Parameter Measurement and Calibration in Discrete Element Simulation of Broken Sweet Potato Seedlings

Corresponding Author: Zhaoqin Lv College of Mechanical and Electrical Engineering, Shandong Agricultural University, Tai’an 271018, China E-mail: lzqsdau2020@163.com Abstract: Given the lack of accurate parameter values in discrete element simulation of sweet potato seedling mechanized recovery, a direct measurement and virtual calibration method was used to study the Discrete Element Method (DEM) simulation parameters of broken sweet potato stems and leaves. The intrinsic parameters, collision recovery coefficient and static friction coefficient of broken seedlings were acquired by physical experiments. Different parameter combinations were designed for DEM simulation. The intrinsic parameters of sweet potato leaves and other unmeasurable DEM simulation parameters were determined by stacking angle optimization simulation. Plackett-Burman test shows that the static friction coefficients of stem-stem and stem-steel and the rolling friction coefficients of stem-stem and stem-leaf all significantly influence the accumulation angle. The parameters that significantly influence the stacking angle of broken seedlings were sent to steepest ascent test and Box-Behnken test. The average stacking angle of 40.51° and the relative error of 0.972% indicate it feasible to calibrate DEM parameters by physical test and optimization simulation and the calibrated parameters can be used in DEM simulation of broken sweet potato stems and leaves.


Introduction
Sweet potato vines are excellent fresh feeds and silage and thus their mechanized recycling has economic and social benefits (Kakahy et al., 2014;Zhao and Gao, 2012;Guizhi et al., 2019). Research on the action mechanism of sweet potato vines and harvesting machinery based on the Discrete Element Method (DEM) provides a theoretical basis for machinery design and optimization. DEM simulation requires many parameters, including intrinsic parameters (e.g., density, shear modulus and Poisson's ratio of sweet potato seedlings) and contact parameters (e.g., collision recovery coefficients, rolling friction coefficients and static friction coefficients between seedling particles and between particles and machine) (Boac et al., 2009;Ucgul et al., 2014;Leblicq et al., 2016). How to determine these parameters is the premise of applying DEM to the research on mechanized recovery of sweet potato vines.
Much research has been conducted to obtain DEM simulation parameters, mainly including direct measurement and virtual calibration (Martin et al., 2003;Horabik and Molenda, 2016;Sweijen et al., 2020). Grima and Wypych (2011) changed a cylinder lifting device to the left and right separation method and calibrated particle discrete element simulation parameters using the improved collapse test. González-Montellano et al. (2012) used direct measurement method to study some parameters in discrete element simulation. Junxiao et al. (2015) simulated straw particle accumulation and mixing movement in the rotating drum and calibrated the discrete element parameters of straw particles by comparison with actual experiments. Santos et al. (2015) obtained the dynamic angle of acerola residue by rotating drum experiment and calibrated the parameters needed in the discrete element simulation based on response surface method. Lee and Park (2019) designed four simulation friction tests to measure the static and rolling friction coefficients between materials and containers.
At present, no scholar has studied the discrete element simulation parameters of sweet potato seedlings. The above studies indicate that the intrinsic parameters of materials can be acquired direct measurement, but directly measuring and obtaining accurate contact parameters is difficult. In this study, physical tests were conducted to obtain the intrinsic parameters of broken sweet potato seedling stems, collision recovery coefficient and the static friction coefficient range of seedling particles. The intrinsic parameters of sweet potato leaves and other unmeasurable discrete element simulation parameters were simulated. The parameters were calibrated by simulation of crushed seedling particle accumulation optimization design. Through the Plackett-Burman test, the steepest climbing test and the Box-Behnken optimization test, the basic contact parameters were calibrated. The simulation data were compared with the physical test data, which provides a reference for the measurement and calibration of discrete element simulation parameters of sweet potato seedlings.

Group Measurement
The broken potato seedlings harvested by a sweet potato seedling recycling machine were classified mainly into broken leaves, short stems and impurities (e.g., dry leaves, weeds, soil blocks). Five groups of mixtures were randomly selected and the average proportions of leaves, stems and impurities were 36.94, 59.2 and 3.85% (very low), respectively. Clearly, seedling leaves and stems were the main particle components used in discrete element simulation. In fact, leaves and short stems were taken as the research objects.
Five samples of crushed sweet potato seedlings were randomly selected after removing impurities. Then leaf areas were measured and calculated using graph paper and the length and diameter of stems were detected using vernier calipers. The coefficients of variation in the measurements of sweet potato leaf area and stem length are larger than 15. The S-W tests show neither the measured leaf areas nor stem lengths satisfy normal distribution. To simplify the modeling, further classification and counting were adopted. The leaves were divided by area into two types: Broken leaves (area >2 cm2) and finelyshredded leaves (area <2 cm2). According to statistics, the average areas of broken leaves and finely-shredded leaves are 2.40 and 1.5 cm 2 , respectively and the coefficients of variation are 6.13 and 4.35%, respectively. The stems were divided by length into long stems (length >20 mm) and short stems (length <20 mm). The average length and diameter of the long stems are 35.73 and 6.7 mm, respectively and the coefficients of variation are 10.06 and 6.77%, respectively. The average length and diameter of the short stems are 14.56 and 4.56 mm, respectively and the coefficients of variation are 8.35 and 3.72%, respectively. The statistical results of mass proportion of each component are shown in Table 1.

