Parameters of a discrete element ballasted bed model based on a response surface method

The discrete element method (DEM) is an effective tool for obtaining qualitative and quantitative information on particle motion, which aids in the design and optimization of agricultural equipment structures. The accuracy of the DEM simulation parameters significantly impacts the simulation results. This study employed a combination of high-speed camera measurement, DEM simulation, and validation tests to determine the material and interaction property parameters for fertilizer particles. The basic parameters (triaxial size, bulk density, density, and coefficient of static friction) and coefficients of restitution between fertilizer and material were measured for three fertilizer varieties. There was a significant difference in the angle of repose between various material plates and fertilizer particles. The calibration values of coefficients of restitution and coefficients of rolling friction between fertilizer particles were optimized using the Box–Behnken method. The angle of repose was significantly affected by the coefficient of static friction and the coefficient of rolling friction between the fertilizer particles. The determined values for the coefficient of restitution, coefficient of static friction, and coefficient of rolling friction between the fertilizer particles were 0.323, 0.381, and 0.173, respectively. The error in the angle of the repose test was less than 3.0%, and the variation coefficient for each row consistency was less than 1.68 percentage points under the optimal simulation parameters. DEM simulations of the angle of repose and each row consistency variation coefficient test using the measured parameters can accurately predict the experimental results. The findings of this paper provide a theoretical basis for the DEM study of fertilizer particles.

To improve the accuracy of contact parameters in discrete element simulations of seed metering devices and avoid errors arising during parameter measurement, this paper does not determine the values of each parameter in advance during parameter calibration. Instead, it directly uses the sliding friction angle, angle of repose, and rebound height as indicators, and employs regression analysis to calibrate the static friction coefficient, rolling friction coefficient, and restitution coefficient. The accuracy of the simulation parameters is verified through comparative experiments with the seed metering device. The results show that: the static friction coefficient is proportional to the sliding friction angle, and the correlation between the two is independent of material properties. The calibrated static friction coefficients between seeds, PMMA, and PLA are 0.39, 0.43, and 0.54, respectively; the rolling friction coefficient of seeds is exponentially related to the angle of repose, and the rolling friction coefficient between seeds is 0.029; the restitution coefficient is quadratically related to the rebound height in drop tests, and the calibrated restitution coefficients of seeds with PMMA and PLA are 0.33 and 0.32, respectively; the verification experiments demonstrate that the motion patterns of seed populations in simulation and physical experiments are similar, and the differences in seed filling rates between the two are not significant, proving the reliability of the calibrated simulation parameters.

To obtain the contact parameters of the moist bulk of shotcrete accurately and quickly, this study calibrated the contact parameters of the moist bulk of shotcrete by physical stacking test and simulation method. Based on the Hertz–Mindlin with JKR (Johnon–Kendall–Roberts) model, the discrete element simulation is carried out. Using P-BD to screen seven initial parameters, it is found that JKR surface energy, rolling friction coefficient between particles and restitution coefficient of particle impact have significant effects on the angle of repose of the moist bulk of shotcrete. According to B-BD, the second-order regression model of angle of repose and significance parameters was established. Three significant parameters were obtained: JKR surface energy 0.418 J/m2, rolling friction coefficient 0.06 and static friction coefficient 1. The angle of repose obtained by simulation is compared with the physical test value, and the relative error is 1.88%. The results show that the calibration method proposed in this study can accurately simulate the physical stacking test, and can provide a reference for the calibration of contact parameters of the moist bulk of shotcrete.

The discrete element method (DEM) for modeling the behavior of particulate material is highly dependent on the use of appropriate and accurate parameters. In this study, a seed metering DEM simulation was used to measure, calibrate, and verify the physical and interactional parameters of rapeseed. The coefficients of restitution and static friction between rapeseeds and three common materials (aluminum alloy, acrylic, and high-density polyethylene) were measured using free drop and sliding ramp tests, respectively. The angle of repose was determined using a hollow cylinder experiment, which was duplicated using a DEM simulation, to examine the effects of static and rolling friction coefficients on the angle of repose. Response surface optimization was performed to determine the optimized model parameters using a Box–Behnken design test. A metering device was made with three materials, and rapeseed seeding was simulated at different working speeds to verify the calibrated parameters. The validation results showed that the relative errors between the seed metering model and experiments for the single qualified seeding, missed seeding, and multiple seeding rates were −0.15%, 3.29%, and 5.37%, respectively. The results suggest that the determined physical and interactional parameters of rapeseed can be used as references for future DEM simulations.

