Experimental Characterization and Computational Simulation of Powder Bed for Powder Bed Fusion Additive Manufacturing

Abstract

The packing density of powder bed is one of the critical parameters affecting the quality of the final parts fabricated via powder bed fusion additive manufacturing. In this study the packing density of the first layer of the powder bed was experimentally estimated from the packing densities of recoated powder with different number of layers. It is found that the packing density of the first layer is much lower than the apparent density of powder and the macro-scale packing density increases as the number of recoated layer increases. Furthermore, recoating simulation using discrete element method (DEM) was conducted to investigate the deposition mechanism of the powder at the particulate-scale. The simulation results showed the packing density of powder bed increases as the number of recoated layer increases, similar to the experimental results. This is caused by the rearrangement of the powder in the powder bed stimulated by the supplied powder. Also, the packing density of the powder bed was not uniform in the thickness direction, and the top surface layer which affects the quality of manufactured parts had almost the same packing density as that of the first recoated layer independently of the number of recoated layers.

 

This Paper was Originally Published in Japanese in J. Jpn. Soc. Powder Powder Metallurgy 68 (2021) 457–463.

1. Introduction

The powder bed fusion (PBF) technique, which is an additive manufacturing (AM) process, is expected to be utilized in various fields such as the aerospace, automobile, and medical fields.¹⁾ Generally, PBF consists of repetitions of two processes. One of them is recoating, which is a process of spreading a thin layer of powder referred to as powder bed, while the other is building, which is a process of melting of a powder into the desired pattern by irradiation with a laser or electron beam. Thus, to obtain high-quality final products manufactured using PBF, the control of various process parameters in both recoating and building processes is required. Numerous studies have been carried out on the optimization of building process parameters such as beam power and scanning speed.²⁾ Moreover, crystal textures peculiar to metal products manufactured by PBF have been actively studied.^3,4) However, there have been few reports on the factors related to the recoating process. Although it is generally accepted that denser powder layers lead to higher final part qualities,^5,6) an optimization technique to obtain a higher packing density of the powder bed, referred to as powder bed density, has not been established. This can be attributed to the difficulty in controlling the powder bed density by optimizing only the recoating process parameters. The powder bed density depends on not only the recoating process but also the powder characteristics, such as the powder size distribution. Furthermore, one of the obstacles preventing the studies on the recoating process is the difficulty in directly measuring the packing density of one layer of powder bed, which is a very thin powder layer.

Recently, numerical simulations attracted considerable attention to evaluate the powder movement behavior during the recoating process using the discrete element method (DEM). The effects of the recoating speed, thickness of the powder bed, and powder characteristics, such as particle size distribution and cohesion force between particles, on the conditions of the powder bed have been evaluated.^5,7–12) One of the common results of these simulations is that the powder bed density is considerably lower than the packing density of the powder, which is defined as one of the powder characteristics. Moreover, the powder bed density depends on the thickness of the powder bed and increases and converges to a fixed value as the thickness of the powder bed increases.⁷⁾ However, further studies are needed to confirm whether the simulation results and experimental data exhibit similar behaviors.

The objective of this study is to experimentally obtain the packing density of one layer of powder bed, which is necessary for the optimization of the recoating process. For this purpose, the packing density of the first layer of the powder bed was experimentally estimated from the powder bed densities with different numbers of layers based on the simulation results, which show that the packing density of the powder bed depends on its thickness. Furthermore, a recoating simulation was carried out using DEM to investigate the deposition mechanism of the powder at the particulate scale. The experimental data and simulation results were compared for the changes in packing density as the number of powder bed layers increased. The packing density distribution in the powder bed and powder movement behavior during the recoating process were analyzed.

2. Experimental Section

2.1 Powder

A gas-atomized Ti–6Al–4V powder (CL41: Concept Laser) was used for the experiments. Figure 1 shows a scanning electron microscopy (SEM) image and size distribution measured by a laser diffraction particle size analyzer, where Q3 and q3 represent the cumulative distribution and density distribution, respectively.¹³⁾ The Ti–6Al–4V powder apparent density and tapping density measured after 1250 times of tapping were 2.56 g·cm⁻³ and 2.72 g·cm⁻³, respectively. Thus, the relative apparent density and relative tapping density were calculated to be 57.8 vol% and 61.4 vol%, respectively, considering that the true density of Ti–6Al–4V is 4.43 g·cm⁻³.¹⁴⁾

Fig. 1

A SEM image and particle size distribution of Ti–6Al–4V powder.

