VasiliBaranov/packing-generation

Binder Jetting Powder Bed

Paolo92 opened this issue · 9 comments

Paolo92 commented

Good afternoon Mr. Vasili,

I'm a Master Degree Student from Politecnico di Milano and I'm working on my degree thesis which is about Additive Manufacturing and in particular Binder Jetting 3D Printing.

To this purpose, I'm writing to you in order to understand if your code could be capable to predict the powder bed density and the so called "avarage coordination number" (intended as the averege number of contacts between a single particle of powder (sphere) and the surrounding particles) on the basis of a known powder size distribution (PSD).

My aim is to define an optimal PSD in order to achieve good mechanical properties of the printed green part and of the sintered final part.

Thank you for your attention.

Best Regards,

Paolo

VasiliBaranov commented

Hi Paolo,

yes, the code is able to generate packings of arbitrary polydispersity. If you finish packing generation with the option -lsgd (or just generate them with a very low compression rate with option -ls), they will be mechanically stable for friction = 0. Depending on the compression rate, the final density will be from the lower to the upper boundary of the Random Close Packing limit, see https://pubs.rsc.org/en/content/articlehtml/2014/sm/c3sm52959b

One can get the contact number distribution with the option -connumdist (not mentioned in https://github.com/VasiliBaranov/packing-generation#3-post-processing, but available in the code). Please read this section before using this option: https://github.com/VasiliBaranov/packing-generation#21-note-on-final-diameters

BUT. The average coordination number for mechanically stable frictionless packings is always six due to the isostaticity condition (in general, it shall be z=2*dimensionality). Please see Section 4 here https://arxiv.org/pdf/0808.2196.pdf or Appendix A here https://arxiv.org/pdf/1602.04369.pdf.

To get the average coordination number different from six for mechanically stable packings one needs to add friction to simulations. Please see the paper A phase diagram for jammed matter for a general overview.

Adding friction shall be done by another program (after an initial packing is generated by my or equivalent program; this packing shall not even be mechanically stable in any sense, just some configuration with sufficiently high density). Please see the Appendix I here https://arxiv.org/pdf/1001.5287.pdf. The program that they use to simulate friction can be found here: https://hmakse.ccny.cuny.edu/software-and-data/ . Search for "Research on the phase diagram for jammed matter" on the page, in this section follow the links "Algorithm and simple instructions", http://www-levich.engr.ccny.cuny.edu/~hmakse/GRANULAR/trubal.zip and "the instruction manual" http://www-levich.engr.ccny.cuny.edu/~hmakse/GRANULAR/trubal-instructions.pdf

Hope this helps!

Best Regards,
Vasili

Paolo92 commented

Dear Mr. Vasili,

Thank you for your comprehensive answer. It will be very useful.

Best Regards,
Paolo

Paolo92 commented

Dear Mr. Vasili,

I tried to run the code with Visual Studio but it returns me several errors (which are in particular the C2373 and the C2447).

image

Could it be related to the issue "makefile/Cygwin" explained in "2.2. Direct makefile compiling and linking"? Because if it is, I Honestly don't understand what to do.

Thank you for answering my questions.

Paolo

VasiliBaranov commented

Dear Paolo,

if you are compiling on Windows with Visual Studio, then makefile/Cygwin issues shall not have any effect.

First, you can download a compiled executable for windows: https://github.com/VasiliBaranov/packing-generation/releases/tag/v1.0.1.28 and just use it.

Also, you can try to unload the Tests project before compiling.

Also, I tested compilation recently with Visual Studio 2017, and it worked fine (and the project shall definitely work with Visual Studio 2010). Maybe the difference comes from the new version of the compiler and standard library (every VS has a new version and sometimes the standard library uses slightly different default macros or file locations). What you can try is to go to Visual Studio Installer -> Modify -> Individual Components -> select smth like Visual Studio 2017 or C++ Toolchain 15 (15 is the version of the tools for 2017). You will probably have to open the original project from the git again, so that VS suggests you to convert it either to 2019 or to 2017. And then you can try to compile it. I think it shall work. In the worst case, you can install the 2010 toolchain (version 14) and reopen the project from git. It shall work for sure.

