic has received increasing amounts of attention from both scholars and industry. Many institutions around the world have researched the microstructures and properties of built parts [24], process design [25], in situ material synthesis [26], process simulation [27], online monitoring and control [28], [29], and equipment development [12] related to EB-DED, promoting the understanding of the process characteristics and deposition laws of this technology. In terms of monitoring and testing, machine vision-based methods were first applied [17], [30], and in recent years, other signal source methods have been studied and implemented [31], [32], [33]. The parts produced by EB-DED have also been applied in many fields such as land, sea, air, and space, showing good prospects for development [34]. However, compared to those of other types of AM technology, the number of institutions and related research works on the development of EB-DED are still relatively low, and EB-DED is still in the early stages of development. Limited by extreme conditions, such as a closed vacuum environment, research on the physical laws of the EB-DED deposition process is still insufficient.
The aim of comprehending the underlying physical mechanisms of AM is to develop uninterrupted and efficient deposition procedures and superior part quality, thereby facilitating its extensive implementation in the production of intricate and high-performance components. Lattice structures are widely recognized as the most intricate type of component, and they have significant potential for being structurally lightweight [35]. Conventional manufacturing techniques, such as casting and machining, are not viable options for producing lattice structures. However, AM has been deemed a suitable method for manufacturing intricate components [1]. The production of metal lattice structures through PBF has reached a relatively mature stage, and recent research has shifted its focus from the forming process to the development of lattice structure design methods, structural optimization, mechanical properties, and application prospects [36], [37], [38]. Despite the high precision of producing various lattice structures using PBF, its manufacturing efficiency is relatively low, which poses challenges in producing large parts. However, large lattice structure parts offer good mechanical properties, sufficient space for multifunctional integration, and broad engineering application prospects [39]. The uniform droplet deposition method has been developed for forming metal lattice structures [40]. Serveral researchers have explored the parameter selection [41], [42], effect of heat accumulation [43], suppression of landing error between different droplets [44], and flight and impingement behaviors of droplets [45]. However, this method is now commonly used for low-melting metals such as aluminum alloys and tin-lead alloys. Wire-based DED is gradually becoming an ideal choice for the rapid formation of medium-to-large freeform metal lattice structures because of its high formation rate and good density, especially for high-melting-point metals [46]. Scholars have reported on manufacturing lattice structures by wire and arc AM (WAAM), mainly exploring the influences of various process parameters, such as arc voltage, current, and welding torch offset on the interlayer geometric shape and size [46], [47], [48]. The microstructures and properties of the formed parts [49] and the planning of forming strategies [46] have also been investigated.
Compared to WAAM, EB-DED has several unique advantages, including higher energy efficiency [50], superior material properties [51], and the potential for on-orbit manufacturing in space [52]. However, preparing lattice structure parts by EB-DED has not been explored in the literature. This lack of research is primarily because of the limited number of researchers in this field who have focused mainly on exploring material microstructures and properties by manufacturing simple parts, such as thin-walled and solid parts [53], [54], [55]. The use of using EB-DED to prepare lattice structures has potential advantages in terms of part size, deposition efficiency, density, avoidance of splashes, interlayer consistency, and adaptability to refractory metals. Our attempts to use EB-DED to prepare the basic strut structure needed for lattice parts reveals that pendant droplets oscillate on the metal wire before dropping. Droplet oscillation involves a pendant droplet swinging around the junction between the wire and the droplet. This phenomenon affects the accuracy and stability of droplet transfer to the molten pool, ultimately hindering the formation of the strut structure. While previous research has focused on the flow and temperature fields of molten pool [15], [56], [57] and droplet transfer [16], [58] processes, little attention has been given to wire melting and droplet behavior. We found only one study [59] on oscillation; in that study, the authors analyzed the causes of the oscillation to a certain extent but did not discover any suppression methods. We believe that there is still a gap in understanding the droplet oscillation phenomenon, which is critical in preparing lattice structures. In our study, we aimed to address this gap by investigating the behaviors and factors influencing droplet formation and oscillation in EB-DED processes. We employed machine vision and the dual-channel absorbed current monitoring method [33] to explore the characteristics of droplet formation and oscillation and the influences of the EB and metal vapor on droplet behavior. We also combined thermal fluid simulation to explain the mechanism of droplet oscillation. Then, we proposed an oscillation suppression technique and prepared the strut structures. Through this study, we could contribute to the understanding of the droplet oscillation phenomenon in the EB-DED process. In addition, we could provide a physical basis for interpreting the mechanism of an EB acting on a droplet and a technical basis for using the EB-DED process to prepare complex lattice structure parts.
2. Methods
Commercial bypass wire-feeding EB-DED equipment (ZCompleX 3; DMAMS Co., Ltd., China) was used in this study. The electron gun had a maximum accelerating voltage of 60 kV and a maximum beam current of 250 mA, and the vacuum chamber operated at a pressure of less than 5 × 10−2 Pa. The electron gun and bypass wire-feeding mechanism were fixed, and the manufacturing process was partially achieved through the movement of a 5-axis workbench. The structure of the equipment was demonstrated in our previous work [33]. The material used for both the substrate and wire was Ti6Al4V (Institute of Metal Research, Chinese Academy of Sciences, China); the wire had a diameter of 2 mm.
The dual-channel absorbed current monitoring system, as shown in the middle panel of Fig. 1(a), could be applied to obtain absorbed current signals (ACS) from both the substrate end and metal wire. The hardware compositions, signal sources, and acquisition principles of the system were introduced in our previous work [33]. A data acquisition card (PCIE-1840; Advantech Co., Ltd., China) was used to collect the ACS at a sampling frequency of 10 kHz. In this study, we defined the positive direction of the current as the direction of electronic directional movement. We employed the locally weighted scatter-plot smoothing algorithm (LOWESS) to reduce the noise in the raw ACS [33], [60]. The energy spectrum was obtained by the fast Fourier transform (FFT) of the processed ACS. Time-frequency analysis of the processed ACS was conducted by variational mode decomposition (VMD) and the Hilbert-Huang transform (HHT).