2.2 Experimental procedure

The packing density of the powder bed was measured using a selective laser melting apparatus (Mlab cusing R: Concept Laser). Figure 2 shows a schematic of the experimental procedure, while Table 1 lists the recoating conditions. The Ti–6Al–4V powder was recoated on a sand-blasted Ti substrate for a predetermined number of layers. The recoated powder was then collected in a bottle and weighed (M_powderbed). The volume of the powder bed V_powderbed was calculated from the area of the substrate and height of the powder. Finally, the packing density of the powder bed ρ_powderbed was calculated using eq. (1). These recoating experiments were carried out three times under the same conditions. The average value for each condition was employed.   

\begin{equation} \rho_{\textit{powderbed}} = M_{\textit{powderbed}}/V_{\textit{powderbed}} \times 100\%. \end{equation} (1)

Fig. 2

Schematic illustration of experimental procedure.

Table 1 Conditions for recoating process.

2.3 Simulation method

2.3.1 DEM

DEM^15,16) is a technique that sequentially tracks the motion of each particle based on the solution of equations of motion considering the mechanical contact, slip, cohesion, and gravity of individual particles. In this study, spherical powder particles were used, where m_i, R_i, I_i, r_i, and $\boldsymbol{\omega}_{i}$ are the mass, radius, moment of inertia, position vector, and angular velocity of the i^th particle, respectively. The size of each particle followed the measured particle size distribution. The force F_i and torque T_i acting on the i^th particle are expressed by   

\begin{align} \boldsymbol{F}_{i} &= m_{i}\frac{d^{2}\boldsymbol{r}_{i}}{dt^{2}} = m_{i}\boldsymbol{g} + \sum\nolimits_{j}(\boldsymbol{F}_{n,ij} + \boldsymbol{F}_{t,ij} + \boldsymbol{F}_{c,ij})\\ &\quad - 6\pi \mu R_{i}\frac{d\boldsymbol{r}_{i}}{dt}, \end{align} (2)

  

\begin{equation} \boldsymbol{T}_{i} = I_{i}\frac{d\boldsymbol{\omega}_{i}}{dt} = \sum\nolimits_{j}(\boldsymbol{R}_{ij} \times \boldsymbol{F}_{t,ij}), \end{equation} (3)

where g is the gravity vector, μ is the coefficient of viscosity of air, and R_ij is the vector from the center of the i^th particle to the contact point between the i^th particle and j^th particle. The normal and tangential contact forces between the i^th particle and j^th particle, F_n,ij and F_t,ij, are   

\begin{equation} \boldsymbol{F}_{n,ij} = -\frac{4}{3}E^{*}\sqrt{R^{*}|\boldsymbol{\delta}_{n,ij}|} \boldsymbol{\delta}_{n,ij} - 2\frac{\ln (\varepsilon)}{\sqrt{\ln^{2}(\varepsilon) + \pi^{2}}}\sqrt{\frac{5}{3}E^{*}\sqrt{R^{*}|\boldsymbol{\delta}_{n,ij}|}}\boldsymbol{v}_{n,ij}, \end{equation} (4)

  

\begin{equation} \boldsymbol{F}_{t,ij} = \begin{Bmatrix} - 8G^{*}\sqrt{R^{*}|\boldsymbol{\delta}_{n,ij}|} \boldsymbol{\delta}_{t,ij} - 4\dfrac{\ln(\varepsilon)}{\sqrt{\ln^{2}(\varepsilon) + \pi^{2}}}\sqrt{\dfrac{5}{3}G^{*}\sqrt{R^{*}|\boldsymbol{\delta}_{n,ij}|}} \boldsymbol{v}_{t} & \text{when $|\boldsymbol{F}_{t,ij}| < \mu_{s}|\boldsymbol{F}_{n,ij}|$}\\ - \mu_{s}|\boldsymbol{F}_{n,ij}|\boldsymbol{t}_{ij} & \text{when $|\boldsymbol{F}_{t,ij}| \geq \mu_{s}|\boldsymbol{F}_{n,ij}|$} \end{Bmatrix} , \end{equation} (5)

