**1. Introduction**

The DEM is widely used in the field of agricultural engineering, and its parameters are crucial to the simulation results [1–10]. For soybean seed particles, parameters play a crucial role in the simulation results when DEM is used to analyze the movement of the particles, the contact interaction between the particles, and between the particles and the boundary.

Nguyen, et al. [11] studied soybean seed particles of one variety, which were approximated as being spherical. The physical properties of the soybean (particle size distribution and weight properties) and the static friction coefficient between the particles and the material surface were determined by test. The rest of the DEM simulation parameters were calibrated by different particle flow tests. In fact, with such a calibration method, there are multiple combinations of parameters that meet the requirements. The applicability of such parameter results needs further analysis when the calibration is performed without determining whether the calibration test is sensitive to only one of the parameters.

Bhupendra et al. [12] used a spherical soybean seed particle as their study object. A set of calibration results were obtained by stacking tests, as follows: the restitution coefficient, static friction coefficient, and rolling friction coefficient between the particles, and the restitution coefficient, static friction coefficient, and rolling friction coefficient between the particles and the boundary. However, the restitution coefficient and static friction coefficient between the particles obtained by calibration were quite different from the actual values. In order to make the simulation closer to the test and accurately analyze the particle

**Citation:** Yan, D.; Yu, J.; Wang, Y.; Sun, K.; Zhou, L.; Tian, Y.; Zhang, N. Measurement and Calibration of DEM Parameters of Soybean Seed Particles. *Agriculture* **2022**, *12*, 1825. https://doi.org/10.3390/ agriculture12111825

Academic Editors: Vadim Bolshev, Vladimir Panchenko and Alexey Sibirev

Received: 14 September 2022 Accepted: 28 October 2022 Published: 1 November 2022

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

population movement, the restitution coefficient and static friction coefficient between the particles can be determined by the test method.

Some scholars [13,14] believe that non-spherical particles do not need to consider the rolling friction coefficient, and only need to calibrate the corresponding sliding friction coefficient to meet testing requirements. However, others believe that the effect of rolling friction coefficient on the test results is significant even for non-spherical particles [15–17]. For soybean seed particles of ellipsoidal shape [18,19], how much the rolling friction coefficient affects the particle population motion and whether the rolling friction coefficient needs to be accurately calibrated requires further study.

Long Zhou [15] demonstrated that the rolling friction coefficient has a significant effect on test results using sensitivity tests during the modeling of different shapes of corn seeds, and further calibrated the rolling friction coefficients between particles, and between particles and boundaries through a piling angle test. For soybean seed particles, the sensitivity of the rolling friction coefficient to the test results needs to be determined further, and the calibration method of the sensitivity parameter also needs to be studied in-depth.

Based on the above problems, in this paper, we verified the importance of the parameters for the first time, and a method for calibrating the above simulation parameters was proposed and verified by tests. Three representative soybean varieties, SN42, JD17, and ZD39, were used in this study. Some parameters of soybean seed particles were measured by test methods. The effect of RFCP-P and RFCP-B on powder motion was analyzed by a repose angle test and self-flow screening simulation. After analyzing the sensitivity of parameters, the test method of parameter calibration was determined and parameter values were calibrated. The accuracy of the parameters was verified using a rotating cylinder test and self-flow screening test. This paper provides some reference for the calibration of parameters for soybean seed particles.

#### **2. Measurement of Soybean Seed Particle Parameters**

In this section, the moisture content, triaxial dimensions, particle density, stiffness coefficient, elasticity modulus, restitution coefficient, and static friction coefficient of soybean seed particles are measured by test measurements; Poisson's ratio is taken to be 0.4, according to reference [20].

#### *2.1. The Moisture Contents of Soybean Seed Particles*

The moisture content of soybean seed particles was measured using XY-102MW type halogen moisture meter (accuracy 0.001), and the test was repeated 5 times for each variety, The moisture content was 10.31, 8.08, and 11.1% for SN42, JD 17, and ZD39, respectively.

#### *2.2. Particle Density of Soybean Seed Particles*

In this paper, the particle density of soybean seeds were measured by the pycnometer method, and the calculation formula is as follows:

$$
\rho\_0 = m\_0 / V\_0 \tag{1}
$$

where *ρ*<sup>0</sup> is the density of soybean seed particles, g/cm3; *m*<sup>0</sup> is the mass of soybean seeds particles, g; *V*<sup>0</sup> is the volume of soybean seed particles, cm3. The formula for the volume of soybean particles is as follows:

$$V\_0 = \frac{(m\_2 - m\_1)(m\_3 - m\_1 - m\_0)}{\rho\_w} \tag{2}$$

where *m*<sup>1</sup> is the mass of the dry specific gravity bottle, g; *m*<sup>2</sup> is the mass of the specific gravity bottle filled with water, g; *m*<sup>3</sup> is the mass of soybean seed particles, water, and specific gravity bottle, g; and *ρ<sup>w</sup>* is the density of water, g/cm3.

#### *2.3. Stiffness Coefficients of Soybean Seed Particles*

The stiffness coefficients of the three varieties were measured using the compression test method [21,22]. As soybean seed particles are ellipsoidal particles with three unequal axes, their stiffness coefficients are different in all directions. Test measurements with three different placement methods (horizontal, lateral, and vertical) are shown in Figure 1. The average value was obtained and used as its final stiffness coefficient.

**Figure 1.** Placement of soybean seed particles.

Taking SN42 as an example, during the loading process, the test force was gradually increased with an increase in deformation before the abrupt change of the test force. The curve is divided into three sections for discussion. In the first section, the deformation (0–0.01 mm) is very small, the test force is small and the growth trend is not obvious; in the second section, the deformation (0.01–0.05 mm) is small, and the test force increases slowly in this range; in the third section, the deformation (0.05–0.4 mm)is larger, and the test force basically grows linearly, as shown in Figure 2.

**Figure 2.** The force–deformation relationship of SN42 soybean seeds.

In our study, the deformation caused by collision during particle movement were within a small range of changes (0.01–0.05 mm) [21]. Therefore, the second section of the curve in the range of smaller deformations was analyzed and processed in this paper. This segment of data was processed in an Excel sheet and a straight line was fitted, as

shown in Figure 3. The slope of this straight line is the stiffness coefficient of the soybean seed particles.

**Figure 3.** The force–deformation relationship of SN42 soybean seeds when the deformation is small.

#### *2.4. Elastic Modulus of Soybean Seed Particles*

The elasticity modulus of soybean seed particles was measured by compression tests [23]. Soybean seed particles are approximately ellipsoidal in shape, so the radii of curvature of soybean seed particles in contact with the upper and lower surfaces of the platen are the same. According to the standard ASAE S368.4 DEC2000 (R2008) [20], the elasticity modulus was calculated as follows:

$$E = \frac{0.338F(1-\mu^2)}{D^{3/2}} \left[ 2K\_{ll} \left( \frac{1}{R} + \frac{1}{R'} \right)^{1/3} \right]^{3/2} \tag{3}$$

where *E* is the modulus of elasticity of soybean seed particles, Pa; *D* is the amount of deformation, mm, which is the middle value of the deformation corresponding to the previous measurement of the stiffness coefficient; *F* is the test force corresponding to the current deformation, N, which can be directly found in the Excel database; *μ* is the Poisson's ratio, with a value of 0.4; *R* and *R'* are the primary and secondary curvature radii when soybean seed particles come in contact with the surface of the plate, m; and *KU* is the coefficient.

#### *2.5. Restitution Coefficient of Soybean Seed Particles*