The machine vision monitoring system in the vacuum chamber utilized an industrial camera (DMK 23GV024; The Image Source Asia Co., Ltd., China), with a resolution of 640 px × 480 px (pixel) and a frame rate of 100 fps (frame per second). Each pixel corresponded to an actual size of approximately 0.125 mm. To extract the contour and centroid of the droplet, we developed an image processing algorithm that segmented the image based on grayscale contrast, applied the Gaussian blur algorithm for noise reduction, and performed threshold segmentation. We also adopted a multiphysics thermal-fluid flow model to simulate the formation processes and oscillation behaviors of the molten droplets. The simulation model and parameter settings are described in Appendix A Description S1.
3. Droplet oscillation phenomenon
3.1. Necessity of introducing pendant droplets
The high power density and vacuum environment of EB-DED present a significant challenge in terms of heat dissipation conditions, necessitating careful consideration of heat input during the manufacturing of lattice structures. Simple components, such as thin walls, are deposited by the relative motion between the substrate and wire. This motion can impede continuous exposure of the EB at the same position, resulting in the stable formation of multilayer wall components. The strut element has an axial dimension greater than the radial dimension, and the formation process by wire-based DED does not require the aforementioned relative motion but instead requires motion in the axial direction [47], as shown in the middle panel of Fig. 1(a). Hence, the position of the EB remains fixed on the substrate plane, and heat dissipation occurs primarily along the axial direction. When employing a continuous forming process similar to that used for Czochralski monocrystalline silicon, only the spherical crown structure is obtained, as depicted in the left panel of Fig. S1 in Appendix A. Conversely, the utilization of an interlayer cooling process yields a strut structure, as illustrated in the right panel of Fig. S1. Even for the WAAM method which has a relatively low power density and good heat dissipation conditions, the recently proposed high-throughput continuous 3D printing technology still needs to halt heat input when fabricating helical structures [61]. Hence, the use of EB-DED for strut preparation without the need for excessive cooling equipment requires interlayer cooling. The process sequence employed in this study is illustrated in the left panel of Fig. 1(a), where the EB and wire-feeding processes act simultaneously, and the workbench position remains unchanged. Upon completion of one layer, the EB and wire feeding processes are suspended, and the workbench position is adjusted for the next layer.
The layer-by-layer deposition technique requires careful attention to interlayer consistency, which is influenced by droplet transfer [31]. Four distinct droplet transfer modes can be identified based on the difference between the time needed for droplet growth before contact with the molten pool (tg) and the time needed for droplet-molten pool contact before dropping (tc), as shown in the right panel of Fig. 1(a) [33]. The liquid bridge transfer mode (DT1), which ensures a stable connection between the wire and molten pool during relative motion, is considered the most effective method for achieving a consistent layer size among simple parts [16]. For strut elements, it is necessary to ensure the consistency of each layer in the axial direction. As mentioned earlier, the strut cannot be continuously formed in the axial direction. Therefore, it is not essential to rely on the DT1 mode to ensure consistency. In addition, DT1 is influenced by multiple parameters, such as the distance d, the wire-feeding speed vw, and the beam current Ib, as shown in the middle panel of Fig. 1(a); moreover, its process window is narrow, making it difficult to maintain throughout the multilayer deposition process [12], [33]. A deviation from the DT1 mode can cause splashing or residual droplets that affect interlayer consistency and may even lead to interruption. Thus, we believe that the utilization of the liquid bridge transfer mode can be deemed dispensable and that other transfer modes should be considered.
The instability of DT1 is closely associated with the coupling between the processes of wire melting and metal transfer to the molten pool. Decoupling these two processes can enhance the stability and repeatability of the deposition [12]. In the small droplet transfer (DT2) mode or large droplet transfer (DT3) mode, a connection between the wire and molten pool is established before the molten droplet falls. This finding indicates that droplet transfer is still influenced by the molten pool. However, in the noncontact transfer (DT4) mode, the pendant droplet formed at the wire end does not touch the molten pool before dropping, resulting in complete decoupling of the droplet formation and transfer processes. This mode expands the selection window for d, making the mode easier to sustain. The stability of single-layer deposition in this mode is solely determined by the size (melting time) and landing point of the droplet. Furthermore, a larger d can prevent wire sticking and provide greater processing space for unexpected phenomena, such as wire deviation. Therefore, selecting DT4 for preparing lattice parts using EB-DED meets the requirements of axial interlayer stability and possesses sufficient robustness. Hence, the formation and dropping behavior of the pendant droplet in this mode becomes the critical physical process.
It should be noted that, as mentioned in Section 1, the EB-DED has unique application advantages in space. However, the DT4 mode mentioned above requires gravity to achieve transfer. Hence, it may be difficult to prepare lattice structural parts in space by relying on this mode. The focus of this study is to explore the influence of an EB on droplets in a ground environment. The influences in the weightless environment of space are beyond the scope of this article and will be explored in future work.
3.2. Characteristics of droplet oscillation
We monitored the formation and dropping processes of droplets under an accelerating voltage (Ub) of 60 kV, a beam current (Ib) of 30 mA, and a wire-feeding speed (vw) of 0.5 m∙min−1. The pendant droplet exhibits violent oscillation before dropping, as demonstrated in Fig. 1(b) and Appendix A Video S1. This oscillation behavior primarily occurs in the oscillation plane, which is defined as the plane formed by the axis of the wire and EB. The obtained images are projections of the droplets in the oscillation plane. By analyzing the droplet behavior through the change in the droplet centroid position [62], we found that the droplet mainly oscillates horizontally with a maximum amplitude of approximately 4.5 mm, which is similar to its size.
