Calibration and Testing of Discrete Element Modeling Parameters for Fresh Goji Berries

: This paper aims at the standard grading of fresh goji berries and develops a variable gap-type fresh goji berry grading machine. To establish a complete simulation model, the discrete element parameters of the model were calibrated by a combination of physical experiments and simulation experiments. The outline of the goji berry was extracted by the SFM-CMVS technique, and a goji berry model was obtained using the multi-spherical particle model ﬁlling method in the EDEM software. By designing the free-fall, suspension collision, slope slip, and slope rolling experiments, we obtained the discrete element simulation parameters: the inter-particle collision restitution coefﬁcient was 0.158, the collision restitution coefﬁcient of fresh goji berry–silicone rubber material was 0.195, the static friction coefﬁcient of fresh goji berry–silicone rubber material was 0.377, and the rolling friction coefﬁcient of fresh goji berry–silicone rubber material was 0.063. By designing the steepest ascent search and central composite design experiments with the angle of repose (AoR) value obtained from the physical experiment as the target value (31.27 ◦ ), we determined the inter-particle static friction coefﬁcient to be 0.454 and the inter-particle rolling friction coefﬁcient to be 0.037. Validation tests were conducted on the calibrated discrete element modeling parameters, and the results showed that the established fresh goji berry model and the optimally calibrated parameter combination are effective for discrete element studies on fresh goji berries.