Density Measurement
The true density of particles is an important parameter of discrete element simulation. The densities of sweet potato stems and leaves were measured by the overflow equal volume method. Firstly, 50 stems each in length of 20 mm and 50 leaves were randomly selected and every 10 stems and every 10 leaves were bundled together with filaments. Then the stem or leaf quality was measured and the volumes were measured by the immersion method (Fig. 1). Water will overflow after putting the stems in a measuring cup full of pure water. Since the density of fresh sweet potato stems is less than that of water, the top was covered with a flat plate to ensure that all the stems can penetrate water. After the measuring cup was removed, the quality of the overflowing water was measured and the volume of water was calculated, which is the volume of the stems. The average density of sweet potato stems measured from five groups is 987.91 kg/m 3 and the coefficient of variation is 3.34%. The density of sweet potato leaves measured by the same method is 785.36 kg/m 3 and the coefficient of variation is 3.69%.

Determination of Poisson's Ratio of Stems
At each time, a stem with a diameter of about 7 mm in the middle section of a sweet potato seedling at the mature stage was made into a sample with a length of 20 mm (Fig. 2a). The sample was sent to a compression test on a WDW-5E microcomputer controlled universal testing machine (Fig. 2b). The compressive stress-strain curve of each sample was acquired at the loading speed of 5 mm/min and each test was repeated 10 times. The shear modulus of the sweet potato stem calculated at the mature stage is 6 MPa, the elastic modulus is 15.34 MPa, Poisson's ratio is 0.28 and the coefficients of variation are 7. 45, 9.32 and 8.77% respectively.

Determination of Contact Parameters of Crushed Sweet Potato Seedlings Collision Recovery Coefficient
The length-to-diameter ratio of sweet potato stems is large. If free fall collision test is used to measure the collision recovery coefficient, vertical rebound does not easily occur, which seriously affects the measuring accuracy. Hence, the stem-stem/leaf/45 steel collision recovery coefficient was measured by the inclined plate collision method (Huang et al., 2014) and the measurement principle is shown in Fig. 3.
At each time, a stem sample makes a free-fall motion from height h0 and after colliding with the collision material (45 steel, leaf, or stem) installed on the collision slope (vn-instantaneous velocity after particle collision), it makes a parabolic motion and falls on the receiving plate. When the relative height between the collision point o and the receiving plate is h1 (or h2), the measured horizontal displacement of the stem is s1 (or s2). The backward movement only has x-direction displacement. At this time, the coefficient e of restitution between the stem and the inclined plate is calculated as Eq. (1) where, v0-instantaneous velocity before particle collision, mm/s; vx and vy-horizontal and vertical velocity components after particle collision, respectively, mm/s. The v0, vx and vy in Eq.
(2) and (3): A self-made collision coefficient measuring device is shown in Fig. 4. In the measurement of stem-stem recovery coefficient, the tested stem is prone to rotation after colliding with the stem stuck on the collision slope. As a result, displacement occurs in both the x and y directions of the splice plate. This fact is inconsistent with the calculation assumption that the stem has only xdirection displacement. Therefore, a 50-mm-wide layer of glue is applied to the splice plate to "capture" the stem. The stem reduces collision and rebound.
when the stem falls outside the range of the red line on the splicing plate, it is an invalid test and the drop point distribution of the sample is shown in Fig. 4b. Totally 50 stems were selected for measurement, 25 in one group and the height of the splicing plate was changed for two tests. The average value of x-direction displacement was recorded in each group and the recovery coefficient was calculated by Eq. (1)-(3). The measurement and calculation determine that the recovery coefficients of stem-stem, stem-leaf and stem-steel plate collision are 0.32, 0.28 and 0.44, respectively and the coefficients of variation are 6.33, 8.36 and 9.03% respectively.