To address the lack of contact and breakage parameters in the discrete element method (DEM) simulation of potato seed cutting and sorting processes, this study took the ‘Atlantic’ potato seed as the research object and constructed a crushable potato model using EDEM. Through physical experiments, the mean average diameter, moisture content, density, Poisson’s ratio, and elastic modulus were measured. The coefficients of collision restitution, static friction, and rolling friction between the potato seed and the Q235 steel plate were determined as 0.576, 0.559, and 0.073, respectively. Using the actual repose angle of 22.89° as the response target, and combining the steepest ascent test with the Box–Behnken design, the non-cohesive contact parameters between potato seed particles were calibrated. The resulting coefficients of collision restitution, static friction, and rolling friction between particles were determined as 0.404, 0.412, and 0.0156, respectively. Finally, based on physical shear tests (maximum shear force 23.56 N), significant influencing factors were identified through Plackett–Burman screening as the bonding radius ratio r and the normal stiffness per unit area Kn. Using the steepest ascent test and the Box–Behnken response surface method, the key bonding parameters of the Bonding V2 model were calibrated as follows: r = 1.098, Kn = 8.597 × 107 N·mm−3, tangential stiffness per unit area Kt = 3.250 × 106 N·mm−3, critical compressive stress σn = 5.500 × 105 Pa, and shear strength τt = 3.000 × 104 Pa. The relative error between the simulated and actual maximum shear forces was 0.89%, which is small. The calibrated flexible model accurately represents the physical characteristics of potato seeds and provides a reliable reference for the design of mechanized potato seed cutting and sorting equipment.

In view of the large difference in moisture content of cotton stalk in autumn in Xinjiang, the existing process of obtaining discrete element simulation parameters of cotton stalk is low in accuracy and complicated in operation, leading to the problems of poor universality and low accuracy in regard to the discrete element simulation parameter-calibration method in the process of mechanized transportation, throwing and returning to the field. Therefore, the experimental study on cotton stalk with different moisture content was carried out with the accumulation angle as the response value, so as to construct a parameter model that can quickly and accurately calibrate cotton stalk with different levels of moisture content. The model has high applicability and flexibility, and it can be widely used in the simulation test of various cotton field-operation machinery, such as a residual film-recycling machine, cotton picker, crushing and returning machine and other equipment. The water content–accumulation angle model was established by the cylinder-lifting method, and the correlation coefficient of the model was 0.9993. Based on EDEM 2020 software, the Hertz–Mindlin model was used to simulate the stacking angle of cotton stalk, and the rolling friction coefficient, static friction coefficient and collision recovery coefficient between cotton stalk and cotton stalk–steel were obtained. Through the Plackett–Burman test, climbing test and Box–Behnken test, three significant parameters, namely the rolling friction coefficient, static friction coefficient and static friction coefficient between cotton stalk and steel, were selected from discrete element simulation parameters to characterize the moisture content of cotton stalk, and the accumulation angle–discrete element parameter model was established. The p-value of the model was less than 0.0001, and the relative error was only 2.67%. Based on the moisture content–stacking angle model and the stacking angle–discrete element parameter model, the moisture content–discrete element parameter model was constructed. The model was verified by the cylinder-lifting method and the plate-drawing method, and the relative error was only 2.79%. Finally, the model was further verified by comparing the effect of the throwing uniformity between the mechanical simulation test and field test, and the relative error was only 4.75%. The test proves that the moisture content–discrete element parameter model is accurate and reliable, not only providing the design basis and support for the mechanization research of cotton stalk conveying and returning to the field in Xinjiang but also providing ideas for the calibration of discrete element simulation parameters of other crop straws.

To establish a fundamental property database for discrete elements targeting long-fiber materials and address the issue of response surface methodology (RSM) being prone to local optima in high-dimensional nonlinear optimization, this study conducted parameter calibration experiments and validated the calibrated parameters through a combined approach of simulation and physical testing. The Plackett–Burman design and steepest ascent test were employed to screen significant factors. Using the angle of repose (42.3°) obtained from physical experiments as the response value, response surface methodology (RSM) and a particle swarm optimization–back propagation (PSO-BP) neural network model were independently applied to optimize and compare the critical parameters. The results demonstrated that the dynamic friction coefficient between wheat straw particles, the static friction coefficient between wheat straw and steel plate, and the JKR surface energy were the most influential factors on the simulated angle of repose. The PSO-BP model exhibited superior optimization performance compared to RSM, yielding an optimal parameter combination of 0.17, 0.46, and 0.03. The simulated repose angle under these conditions was 41.67°, exhibiting a relative error of only 1.5% compared to the physical experiment. These findings provide a robust theoretical foundation for discrete element simulations of wheat straw feedstock.