Introduction
Goji berry is a tonic quality Chinese herbal medicine with good health effects and is also one of the characteristic crops in the northwest of China [1]. Currently, processed Chinese goji berry products are sought after by domestic and foreign consumers of all ages, and China's fresh goji berry planting area has exceeded 160,000 hectares. The mechanized grading process of fresh goji berries is crucial to improve their drying quality and economic efficiency, but mature fresh goji berries are characterized by thin skin, tender flesh, and high water content as well as short storage time [2]. There is no grading method for fresh goji berries for the time being.
The grading machines in agriculture can be divided into five types according to their working principles: hole, roller-shaft, wind, weighing, and visual recognition. Li et al. [3,4] designed a vibratory grading machine with a differential queuing method for counting to meet the integrated needs of grading and counting scallop seedlings. The high-speed vibration of the screen affects the activity of scallop seedlings, and it is suitable for grading small and hard-shelled crops. Dai et al. [5] added dual front and rear air ducts to the vibratory grading machine to achieve separation and cleaning of the flax threshing material. Lü et al. [6,7] proposed a roller-shaft grading machine for potato grading. The device controls the grading range by changing the lifting angle through a differential grading device, and the equipment is highly productive. However, the fruit rotates forward in the gap between two rollers, and the friction between them causes damage to the fruit where D p is the equivalent diameter of fresh goji berry (mm); ϕ is the sphericity of fresh goji berry (%); and L, W, and T are the average length, width, and thickness of fresh goji berry, respectively (mm).
Appl. Sci. 2022, 12, x FOR PEER REVIEW the data, the equivalent diameter and sphericity of fresh goji berries were calculat 14.03 mm and 54.24% from Equations (1) and (2). As shown in Figure 1, the fresh go has a distinct ellipsoidal appearance.
where Dp is the equivalent diameter of fresh goji berry (mm); φ is the sphericity goji berry (%); and L, W, and T are the average length, width, and thickness of fr berry, respectively (mm). To measure the intrinsic parameters (Poisson's ratio, shear modulus, and elas ulus) of fresh goji berries, compression experiments were performed on sample berries using a texture analyzer (Stable Micro Systems) in the mechanics laborato In the compression experiment, pressure was applied to the W direction of berry until it reached the maximum critical deformation (Figure 2), and the loadin was 8 mm/min [24]. The loading force and transverse deformation of the sample tained by post-processing, and the longitudinal deformation was measured by a vernier caliper. The Poisson's ratio (ν) of the goji berry can be calculated as 0.420 b tion (3), the elastic modulus (E) can be calculated as 2.217 × 10 6 pa by Equation (4), shear modulus (G) can be calculated as 7.807 × 10 5 pa by Equation (5). To measure the intrinsic parameters (Poisson's ratio, shear modulus, and elastic modulus) of fresh goji berries, compression experiments were performed on samples of goji berries using a texture analyzer (Stable Micro Systems) in the mechanics laboratory.
In the compression experiment, pressure was applied to the W direction of the goji berry until it reached the maximum critical deformation (Figure 2), and the loading speed was 8 mm/min [24]. The loading force and transverse deformation of the sample was obtained by post-processing, and the longitudinal deformation was measured by a digital vernier caliper. The Poisson's ratio (ν) of the goji berry can be calculated as 0.420 by Equation (3), the elastic modulus (E) can be calculated as 2.217 × 10 6 pa by Equation (4), and the shear modulus (G) can be calculated as 7.807 × 10 5 pa by Equation (5).
where ν is the Poisson's ratio of fresh goji berry; ε 1 is the strain in the loading direction; ε 2 is the strain in the vertical direction; L 1 is the original length of the sample (mm); L 2 is the length of the sample after compression (mm); W 1 is the original width of the sample (mm); W 2 is the length of the sample after compression (mm).
where E is the elastic modulus of fresh goji berries (Pa); F is the loading force when the sample reaches the critical elastic deformation state (N); S is the cross-sectional area of the sample, with the cross-sectional approximation of an ellipse (mm 2 ).
where G is the shear modulus of fresh goji berries (Pa).
berry until it reached the maximum critical deformation (Figure 2), and the loadin was 8 mm/min [24]. The loading force and transverse deformation of the sample tained by post-processing, and the longitudinal deformation was measured by vernier caliper. The Poisson's ratio (ν) of the goji berry can be calculated as 0.420 b tion (3), the elastic modulus (E) can be calculated as 2.217 × 10 6 pa by Equation (4), shear modulus (G) can be calculated as 7.807 × 10 5 pa by Equation (5). The intrinsic parameters of the fresh goji berries show that the fresh goji berries are characterized by thin skin and tender flesh. For non-destructive grading of fresh goji berries, we designed the variable gap-type fresh goji berry grading machine.
The variable gap-type fresh goji berry grading machine is mainly composed of the sieving unit, the orientation device, the grading range adjustment component, the frame structure, and the driving component, as shown in Figure 3. In the operation process, the sieving unit is driven forward by the driving component. The fresh goji berries enter the sieve surface and move forward together with the belts, and there is no relative movement between them. The gap between the belts gradually increases from 5 mm to 20 mm. The goji berries fall into the basket through the belt conveyor. Finally, they are divided into several grades according to the size of the horizontal diameter.
Appl. Sci. 2022, 12, x FOR PEER REVIEW where E is the elastic modulus of fresh goji berries (Pa); F is the loading force w sample reaches the critical elastic deformation state (N); S is the cross-sectional ar sample, with the cross-sectional approximation of an ellipse (mm 2 ).
( ) where G is the shear modulus of fresh goji berries (Pa). The intrinsic parameters of the fresh goji berries show that the fresh goji be characterized by thin skin and tender flesh. For non-destructive grading of fresh ries, we designed the variable gap-type fresh goji berry grading machine.

Design of
The variable gap-type fresh goji berry grading machine is mainly compose sieving unit, the orientation device, the grading range adjustment component, th structure, and the driving component, as shown in Figure 3. In the operation pro sieving unit is driven forward by the driving component. The fresh goji berries e sieve surface and move forward together with the belts, and there is no relative mo between them. The gap between the belts gradually increases from 5 mm to 20 m goji berries fall into the basket through the belt conveyor. Finally, they are divi several grades according to the size of the horizontal diameter.

