Tablet press model

EDEM Tutorial: Tablet press model

EDEM Tutorial: Tablet Press

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Introduction This is an advanced tutorial suitable for users with a significant level of acquaintance with EDEM. In case of any uncertainties or problems, refer to previous tutorials or EDEM Help section. This exercise demonstrates the capabilities of the Hysteretic and ECM contact models through the simulation of a pharmaceutical tablet press. The main concepts investigated here are:  



Importing geometry in EDEM and exporting a simulation deck. 



Importing a custom contact model in EDEM and defining its input parameters.



Showcasing the use and capabilities of the Hysteretic spring and ECM contact models.   Plotting graphs with custom model properties.

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Problem description A pharmaceutical company is experiencing problems with their tablet production. They suspect that their tabletting press does not produce enough compaction and/or their powder mix is not cohesive enough, leading to tablets falling apart. They would like to simulate the process to gain a better insight into the problem. The tablet press consists of a die and upper and lower punches which compact the tablet material. You can see the geometry setup in the pictures below.

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Part 1: Setup with the Hysteretic Spring contact model EDEM Creator: Setting up the model Introduction The Hysteretic Spring contact model allows plastic deformation behaviors to be included in the contact mechanics equations. The model approximates elasto-plastic deformation by defining a yield strength for the material and calculating a loading stiffness based on that yield strength. A higher unloading stiffness is then defined based on the material’s coefficient of restitution which leads to the plastic deformation δ0. The model does not include cohesion forces and is therefore suitable for simulation of non-cohesive plastic materials only. However, It can be combined with the Linear Cohesion model to simulate an elastic-plastic cohesive material.

Uncompressed

Compressed

Unconfined

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EDEM Tutorial: Tablet Press In the case of the tablet press we can use the Hysteretic spring model to simulate compaction in the press without cohesion so: 1. Start EDEM and save your project as Tablet_Press_Hysteretic.dem in the tutorial folder. 2. Remember to often Save the model when setting up the simulation.

Step 1: Set the Global Model Parameters Choose the units and name the model 1. Set the measurement units as follows: 

Velocity: m/s



Length: mm

2. In the Globals tab, enter the simulation title Tablet_Press_Hysteretic.

Step 2: Set the gravity, define the materials and interactions 1. Check that gravity is set to -9.81 m/s2 in the z direction. 2. Create two new materials with the following specifications and interactions:

The low friction coefficients of the powder steel interaction correspond to the low friction material of the die and punches. Adhesion and friction is minimized in the tabletting process.

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Step 3: Define the Base Particles Create a new particle type and define the surfaces and properties 1. In the Particles tab, create a new particle called PowderParticle. The name is important, because the custom model we’ll use later requires an exact particle name to be defined. 2. Create 1 surfaces with a particle radius of 0.2 mm (fine powder). 3. Set the Material to Powder. 4. Click the Calculate Properties button and pick the Surfaces option.

Step 4: Set the Contact Models 1. For the Particle to Particle interaction remove the Hertz-Mindlin model and add the Hysteretic Spring model. 2. Click on the

button and define the following input parameters:

The Damping Factor is a used to scale the normal spring damping force. In this case using a factor of 1 gives us the same damping force to the one in the linear spring contact model.

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EDEM Tutorial: Tablet Press The Stiffness Factor is needed to define the ratio of the tangential force to the normal force of the contact since in the Hysteretic Spring model the tangential force is calculated as a fraction of the normal force. The Yield Strength defines the level of stress at which plastic deformations occur. In the hysteretic spring model the loading stiffness is linearly depended on the yield strength. Therefore the higher the yield strength the stiffer the particles become. However there is plastic strain at all stress values above or below the Yield Strength. To investigate the effect of the different parameters on the model you can look at the Hysteretic models.xlsx Excel table provided with the tutorial.

