Vibratory Powder Feeding for Powder Bed Additive Manufacturing Using Water and Gas Atomized Metal Powders

Commercial powder bed fusion additive manufacturing systems use re-coaters for the layer-by-layer distribution of powder. Despite the known limitations of re-coaters, there has been relatively little work presented on the possible benefits of alternative powder delivery systems. Here, we reveal a feeding technology that uses vibration to control flow for powder bed additive manufacturing. The capabilities of this approach are illustrated experimentally using two very different powders; a ‘conventional’ gas atomized Ti-6Al-4V powder designed for electron beam additive manufacturing and a water atomized Fe-4 wt.% Ni alloy used in powder metallurgy. Single layer melt trials are shown for the water atomized powder to illustrate the fidelity of the melt tracks in this material. Discrete element modelling is next used to reveal the mechanisms that underpin the observed dependence of feed rate on feeder process parameters and to investigate the potential strengths and limitations of this feeding methodology.

that vibration assisted powder feeding has been widely used in the powder metallurgy industry, for laser sintering and for laser cladding applications [22] where irregularly shaped powders are common.
In this work, we have explored the use of a vibratory powder feeder to distribute powder over the build plate with a specific eye towards application to non-conventional powder for additive manufacturing. We start by describing the powder feeding technology used followed by the materials tested in this preliminary study. We characterize the feeder behaviour experimentally using two very different powders; the first a gas atomized Ti-6Al-4V powder conventionally used in electron beam additive manufacturing (see e.g. [23]) and the second a commercial water atomized Fe-4wt%Ni powder conventionally used in powder metallurgy. While the former exhibits a highly spherical powder shape and narrow particle size, the latter exhibits a highly irregular powder shape and very wide size distribution. Experiments combining feeding and electron beam based melting are also described and illustrative single layer squares are produced to illustrate the ability to feed and melt with the Fe-4wt%Ni powder.
To better understand the relationship between feed rate and process parameters for this vibratory feeding approach, discrete element modelling (DEM) is performed. The results of these simulations highlight the potential strengths and limitations.

Experimental Methodology:
In this study, we have used of a recently developed technology (patent pending, Canmora TECH Inc.) for powder delivery in powder bed based additive manufacturing. This technology uses vibration as the means of the controlled metering of metal powder onto a powder bed. Figure 1 illustrates the relatively simple setup of the feeder.
The key part of the feeder is highlighted in blue in figure 1. This inner portion of the feeder can be separated into three parts, a hopper that contains the powder to be fed, a feed channel that ensures powder does not feed when the feeder is off and an exit chute through which the powder is dispersed onto the powder bed. Two voice coils, electromagnetically shielded from the contents of the feeder, are attached as shown. The voice coils are actuated by means of a computer controller and amplifier so as to generate a sinusoidal displacement of specified amplitude (specified as a voltage) and frequency. The displacement of the feeder is monitored independently by a separate displacement sensor mounted between the voice coils. The inner portion of the feeder (blue) rotates on a bearing located close to the bottom exit chute of the feeder. The feeder was used in two separate setups. Feeding was performed both in air as well as within the high vacuum ( < 5 × 10 −5 mbar) LEAM electron beam additive manufacturing facility at the University of British Columbia.
In both cases, the feed rate was calculated by placing a digital scale beneath the feeder and feeding for 10 s. The mass flow rate was then estimated based on the measured mass fed in that time. In all cases feeding was performed starting from the feeder containing the same mass of powder so as to eliminate any variations induced by differences in feeder mass. It was noticed, however, that the feed rate did not significantly change with feeding as long as sufficient powder remained within the feeder so as to allow for continuous feeding. In the case of the single layer melt experiments described below, a single powder layer of controlled thickness was deposited onto the build table by holding the feeder in a fixed position, controlling the feed rate of powder, and moving the build table under the feeder using a computer controlled x-y table.
As mentioned above, two powders were used in this study. The first was an AP&C Ti-6Al-4V grade 23 with a size range of 45 -106 µm and a D50 of 71 µm. The characteristics of this powder have been discussed in previous publications (see e.g. [23]). The powder used had been recycled several times, the exact number not having been reported. However, as can be seen in figure   2 the morphology and size of the powder particles remains very regular and spherical with a relatively small proportion of satelite particles. The second powder, ATOMET 4801, was provided by Rio Tinto Metal Powders. This water atomized Fe-4wt%Ni alloy is conventionally used in powder metallurgy applications. This powder, illustrated in figure 2b, is very irregular in shape with a with a wide size distribution. Sieving produces results showing that 10wt% of particles are larger than 150 µm in size (U.S. mesh +100), 62wt% are larger than 45 µm in size (U.S. mesh +325) and 28wt% are less than 45 µm in size (U.S. mesh -325). The ATOMET powder was used in an un-recycled state.
Finally, the feeder has been used to perform simple single layer melt trials with the two powders. Here we focus only on the results for the Fe-4wt%Ni powder with the aim of illustrating the potential for feeding and melting of this less conventional (for additive manufacturing) powder within electron beam additive manufacturing. An AISI4340 steel build plate was used and a single layer of powder was delivered to the build plate by controlling the feed rate from the feeder and the translation of the build plate (on its x-y translation stage) beneath it. This was done to achieve an approximate layer thickness of 0.2 mm. Seven independent 15 × 15 mm squares were melted using a simple outer contour followed by infill by hatching. Prior to depositing the powder layer, the build plate was heated to 940 • C to eliminate smoking.