Design of Grading Belt
The belt used for grading is one of the key components of the machine, and is shown in Figure 4. The grading belt has no inner core, so it can be freely bent and To restrain the belt from sagging, there is a belt guide below each belt, and the be in the guide. The material of the belt is silicone rubber. Silicone rubber materials a acterized by non-toxicity, softness, and chemical stability, as well as high elasti material parameters are shown in Table 1 [25,26].

Design of Grading Belt
The belt used for grading is one of the key components of the machine, and its shape is shown in Figure 4. The grading belt has no inner core, so it can be freely bent and driven. To restrain the belt from sagging, there is a belt guide below each belt, and the belt slides in the guide. The material of the belt is silicone rubber. Silicone rubber materials are characterized by non-toxicity, softness, and chemical stability, as well as high elasticity. The material parameters are shown in Table 1 [25,26].   The free-fall experiment was used to calibrate the collision restitution coefficient of fresh goji berry-silicone rubber material [27]. The collision restitution coefficient is calculated by Equation (6).
where Ex1 is the collision restitution coefficient of fresh goji berry-silicone rubber plate; v0 is the normal relative approach velocity of fresh goji berry-silicone rubber plate (mm/s); v1 is the normal relative separation velocity of fresh goji berry-silicone rubber plate (mm/s); g is the acceleration of gravity (980 mm/s 2 ); H0 is the initial height of the goji berry (mm); H1 is the maximum rebound height of the goji berry after collision with silicone rubber plate (mm). The experiment was conducted to release a fresh goji berry from a certain height, and to fell onto a horizontally placed silicone rubber plate. The test process is shown in Figure  5. The highest point where the particle rebound up was captured by a high-speed camera, and the highest point was read by graph paper. Changing the initial release height of goji berry has no significant effect on the collision restitution coefficient, and H0 = 300 mm was selected as the initial condition to carry out the experiment. The collision restitution coefficient was calculated by Equation (6). The experiment was repeated five times, and the results were averaged.  The free-fall experiment was used to calibrate the collision restitution coefficient of fresh goji berry-silicone rubber material [27]. The collision restitution coefficient is calculated by Equation (6).
where Ex 1 is the collision restitution coefficient of fresh goji berry-silicone rubber plate; v 0 is the normal relative approach velocity of fresh goji berry-silicone rubber plate (mm/s); v 1 is the normal relative separation velocity of fresh goji berry-silicone rubber plate (mm/s); g is the acceleration of gravity (980 mm/s 2 ); H 0 is the initial height of the goji berry (mm); H 1 is the maximum rebound height of the goji berry after collision with silicone rubber plate (mm). The experiment was conducted to release a fresh goji berry from a certain height, and to fell onto a horizontally placed silicone rubber plate. The test process is shown in Figure 5. The highest point where the particle rebound up was captured by a high-speed camera, and the highest point was read by graph paper. Changing the initial release height of goji berry has no significant effect on the collision restitution coefficient, and H 0 = 300 mm was selected as the initial condition to carry out the experiment. The collision restitution coefficient was calculated by Equation (6). The experiment was repeated five times, and the results were averaged.  The experiment results show that the average maximum rebound height of goji be is 11.5 mm. Under real test conditions, the collision restitution coefficient of fresh g berry-silicone rubber material was 0.196.

Collision Restitution Coefficient of Fresh Goji Berry-Fresh Goji Berry
To determine the collision restitution coefficient between the fresh goji berry pa cles, two fresh goji berries were selected for a suspension collision experiment [28]. T collision restitution coefficient of fresh goji berry-fresh goji berry was calculated by Equ tion (7).
where Ex2 is the collision restitution coefficient of fresh goji berry-fresh goji berry; H the height of fresh goji berry A being lifted (mm); Ha is the maximum rising height of goji berry A after collision (mm); Hb is the maximum rising height of the goji berry B af collision (mm). As shown in Figure 6, the particles A and B were each attached to a nylon rope w a length of 160 mm, and the two particles were at the same height in the natural hangi state. During the experiment, the natural hanging points of particles A and B w adopted as the base point. We lifted particle A (keeping the nylon rope in a stretched sta to the height in the vertical direction of the base point, and the particle B was in a natu hanging state. Releasing particle A with zero initial velocity, it moved to the base po and collided with particle B, and they swung around the nylon rope with a radius of 1 mm. At this time, the maximum heights of particles A and B from the base point in t vertical direction were Ha and Hb, respectively. The whole process was recorded by a hig speed camera.   The experiment results show that the average maximum rebound height of goji berry is 11.5 mm. Under real test conditions, the collision restitution coefficient of fresh goji berry-silicone rubber material was 0.196.