Static Friction Coefficient
The static friction coefficients of stem-stem, stem-leaf and stem-45 steel were measured by the inclined surface sliding method (Fangyuan et al., 2018). The self-made static friction coefficient measuring instrument mainly consists of a lifting plate and a digital display angle measuring instrument (Fig. 5). Sweet potato stems with similar diameters were pasted on the lifting plate to measure the stem-stem static friction coefficient. During measurement, the lifting plate was slowly lifted until it stopped when the stem slided on the inclined surface. Then the inclination angle of the inclined plate on the digital angle measuring instrument installed on one side was read. The static friction coefficient, μ, is calculated as Eq. (4): where, ɑinclination angle of the inclined plate (°). The measured static friction coefficient between stemstem ranges from 0.2 to 0.8. Clean and tidy sweet potato leaves were pasted on the lifting plate. The static friction coefficients between stem-leaf and between leaf-leaf range from 0.3 to 0.6 and from 0.3 to 0.8 respectively. The static friction coefficients between the stem or leaf and the 45 steel measured by the same method range from 0.3 to 0.8 and 0.3 to 0.7, respectively.

Pile Angle of Crushed Sweet Potato Seedlings
The pile-up angle of broken seedling particles was determined by the cylinder lifting method. The broken seedlings harvested by the sweet potato seedling recovery machine (to remove impurities) were collected as samples. According to the test requirements of the cylinder lifting method (Jia et al., 2014), a steel cylinder with an inner diameter of 160 mm and a height of 480 mm was selected and the steel cylinder filled with crushed seedlings was lifted upward at a speed of 0.05 m/s using a CNC milling machine. A pile of crushed seedling particles was formed on the horizontally-fixed bottom plate (Fig. 6). The experiment was repeated 5 times and the average accumulation angle of the crushed seedlings was measured to be 40.12° and the coefficient of variation was 2.36%.

Model of Broken Sweet Potato Seedlings
To make the broken sweet potato seedling model structurally close to the real broken sweet potato seedling, the geometric model of each component of the broken seedling drawn by SolidWorks was imported into EDEM. Then spherical particles were quickly filled to obtain 4 types of particles, including long-diameter stems (length 30 mm, diameter 7 mm), short-diameter stems (length 15 mm, diameter 5 mm), broken leaves (area 2.4 cm 2 ) and finely-broken leaves (area 1.5 cm 2 ) (Fig. 7).

Simulation of Accumulation Angle of Crushed Sweet Potato Seedlings
In EDEM 2018, a virtual cylinder with an inner diameter of 160 mm and a height of 480 mm was established as a pellet factory. Four types of pellets were set in the pellet factory. The pellet factory type was set to be a dynamic factory. According to the actual proportion of crushed seedlings, the generation speeds of long-diameter rod, short-diameter rod, broken leaf and fine broken-leaf were set as 0.33, 0.29, 0.62 and 0.38 kg/s, respectively and the generation time was 7 s. The contact model between particles was a Hertz-Minglin (no-slip) model. After particles of crushed seedlings were formed, the lifting speed of the cylinder was set at 0.05 m/s. After the particles were stationary on the substrate, a pile of crushed seedlings was formed (Fig. 8).

Screening of Influencing Parameters of Particle Stacking Angle of Broken Sweet Potato seedlings
Many parameters are required to simulate the pile-up angle of the broken seedlings. The stem density, leaf density, shear modulus of stems and Poisson's ratio are 998.91 kg/m 3 , 885.36 kg/m 3 , 6 MPa and 0.28 respectively. The coefficients of collision recovery in stem-stem, stem-leaf and stem-steel plate are 0.32, 0.28 and 0.44 respectively based on the measured values. The shear modulus, Poisson's ratio and density of 45 steels are taken as 0.30 and 7850 kg/m 3 . The coefficient of static friction between the grains of crushed seedlings was determined by the test value to determine the parameter ranges. The 14 parameters such as sweet potato leaf shear modulus, Poisson's ratio, rolling friction coefficient between crushed seedling particles and leaf-leaf/45 steel recovery coefficient cannot be tested easily. The value ranges were determined as reported (Lenaerts et al., 2014;Liao et al., 2020). Plackett-Burman test design was carried out on Design-Expert 8.0.6 to immediately screen out the parameter combinations that significantly impact the test results. The minimum and maximum values of the 14 parameters are coded as -1 and +1 levels respectively (Table 2).
In the Plackett-Burman test, the middle value of the high and low levels was taken as level 0 and a center point test was set up. Totally 21 tests were performed. The test design and results are shown in Table 3. The variance and significance analysis of the test results are shown in Table 4. Clearly, the static friction coefficient of stem-stem x3, the static friction coefficient of stem-steel x5, the rolling friction coefficient of stem-stem x8 and the rolling friction coefficient of stem-leaf x9 all significantly affect the stacking angle. Therefore, in the subsequent steepest climb test and Box-Behnken test, only these 4 significant parameters were considered and the other 10 insignificant factors were taken at the intermediate levels. The values of x1,x2,x4,x6,x7,x10,x11,x12,x13 and x14 are 0.35,253,0.5,0.55,0.5,0.15,0.15,0.15,0.3,0.3 respectively.