Fig. 1(c) shows the centroid abscissa curve and the dual-channel ACS obtained during droplet formation. The oscillation phenomenon mainly occurs at the end of the droplet formation process. The amplitude increases gradually. The energy spectra show a frequency of oscillation of approximately 12.8 Hz. The centroid horizontal position remains nearly constant before significant oscillation. By utilizing the centroid vertical direction (i.e., the direction of gravity) of the constant position stage as the demarcation line, the oscillation plane is divided into left (pixel coordinate decrease) and right (pixel coordinate increase) regions. The amplitude and residence time of the droplet in the right region are smaller than those in the left region, indicating an asymmetric oscillation. We further define the spatial region where the EB is present as the EB zone and the remaining space as the plasma zone [63]. The ACS at the substrate has a linear mapping relationship with the small incident beam current, but this relationship gradually deviates as the beam current increases [64]. The ACS at the substrate is slightly greater than 0 before oscillation. This value increases when the droplet moves toward the right region during oscillation, and it returns to the initial value when the droplet moves toward the left region. The ACS at the wire is negative throughout the process, indicating the high density of cations around the droplet. The decrease in its value when the droplet moves toward the right region indicates an increased influence of electrons. These findings suggest that the droplet oscillates between the plasma zone and EB zone. In addition, we conducted the same monitoring experiment using pure Mo, Nb, and Ni wires, and observed similar droplet oscillation phenomena, as shown in Appendix A Fig. S2. This result supports the idea that the droplet oscillation phenomenon is not unique to a specific material.
The droplet oscillation phenomenon has a detrimental effect on the preparation of strut structures, warranting further investigation. As illustrated in Fig. 1(d), once detached from the wire, the droplet with a horizontal velocity follows a parabolic trajectory and lands in the unmelted region of the substrate, which can significantly reduce the interlayer bonding strength. Furthermore, as depicted in Fig. 1(e), the time-space trajectories of the centroids do not coincide among the different droplets. The distances between the centroids of different droplets upon landing on the substrate are even greater than the droplet diameter, thereby resulting in irregularly shaped and poorly bonded structures after solidification, as demonstrated in Fig. 1(f). In the present state, it is difficult to use EB-DED for fabricating lattice structures. Therefore, it is imperative to take measures to suppress droplet oscillation, ensuring that droplets fall vertically into the molten pool. To achieve this goal, a thorough understanding of the factors influencing droplet oscillation and a further analysis of the underlying mechanism are necessary.
4. Variations in droplet oscillation
To better analyze the droplet oscillation, we further explored the variations in droplet oscillation behavior under different parameters in Fig. 4. The droplet oscillation phenomenon in EB-DED has been previously reported [59], suggesting that the oscillation is caused by the interaction between the droplet and metal vapor generated from the molten pool and that the corresponding recoil force Fv,m acting on the droplet is in the opposite direction to gravity as illustrated in Fig. 2(g). To validate this viewpoint and further understand the oscillation behavior, we examined the effects of heat and mass input on droplet oscillations by varying Ib and vw. We selected three Ib values (30, 40, and 50 mA) and three vw values (0.5, 1.0, and 1.5 m∙min−1) for combination, as depicted in Fig. 2(g). Notably, in multiple trials, the wire cannot be melted after combining the conditions of Ib = 30 mA and vw = 1.5 m∙min−1. Therefore, we compared and analyzed the results of the other eight parameter groups. By coordinating the optical and absorbed current information, we monitored multiple droplets in each parameter group. Fig. 2(a) displays an example of the time-domain waveform of the dual-channel ACS and the curve of droplet centroid coordinates during a single droplet duration for each of the eight parameter groups. Given that the ACS can have a relatively high sampling frequency and simultaneously reflect information about droplet oscillations and spatial plasma, we conducted a quantitative analysis of the ACS, and the results are shown in Figs. 2(b)-(f).
The average value of the ACS at the wire during a single droplet duration, as shown in Fig. 2(b), can reflect the generation of metal vapor and plasma around the droplet. The average value is negative for all parameter groups, indicating that metal vaporization and ionization occur violently, resulting in a positive space potential at the droplet because of space-charge overcompensation [65]. The numerical value of the average ACS at the wire increases with increasing Ib. The mass of metal vaporization per unit time and per unit area from the molten pool (ṁevp) under high vacuum conditions can be described by the simplified Hertz-Knudsen equation, as shown in Eq. (1) [66]. Plasma mainly comes from thermal ionization and electron-impact ionization of metal vapor. The degree of thermal ionization (αT) can be described by the Saha equation, as shown in Eq. (2), and the degree of electron-impact ionization (αE) can be described by Eq. (3) [67]. The vaporization rate and ionization degree of metal vapor increase with increasing Ib, leading to an increase in the numerical value of the ACS at the wire. Therefore, the results demonstrate that increasing Ib can intensify the production and ionization of metal vapor.
$ \dot{m}_{\mathrm{evp}}=\alpha_{\mathrm{evp}} P_{\mathrm{s}} \sqrt{\frac{M}{2 \pi R T}}$
where, αevp, T, Ps, M, and R are the evaporation coefficient, temperature, saturated vapor pressure at T, molar mass, and ideal gas constant, respectively; C, e, ∊, and kB are the constant, elementary charge, ionization potential, and Boltzmann constant, respectively; and σeb, lE, uv, and SE are the electron-impact ionization cross section, effective interaction length of beam electrons with vapor, vapor speed, and area of the EB spot, respectively.