Frequency Controlled Feeding of Powders:
The construction of the feeder is such that powder only flows when the voice coil is activated, and even then only when the correct conditions are imposed.
We have evaluated this under two sets of conditions. First, Figure 3 shows the resulting feed rate for the two powders, fed in air, for different imposed frequencies of the voice coil at fixed driving amplitude (fixed imposed voltage maximum to voice coil). While the results in figure 3 show a general trend of increasing feed rate with reduced frequency, significant scatter exists within the data. As the voice coil induced oscillations are imposed via its coupling to the feeder, control of the feed rate by varying voice coil frequency at fixed amplitude was found to be challenging. In the setup used here it was found that it was not possible to independently control the feeder's vibration frequency and displacement as the system behaves as a driven, damped harmonic oscillator. This can be shown by means of figure 4. Here, the measured feeder displacement is shown as a function of frequency for the same conditions as in figure   3, the same color scheme being used to indicate the results from the two different powders. Here, although the amplitude (voltage) imposed on the voice coil was fixed to be constant, the measured feeder displacement was found to increase strongly with decreasing frequency, independent of the type of powder used. This dependence is exactly the one that would be expected for a driven, overdamped harmonic oscillator. A system of mass m driven through a spring (constant k) and dashpot (damping coefficient ν) by a source with amplitude X 0 and frequency ω will respond with an amplitude x 0 such that, where ω 0 = k/m is the natural frequency of the system. This relationship is plotted as a line on figure 4 with assumed values for X 0 and ω 0 . As can be seen this explains this data well under the condition that the feeder contains the same mass (m) of the two powders as noted above. This result also implies that when ω = ω 0 resonance will occur. Evidence of this was observed experimentally as, at certain combinations of imposed voice coil frequence/amplitude, the measured displacement signal was found to change from a well controlled, regular sinusoidal variation, to a more chaotic pattern indicative of ω → ω 0 . Also plotted as a solid line is the predicted behaviour assuming the feeder/voice coil system as a driven, damped harmonic oscillator.

Displacement Controlled Feeding:
The results in figure 4 show only a small dependence of feeder displacement on imposed frequencies for frequencies greater than ∼40 Hz. Thus, further experiments and development were focused onto controlling feed rate by fixing imposed frequency, at ω > 40 Hz and varying the displacement of the feeder using the measured displacement from the displacement sensor. Figure 5 shows the resulting feed rates measured in air for the two powders when the voice coil frequency was fixed to 57 Hz and the imposed amplitude varied to give the (fixed) feeder displacements shown. Under these conditions, one can see that the mass flow rate varies nearly linearly with the feeder displacement above a lower threshold displacement for both powders. The mass flow rate for the Ti-6Al-4V powder is higher for all tested displacements, but it is possible to obtain the same stable flow rate for both the highly spherical Ti-6Al-4V and highly irregular ATOMET 4801 powder by the judicious selection of the feeder displacement. While figure 5 was generated from experiments performed in air, the same experiments were repeated for feeding within the vacuum of the LEAM chamber. No significant differences from the feeding in air and vacuum were observed. Figure 5 shows that the feeder operated under displacement control at fixed frequency is not only able to feed conventional gas atomized powder but also the highly irregular Fe-Ni alloy powder with no further modifications. While the flow rate is significantly lower than that of the Ti-6Al-4V powder for a given feeder amplitude, it is still possible to achieve the same flow rate for the two powders by adjusting the feeder's displacement amplitude.

