COMSOL 6.4 - Powder Spreading Using a Moving Roller

Additive manufacturing techniques such as powder bed fusion (PBF) rely on obtaining thin uniform layers of powdered materials. The quality and the consistency of the obtained powder bed has a significant impact on the quality of the manufacturing process. The factors affecting the quality of the bed include its density, homogeneity, and thickness as well as the presence of any defects. This crucial step is most often achieved by first generating a heap of the powdered material in front of the bed. A moving roller is then used to spread the material onto the bed. The geometry and speed of the roller can affect the quality of the powder bed.

This example uses the Granular Flow interface to model the formation of the grain heap and then its subsequent spreading using a cylindrical roller. The roller has a combined rotational and translational motion. The resulting powder bed is then analyzed to determine its quality based on its packing fraction. Additional packing characteristics such as the distribution of the grain center heights and the coordination numbers are also evaluated.

This model also demonstrates the process of restarting the granular flow simulations whereby the information of the grains from one study step is used as the initial conditions for a subsequent study step.

Model Definition

The geometry consists of three rectangular compartments. The first one houses the roller until it is ready to move. The grains are released into the middle compartment. The third compartment represents the powder bed. The length and the width of the middle compartment is 40 mm. The length of the powder bed is set to 200 mm, and the height of all the compartments is 60 mm. The roller has a diameter of 15 mm and is initially situated in the first compartment such that it has a gap of 3 mm from both its walls in the x direction. The geometry is presented in Figure 1. The two boundaries that separate the middle compartment from the other two represent gates that can be added and removed to alter the geometry.

A total of 20,000 grains, each having a diameter of 1 mm, are first released randomly into the middle compartment. The grains initially settle under the influence of gravity for 0.25 s to form a compact bed since the two gates are closed. Periodic boundary conditions are applied along the y directions to isolate the wall effects in this direction. Once the grains are settled, the two gates are lifted to allow the grains to form a stable heap. The heap formation time is 0.4 s.

Figure 1: Model geometry.

Finally, the roller blade is allowed to move with a translational speed of 100 mm/s for a total linear traversal length of 163 mm. The roller also rotates with an angular speed of 6 rad/s around its axis. This action causes the powder spreading and the formation of a compact powder bed.

Notes on COMSOL Implementation

The model is solved using three studies. In the first study, the grains are released into the middle compartment and are allowed to settle. The degrees of freedom of the grains at the end of this study are used to initialize the second study in which the gates are removed instantaneously to allow for the heap formation. The removal of these gates is achieved by using the feature. Once the heap is stable, the degrees of freedom are then used to initialize the third study wherein the roller is allowed to move. The motion of the roller is controlled by the settings in the feature. The feature is used in the y direction to eliminate the wall effects in that direction.

Once the powder bed is generated, its quality is judged based on two parameters: the packing fraction and the height of the grains as a function of the x-coordinate. To calculate the packing fraction, the resultant powder bed is first divided into multiple samples along the x direction with a sample width of 10 mm. A feature is then used to count the number of grains within each sample and the result is stored in a table. An feature is then created to convert the data in this table into a function of the sample index or the x-coordinate representing the center of each sample. The packing fraction in each sample is then evaluated as the product of the number of grains in each sample and the volume of each grain divided by the ideal volume of the sample.

Results and Discussion

Figure 2 shows the grain positions at the end of the first study colored by their speed in m/s. The speeds are very low, indicating that the grains have settled under gravity and have formed a stable pile.

Figure 2: The middle compartment filled with grains. The grains are colored based on their speeds in m/s.

Figure 3 shows the grain positions at the end of the second study, again colored by their speed in m/s. The lifting of the two gates allows the formation of a nearly symmetric heap that can then be rolled over. The speeds of the grains in the heap are again very low, indicating that the grains have formed a stable heap.

Figure 3: Heap of grains formed after the two boundaries are removed. The grains are colored by their speed in m/s.

The grain positions at the end of the third study are shown in Figure 4 and are colored by their coordination numbers. It is visually evident that the powder bed is pretty uniform in density without any major gaps in the bed. This property of the bed quality is quantified by the packing fraction, which is plotted as a function of the x-coordinate in Figure 5. The packing fraction is clearly almost constant for every sample with a value of roughly 0.47 throughout the bed. This illustrates the density and the uniformity of the powder bed.