As evident from Fig. 2(c), the variation in Ib does not significantly affect the single droplet duration, while the influence of vw is more pronounced. This finding presents the dominance of gravity and surface tension in the critical condition of droplet detachment. If the single droplet duration is only affected by the relationship between gravity and surface tension, it should exhibit a linear negative correlation with increasing vw. However, the ideal linear relationship is not reflected in Fig. 2(c), which is caused by the violent oscillation. Fig. 2(d) shows the peak frequency (fp) of the energy spectrum of the ACS at the substrate during droplet oscillation. The fp is approximately 15 Hz for all parameter groups. With increasing vw, as depicted in the droplet centroid change curve on the right side of Fig. 2(a), the rapid increase in droplet mass reduces the regularity of oscillation, shortens the position constant stage before oscillation, and intensifies the instability of droplets, which may cause a slight increase in fp. However, the variation in Ib has little influence on fp.
Fig. 2(e) displays the ratio of the energy of the ACS at the substrate within the frequency range of fp ± 2.5 Hz to the total signal energy, which can reflect the relative amplitude of the oscillation. The ratio gradually decreases with increasing Ib. Combined with the time-domain ACS shown on the left of Fig. 2(a), the decrease in the ratio primarily occurs because of the significant decrease in the amplitude of the ACS. However, the centroid coordinate curves shown on the right of Fig. 2(a) indicate that an increase in Ib does not significantly decrease the actual amplitude of droplet oscillation. Therefore, an increase in Ib exacerbates the generation and ionization of metal vapor, and intensifies overcompensation, resulting in a decrease in the amplitude of the ACS. Finally, we used the HHT to perform a time-frequency analysis on the ACS at the substrate. The results in Fig. 2(f) present the ratio of the time spent in the frequency range fp ± 2.5 Hz to the single droplet duration, which can reflect the relative time of the droplet oscillation and can be considered the early or late start of the oscillation. When vw increases, the droplet begins to oscillate earlier, and the time ratio of the oscillation is greater. However, an increase in Ib does not significantly affect the duration of the oscillation.
The results obtained from Figs. 2(b) and (e) suggest that an increase in Ib intensifies the generation and ionization of metal vapors. As the positions of the substrate and molten pool remain fixed, an increase in Ib inevitably increases the heat input and temperature of the molten pool. Hence, the intensified space-charge overcompensation is related to the evaporation of the molten pool. Therefore, an increase in Ib increases the recoil force Fv,m generated from the molten pool. According to Ref. [59], changes in the recoil force generated by the molten pool should affect the oscillation behavior, including the single droplet period, amplitude, and oscillation start time. However, we did not observe any significant influence on the droplet oscillation behavior during Ib variation, as shown in Fig. 2. Additionally, we demonstrated the droplet oscillation behaviors at different distances d (reflecting the distance between the droplet and molten pool) in Appendix A Fig. S3. The results showed that as d increases, the value of the ACS at the wire decreases, indicating that the cation density in the space around the droplet decreases. Thus, the influence of the recoil force generated from the molten pool on the droplet should decrease, but the behaviors of the droplet oscillation, such as its amplitude and duration, should be almost unaffected. Conversely, according to Ref. [59], when the droplet moves above the molten pool (within the EB region), it should tend to move in the direction opposite to gravity. However, we did not observe this phenomenon. Moreover, this force cannot explain the asymmetric oscillation shown in Fig. 1(c). In summary, based on our experimental results on the oscillation behaviors under different parameters, we believe that the recoil force generated by the molten pool is the main driving force of droplet oscillation proposed in Ref. [59] may not be accurate. Hence, we further explored the reasons and driving forces for the generation of droplet oscillations.
5. Generation of droplet oscillation
5.1. Oscillation mechanism
The droplet oscillation phenomenon is distinguished by escalating and asymmetric amplitudes and is markedly different from the natural vibration of a pendant liquid droplet that is controlled by surface tension and gravity [68]. This finding indicates that there is a continuous input of energy and momentum during oscillation, and the kinds of restoring forces applied during reciprocating motion vary rather than merely changing the force direction in a simple pendulum system. To gain additional intuitive insight into the generation of droplet oscillations, we conducted further exploration via simulation. We established a multiphysics thermal-fluid flow model to describe wire melting and droplet oscillation. The model and simulation settings are described in Description S1.1-S1.4 (Figs. S4-S6 in Appendix A). By comparing the experimental and simulated droplet behaviors under different parameters, we verified the suitability of our model for describing wire melting and droplet oscillation behavior, as shown in Description S1.5 (Fig. S7 in Appendix A).
Initially, we focused on the temperature field of the droplet during oscillation, as depicted in Fig. 3(a). When the droplet moves into the EB zone along the +Y direction, the temperature of the droplet surface area directly affected by EB increases rapidly (up to several hundred degrees Kelvin (K)) within 10-20 ms. Subsequently, as the droplet moves away from the EB zone in the −Y direction, the temperature in the area decreases within 10-20 ms, and the temperature of the entire droplet tends to be uniform. Fig. 3(b) provides a more intuitive demonstration of the periodic variation in the droplet temperature during oscillation, as evidenced by the curves of the average fluid temperature (including the wire that has not yet melted in the calculation domain), by the temperature of a point in the droplet, and by the abscissa of the droplet centroid over multiple oscillation cycles. The average fluid temperature shows an overall upward trend during oscillation.
From the liquid flow behavior in the longitudinal section of the droplet during the oscillation depicted in Fig. 3(c), we observed a counterclockwise vortex flow inside the droplet, which can accelerate heat transfer and homogenize the temperature, consistent with the rapid decrease in the temperature mentioned above. On the −Y side of the droplet, the Marangoni effect induced by the surface tension gradient (caused by the temperature gradient) in the area connected with the wire generates a thermocapillary force in the −Z direction, which, together with gravity, drives the liquid to flow in the −Z direction. On the +Y side of the droplet, the direction of the thermocapillary force changes to the +Z direction because of the EB. Therefore, the liquid flows in a counterclockwise pattern, and the flow velocity on the −Y side is greater.