where E^*, G^*, R^*, and m^* are the equivalent Young’s modulus, equivalent shear modulus, equivalent radius, and equivalent mass for the i^th and j^th particles, respectively.¹⁷⁾ $\boldsymbol{\delta}_{n,ij}$ and $\boldsymbol{\delta}_{t,ij}$ are the normal and tangential displacements, respectively, v_n,ij and v_t,ij are the normal and tangential relative velocities, respectively, and t_ij is the tangential unit vector between the i^th and j^th particles. μ_s is the friction coefficient, while ε is the coefficient of restitution. The cohesion force F_c,ij between the i^th and j^th particles is expressed using the Johnson–Kendall–Roberts (JKR) cohesion model:¹⁸⁾   

\begin{equation} \boldsymbol{F}_{c,ij} = 4\sqrt{\pi\gamma E^{*}a^{3}} \frac{\boldsymbol{\delta}_{n,ij}}{|\boldsymbol{\delta}_{n,ij}|}, \end{equation} (6)

where γ is the surface energy density and a is the radius of the contact surface between the i^th and j^th particles. The air resistance is expressed as Stokes’ drag force, assuming that the air around the particle exhibits laminar flow.

The simulation was performed using the open-source software LIGGGHTS-PUBLIC3.6.0, as it can introduce any physical laws due to its open source code that anyone can modify.

2.3.2 Models and simulation conditions

Figure 3 shows the simulation model for powder recoating. The width of the model W, length of the dose chamber L_D, and length of the build chamber L_B are 600 µm, 7200 µm, and 3600 µm, respectively. A periodic boundary condition was applied in the x direction to approximate the actual experimental equipment. In the simulation, the recoating blade was rigid and moved in the y direction from the end of the model at a velocity of 75 mm·s⁻¹ or 150 mm·s⁻¹. The dose chamber is filled with particles prepared for the recoating (Fig. 3) by the following procedure. Particles are randomly generated above the dose chamber with a depth H_D of 200 µm and deposited in the chamber by free fall under the gravity. The recoating blade then moves at a height H′_D of 50 µm, 250 µm away from the bottom of the dose chamber. Excess particles were removed. The initial particle layers were prepared in the chamber. The initial particle layer was restored after each layer recoating process. The depth of the build chamber H_B was 100 µm for the first layer and increased by 25 µm from the second layer. With the increase in the depth of the build chamber, both recoated particles and bottom of the build chamber moved downward simultaneously. The depth of the build chamber for the first layer of 100 µm was selected according to the recoating experiment, where the position of the substrate for the first layer was set so that the thinnest powder layer could be recoated. The relative powder bed density was calculated using the total volume of recoated particles in the build chamber after each layer recoating process,   

\begin{equation} \rho_{\textit{powderbed}} = \frac{\displaystyle\sum\nolimits_{i}(4\pi R_{i}^{3}/3)}{WL_{B}H_{B}} \times 100\%. \end{equation} (7)

Fig. 3

Simulation model for powder recoating.

Table 2 lists the parameters used for the recoating simulation. The material properties of bulk Ti–6Al–4V^9,14) are employed for each particle, except the Young’s modulus, which is set as 10⁶ times smaller than that of bulk Ti–6Al–4V to reduce the simulation cost. The friction coefficient and surface energy density, which are affected by the surface conditions of the powder, were determined from the results of the powder packing simulation and powder tapping simulation shown in Fig. 4. Regarding the powder packing simulation, approximately 4000 particles were randomly generated at the top of the analysis region of 400 µm × 400 µm × 5000 µm and fell freely. After all particles were deposited, the relative density of the packed region was calculated from the volume of packed particles as the packing density. Regarding the powder tapping simulation, particles after the packing simulation were tapped 20 times. The density after 1000 times of tapping was estimated from these results using the Kawakita equation¹⁹⁾ as the tapping density. In calculating the packing density and tapping density, to avoid the wall effect,^5,12) the density was calculated using the center region where the apparent density was almost constant. In this study, the surface energy density and friction coefficient were determined to be 0.06 J·m⁻² and 0.3, respectively, from the results of the packing and tapping simulations. When these values were employed, the calculated relative packing density and relative tapping density were 57.98% and 60.69%, respectively, which implies that the actual powder characteristics such as flowability can be well simulated because the calculated densities almost match the measured values.