Figure 6 shows the normalized histogram of the z-coordinates of the grains in the powder bed. The x-axis in the plot is the z-coordinate normalized by the grain diameter. There are three distinct peaks in the distribution. The first peak occurs at 0.5 indicating the first layer is in contact with the base of the bed. The second peak occurs at 1.3 which is approximately equal to

which would be expected from a closely packed periodic structure. The broadness of this peak also denotes some additional variance in the height of the second layer. Finally, there is an additional much broader third peak at 2.1 which is approximately equal to

which corresponds to the third layer in a closely packed periodic structure. Note that these peaks are identical to the ones observed in Ref. 1 where the powder spreading is achieved through the linear translation of a rectangular blade.

Figure 4: The powder bed formed due the motion of the roller. The grains are colored by their coordination numbers.

Figure 7 shows the normalized histogram of the grain coordination numbers. The plot has a strong peak at three, thus indicating that a large portion of the grains are in contact with three additional grains. However, there is also a very small fraction of the grains that are in contact with nine additional grains. This is indicative of the pockets of high compaction in the powder bed.

Figure 5: Packing fraction of the grains as a function of the x-coordinate in the powder bed.

Figure 6: Distribution of grain heights in the powder bed.

Figure 7: Distribution of grain coordination numbers in the powder bed.

Reference

1. Y.M. Fouda and A.E. Bayly, “A DEM study of powder spreading in additive layer manufacturing,” Granular Matter, vol. 22, no. 1, p. 10, 2020.

Granular_Flow_Module/Transport/powder_spreading

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > .

Click .

Click

In the tree, select > .

Click

Global Definitions

Model Parameters

In the window, under click .

In the window for , type Model Parameters in the text field.

Locate the section. Click

Browse to the model’s Application Libraries folder and double-click the file powder_spreading_parameters.txt.

Definitions

Variables 1

In the toolbar, click

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Unit	Description
roller_disp	roller_v*(t-t_heap)	m	Roller displacement

Geometry 1

Block 1 (blk1)

In the toolbar, click

In the window for , locate the section.

In the text field, type roller_dia+2*roller_gap+5*Lx.

In the text field, type Ly.

In the text field, type Lz.

Locate the section. In the text field, type -(roller_dia+2*roller_gap).

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (m)
Layer 1	roller_dia+2*roller_gap
Layer 2	Lx

Find the subsection. Select the checkbox.

Clear the checkbox.

Cylinder 1 (cyl1)

In the toolbar, click

In the window for , locate the section.

In the text field, type roller_dia/2.

In the text field, type Ly.

Locate the section. In the text field, type -(roller_dia/2+roller_gap).

In the text field, type roller_dia/2+roller_gap.

Locate the section. From the list, choose .

Click

Click the

button in the toolbar. The geometry should look like Figure 1.

Granular Flow (gran)

Grain Properties 1

In the window, under > click .

In the window for , locate the section.

From the ρg list, choose . In the associated text field, type rho.

From the Eg list, choose . In the associated text field, type E.

From the νg list, choose . In the associated text field, type pois.

Locate the section. In the dg text field, type dg.

Wall 1

In the window, click .

In the window for , locate the section.

From the E list, choose . In the associated text field, type E.

From the ν list, choose . In the associated text field, type pois.

Contact Between Grains 1

In the window, click .

In the window for , locate the section.

In the en text field, type e.

In the et text field, type e.

In the μs text field, type mu_s.

In the μr text field, type mu_r.

In the μtw text field, type mu_tw.

Contact with Walls 1

In the window, click .

In the window for , locate the section.

In the en text field, type e.

In the et text field, type e.

In the μs text field, type mu_s.

In the μr text field, type mu_r.

In the μtw text field, type mu_tw.

Release 1

In the toolbar, click

and choose .

Select Domain 3 only.

In the window for , locate the section.

In the table, enter the following settings:


Released grain properties	Number of grains
Grain Properties 1	N

Outlet 1

In the toolbar, click

and choose .

Select Boundaries 12 and 17 only.

Roller

Next, add a node to specify the settings for the motion of the roller.

In the toolbar, click

and choose .

In the window for , type Roller in the text field.

Select Boundaries 6, 7, 10, and 11 only.