We subsequently investigate the variation in the vapor recoil force Fv,d generated by evaporation at the droplet surface within one oscillation cycle, as depicted in Fig. 3(d). The results showed that the Fv,d also exhibits the same oscillation pattern as the temperature. To date, various models have been developed to describe the metal vapor recoil force, but they all involve the value of the force being positively correlated with the surface temperature [69], [70]. Therefore, the rapid change in temperature in the local area of the droplet surface leads to a rapid change in evaporation of the droplet surface, causing periodic variation in the recoil force from the droplet. Scholars have previously reported the spontaneous trampoline-like bouncing of droplets on superhydrophobic surfaces under low-pressure conditions [62] or on high-temperature surfaces under normal pressure conditions [71], also exhibiting an escalating and asymmetric amplitude. These studies suggest that the droplets are propelled off the surface because of vapor overpressure caused by low-pressure environments or the Leidenfrost phenomenon. In our study, droplets are formed under high-temperature and low-pressure conditions. Based on the simulation results in Figs. 3(a)-(d), we propose that the vapor recoil force Fv,d caused by intense droplet surface evaporation is the primary force driving droplet oscillation. Each time the droplet enters the EB zone, Fv,d provides momentum to the droplet in the −Y direction, decelerating its motion toward the EB zone (along the +Y direction) and pushing it back to the plasma zone (along the −Y direction). When the droplet leaves the EB zone, similar to droplet trampolining, Fv,d diminishes and the surface tension becomes the main restoring force. Like in the case of gravity in the pendulum and droplet trampolining, the surface tension presents throughout the oscillation and undergoes directional changes along the Y-axis. In contrast, Fv,d only exists when the droplet is in the EB zone and the force direction remains constant in the −Y direction. Therefore, the Fv,d, which serves as the driving force, can effectively account for the escalating and asymmetric amplitudes. The rapid increases in and uneven distributions of the local surface temperatures of the droplets are the fundamental characteristics that induce droplet oscillation.
To further substantiate this proposition, we deliberately omit the vapor recoil force Fv,d from our simulation model. As depicted in the left panel of Fig. 3(e), the droplet fails to exhibit the oscillation phenomenon observed in its natural state (with Fv,d present, as shown in Fig. 3(a)). Instead, the droplet descends slowly because of the accentuation of gravity. Once detached from the wire, the droplet follows a nonparabolic, free-fall trajectory along the −Z direction, as opposed to the parabolic path observed in the natural state (as presented in Appendix A Description S1.5). Moreover, the duration of a single droplet in the natural state is approximately 3000 ms, whereas it increases to approximately 5600 ms in the absence of Fv,d. As the droplet expands, the Bond number Bo assumes a time-dependent character, as shown in Eq. (4), in which the characteristic length of the droplet is defined as the equivalent diameter Deq(t) (as presented in Eq. (5) [72]). In the natural state, the Bo before detachment is approximately 0.65, while in the Fv,d absence state, it was approximately 1 (the values of σ and ρ are 1.68 N∙m−1 and 4000 kg∙m−3, respectively [73], [74]). Consequently, in the absence of Fv,d, the droplet detaches from the wire spontaneously because of the enhanced effect of gravity. The presence of Fv,d is tantamount to an amplification of the gravitational force, leading to a reduction in the duration of a single droplet.
$ \mathrm{Bo}(t)=\frac{\rho g D_{\mathrm{eq}}^{2}(t)}{\sigma}$
where, ρ, σ, and g are the density of the droplet, surface tension coefficient, and acceleration due to gravity, respectively, and t and rw are the duration and radius of the metal wire, respectively.
Furthermore, we conducted a comparison of the average fluid temperature and kinetic energy per unit mass between the two scenarios, as depicted in the right panel of Fig. 3(e). In the natural state, droplet oscillation impedes the heating rate because of the intermittent exposure of the droplet surface to EB, while the presence of Fv,d augments the kinetic energy. In the absence of Fv,d, the droplet remains stationary, and the EB acts on the droplet continuously, increasing the average temperature and heating rate. In practice, the temperature of a droplet cannot increase indefinitely owing to the liquid-vapor phase transition. We contend that the locally transient surplus heat input from the EB is spontaneously transformed into kinetic energy that propels droplet oscillation through the action of Fv,d, which is generated by intense evaporation, thereby minimizing the nonuniformity and maintaining the consistency of temperature within the droplet. However, the supply of kinetic energy elevates the dynamic instability of the droplet, resulting in its detachment from the wire at an earlier stage. Since the droplet is a fluid entity rather than a rigid object, there is inherent uncertainty in the interplay between Fv,d, gravity, and surface tension, leading to indeterminacy in droplet oscillation behavior and resulting in uncertainty in the droplet trajectory after detachment, as demonstrated in Fig. 1(e).
To further validate the rationality of Fv,d as the driving force for oscillation, simulations were conducted to investigate the differences in the impacts of Ib and vw on droplet oscillation, as depicted in Fig. 2. The simulated droplets and molten pool images when Ib is either 30 or 50 mA (with other parameters identical to those in Fig. 3(a)) are presented in the left panel of Fig. 3(f). With an increase in Ib, an increase in the molten pool size on the substrate can be observed, and the stable melting position of the droplet on the wire shifts toward the unmelted wire. According to the right panel of Fig. 3(f), the fluid temperature at a current of 50 mA increases faster than that at 30 mA, and the average temperature increases (approaching a 300 K difference) at the beginning of droplet formation. As the droplet grows, the temperature difference between the two conditions decreases, and at the droplet oscillation stage, the temperatures are nearly the same. Hence, changes in Ib can modify the thermal conduction of the droplet to the wire, leading to a spontaneous adjustment of the stable melting position. The droplet has a uniform temperature distribution and a similar average temperature under different Ib values, resulting in Fv,d having a comparable impact on droplet behavior.
