Development of a Non-Spherical Polymeric Particles Calibration Procedure for Numerical Simulations Based on the Discrete Element Method

Abstract

The manufacturing industry, in general, and the plastic industry, in particular, have been developing new materials and process methods that need a correct study and optimization. Nowadays, the main approach to optimize these processes is using numerical methods and, in the case of particulate materials, the Discrete Elements Method to estimate the particles interactions. But those mathematical models use some parameters that depend on the material and must be calibrated, thus requiring an important computational and experimental cost. In this study, we integrate different speed-up procedures and present a general calibration method of Low-Density Polyethylene particles, to obtain the calibrated solid density and Poisson's ratio of the material, the restitution, static and rolling friction factors in the particle-to-particle and particle-to-wall interactions, and the contact model variables (damping factor, stiffness factor, and energy density). For this calibration, four different tests were carried out, both experimentally and with simulations, obtaining the bulk density, the repose and shear angles, and the dropped powder. All these response variables were compared between simulations and experimental tests, and using genetic algorithms, the input parameters (design variables) were calibrated after 85 iterations, obtaining a Mean Absolute Percentage Error of the response variables lower than 2% compared to the experimental results.

Keywords: discrete element method; genetic algorithms; material calibration; polymeric powder calibration.

Figure 1

Experiment flow chart.

Figure 2

Vacuum powder disperser (a) and slide with dispersed powder (b).

Figure 3

Tap density test machine.

Figure 4

Alternative bulk density measuring device in initial position (a) and device sectioned with the selected amount of powder for mass measuring for determining the bulk density (b).

Figure 5

Hollow cylinder machine.

Figure 6

Hollow cylinder test principle starting test (a) and finishing test with the measured angles (b).

Figure 7

Ledge box test principle starting test (a) and finishing test with the measured angles (b).

Figure 8

Drawdown test principle starting test (a), finishing test with the measured angles (b).

Figure 9

Schema of interaction representation between particles (a) and representation of the overlap in the contact point and their principal measures (b).

Figure 10

Contact force–displacement function of Hert-Mindlin (HMCM) (a), hysteretic spring (HSCM) (b), and Edinburgh elasto-plastic adhesion (EEPACM) (c) models.

Figure 11

Capture of microscope visualization with aspect ratio measurements examples.

Figure 12

Direct bulk density measurement in test simulation.

Figure 13

Hollow cylinder process in software for four different time steps.

Figure 14

Ledge box process in software for four different time steps.

Figure 15

Drawdown process in software for four different time steps.

Figure 16

Image processing method: initial picture (a), sectioned part (b), binarized section (c), and boundary with fitted equation (d).

Figure 17

Flow chart calibration process.

Figure 18

Particle size distribution of LDPE powder.

Figure 19

Representation of the particle shape used for the study.

Figure 20

Trend of the results of the calculated equations (MAPE) for the different iterations.