Single Layer Melt Trials on ATOMET 4801 Water Atomized Powder
With this result in mind, single layer melt trials were conducted to illustrate the potential for feeding of the Fe-4wt%Ni powder. Figure 6a shows  tracks observed for all other squares, save square 7. Square 7 (6c), on the other hand showed clear evidence of balling due to insufficient input power for consistent melting. Figure 7 shows a cross-section through square 3 showing the uniformity of the melt depth and the lack of evidence for large scale defects (e.g. lack of fusion or 'key hole' formation). This was consistent for all squares, save square 7.

Interpreting Feeder Behaviour using DEM simulations
In order to understand the behaviour exhibited by the feeder described above, particularly the response exhibited in figure 5, we have used discrete element (DEM) simulations. This follows on a large body of work using DEM simulations to understand powder flow in additive manufacturing (see e.g. [9,13,8,26,27,11] Rather than attempt to quantitatively predict the experimental results, the aim of the simulations performed here was to reveal the Simulations were performed using the LIGGGHTs DEM package [28] built on of the LAMMPS simulation platform [29]. Simulations used a Hertz-Mindlin noslip contact model with a simplified JKR cohesion model to simulate particleparticle adhesion. Briefly, the equations of motion for each particle i of mass m i are solved according to, where g is acceleration to due gravity and the normal force is calculated for particles of a single type and size (radius, R) as, and the tangential force is, The parameters δ n and δ t correspond to the normal and tangential overlap of contacting surfaces. The damping coefficients η n and η t used above follow the dependence on the coefficient of restitution as described in [30].
Rather than use the simplified JKR model implemented in LIGGGHTS, we modified this model to use it in its conventional form, where γ coh here is a material parameter that measures the cohesive strength of the interaction (see e.g. [13]).
The material parameters used here are defined in Table 1, these having been strongly inspired by the experimental and simulation work on Ti-6Al-4V powders as reported in the work of Meier et al. [13]. An inherent limitation of DEM simulations applied to 'stiff' materials, is the short time scale required to resolve particle-particle interactions [31,32]. Taking properties consistent with titanium would require one to use a time step of <10 ns, this requiring 100 million time-steps to simulate 1 second of feeder operation. To overcome this timescale limitation, we follow the convention in the field using a 'soft particle' approximation. Rather than using the actual modulus for Ti, the particles are assumed to have a much reduced elastic modulus, this leading to a much longer interaction time during particle contact. It has been shown that for conditions similar to those used here the effect on predictions is small (see e.g. [31,13]).
Time-steps were selected to be sufficiently small so as to satisfy the Rayleigh criterion [32]. Most simulations shown here were performed with mono-sized, spherical particles. A relatively large particle radius of 120 µm was used to again reduce the total number of particles simulated and thus the total required simulation time. Tests performed for particle radii down to 50 µm showed no appreciable difference in the qualitative trends illustrated below.