The simulation results for vw values of 0.5 and 1.0 m∙min−1 (with other parameters identical to those in Fig. 3(a)) are depicted in Fig. 3(g). An increase in vw reduces the linear energy density acting on the wire, causing the stable melting position to shift along the wire-feeding direction. Although the droplet mass grows at twice the rate at 1.0 m∙min−1 compared to 0.5 m∙min−1, the single droplet duration decreases by more than 50%. Interestingly, the mass of the droplet before dropping at 1.0 m∙min−1 is approximately 15% lower than that at 0.5 m∙min−1, and the surface area differs by approximately 5%. The total thermal energy of the droplets at 1.0 m∙min−1 is greater than that at the other speeds, and the average temperature increases faster. We postulate that the elevated temperatures of the droplets reduce the surface tension, intensifying the impact of gravity, deforming the droplet, and increasing the droplet surface area. Increases in temperature and contact area with EBs can result in collective intensification of the effect of Fv,d. Therefore, the effect of vw on droplet behavior is more pronounced and nonlinear, which is consistent with the experimental findings depicted in Fig. 2. Hence, the utilization of Fv,d as the driving force for oscillation can clarify the effects of changes in Ib and vw on droplet behavior observed in the experiment.
5.2. Typical droplet formation process
Following an analysis of the mechanism of droplet oscillation, we examined the complete process of droplet formation in the DT4 mode. The typical procedure of droplet formation can be classified into three stages: the initial stage, the quasistatic stage, and the oscillation stage (depicted in Fig. 4 and Video S1).
In Fig. 4(a), the initial stage can be decomposed into three substages. The first substage is the droplet-forming stage, where the metal wire enters the EB zone before fully melting to form a droplet. A temperature gradient is established at the wire end as illustrated in Fig. 4(d). The Marangoni effect and surface tension mainly act on the front end of the partially melted wire, preventing the melted part from leaving the EB zone. Upon continuous accumulation of heat, the initially fed wire undergoes complete melting to form a droplet, transitioning into the droplet retracting stage. Due to the relatively large curvature and small gravity of the droplet, surface tension emerges as the dominant force, which is supported by the simulation and Bond number (Bo ≈ 0.171 < 1, at t = 400 ms) [75]. The droplet retracts in the opposite direction to the wire feeding. As the droplet grows, the influence of gravity increases, and the centroid of the droplet begins to deviate from the axis of the wire, ultimately attaining a natural drooping state (the droplet drooping stage).
The quasistatic stage of the formation process is characterized by minor horizontal oscillations of the droplet, with amplitudes that are considerably smaller than the droplet size (Fig. 4(b)). Consequently, the horizontal position of the droplet is deemed stable, while the centroid of the droplet gradually shifts downward in the vertical direction. Although some conditions necessary for droplet oscillation, such as gravity, surface tension, and vapor recoil force necessary for droplet oscillation are present during the quasistatic stage, oscillation does not occur. The droplet profile is almost spherical during the quasistatic stage and pyriform during the oscillation stage, as illustrated in Fig. 4(e). Hence, surface tension plays a dominant role during the quasistatic stage. The internal pressure of the droplet during the quasistatic stage is greater than that during the oscillation stage. This difference suggests that the resistance within the droplet due to surface tension and viscosity can counteract the influence of the vapor recoil force. Moreover, the temperature of the droplet during the quasistatic stage decreases, and the effective area of the EB decreases, as shown in Fig. 4(e). Hence, the impact of the vapor recoil force during the quasistatic stage is smaller than that during the oscillation stage. Therefore, the droplet formation process can undergo a quasistatic stage without droplet oscillation.
Finally, the droplet undergoes significant oscillations before ultimately detaching from the wire and depositing onto the substrate. This phenomenon can be attributed to several key factors, including the vacuum environment, which reduces the boiling point of the metal; the high power density of the EB, which facilitates rapid heating; and the nonuniform interaction between the EB and the droplet resulting from the bypass wire feeding mechanism. Because of the aforementioned conditions, the surfaces of the droplets experience nonuniform temperature distributions and vapor recoil forces, ultimately generating droplet oscillation. This phenomenon has yet to be reported in AM processes using other heat sources, as the aforementioned conditions are not simultaneously present in such methods.
6. Suppression of droplet oscillation
6.1. Oscillation-suppressing technique
Through a comprehensive analysis of the underlying mechanisms and influencing factors of droplet oscillation, we endeavor to effectively mitigate this phenomenon to ensure the stable transfer of droplets into the molten pool. We observe that the vapor recoil force can modulate the behavior of the droplet, as evidenced by the escalating and asymmetric amplitude. This finding suggests that improving the uniformity of the temperature distribution on the surface of the droplet is the key to suppressing droplet oscillation. We propose that an EB should be applied uniformly across all parts of the droplet, with the center of the droplet being positioned as close as possible to the axis of the EB.