Collision Restitution Coefficient of Fresh Goji Berry-Fresh Goji Berry
To determine the collision restitution coefficient between the fresh goji berry particles, two fresh goji berries were selected for a suspension collision experiment [28]. The collision restitution coefficient of fresh goji berry-fresh goji berry was calculated by Equation (7).
where Ex 2 is the collision restitution coefficient of fresh goji berry-fresh goji berry; H 2 is the height of fresh goji berry A being lifted (mm); H a is the maximum rising height of the goji berry A after collision (mm); H b is the maximum rising height of the goji berry B after collision (mm). As shown in Figure 6, the particles A and B were each attached to a nylon rope with a length of 160 mm, and the two particles were at the same height in the natural hanging state. During the experiment, the natural hanging points of particles A and B were adopted as the base point. We lifted particle A (keeping the nylon rope in a stretched state) to the height in the vertical direction of the base point, and the particle B was in a natural hanging state. Releasing particle A with zero initial velocity, it moved to the base point and collided with particle B, and they swung around the nylon rope with a radius of 160 mm. At this time, the maximum heights of particles A and B from the base point in the vertical direction were H a and H b , respectively. The whole process was recorded by a high-speed camera. The experiment results show that the average maximum rebound height of goji ber is 11.5 mm. Under real test conditions, the collision restitution coefficient of fresh g berry-silicone rubber material was 0.196.

Collision Restitution Coefficient of Fresh Goji Berry-Fresh Goji Berry
To determine the collision restitution coefficient between the fresh goji berry par cles, two fresh goji berries were selected for a suspension collision experiment [28]. T collision restitution coefficient of fresh goji berry-fresh goji berry was calculated by Equ tion (7).
where Ex2 is the collision restitution coefficient of fresh goji berry-fresh goji berry; H the height of fresh goji berry A being lifted (mm); Ha is the maximum rising height of t goji berry A after collision (mm); Hb is the maximum rising height of the goji berry B af collision (mm). As shown in Figure 6, the particles A and B were each attached to a nylon rope w a length of 160 mm, and the two particles were at the same height in the natural hangi state. During the experiment, the natural hanging points of particles A and B we adopted as the base point. We lifted particle A (keeping the nylon rope in a stretched sta to the height in the vertical direction of the base point, and the particle B was in a natu hanging state. Releasing particle A with zero initial velocity, it moved to the base po and collided with particle B, and they swung around the nylon rope with a radius of 1 mm. At this time, the maximum heights of particles A and B from the base point in t vertical direction were Ha and Hb, respectively. The whole process was recorded by a hig speed camera. Varying the initial release height of particle A had no significant effect on the val of the interparticle collision restitution coefficient, thus H2 = 60 mm was selected as t initial condition for the suspension collision experiments. The experiment results sho that the average maximum rising height of fresh goji berry B was 18.0 mm, and t Varying the initial release height of particle A had no significant effect on the value of the interparticle collision restitution coefficient, thus H 2 = 60 mm was selected as the initial Appl. Sci. 2022, 12, 11629 7 of 23 condition for the suspension collision experiments. The experiment results show that the average maximum rising height of fresh goji berry B was 18.0 mm, and the average maximum rising height of fresh goji berry A was 9.5 mm. After the calculation of Equation (7), the collision restitution coefficient of fresh goji berry-fresh goji berry was 0.150.