Hope this helps.

Best Regards,
Vasili

Paolo92 commented
VasiliBaranov commented

Hi Paolo,

for the LS algorithm, you do not even need this estimation. Particles will be scaled proportionally to their initial radii during the simulation and their final diameter will be greater then the initial one. The final density is controlled only by the compression rate. To get the highest possible density, you need to specify a very low compression rate (which is controlled by the time you can realistically spend on packing generation).

For the FB algorithm, the expected final density is another parameter that determines the real final density (along with the compression rate). Here you might indeed have to make several attempts (but see below).

The exact parameters that i used are described here: https://github.com/VasiliBaranov/packing-generation#14-note-on-final-diameters (last paragraph). You can in principle estimate the polydispersity of your system, then go to Fig. 2 https://pubs.rsc.org/en/content/articlehtml/2014/sm/c3sm52959b#imgfig2 and then check the compression rate that has to be used to achieve the desired density. To reach the desired (maximum possible) density with the FBA algorithm, you have specify the expected density that is for sure higher than the real maximum density. You can get the real maximum density from Fig. 2 as well. You can get the expected densities that i used for the FBA algorithm from the formula described here https://github.com/VasiliBaranov/packing-generation#14-note-on-final-diameters (in the last paragraph).

Hope this helps!

Best Regards,
Vasili

Paolo92 commented
VasiliBaranov commented

Dear Paolo,

no problem, i'm happy to help as much as i can.

  1. Please see, for example, this paper: https://arxiv.org/pdf/cond-mat/0608362.pdf (one co-author, Stillinger, is the author of the original algorithm). A pretty cool guy actually: https://en.wikipedia.org/wiki/Frank_Stillinger Anyway, please see Fig. 4 there. They stop simulation at reduced pressure Z=10^12. They explain the logic pretty well in this paper: high reduced pressure means that spheres are colliding very very often, which means that they are very close and the system is almost jammed. One can estimated the difference between the expected jamming density and the current density by this pressure (see Eqs. 3 and 4 in this paper), they are derived in a very old paper https://aip.scitation.org/doi/abs/10.1063/1.1733163 . Please note that these equations are valid when the compression rate is small (explained in the paper of Stillinger as well).

  2. Seed is just the value used to start random number generation. See e.g. http://www.cplusplus.com/reference/cstdlib/srand/ Random numbers are used to place particles and set their velocities. If you use the same seed, the algorithm will start and proceed every time in exactly the same way (for the same starting radii).

  3. Time is some internal simulation time (in simulation units of measurement), a.u. (arbitrary units). In this algorithm, particles grow and fly, like atoms or molecules, so temperature and pressure have usual meaning of the kinetic theory of gases. Temperature = m <v^2> / 2. Masses of all particles are set to unity. Reduced pressure is Z = p V/ N k T. Pressure P is measured by the momentum exchange between particles (when they collide), i can check for the exact equation. V is the volume of the box where particles are, k is the Boltzmann constant which in these units is set to unity. Z is very convenient, because it is dimensionless and does not depend on the units of measurements (k is present in p and cancels out, unit of time is present in p and and T and also cancels out). For the ideal gas, Z=1, for hard spheres Z is higher and possibly infinite. Temperature is set to 0.2 (this is basically how velocities relate to the compression factor you specify). Velocities are sampled from the Maxwell-Boltzmann distribution (equilibrium distribution).

  4. "steps to write" is how often an intermediate simulation result is written as packing.xyzd, so that you can restart the simulation if anything breaks. How often==how many collision events pass.

Hope this helps!

Wishing you a merry Christmas and a happy New Year!

Best Regards,
Vasili

Paolo92 commented