Calibration of parameters of wheat required in discrete element method simulation based on repose angle of particle heap

Abstract: In this study, we determined the parameters of wheat required in discrete element method (DEM) simulation by the response surface method. The repose angle is a macroscopic parameter, which is used to describe the friction and flow properties of particle material and widely applied in DEM parameter calibration for it can be measured easily. In this research, the heap of wheat was formed through the bottomless cylinder method and the repose angle was measured using a computer graphic technology. The calibration tests were conducted in laboratory and by simulation using EDEM 2.7.0 software. According to previous research, an acrylic cylinder with an inner diameter of 39 mm and a height of 120 mm was used. The wheat particles were filled into the cylinder using the "rainy method" through a square-opening sieve with 12 mm aperture and lifted with a speed of 0.05 m/s. For DEM simulation, different parameter combination tests were designed. Specifically, the Plackett-Burman test was performed to screen the significant parameters from the 8 selected parameters. It was found that the static friction for wheat-wheat and wheat-acrylic contact and the rolling friction for wheat-wheat contact had a significant effect on the repose angle, while the other 5 parameters' influence was negligible. Then the steepest ascent test was used to determine the optimal value range of the significant parameters. In the steepest ascent test, the 5 non-significant parameters were the mid-value of the corresponding initial region, while the 3 significant parameters increased progressively until the relative errors between the simulated and the test value reached the minimum. Based on the result of the Box-Behnken test, a quadratic polynomial model for the repose angle and the 3 significant parameters was created. The analysis of variance (ANOVA) of the quadratic polynomial model showed that the model was significant and the lack-of-fit was non-significant. This means the model can be used to determine the best parameter combination. However, some terms in the quadratic polynomial model were non-significant. So, a modified regression model was established by deleting these non-significant terms. The ANOVA of the modified model showed all of the terms were desirable, and the first-order term of the 3 significant parameters, the interactive term of the wheat-wheat static friction coefficient and wheat-acrylic static friction coefficient, and the quadratic term of wheat-acrylic static friction coefficient had a significant effect on the repose angle. The interaction of the static friction coefficient for the wheat-wheat and wheat-acrylic contact was also analyzed, and it was found that the repose angle increased with the increase of the 2 parameters. However, when one of the 2 parameters (the static friction coefficients for the wheat-wheat A and wheat-acrylic B contact) was low, the growth rate of repose angle with the other parameter was larger than that when one of the 2 parameters was high. This showed that the interaction between the parameters of A and B was more significant when they were low. By solving the modified regression equation, the best combination of the parameters was obtained: wheat-wheat static friction coefficient of 0.58, wheat-acrylic static friction coefficient of 0.61 and wheat-wheat rolling friction of 0.08. The best parameter combination was validated through comparing the DEM simulation results with the test values, and it was found that there was no significant difference between them. The research shows that the parameter calibration method based on the response surface method is feasible. Meanwhile, the best parameter combination can be used as reference values when choosing the simulation parameters of wheat required in DEM.