Step 5: Define the Geometry Import the tablet press geometry The tablet press geometry has been created using a CAD package. 1. Go to the Geometry tab and import the Bottom_Punch.igs, Top_Punch.igs and Factory_And_Walls.igs from the tutorial folder, select units mm. When importing the top and bottom punch geometry make sure to select the merge sections option. Do not merge the walls and factory sections. 2. Set Material to Steel for all parts of the geometry, except the Factory Plate which should be Virtual. 3. Rename the sections of the geometry as shown in the image below:

Top Punch Factory Plate

Walls

Bottom Punch

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EDEM Tutorial: Tablet Press 4. Set the geometry domain to the values below (deselect update from geometry check box):

Define the geometry dynamics 1. Add three linear translations to the Top Punch with the following parameters:

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2. Add one linear translation to the Bottom Punch with the following parameters:

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Step 6: Create the Particle Factory 1. In the Factories tab, create a new factory called Powder. 2. Set the Factory Type to dynamic, select Total Number and specify 6000 particles. 3. In the Generation Rate section, select Target Number and set the value to 100000 particles/s. 4. In the Parameters section, select Factory Plate from the Section pull-down. 5. Set the Velocity to fixed with the following parameters:

EDEM Simulator: Running Simulation In tabletting the compactions happen fairly quickly (in less than one second) so we’ll need to take this into account when choosing the target save interval and the simulation run time. 1. Set the simulation time to 0.25 s. 2. Set the time step to 20% of the Rayleigh value. 3. Set the target save interval to 0.001 s. 4. Make sure the Simulator Grid Cell Size is set to 3 Rmin. 5. Run the simulation.

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EDEM Analyst: Analyzing the Results Review tablet breakage 1. Go to the Analyst and play through the simulation. Notice how the powder is compacted and exhibits plastic behavior but there is no cohesion. What is keeping the particles together is the interparticle friction only. When minimal force is applied the tablet falls apart.

Plot a graph of average normal overlap with time To verify that the particle have plastic behavior we can plot the average normal overlap with time. 1. Go to Analyst and press the Create Graph button

.

2. Choose the Line Graph tab. 3. On the X axis choose a time range from 0.086 s to 0.11 s. 4. On the Y axis choose Contact group, Normal Overlap as primary attribute and select Average in component. 5. Create the graph. You should get something similar to the graph below:

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Notice how the normal overlap increases during compression and reaches a maximum 1 milliseconds after the end of compaction, the delay being due to the remaining kinetic energy of the punch. Afterwards the normal overlap levels off to a more or less constant value with no force being applied to the sample. The minor fluctuations are due to the dynamics of the setup

Save the deck The setup for Part 2 is similar to this one so you can save it for reuse. 1. Go to Creator tab and set the Current Time to 0 s. 2. Go to File>Save As and save the file in the tutorial folder as Tablet_Press_ECM.dem

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Part 2: Setup with the ECM contact model Introduction On the meso scale, many compressed granular materials exhibit a behavior which can be characterized by elasto-plastic deformation accompanied with an increase in cohesion. Such materials include soil, fine dry powders, organic material, ore fines etc. To address the need to simulate such materials, the Edinburgh Elasto-Plastic Cohesion (ECM) model has been developed at The University of Edinburgh. It is a versatile non-linear model which incorporates hysteresis, cohesion and Van der Waals type forces in the contact mechanics equations. You can see the model’s contact function and a simple example in the figures below.

Initial

Compressed

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Uncompressed


Importing custom contact models in EDEM Like all custom contact models, the ECM model has been written in C++ using the EDEM Application Programming Interface (API) and compiled as a .dll file. The model’s input parameters are defined in a separate .txt file which should always be in the same directory as the model .dll file and should not be renamed. To import the ECM contact model into EDEM, please complete the following steps: 1. Open Tablet_Press_ECM.dem 2. Go to Tools>Options>File Locations and under Contact Models press Browse and navigate to the folder which contains ECM_v2_2014.dll, ECM_v2_2014.so and ECM_Parameters.txt files.

3. Go to the Global Tabs in Creator and delete the Hysteretic Spring model under Particle-Particle contacts. 4. Add the ECM_v2_2014 model and save the simulation.