Static Friction Coefficient of Fresh Goji Berry-Silicone Rubber Material
The static friction coefficient of fresh goji berry-silicone rubber material was calibrated by the slope slip method. The static friction coefficient of fresh goji berry-silicone rubber material can be calculated by Equation (8).
where µ s1 is the static friction coefficient of fresh goji berry-silicone rubber material; m is the mass of the goji berry (kg); θ is the angle between silicone rubber plate and horizontal direction when the fresh goji berry sliding occurs ( • ). A silicone rubber plate was placed on the support plate to form the experimental slope, as shown in Figure 7. To prevent the single fresh goji berry from rolling on the slope, three fresh goji berries were bonded together and placed on the plate. One side of the slope and the horizontal experimental bench always fit, and we slowly and uniformly lifted the other side. When the fresh goji berries started to slide on the plate, the angle between the plate and the test bench was measured with an angle ruler (range: 0 •~3 60 • , accuracy: 0.05 • ). The slope slip experiment was repeated five times, and the average of the results was taken.
average maximum rising height of fresh goji berry A was 9.5 mm. After the calcul Equation (7), the collision restitution coefficient of fresh goji berry-fresh goji be 0.150.

Static Friction Coefficient of Fresh Goji Berry-Silicone Rubber Material
The static friction coefficient of fresh goji berry-silicone rubber material w brated by the slope slip method. The static friction coefficient of fresh goji berryrubber material can be calculated by Equation (8).
where μs1 is the static friction coefficient of fresh goji berry-silicone rubber mater the mass of the goji berry (kg); θ is the angle between silicone rubber plate and ho direction when the fresh goji berry sliding occurs (°). A silicone rubber plate was placed on the support plate to form the exper slope, as shown in Figure 7. To prevent the single fresh goji berry from rolling on th three fresh goji berries were bonded together and placed on the plate. One sid slope and the horizontal experimental bench always fit, and we slowly and un lifted the other side. When the fresh goji berries started to slide on the plate, th between the plate and the test bench was measured with an angle ruler (range: 0 accuracy: 0.05°). The slope slip experiment was repeated five times, and the averag results was taken. The slope slip experiment results show that the average slope angle was 21.7 der real test conditions, the static friction coefficient of fresh goji berry-silicone material was 0.340.

Rolling Friction Coefficient of Fresh Goji Berry-Silicone Rubber Material
The rolling friction coefficient of fresh goji berry-silicone rubber material w brated by the slope rolling method [28]. In the process of the experiment, without ering the influence of static friction, Equation (9) can be obtained from the law of vation of energy, and the rolling friction coefficient can be calculated from Equati where μr1 is the rolling friction coefficient of fresh goji berry-silicone rubber plate; angle of inclination of the slope (°); S is the rolling distance of the goji berry on th (mm); Y is the rolling distance of the goji berry on the horizontal plate (mm). The slope slip experiment results show that the average slope angle was 21.77 • . Under real test conditions, the static friction coefficient of fresh goji berry-silicone rubber material was 0.340.