Evaluation of particle models of corn kernels for discrete element method simulation of shelled corn mass flow

The understanding of the behavior of the particles inside the rotating drum is fundamental for the improvement of its efficiency. By allowing the individual monitoring of each particle, the Lagrangean numerical approach is an excellent tool to aid studies in particulate systems. Thus, the purpose of this work was to determine the combinations of the numerical parameters of the Lagrangean approach that best represent the dynamics of the particles inside a rotating drum for different types of materials under different operating conditions. Experimental methodologies for the determination of the coefficients of restitution, static friction and rolling friction were tested and validated for particle-particle and particle-wall interactions. The experimental values of these coefficients were applied in the model to verify if they would be representative in a bulk effect in the rotatory drum. A calibration process was also performed to determine the best combination of parameters and to compare it with the results of the experimental coefficients. The experimental apparatus used was suitable for the measurement of each of the coefficients. Since the value of the coefficient of restitution depends on the thickness of the material in which the particles are colliding, while in order to determine the coefficient of static friction correctly it is necessary to use the glued spheres to avoid rolling and to ensure correct measurement of the parameter. The values found in the calibration and the values of the measured parameters showed good agreement when compared with the experimental data and the Eulerian approach reported in the literature, for materials of different physical properties under different operating conditions. These were also able to successfully describe the transitional phenomena of different flow regimes. The values found in the calibration process were: 0.80 and 0.50 for the coefficient of static friction, 0.03 and 0.06 for the coefficient of rolling friction, particle-particle and particle-wall respectively, while for the measured experimentally were 0.80 and 0.49 for particle-particle and particle-wall static friction and 0.011 and 0.054 for particle-particle and particle-wall friction respectively. The results were close, showing that the calibration process was able to preserve the physical meanings of the parameters.

This study was undertaken to 1. develop an apparatus to rapidly measure coefficient of friction (COF) on soft contact lenses; 2. determine if COFs measured on two daily-disposable lens models before and after wear are consistent with changes in lens surface morphology observed in parallel atomic force microscopy (AFM) images. Methods: A stress rheometer was adapted to measure COF on a soft contact lens by custom fabrication of a rapid-mount sample stage for increased throughput. Five subjects were randomly assigned to wear daily disposable nesofilcon A and delefilcon A contact lenses bilaterally for 4 hours, after which time lenses were removed. Static and kinetic COFs of lenses worn on left eyes was measured, while lenses worn on right eyes were imaged in parallel by AFM in tapping mode. Root mean square (RMS) surface roughness was calculated for all lenses to determine the effect of wear on surface topography. Results: Both static and kinetic COFs measured on unworn delefilcon A silicone hydrogel lenses were greater than on nesofilcon A traditional hydrogel lenses. Static COF on nesofilcon A increased significantly after wear, while kinetic COF trended higher but did not change significantly. Similarly, static COF on delefilcon A also increased significantly after wear, and kinetic COF trended higher but did not change significantly, both remaining greater than on worn nesofilcon A. Parallel AFM analysis demonstrated that nesofilcon A lenses are smoother than are delefilcon A out of the package. Both lenses attracted deposits during wear, but the nesofilcon A surface was less altered by on-eye wear than was the delefilcon A surface. Conclusion: A system to rapidly measure static and kinetic COFs was successfully developed. Static and kinetic COFs measured on delefilcon A were greater than on nesofilcon A lenses. More deposits and greater surface roughness were observed after wear on delefilcon A relative to nesofilcon A. Parallel AFM images of worn and unworn lenses were not predictive of measured COFs, but increased roughness visible by AFM was consistent with observed increases in COF, although not all increases were statistically significant.

Addressing the problem of lacking accurate and reliable contact parameters and bonding parameters in the simulation of the mashing process during the harvesting of alfalfa, this study takes the stems of alfalfa at the harvesting stage as the research object. The geometric dimensions and related intrinsic parameters of the stems were measured. Using the Enhanced Discrete Element Method (EDEM) software, a multi-scale discrete element flexible bonding model of alfalfa stems was established based on region-specific parameters. The entire alfalfa stem was divided into three parts: the top, middle, and root sections. A multi-scale particle aggregation model of hollow stems was created using the Hertz-Mindlin with bonding model. The contact parameters between alfalfa stems at the harvesting stage and PU rubber were determined using a mathematical model based on quadratic polynomial fitting curves. The results showed that the shear modulus of the top, middle, and root sections of the alfalfa stems were 24.96 MPa, 29.60 MPa, and 10.48 MPa, respectively. The coefficients of restitution between the top, middle, and root sections of the alfalfa stems and PU rubber were 0.426, 0.375, and 0.386, respectively; the static friction coefficients were 0.613, 0.667, and 0.422, respectively; and the rolling friction coefficients were 0.213, 0.226, and 0.292, respectively. The relative error between the simulated and measured values of the angle of repose was less than 3%, effectively representing the mechanical characteristics of alfalfa stems at the harvesting stage bending and breaking under impact. This study aims to establish a discrete element flexible model of alfalfa stems at the harvesting stage and accurately calibrate the contact parameters with typical rubber materials, thereby addressing the lack of reliable bonding and contact parameters in existing simulations of the mashing process.

