*6.1. Rotating Cylinder Test*

The rotating cylinder test apparatus is shown in Figure 17a, where the inner diameter of the cylinder is 160 mm and the height is 40 mm. Taking SN42 as an example, the soybean seed particles were first filled through the inlet, and when the height of the soybean seed particle filling in the cylinder reached 40–50 mm, it met the particle filling requirements of the rotating cylinder test, as shown in Figure 17b.

**Figure 17.** (**a**) The rotating cylinder test apparatus and (**b**,**c**) the screenshot of test process.

After the test device was installed, the power supply was connected, and the speed controller was adjusted to make the drum speed 7.5 rpm. After the speed was stable, the soybean seed particles in the drum formed a dynamic repose angle, such as Figure 17c, recording the dynamic piling process for 30 s. The cylinder speed was adjusted to 11.5 and 15.5 rpm, respectively, and the dynamic stacking process was recorded for 30 s. At the end of the test, the soybean seed particles were weighed for mass. Three replicate tests were conducted for each variety.

For the simulated rotating cylinder test, the soybean seed particle model was equal to the actual soybean seed particle mass. Taking SN42 as an example, the drum speed was 7.5 rpm. Figure 18a,b shows the test photo and binarization image, respectively. Figure 18c,d shows the simulation screenshot using the calibration parameters and binarization image, respectively. Figure 18e,f shows the simulation screenshot without considering the rolling friction coefficient and binarization image, respectively.

**Figure 18.** (**a**) The test photo of the rotating cylinder and (**b**) its binarization image; (**c**) simulation result snapshot using calibration parameters and (**d**) its binarization image; and (**e**) simulation result snapshot without considering rolling friction coefficient and (**f**) its binarization image.

Figure 19 shows the dynamic angle of repose versus cylinder speed for each variety. For SN42, the relative errors between the simulation results using the calibration parameters and experimental results were 2.28, 6.93, and 4.78% for rotational speeds of 7.5, 11.5, and 15.5 rpm, respectively, whereas the relative errors between the simulation results ignoring the rolling friction coefficient and experimental results were 13.85, 17.08, and 12.83% for rotational speeds of 7.5, 11.5, and 15.5 rpm, respectively, as shown in Figure 19a.

**Figure 19.** The relationship between dynamic angle of repose and rotational speed for (**a**) SN42, (**b**) JD17, and (**c**) ZD39.

For JD17, the relative errors between the simulation results using the calibration parameters and experimental results were 2.56, 4.1, and 2.84% for rotational speeds of 7.5, 11.5, and 15.5 rpm, respectively, whereas the relative errors between the simulation results ignoring the rolling friction coefficient and experimental results were 7.15, 9.11, and 9.11% for rotational speeds of 7.5, 11.5, and 15.5 rpm respectively, as shown in Figure 19b.

For ZD39, the relative errors between the simulation results using the calibration parameters and experimental results were 2.43, 3.25, and 3.62% for rotational speeds of 7.5, 11.5, and 15.5 rpm, respectively, whereas the relative errors between the simulation results ignoring the rolling friction coefficient and experimental results were 9.55, 6.94, and 7.28% for rotational speeds of 7.5, 11.5, and 15.5 rpm, respectively, as shown in Figure 19c.

The analysis shows that the relative error between the simulation results using calibration parameters and experimental results was small and within the error range of the experimental results. The simulation results without taking the rolling friction coefficient into account were much smaller than the experimental results, and were not within the experimental error range.

#### *6.2. Self-Flow Screening Tests*

According to previous studies, the inclination angles of the self-flow screening devices were 7, 11, and 15◦ for SN42, JD17, and ZD39, respectively. The material of the device was organic glass and the aperture size was 8 mm. Figure 20a–c shows the test photo for self-flow screening, the simulation screenshot using the calibrated parameters, and the simulation screenshot without considering the rolling friction coefficient, respectively.

**Figure 20.** (**a**) The test photo, (**b**) the simulation screenshot using the calibrated parameters, and (**c**) the simulation screenshot without considering the rolling friction coefficient for self-flow screening test.

Figure 21a–c shows comparisons of the simulation results with experimental results of the percentage passing into the five statistic areas for the three varieties. The analysis shows that the simulation results using the calibrated parameters, simulation results without considering the rolling friction coefficient, and experimental results have similar trends.

**Figure 21.** Comparisons of the simulation results with the test results of the percentage passing from different statistic areas in the "self-flow screening" for (**a**) SN42, (**b**) JD17, and (**c**) ZD39.

Further analysis of the percentage passing of the simulation and experimental results for the three varieties is shown in Figure 22.

For the SN42, the simulation results using the calibrated parameter was slightly smaller than the experimental results, with a relative error of 0.7%. The difference between the simulation results ignoring the rolling friction coefficient and experimental results was larger, with a relative error of 3.3%.

For the JD17, the simulation results using the calibrated parameter was slightly smaller than the experimental results, with a relative error of 0.1%. The difference between the simulation results ignoring the rolling friction coefficient and experimental results was larger, with a relative error of 4.9%.

For the ZD39, the simulation results using the calibrated parameter was slightly larger than the experimental results, with a relative error of 0.27%. The difference between the simulation results ignoring the rolling friction coefficient and experimental results was larger, with a relative error of 5.23%.

**Figure 22.** The percentage passing of the simulation and experimental results for three varieties.

Therefore, for the self-flow screening test, the simulation results using the calibrated parameters were closer to the experimental results.

Through the comprehensive analysis of the simulated and experimental results of the rotating cylinder test and self-flow screening test, our results showed that, for the three varieties of soybean seed particles, the simulation results using calibrated parameters were closer to experimental values than simulation results without the rolling friction coefficient. At the same time, the simulation results using the calibrated parameters were within the error range of the experimental results. Therefore, the results of the parameter calibrations in this paper were high in accuracy.

#### **7. Conclusions**

In this paper, the physical parameters of soybean seed particles of different varieties were tested, and the rolling friction coefficients, which could not be measured by test, were determined by calibration methods. The accuracy of the calibration parameters was verified by rotating cylinder test and self-flow screening test. The conclusions are as follows:


In summary, parameters are important for simulation. It is particularly important to select and calibrate the relevant parameters accurately. Though the experimental apparatus in this paper is not necessarily applicable to other research subjects, a similar research methodology could be adopted. In addition, there are various methods for modelling particles when the object of study is a different shape. Due to time constraints, only the multi-sphere method was used to model particles in this paper; therefore, other methods for modelling particles and more in-depth analytical studies on the calibration of parameters should be considered for the next step of research. This paper could provide some reference for relevant areas of inquiry.

**Author Contributions:** Conceptualization, D.Y.; methodology, D.Y.; validation, D.Y. and Y.T.; investigation, K.S. and resources, N.Z. and K.S.; writing—original draft preparation D.Y.; writing—review and editing, Y.W.; supervision, L.Z.; project administration, J.Y.; funding acquisition, D.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors are grateful to the National Natural Science Foundation of China (No. 52130001) for the financial support of this work.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