To achieve this goal, the factors that affect the initial complete melting position of the wire during the initial stage are analyzed. The initial complete melting position is defined as the spatial position of the wire when heated from the ambient temperature (Ta) to the melting point (Tm). This position is also dictated by the time (tw) needed for the wire to heat to the melting point after entering the EB zone. Our objective is to extend tw so that the droplet can be completely within the EB zone in the quasistatic state. We adopt a wire element with a mass of Δm at the front end of the wire for analysis and assume that its feeding direction passed through the axis of the EB, as shown in Fig. 5(a). An energy conservation equation is employed to describe the process from the entry of the wire into the EB zone (upper figure of Fig. 5(a)) to its melting (lower figure of Fig. 5(a)), as shown in Eq. (6). This equation includes the energy input from the EB (Qeb), the energy gained/lost by heat conduction (Qcon), and the heat loss by thermal radiation (Qrad). Qcon and Qrad are passive regulation factors that become increasingly negative with increasing Qeb. Hence, adjusting Qeb is the most convenient approach for changing tw. We adopt a Gaussian distribution surface heat source model [76] and ignore the influence of the wire surface curvature on the energy absorptivity η. Qeb is described by Eq. (7) and the power density distribution W(t) on the element Δm is given by Eq. (8). Increasing tw requires reducing the power input to the wire while keeping vw constant. However, increasing the rb may lead to difficulties in melting the wire by reducing the power density applied directly to the wire surface. Hence, this method may not be an optimal solution.
where cp, Lm, and S are the specific heat, specific latent heat of melting, and direct interaction area of the EB, respectively; and N, rb, and θ are the concentration coefficient of the EB, radius of the EB, and wire-feeding angle, respectively.
In this study, we proposed the EB-dynamic surrounding melting (DSM) technique to suppress droplet oscillation. A notable difference between EBs and other high-energy beams is that EBs can be deflected simply and cost-effectively under the action of electric or magnetic fields [77]. In the EB-DSM technique, two sets of sinusoidal driving signals with the same amplitude and frequency and a phase difference of 90° are applied to two pairs of deflection coils, causing the EB to move along a circular trajectory, as depicted in Fig. 5(b). Figs. 5(c-i) and (c-ii) show the desired position relationship between the deflected EB and the droplet. The EB-DSM technique can be applied to adjust the centroid of the droplets to be close to the axis of the EB zone, as confirmed by Fig. 5(c-iii) and to obtain a larger molten pool size under the same EB power (the X-axis width of the molten pool in Fig. 1(d) is approximately 11.4 mm, while that in Fig. 5(c-iii) is approximately 15.3 mm). The results in Fig. 5(d) show that the EB-DSM technique can reduce the oscillation amplitude by one order of magnitude. Fig. 5(e) shows that the droplet can fall freely after detaching from the wire and accurately transfer into the molten pool. The whole droplet formation process under EB-DSM is shown in Appendix A Video S2. The EB-DSM technique makes it possible to use EB-DED to prepare lattice structures. By utilizing the EB-DSM technique and the process sequence shown in the left panel of Fig. 1(a), we successfully prepare a high-quality strut structure, as illustrated in Appendix A Fig. S8.
Subsequently, we further analyze the characteristics of the EB-DSM technique performed by the ACS. The frequency energy spectrum of the ACS at the substrate is shown in the upper part of Fig. 5(f), with a peak frequency of 200 Hz, which is the same as the setting deflection frequency. The time-frequency analysis energy spectrum in the lower part of Fig. 5(f) shows that a frequency component of 200 Hz is present throughout the droplet formation process. This frequency component is caused by the partial obstruction of the EB when it moves to the wire indicating that the EB passes through the wire only once per cycle, confirming the circular motion around the droplet of the EB desired in Fig. 5(c). Fig. 5(g) shows that neither ACSs display oscillation features similar to those in Fig. 1(c), confirming the oscillation suppression effect of the EB-DSM. After the introduction of the EB-DSM, the value of ACS at the substrate significantly increases, and the value of ACS at the wire changes from negative to positive. This change indicates a reduced degree of metal vapor generation and ionization and no occurrence of the overcompensation phenomenon. This finding suggests that the EB-DSM technique may reduce the temperature of the droplet and molten pool. Hence, the oscillation suppression of droplets by EB-DSM may be achieved by simultaneously reducing the droplet temperature and homogenizing the droplet temperature distribution.
The droplet formation process under the action of the EB-DSM technique can be categorized into the aforementioned three stages, as shown in Fig. 5(h). The initial stage (including its three substages) and quasistatic stage are both significantly longer than those in Fig. 1(c). During the quasistatic stage, the horizontal coordinate of the droplet centroid only moves to the left by approximately 1.75 mm, and the whole droplet remains within the EB area. However, during the oscillation stage, the uniformity of the EB action on the droplet slightly decreases. This leads to a small segment of droplet oscillation with an amplitude of approximately 0.25 mm. The droplet does not move outside the EB zone. Compared with the droplet oscillation amplitude shown in Fig. 1(c), the EB-DSM technique reduces the amplitude by approximately 94%. The leftward shift of the droplet and the increase in droplet volume both increase the obstruction degree of EB to the molten pool, resulting in larger amplitude fluctuations of ACS at the substrate. This phenomenon explains why the energy at a frequency of 200 Hz in Fig. 5(f) increases significantly during the oscillation stage. The single droplet duration significantly increases to approximately 6500 ms, and the Bo before dropping is approximately 1.1, indicating that the balance between surface tension and gravity contributes more to the critical conditions of droplet detachment. According to Fig. 5(g), the intensity of the metal vapor evaporation decreases. Based on Ref. [59], the role of the recoil pressure in resisting gravity on droplets should decrease, thereby shortening the duration of a single droplet. However, the prolonged duration shown in Fig. 5(h) shows that the vapor recoil force from the molten pool is not the driving force of droplet oscillation.