Table 2 Parameters for recoating simulation.

Fig. 4

Sequence of powder packing simulation (a) and powder tapping simulation (b).

3. Results

3.1 Experimentally obtained powder bed density

Figure 5(a) shows the relationship between the relative powder bed density and number of recoating layers obtained from the recoating experiments. Regardless of the recoating speed, the relative powder bed density was considerably smaller than the apparent density of the Ti–6Al–4V powder when the number of recoating layers was small, increased as the number of recoating layers increased, and finally converged to the apparent density of the Ti–6Al–4V powder. Moreover, the relative packing density decreased as the recoating speed increased.

Fig. 5

Measured packing density (a) and Kawakita plot for blade speed 75 mm·s⁻¹ (b) and 150 mm·s⁻¹ (c).

In this study, the relationship between the relative powder bed density and number of recoating layers was fitted to the Kawakita equation¹⁹⁾ for a quantitative evaluation. However, the Kawakita equation has been mainly applied only for powder compaction and powder tapping. Therefore, in this study, the degree of volume reduction in the Kawakita equation was replaced with the relative powder bed density and the compaction pressure or number of taps in the Kawakita equation was replaced by the number of recoating layers. Figure 5(b) and (c) show the number of recoating layers N divided by the relative powder bed density V_f. N/V_f seems proportional to N, and thus the following equation is almost satisfied when a, b are constant:   

\begin{equation} \frac{N}{V_{f}} = aN + b. \end{equation} (8)

If we denote a = 1/A, b = 1/AB, eq. (8) can be expressed as   

\begin{equation} V_{f} = \frac{ABN}{1 + BN}. \end{equation} (9)

Equation (9) has the same form as the Kawakita equation. Thus, when eq. (8) is satisfied, the relationship between the relative powder bed density and number of recoating layers could be fitted to the Kawakita equation. Figure 5(a) shows the result of fitting the powder bed density to the Kawakita equation at each recoating speed. However, the relationship between the relative powder bed density and number of recoating layers obtained in this study is a fitting result from the experimental data, not equation based on physical phenomena. There have been few reports on the Kawakita equation applied to the relative powder bed density. Thus, further investigations should be carried out to evaluate whether this relationship is true. The relative packing density of the first layer of the powder bed was estimated to be 30.2% and 20.3% using the Kawakita equation when the recoating speed was 75 and 150 mm·s⁻¹, respectively. Thus, the packing density of one layer of the powder bed was considerably lower than the apparent density of the powder, as reported earlier.⁵⁾

3.2 Powder bed density calculated using DEM

Figure 6(a) shows the relationship between the relative powder bed density and number of recoating layers. The experimentally obtained relative powder bed densities are presented in the same graph. The comparison of the powder bed densities shows that the simulation results are considerably lower than the experimental results. However, the tendency of the relative powder bed density to increase as the number of recoating layers increased and converge to the apparent density of the powder was in agreement. Moreover, the tendency of the relative powder bed density to decrease as the recoating speed increased was also in agreement for both experimental and simulation results. Figure 6(b) and (c) show the number of recoating layers N divided by the relative powder bed density V_f. Similar to the experimental data, N/V_f seems proportional to N. Thus, the tendency of the simulation results was in agreement with the experimental results, although there were some deviations between them, which implies that the powder movement behavior during the recoating process could be reasonably reproduced by this simulation.

Fig. 6

Simulationally obtained packing density (a) and Kawakita plot for blade speed 75 mm·s⁻¹ (b) and 150 mm·s⁻¹ (c).