Rolling Friction Coefficient of Fresh Goji Berry-Silicone Rubber Material
The rolling friction coefficient of fresh goji berry-silicone rubber material was calibrated by the slope rolling method [28]. In the process of the experiment, without considering the influence of static friction, Equation (9) can be obtained from the law of conservation of energy, and the rolling friction coefficient can be calculated from Equation (10). where µ r1 is the rolling friction coefficient of fresh goji berry-silicone rubber plate; α is the angle of inclination of the slope ( • ); S is the rolling distance of the goji berry on the slope (mm); Y is the rolling distance of the goji berry on the horizontal plate (mm).
As shown in Figure 8, a silicone rubber plate was placed at an inclined angle of 30 • . A fresh goji berry was released along the slope at the initial velocity of 0. The fresh goji berry rolled down along the slope, and the rolling distance of the particle on the slope was 30 mm. Due to the rolling friction, the goji berry rolled on the horizontal plate for a distance, and finally it stood still. The rolling distance (Y) of the particle on the horizontal plate was measured by a tape measure.
Appl. Sci. 2022, 12, x FOR PEER REVIEW r1 S sin α μ = S cos α Y + As shown in Figure 8, a silicone rubber plate was placed at an inclined angl A fresh goji berry was released along the slope at the initial velocity of 0. The fr berry rolled down along the slope, and the rolling distance of the particle on the sl 30 mm. Due to the rolling friction, the goji berry rolled on the horizontal plate fo tance, and finally it stood still. The rolling distance (Y) of the particle on the ho plate was measured by a tape measure. The slope rolling experiment results show that the average horizontal rolling was 237.2 mm, and the rolling friction coefficient of fresh goji berry-silicone rubb rial under real test conditions was 0.057.

Angle of Repose Experiment
The AoR of fresh goji berries was measured by the cylinder lifting method [ poured 1 kg of fresh goji berries from the top of a hollow cylinder. After all of the ing, the hollow cylinder was lifted up at a speed of 5 mm/s. The fresh goji ber naturally due to gravity and gathered at an angle on the silicone rubber plate, as in Figure 9a. We used Python (version 3.7) for grayscale processing (Figure 9b [30]. The average AoR from the phy periment of fresh goji berries was obtained at 31.27°.  The slope rolling experiment results show that the average horizontal rolling distance was 237.2 mm, and the rolling friction coefficient of fresh goji berry-silicone rubber material under real test conditions was 0.057.

Angle of Repose Experiment
The AoR of fresh goji berries was measured by the cylinder lifting method [29]. We poured 1 kg of fresh goji berries from the top of a hollow cylinder. After all of the dumping, the hollow cylinder was lifted up at a speed of 5 mm/s. The fresh goji berries fell naturally due to gravity and gathered at an angle on the silicone rubber plate, as shown in Figure 9a. We used Python (version 3.7) for grayscale processing (Figure 9b As shown in Figure 8, a silicone rubber plate was placed at an inclined angle of 30°. A fresh goji berry was released along the slope at the initial velocity of 0. The fresh goji berry rolled down along the slope, and the rolling distance of the particle on the slope was 30 mm. Due to the rolling friction, the goji berry rolled on the horizontal plate for a distance, and finally it stood still. The rolling distance (Y) of the particle on the horizontal plate was measured by a tape measure. The slope rolling experiment results show that the average horizontal rolling distance was 237.2 mm, and the rolling friction coefficient of fresh goji berry-silicone rubber material under real test conditions was 0.057.

Angle of Repose Experiment
The AoR of fresh goji berries was measured by the cylinder lifting method [29]. We poured 1 kg of fresh goji berries from the top of a hollow cylinder. After all of the dumping, the hollow cylinder was lifted up at a speed of 5 mm/s. The fresh goji berries fell naturally due to gravity and gathered at an angle on the silicone rubber plate, as shown in Figure 9a. We used Python (version 3.7) for grayscale processing (Figure 9b

Simulation Experiments for the Calibration of Contact Parameters
The discrete element parameters were calibrated using the DEM. We built the simulation test models in EDEM 2020 software (DEM Solutions Ltd., Edinburgh, Scotland, UK),

Simulation Experiments for the Calibration of Contact Parameters
The discrete element parameters were calibrated using the DEM. We built the simulation test models in EDEM 2020 software (DEM Solutions Ltd., Edinburgh, Scotland, UK), and designed single-factor simulation experiments. The simulation experiments were performed in the same way as the physical experiments.