6.2. Oscillation suppression mechanism of EB-DSM
Based on the aforementioned results, we propose that the EB-DSM technique suppresses droplet oscillation through two mechanisms. First, the uniform action of the EB reduces the temperature difference throughout the droplet, allowing the vapor recoil force to uniformly act on all parts of the droplet. Second, the local energy input is reduced because of the deflection, reducing the droplet temperature and the vapor recoil force. To further confirm the underlying mechanism, we simulate the melting process using the EB-DSM technique. As shown in Fig. 6(a), the droplet temperature exhibits an upward trend during the formation process, but the input heat energy of the fluid is significantly reduced via the EB-DSM technique. Compared to the droplet surface temperature distributions near and far from the EB given in Fig. 3(a), Fig. 4(d), and Fig. 6(b), the EB-DSM process increases the uniformity of the temperature distribution of the droplet. The highest surface temperature of the droplet is lower than that without the EB-DSM. The temperature gradient shown in Fig. 6(c) further illustrates the uniform effect of the EB-DSM process on the temperature distribution. Fig. 6(d) shows that the flow velocity inside the droplet under the action of EB-DSM is significantly lower than that in Fig. 3(c). Moreover, the counterclockwise flow tendency inside the droplet also decreases as the droplet grows, indicating that EB-DSM can stabilize the flow inside the droplet. The simulation results confirm that the EB-DSM technique suppresses droplet oscillation by reducing the highest temperature and improving the uniformity of the temperature distribution.
The EB-DSM technique may not always achieve optimal suppression effects. We vary the parameters shown in Fig. 5, increasing Ib (from 30 to 50 mA), reducing the deflection range (from a deflection radius of 3.5 to 2.5 mm), decreasing the deflection frequency (from 200 to 100 Hz), and changing the deflection pattern (from a circular pattern to a lemniscate pattern). Fig. 6(e) shows that the horizontal distance between the droplet centroid and the EB deflection axis (molten pool centroid) increases in all four cases. Correspondingly, the amplitude of the droplet oscillation also increases, with each maximum amplitude being different but less than the maximum amplitude without the application of the EB-DSM technique, as shown in Fig. 1(c). In Figs. 6(f) and (g), we simulate the temperature field with increasing Ib and decreasing deflection range conditions, respectively. The side of the droplet near the EB zone exhibits a significantly increased temperature, thereby decreasing the temperature field uniformity and increasing the recoil pressure of the metal vapor acting on that side of the droplet. In other words, the above four changes in parameters all increase the temperature of the droplet side near the EB and reduce the uniformity of the temperature distribution. Therefore, the most critical aspect of achieving stable suppression of droplet oscillation is to control the value and distribution of the heat input (by adjusting the beam current, deflection pattern, deflection area size, deflection frequency, etc.) to ensure that the droplet center is close to the axis of the EB region. This finding provides criteria that can guide and increase the effectiveness of developing other types of oscillation suppression methods. Based on our experimental results, for a 2.0-mm-long Ti6Al4V wire at an approximately 45° wire-feeding angle, the parameter combination of a Ub of 60 kV, an Ib of 30 mA, a circular deflection frequency of 200 Hz, and a deflection radius of 3.5 mm can enhance the droplet oscillation suppression effect. The strut structure illustrated in Fig. S8 is prepared by applying these parameters.
The focus of this study is on the mechanism and suppression methods of the droplet oscillation phenomenon. Our results can be considered to provide a physical basis for interpreting the mechanism of the EB acting on the droplet and a technical basis for applying EB-DED to prepare complex lattice structure parts. We demonstrate the preparation of only the basic strut components of the lattice structure, intending to preliminarily verify the effectiveness of EB-DSM. However, we must note that there is still a significant gap between strut components and complex lattice structure parts, and additional research is still needed. Based on this work, we will further explore the use of EB-DED to prepare large and complex lattice structure parts in the future.
7. Conclusions
In this study, we investigated the droplet oscillation phenomenon that significantly impacts the feasibility of preparing lattice structures by EB-DED. We used optical and absorbed current information to conduct fusion monitoring to thoroughly uncover the characteristics of and factors influencing droplet oscillation. In addition, we adopted a multiphysics thermal-fluid flow model to simulate the droplet formation process. By using the findings of the simulation and monitoring, we explained the mechanism of droplet oscillation. We also proposed the EB-DSM technique to suppress droplet oscillation, and we clarified its suppression mechanism. By using this technique, we could accurately transfer the droplet into the molten pool, which allowed us to construct strut structures using a specially designed process sequence. Our research shed important light on droplet oscillation and offered a practical method for its suppression, increasing the viability of preparing lattice structures by EB-DED. Our main findings were as follows:
(1) The droplet formation process is typically characterized by an initial stage, quasistatic stage, and oscillation stage. During the oscillation stage, the droplet oscillates between the inside and outside of the EB zone, exhibiting escalating and asymmetric amplitudes. Changes in mass input have a more significant impact on droplet oscillation than changes in heat input. Once the droplet detaches from the wire, it undergoes parabolic motion and cannot transfer to the molten pool.
(2) The direct driving force of droplet oscillation is the metal vapor recoil force generated by the direct action of the EB on the local surface of the droplet. The physical principle of this force is the rapid increase in and uneven distribution of the local surface temperature of the droplet, which is a result of the vacuum environment, high power density, and bypass wire feeding characteristics. The interaction between the EB and droplet inputs both thermal and kinetic energy, increasing the instability of the droplet.
(3) Achieving uniformity of the temperature distribution and reducing the temperature of the droplet are critical to suppressing droplet oscillation. The proposed EB-DSM technique effectively reduces the droplet temperature and temperature gradient by symmetrically deflecting the EB around the droplet. The EB-DSM can position the droplet close to the axis of deflection of the EB, resulting in a reduction in the droplet oscillation amplitude by one order of magnitude and the droplet can be accurately transferred to the molten pool in a free-fall manner.
In the future, we plan to further optimize the EB-DSM technique, deepen the design of the process sequence for lattice structures, and conduct path planning research to achieve the production of large and complex lattice structure parts by EB-DED.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (52375349) and the Beijing Municipal Natural Science Foundation (3222008).
Compliance with ethical guidelines
Zhiyue Liang, Zhenyu Liao, Haoyu Zhang, Zixiang Li, Li Wang, Baohua Chang, and Dong Du declare that they have no conflict of interest or financial conflicts to disclose.
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