Figure 7 shows a side view of the powder bed after a 50-layer recoating. The surface roughness increased as the recoating speed increased. The surface roughness R_a calculated from the side view was 13 and 16 µm when the recoating speed was 75 and 150 mm·s⁻¹, respectively. It is considered that, when the surface roughness is large, the possibility that the final product includes some defects increases because the powder layer melted by a laser or electron beam has a large deviation. Therefore, to explain the surface roughness increase with the recoating speed, the speed distribution of particles in the powder bed during the recoating process is presented in Fig. 8, where only the center points of the particles are presented to improve the visualization of the results. Figure 9 shows the horizontal (x–y direction) and tangential (z direction) speeds of the recovered particles v_h and v_t averaged by each distance from the surface of the powder bed. v_h and v_t were calculated using the particles whose center point was at a distance of d from the surface of the powder bed.   

\begin{equation} v_{h}(d) = \frac{\displaystyle\sum\nolimits_{i,z \in d}\sqrt{v_{xi}^{2} + v_{yi}^{2}}}{n(d)}, \end{equation} (10)

  

\begin{equation} v_{t}(d) = \frac{\displaystyle\sum\nolimits_{i,z \in d}v_{zi}}{n(d)}, \end{equation} (11)

where v_xi, v_yi, and v_zi are the speeds of the i^th particle in each direction, while n is the number of recoated particles. Figure 9 shows that the absolute value of the speed of the recoated particles increased and that the recoated particles at a deeper position moved with the increase in recoating speed. Thus, the higher recoating speed led to a larger surface roughness as the recoated particles in the powder bed at a deep position can move because a larger friction force was applied to the powder bed owing to the higher velocity of the supplied particles. However, no significant difference in the surface roughness of the powder bed was experimentally observed under the experimental conditions of this study. This could be explained as the difference in surface roughness in this study was too small to detect or as the rubber recoater exhibited a different mechanical behavior from the rigid structure. Further consideration is required for the relationship between the surface roughness and recoating speed, including the material of the recoater blade.

Fig. 7

Side view of powder bed recoated 50 layers at blade speed of 75 mm·s⁻¹ (a) and 150 mm·s⁻¹ (b).

Fig. 8

Speed of recoated powder in powder bed for blade speed 75 mm·s⁻¹ (a) and 150 mm·s⁻¹ (b). Higher magnification of (a) and (b) are shown in (c) and (d) respectively.

Fig. 9

Horizontal (a) and tangential (b) speed distribution for recoated powder in powder bed.

4. Discussion

4.1 Difference in powder bed density between experiments and simulation

As shown in Fig. 6(a), the simulation results for the relative powder bed density did not agree with the experimental data, although they indicated a similar tendency. One of the reasons for this result is the error in the simulation parameters. The friction coefficient and surface energy density, which are one of the DEM parameters that determine the friction force and cohesion force, respectively, depend on the surface conditions of the powder. The manufacturing powder and powder storage conditions also affect them. Because the friction and cohesion forces affect the powder flowability, there is a difference in the powder movement behavior between the experiments and simulations unless the parameters can be determined to reproduce the flowability of the powder. In this study, powder packing and tapping simulations were performed in advance and the DEM parameters were determined so that the experimental data and simulation results indicated almost the same apparent density and tapping density. However, in addition to these factors, there are many evaluation values for powder such as angle of repose²⁰⁾ and flow rate measured by a Hall flowmeter.²¹⁾ Further consideration is required to determine which evaluation value is suitable to determine the DEM parameters to accurately reproduce the powder moving behavior. Also, a careful consideration is required to determine DEM parameters experimentally. Some DEM parameters, such as the surface energy density, can be determined experimentally. However, when a Young’s modulus smaller than the actual value is used, experimentally obtained parameters might lead to a completely different powder movement behavior and cannot be applied directly to the simulation, because the effect of DEM parameters on the powder movement behavior depends on the Young’s modulus.¹⁸⁾

Another reason for the difference between the experimental data and simulation results was the size of the simulation model, particularly the length of the build chamber L_B and length of the dose chamber L_D. Because it is considerably smaller than the actual experimental equipment, the simulation results can be affected, which needs a careful consideration in the future.