Steepest Climb Test
Since the accumulation angle of broken sweet potato seedling particles is enlarged with the increase of 4 significant parameters, 6 sets of steepest climbing experiments were designed and the values of the 4 parameters increased uniformly. The experimental design and results are shown in Table 5. With the gradual increase of the 4 test parameters, the relative error between the simulation and physical test of accumulation angle first decreases and then increases. The relative error of the accumulation angle is the smallest in test No. 3, so the optimal parameter is near test No. 3.

Box-Behnken Test and Analysis of Significant Contact Parameters
In the steepest climbing test, the 4 significance parameters in test No. 3 were taken as the intermediate level (0) and the corresponding parameters in tests No. 2 and No. 4 were taken as the low level (-1) and the high level (+1) respectively. The values of the other 10 parameters are the same as the steepest climbing test. Response surface test was designed on Design-Expert 8.0.6 to obtain the optimal values of the 4 significant contact parameters. The Box-Behnken experiment design and results are shown in Table 6.
The test results in Table 6 were fitted on Design-Expert 8.0.6 and the quadratic regression full model of the broken sweet potato seedling particle packing angle and the 4 significant contact parameters was expressed as Eq. (5) The variance analysis of the model test results is shown in Table 7. The fitted model P<0.0001 and the coefficient of determination R 2 = 0.9938 close to 1 indicate the regression model is extremely significant and can predict the target accumulation angle. The lack of fit term P = 0.181>0.05 and the low coefficient of variation CV = 0.39% indicate the regression equation has a good fit.

Verification and Determination of Simulation Optimal Parameter Combination
With the optimization module in Design-Expert 8.0.6, Eq. (7) was optimized with the tested accumulation angle of 40.12° as the target value. The values of x3, x5, x8 and x9 are 0.41, 0.53, 0.17 and 0.13, respectively. The result is the best when the remaining non-significant parameters are taken at the middle values. To test the accuracy of the optimal parameter combination, the above parameter values were used to carry out 5 particle accumulation simulation tests. The average value of particle accumulation angle of crushed sweet potato seedlings was measured to be 40.51° and the relative error between the accumulation angle 40.12° and the actual physical test was 0.972%, indicating the calibrated granular parameters of crushed seedlings are feasible. The values of each parameter are shown in Table 8.

Conclusion
The stem density of sweet potato measured by the overflow equal volume method is 987.91 kg/m 3 and the coefficient of variation is 3.34%. The leaf density is 785.36 kg/m 3 and the coefficient of variation is 3.69%. The coefficients of recovery from the collision between stem-stem, stem-leaf and stem-steel plate are 0.32, 0.28 and 0.44, respectively and the coefficients of variation are 6.33, 8.36 and 9.03%, respectively. The elastic modulus, shear modulus and Poisson's ratio of the mature sweet potato seedling stems measured by the compression test are 15.34, 6 MPa and 0.28, respectively and the coefficients of variation are 7.45, 9.32 and 8.77%, respectively. Through cylinder lifting method particle accumulation test, the average accumulation angle of broken sweet potato seedlings is 40.51° and the coefficient of variation is 2.36%.
Plackett-Burman simulation shows the static friction coefficient and rolling friction coefficient significantly affect the accumulation angle. Box-Behnken test was performed on the significant parameters on the stacking angle of crushed sweet potato seedlings and a secondorder regression model between stacking angle and significance parameters was established. The optimization was performed with the goal of 40.12° and the optimal solution was obtained. The stem-stem, stem-steel static friction coefficients and the stem-stem, stem-leaf rolling friction coefficients are 0.41, 0.53, 0.17 and 0.13, respectively. With the obtained contact parameters, a simulation test of the particle accumulation of crushed sweet potato seedlings was carried out. The measured average accumulation angle is 38.71° and the relative error between the simulation result and the measured value is 0.972%, indicating the optimal parameter combination is desirable.
Although the accumulation angle of broken sweet potato seedling particles is determined by the typical lifting method, the stalk length of the broken sweet potato seedling particles is relatively large and it is difficult to form a continuous flow boundary. The calibration results may be affected by the calibration test and the shape of the particles.
In the future research, more virtual calibration experiments and particle shapes should be selected to further study the calibration of simulation parameters, so as to establish a discrete element simulation parameter database of crushed sweet potato.