Property Value
Density, ρ 4.5 g/cm 3   Simulations involved two steps. First, particles were inserted into a region at the top of the feeder via a rain model [33] and allowed fall into the hopper until the hopper was nearly filled. The powder naturally flowed into the feed channel establishing a stable distribution within it. This is illustrated in figure  9a which shows the simulation setup at the end of the feeding step where the characteristic angle adopted by the powder within the feed channel, related via the assumed contact mechanics and cohesion model to the angle of repose for the powder, can be seen. This observation immediately explains why powder does not continuously feed through the feeder without vibration; so long as the feed channel is long enough to contain this characteristic powder angle then the powder will not flow so long as the feeder is not vibrating. Simulation results for particle radius of 50µm, vibration frequency and amplitude of 40 Hz and 0.25 mm. a) represents the initial configuration prior to feeding. e) The number of particles fed as a function of time for different displacement amplitudes of the feeder. In this case the particle size was 120 µm and the vibration frequency was 100 Hz. As one can see, the feed rate remains constant, for a given displacement amplitude and frequency, over the entire range of feeding.
Each simulation of feeding started from the same initial equilibrium distribution of powder within the feeder (figure 9a). To simulate vibration in this case, the entire feeder was subjected to a sinusoidal horizontal displacement in the x-direction, ∆x = A sin (ωt), with amplitude A and frequency ω.  At amplitudes A 0.4 mm one sees that the feed rate deviates away from linear, and for amplitudes above A 0.6 the feed rate is seen to decrease.
We can understand the behaviour in figure   While the experiments presented above were limited to displacement controlled conditions, one may wonder whether frequency control (at fixed displacement) is a viable option for controlling flow. Figure 13 shows that the  A final comment on the potential impact of actual powders that are not monosized spheres but which, as discussed in reference to the two powders studied experimentally here, have size distributions, irregular shapes and/or a range of densities (e.g. if powder mixtures are used). While the effect of particle shape has not been studied within the context of the DEM simulations presented here, the impact of a bi-modal distribution of particle sizes (at constant density) and particle density (at fixed size) has. Vibration induced segregation, often referred to as the 'brazil nut effect', is known to lead to large particles being segregated to the top of a vertically vibrating granular bed [34]. A variety of views exist to explain this effect, but the controlling mechanisms remain a topic of active consideration [34,35]. Two additional sets of simulations were performed, following the same approach as described above, but with two significant differences. In the first set of simulations, during feeding, particles with two distinct sizes (radii of 120 µm and 60 µm) were deposited into the feeder, all other particle properties being held constant. In a second set of simulations, particles with two distinct densities (2.5 g/cm 3 or 9.0 g/cm 3 (two times smaller and larger than the densities of the particles used in the above simulations) were deposited all other particle properties, including particle size, being held the same as those used in previous simulations. Also different from the above simulations was the fact that the powder was deposited onto a moving horizontal surface (properties the same as those used above) to simulate the deposition of a powder layer on a build table.
No evidence of density or size induced segregation was observed within the feeder for either of these simulations. This can be illustrated by measuring the time evolution of the fraction of the particle types within the vertical channel separating the feed channel from the hopper as a function of time, using this as a measure of the 'composition' of the powder being fed from the hopper. This is illustrated for the case where two particle densities were used in figure   14d. Note, the elevated fraction at t ≈ 0.4 − 0.5 corresponds to the layer of higher density particles located at the top of the feeder (see e.g. figure 14a), this being an artifact arising from the 'rain model' method used to fill the feeder.
The lack of discernible segregation based on size or density due to vibration is a consequence of the fact that any vibration induced convection within the hopper is overwhelmed by the downward flow of powder from the hopper into the feed channel. Powder is drawn from across the entire width of the hopper into the feed channel with no evidence of preferential flow of one type of particle.
In the case of the powder bed itself, no evidence of segregation was observed for the case of the powder containing a bi-modal distribution of particle sizes.
It was confirmed that the initial hopper composition and the composition of the powder bed (at all times) remained the same. In the case of the powder with two particle densities, however, a small difference between the powder bed 'composition' and bulk initial 'composition' were observed, this being illustrated in figure 14e. Careful inspection of figures 14e, f and g show that a preferential accumulation of lower density powder occurs to the left of the developing powder bed. Due to the lower mass of these smaller particles, they tend to be ejected to a larger distance upon impact with the build 2% more of the particles with ρ =9.0 g/cm 3 in the powder bed compared to than in the bulk. The same 2% enrichment of the powder bed was observed in a simulation where powder densities of ρ =2.25 and 4.5 g/cm 3 were used.
One way to further improve powder feeding, and to help further mix the powder as it enters the powder bed is to use the bottom surface of the feeder to 'level' the powder bed. In this mode the feeder is much closer to the build table to indicate the position of the feeder's exit chute. g) Shows a higher magnification of (f) illustrating the tendency for lower density particles to segregate to the right of the powder bed. and the powder 'injected' into the powder bed, this leading to both a flatter surface and an additional opportunity for mixing of powders of different densities/sizes within the powder bed. This opens up many further opportunities to think about alternative ways of delivering powder (or powders) during PBF-AM processing, with the potential to overcome many of the limitations discussed in the opening for conventional re-coating technologies.

Conclusions
In this work we have illustrated the use of a vibratory powder feeding system in conjunction with electron beam additive manufacturing. It has been shown to be possible to feed not only 'conventional' gas atomized powders used extensively in additive manufacturing but also a highly irregularly shaped and broadly sized water atomized Fe-Ni powder conventionally used in the powder metallurgy industry. It has been shown that the feed rate, and thus the powder layer height can be accurately controlled thanks to a linear relationship between feed rate and vibration amplitude at fixed frequency. Simulations have revealed the underlying mechanism controlling the feeding behaviour under these conditions including the threshold vibration amplitude below which no feeding occurs. Simulations suggest that size based segregation is not expected but that a small amount of powder based segregation may occur during feeding of particles with very different densities. Careful monitoring would be required in this case to ensure the desired bulk chemistry is obtained. Opportunities to introduce additional powder mixing in the powder bed itself have also been suggested.
The use of a vibratory powder feeder, as introduced here, can overcome some of the limitations inherent in re-coaters, one significant one shown here being the ease with which it can distribute powder that would be considered to difficult to flow (without sizing or mixing with other powders) in conventional electron beam or laser based additive manufacturing. This opens the opportunity for new strategies in powder delivery for additive manufacturing that are not conventionally considered in existing commercial systems.