4.2 Dependence of the relative powder bed density on the number of recoating layers

In this section, we discuss the reason for the relative powder bed density increase with the number of recoating layers. Figure 10 shows a side view of the powder bed and relative powder bed density distribution after the 50-layer recoating at a recoating speed of 75 mm·s⁻¹. The powder bed density was lower than the apparent density near the surface of the powder bed, increased as the position became deeper, and became almost the same as the apparent density where the position was deeper than 200 µm from the surface of the powder bed. Thus, the percentage of the lower relative density region decreased as the number of recoating layers increased, which could be attributed to the relative powder bed density increase and convergence to the apparent density of the powder.

Fig. 10

Side view (a) and packing density distribution (b) of powder bed recoated 50 layers at blade speed of 75 mm·s⁻¹.

4.3 Relative powder bed density distribution in the depth direction

In this section, we discuss the reason for the low value of the relative powder bed density near the surface of the powder bed. The powder bed density decreases because of the wall effect,^5,12) where the voids created between the wall or substrate and particles reduce the powder bed density. In this study, it could be assumed that there was a virtual wall at the top of the build chamber because the height of the build chamber used for the calculation of the powder bed density was constant depending on the number of recoating layers. Thus, we believe that the reduced powder bed density near the surface of the powder bed was induced by the wall effect. However, after the recoating of 50 layers, the density of the powder bed around the substrate was not reduced, although the wall effect should be observed at the bottom of the powder bed. When the number of recoating layers is small, the powder bed density is reduced, which implies that the wall effect around the substrate occurs. This could be attributed to the rearrangement of particles in the powder bed when the powder bed density around the substrate increased as the number of recoating layers against the wall effect.

According to Fig. 8 and 9, it appears that, just below the supplied particles, recoated particles, except those around the surface of the powder bed, moved in the direction of the composite vector of the blade running direction and gravitational direction. Moreover, when the recoating speed was 75 mm·s⁻¹, the relative powder bed density was almost the same as the relative apparent density and the average tangential speed of the recoated particles was almost zero at the position of 200 µm from the surface of the powder bed. Thus, the decrease in the powder bed density due to the wall effect was not observed around the substrate because of the following phenomena. The recoated particles in the powder bed were stimulated by the supplied powder and rearrangement occurred, followed by an increase in the powder bed density to the apparent density.

In this study, the average packing density of the entire powder bed is discussed as the powder bed density. However, the packing density only around the surface of the powder bed where the powder was melted by a laser or electron beam can affect the quality of the manufactured parts. Thus, the packing density around the surface of the powder bed is discussed below. When the recoater speed was 75 mm·s⁻¹, Fig. 10 indicates that the relative packing density around the surface of the powder bed was 35.9%. On the other hand, the relative packing density of the first layer of the powder bed was 29.7%, as shown in Fig. 6. Thus, the relative packing density around the surface of the powder, which affects the quality of the manufactured parts, was almost constant and independent on the number of recoating layers, although the average packing density of the entire powder bed depended on the number of recoating layers.

5. Conclusion

In this study, the packing density of the first layer of the powder bed was experimentally estimated to optimize the recoating process parameters. Furthermore, a recoating simulation using the DEM was carried out. The results of this study can be summarized as follows.

1. (1)    The packing density of the first layer of the powder bed could be experimentally estimated from the packing densities of the recoated powder with different numbers of layers.
2. (2)    The experimentally obtained packing density of the first layer was considerably lower than the apparent density of the powder. Moreover, the average packing density of the entire powder bed increased as the number of recoated layers increased.
3. (3)    The increased recoating speed led to a decreased packing density of the powder bed.
4. (4)    The recoating simulation results obtained using DEM exhibited a tendency similar to that of the experimental results owing to the rearrangement of the powder stimulated by the powder supplied to the powder bed.
5. (5)    The packing density of the powder bed appeared to be nonuniform in the thickness direction. The top surface layer, which affected the quality of the manufactured parts, exhibited an almost constant packing density independent on the number of recoated layers.

Acknowledgments

This work was supported by Council for Science, Technology and Innovation (CSTI), Cross-ministerial Strategic Innovation Promotion Program (SIP), “Materials Integration” for Revolutionary Design System of Structural Materials (Funding Agency: JST).

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