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The model has now been loaded into EDEM with the parameters specified in the ECM_Prefs.txt file. The contents of the preference file should look like this:

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EDEM Tutorial: Tablet Press The input parameters of the model are: Constant pull-off force, f0 (N): This can be used to incorporate ever presents forces that may occur, such as van der Waals type forces or electrostatic force. The magnitude of this force will not change for the simulation duration. Meso-contact Surface Energy, (J/m2): This is the level of adhesion that is used in the calculation of the load dependent adhesive force in the contact model, f min. Contact Plasticity Ratio: this is the level of contact plasticity used in the model and this parameter defines the magnitude the unloading/reloading stiffness k2 as a constant ratio between the initial stiffness k1 and the unloading/reloading stiffness k2. A value of zero represents elastic particle contacts, while a value of 1 leads to perfectly plastic particle contacts. Power Value for k1 and k2 F-D relationship, n: This is used to switch between linear and non-linear force-overlap relationships for the contact model. Power value for adhesion branch, X: This defines the severity of the drop in adhesion force following the peak tensile force being reached. A value of unity gives a linear, more ductile separation curve, whereas a sharp drop in strength is found for values > X = 2. Tangential Stiffness multiplier, Ktm: This allows the tangential stiffness used in the model to be varied. The tangential stiffness is defined as a ratio of the Virgin Loading Stiffness, k1 – a multiplier of 1 gives a tangential stiffness equal in magnitude to the loading stiffness. The preference file specifies contact parameters for specific particles only, in this case PowderParticle so it is important to have the particles in the simulation named accordingly. To get a better idea of how the different input parameters affect the model you can review the Hysteretic models.xlsx Excel table.

EDEM Simulator: Running Simulation 1. Set the simulation time to 0.25 s. 2. Set the time step to 10% of the Rayleigh value (the ECM contact model needs smaller time steps to be stable). 3. Set the Target Save Interval to 0.001 s. 4. Make sure the Simulator Grid Cell Size is set to 3 Rmin. 5. Run the simulation.

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EDEM Analyst: Analyzing the Results Step 1: Play through the simulation 1. Go to the Analyst and play through the simulation. Notice the highly cohesive behavior after compaction leading to the formation of a stiff tablet.

Step 2: Color the tablet using manual selection 1. Go to Analyst>Selection tab and add a new Manual Selection. 2. Set the time to 0.18 seconds. 3. Check the Enable Manual Selection tick box. 4. Change the model view to +X and select the top layer of the tablet. 5. Go to Coloring and under Color by change from Type to Selection 6. Choose a color under Static Coloring and press Apply.

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Step 2: Plot custom properties Custom model properties can be plotted in EDEM using the Analyst. For example the plastic overlap in the ECM model can be plotted against time. 7. Go to Analyst>Create Graph>Line Graph and set the X axis range from 0.08 to 0.1 seconds. 8. Change the element group form Particle to Contact. 9. Under the Y axis tab select ECM Plastic overlap as the primary attribute and Average as the component. 10. Create the graph.

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Notice the similarity in the plastic behavior simulated with the two models. In fact the ECM model is capable of replicating the Hysteretic spring contact model simply by adjusting the input parameters.

Step 3: Investigate relationship between compaction and cohesion The ECM models an increase in cohesion with an increase in compaction. To investigate this behavior you can plot the total force on the top punch during crushing for the current tablet and then for a tablet which has been compacted less. 1. Go to Analyst>Create Graph>Line Graph and set the X axis range from 0.23 to 0.25 seconds. 2. Change the element group from Particle to Geometry and the Section to Top Punch. 3. Under the Y axis tab select Total Force as the primary attribute and Total Magnitude as the component. 4. Create the graph.

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Rerun the simulation with lower compaction 5. Go to Creator and change time to 0 s. 6. Save under a new simulation name and update the following geometry dynamics of the Top Punch:

7. Rerun the simulation from the start with the same simulation parameters. 8. Create the same graph as above.

Notice the decrease in the peak force that the tablet can withstand with lower compaction. You can also see that the tablet is behaving in a more brittle manner during loading.

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Tablet press model

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