A discrete phase approach based on individual wheat kernel characteristics is needed to overcome the limitations of previous statistical models and accurately predict the milling behavior of wheat. As a first step to develop a discrete element method (DEM) model for the wheat milling process, this study determined the physical and mechanical properties of wheat mill streams (wheat kernels, break stream, and wheat flour) required as input parameters. The parameters measured were particle size and size distribution, bulk density, Young’s modulus, static and rolling coefficients of friction, and coefficient of restitution. The effect of moisture content (12% to 16% wet basis) on these properties was
\nevaluated. The density, Young’s modulus, and coefficient of restitution tended to decrease while the coefficients of friction tended to increase with increasing moisture content of wheat kernels. The effect of moisture content on material properties was significant for break stream, but there was no significant (p > 0.05) material property change with moisture content for flour. It was concluded that moisture content had a greater significant effect on physical properties (bulk, true, and tapped densities and particle size) of the mill streams than it did on the mechanical properties (Young’s modulus, coefficients of static and rolling friction, and coefficient of restitution).

Material characterization and inter/intra-particle validation for DEM simulation of urea coating process

The study of Leymus chinensis seed cleaning has been hindered by the lack of accurate discrete-element contact parameters for seed–straw interactions, thereby limiting, to some extent, the optimization of cleaning equipment. To address this issue, the present study analyzed a mixture of L. chinensis seeds and straw, and determined their fundamental physical and contact parameters via laboratory experiments. The Hertz–Mindlin (no slip) discrete element simulation model was employed to calibrate the parameters of the seed–straw mixture. A Plackett–Burman test was used to identify key factors significantly affecting the repose angle, including the seed–seed static friction coefficient and the seed–straw static and dynamic friction coefficients. These factors’ optimal ranges were further refined using steepest ascent experiments. A Box–Behnken design was used to optimize contact parameters, resulting in the following values: a seed–seed static friction coefficient of 0.709, a seed–straw static friction coefficient of 0.281, and a seed–straw dynamic friction coefficient of 0.085. Validation experiments demonstrated an error of less than 2.14%, confirming the reliability of the calibrated parameters. This study offers a theoretical foundation for discrete element simulations in L. chinensis seed cleaning applications.

HighlightsThe relationship between the angle of repose and compound fertilizer particle size distribution and sphericity was revealed.The range of the rolling friction coefficient obtained by different modeling was calibrated by the golden section method.Scanning modeling required 80% of the rolling friction coefficient of spherical modeling to reflect actual motion.The relative error of scanning modeling (7.91%) was better than that of spherical modeling (30.84%).Abstract. The discrete element method (DEM) is widely used to simulate the behavior of granular materials. The accurate establishment of the particle model has a great influence on the accuracy of the simulation. Most of the existing discrete element simulations of granular compound fertilizers use spherical modeling without considering the shape or particle size distribution. To compare the simulation accuracy of spherical modeling (spherical particles with equivalent diameters) and scanning modeling (a three-dimensional model of fertilizers was obtained by a scanner and then automatically filled by EDEM2020 software) on compound fertilizer discharge, three kinds of granular compound fertilizers (Changqingshu, Xinshidai, and Munvhong) were selected as the research objects. The characterization parameters of fertilizer shape and fluidity were measured. Principal component analysis and Pearson correlation analysis were used to analyze the influence of the compound fertilizer characterization parameters on the angle of repose. The results showed that the particle shape and particle size distribution of compound fertilizer were the main factors affecting its angle of repose. Through the golden section method and a single-factor experiment, the rolling friction coefficients of the three granular fertilizers under the two granular modeling methods for spherical modeling and scanning modeling were determined. The results showed that the rolling friction coefficient when using scanning modeling to approximate the actual angle of repose was approximately 80% of that when using the spherical modeling method. The influence of different modeling methods on the total rotational kinetic energy and the formation of the angle of repose was discussed. For the same fertilizer, the total rotational kinetic energy was greater in spherical modeling than in scanning modeling, and the formation time of the angle of repose was longer in scanning modeling than in spherical modeling. The results of an external tank wheel fertilization simulation and bench test showed that considering the scanning modeling of fertilizer shape and particle size distribution, the fertilization variation coefficient obtained from the simulation test was closer to that of the bench test. This research helps to better understand the influence of particle shape and particle size distribution on DEM simulations and provides references for discrete element modeling of other granular fertilizers. Keywords: Compound fertilizer, Modeling method, Shape, Simulated flow characteristics, Size distribution.