Locate the section. From the E list, choose . In the associated text field, type E.

From the ν list, choose . In the associated text field, type pois.

Locate the section. From the list, choose .

Specify the dx vector as


roller_disp	X
0	Y
0	Z

In the ω text field, type roller_om.

In the α0 text field, type -roller_om*t_heap. Note that the roller movement will only be activated at the third study which starts at t_heap. Thus it is important to specify the initial angle of rotation appropriately.

Specify the rbp vector as


-(roller_dia/2+roller_gap)	X
0	Y
roller_dia/2+roller_gap	Z

Specify the eax vector as


0	X
1	Y
0	Z

Periodic Condition 1

In the toolbar, click

and choose .

Select Boundaries 2, 5, 8, 9, 13, 16, 18, and 21 only.

Click the

button in the toolbar.

Study 1: Filling

Set up the first study to release the grains into the domain and to simulate the filling of the domain.

In the window, click .

In the window for , type Study 1: Filling in the text field.

Step 1: Time Dependent

In the window, under click .

In the window for , locate the section.

In the text field, type range(0,t_fill/10,t_fill).

Locate the section. Select the checkbox.

In the tree, select > > and > > .

Click

In the toolbar, click

Results

Grain Positions: Filling

In the window for , type Grain Positions: Filling in the text field.

Click the

button in the toolbar.

Click the

button in the toolbar.

The grain positions at the end of the first study should resemble Figure 2.

Filling

In the toolbar, click

and choose .

In the window for , type Filling in the text field.

Locate the section. From the list, choose .

Click the

button in the toolbar.

Add Study

Next, set up the second study to simulate the heap formation that occurs when the two boundaries of the domain containing the grains are removed.

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Study 2: Heap Formation

In the window for , type Study 2: Heap Formation in the text field.

Step 1: Time Dependent

In the window, under click .

In the window for , locate the section.

In the text field, type range(t_fill,(t_heap-t_fill)/10,t_heap).

Locate the section. Select the checkbox.

In the tree, select > > .

Click

Click to expand the section. Find the subsection. From the list, choose .

From the list, choose .

In the toolbar, click

Results

Grain Positions: Heap Formation

In the window for , type Grain Positions: Heap Formation in the text field.

The grain positions at the end of the second study should resemble Figure 3.

Heap Formation

In the toolbar, click

and choose .

In the window for , type Heap Formation in the text field.

Locate the section. From the list, choose .

Click the

button in the toolbar.

Granular Flow (gran)

Before setting up the final study to simulate the spreading of the grains to form a powder bed due to the motion of the roller, enable the computation of the coordination numbers for the grains.

In the window, under click .

In the window for , locate the section.

Select the checkbox.

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Study 3: Spreading

In the window for , type Study 3: Spreading in the text field.

Step 1: Time Dependent

In the window, under click .

In the window for , locate the section.

In the text field, type range(t_heap,0.1,t_spread).

Locate the section. Find the subsection. From the list, choose .

From the list, choose .

In the toolbar, click

Results

Grain Positions: Spreading

In the window for , type Grain Positions: Spreading in the text field.

Modify the default plot settings to better visualize the roller rotations.

In the window, expand the node.

Color Expression 1

In the window, expand the > > node, then click .

In the window for , locate the section.

In the text field, type gran.Ng.

In the toolbar, click

Surface 1

In the window, under > click .

In the window for , locate the section.

From the list, choose .

Selection 1

In the window, expand the node, then click .

In the window for , locate the section.

Click to select the

toggle button.

In the list, choose and .

Click

Select Boundaries 7 and 10 only.

Surface 2

In the window, under > right-click and choose .

In the window for , locate the section.

From the list, choose .

Selection 1

In the window, expand the node, then click .

In the window for , locate the section.

Click to select the

toggle button.

Click

Select Boundaries 6 and 11 only.

In the toolbar, click

Click the

button in the toolbar. The powder bed at the end of the third study should resemble Figure 4.

Spreading

In the toolbar, click

and choose .

In the window for , type Spreading in the text field.

Locate the section. From the list, choose .

Click the

button in the toolbar.

1D Histogram

Next, a of the x-coordinates of the grains is first computed, and the resultant data is used to set up an function. This function is then used to compute the packing fraction of the grains within the powder bed.

In the toolbar, click