Three-Dimensional Reconstruction of the Fresh Goji Berry Model
In order to establish an accurate 3D model of the fresh goji berry and improve the realism of the simulation, we used the structure from motion coupled with clustering views for multi-view stereo (SFM-CMVS) technique to acquire the model of a fresh goji berry [31,32]. The main steps include: image data acquisition, point cloud data pre-processing, point cloud data materialization, mesh partitioning, and mesh filling.
As shown in Figure 10, we selected a fresh goji berry with near-average size and uniform shape as the object, took 128 2D images with an industrial camera, and imported the images into Visual SFM software to obtain the dense point cloud model of the goji berry. The point cloud filter tool of MeshLab software was used to remove noise and redundant points from the point cloud file and extract the contour area of the goji berry. The solid model of the goji berry was obtained by surface fitting the point cloud data, and the solid model was imported into HyperMesh software for meshing. The mesh was filled as a particle template in the EDEM software. The desired fresh goji berry model was obtained by using the modeling method of multiple spherical cells overlapping to form a particle cluster.
OR PEER REVIEW 9 of 23 and designed single-factor simulation experiments. The simulation experiments were performed in the same way as the physical experiments.

Three-Dimensional Reconstruction of the Fresh Goji Berry Model
In order to establish an accurate 3D model of the fresh goji berry and improve the realism of the simulation, we used the structure from motion coupled with clustering views for multi-view stereo (SFM-CMVS) technique to acquire the model of a fresh goji berry [31,32]. The main steps include: image data acquisition, point cloud data pre-processing, point cloud data materialization, mesh partitioning, and mesh filling.
As shown in Figure 10, we selected a fresh goji berry with near-average size and uniform shape as the object, took 128 2D images with an industrial camera, and imported the images into Visual SFM software to obtain the dense point cloud model of the goji berry. The point cloud filter tool of MeshLab software was used to remove noise and redundant points from the point cloud file and extract the contour area of the goji berry. The solid model of the goji berry was obtained by surface fitting the point cloud data, and the solid model was imported into HyperMesh software for meshing. The mesh was filled as a particle template in the EDEM software. The desired fresh goji berry model was obtained by using the modeling method of multiple spherical cells overlapping to form a particle cluster.
Point cloud data materialization Point cloud data pre-processing Acquire 2D images  As with the physical experiment, the simulation experiment was carried out with H0 = 300 mm as the initial condition. The particle displayed a free-fall motion to the silicone

Simulation Experiment for Collision Restitution Coefficient of Fresh Goji Berry-Silicone Rubber Material
As with the physical experiment, the simulation experiment was carried out with H 0 = 300 mm as the initial condition. The particle displayed a free-fall motion to the silicone rubber plate with 0 initial velocity, as illustrated in Figure 11. The contact model between fresh goji berry and silicone rubber material was taken as Hertz-Mindlin (no slip) in the EDEM software. When setting the contact parameters between the fresh goji berry and contact material, the static friction coefficient and rolling friction coefficient had no effect on the rebound height of the particle; hence, these two parameters were set to 0.
l. Sci. 2022, 12 Table 2 presents the design scheme and results of the simulation experiment, wh the collision restitution coefficient (Ex1) was considered as a factor and the highest bound height (H1) was adopted as an index. As shown in Figure 12, a semicircular hollow pipe with a diameter of 320 mm w added to the EDEM software. In the pipe, two particles were generated at the bottom a 60 mm from the base point in the vertical direction. The intrinsic parameters of the p did not have a significant effect on the experimental process, so the pipe intrinsic para eters were set to be the same as the silicone rubber material. The collision restitution co ficient, static friction coefficient, and rolling friction coefficient were set to 0.  Table 2 presents the design scheme and results of the simulation experiment, where the collision restitution coefficient (Ex 1 ) was considered as a factor and the highest rebound height (H 1 ) was adopted as an index. As shown in Figure 12, a semicircular hollow pipe with a diameter of 320 mm was added to the EDEM software. In the pipe, two particles were generated at the bottom and 60 mm from the base point in the vertical direction. The intrinsic parameters of the pipe did not have a significant effect on the experimental process, so the pipe intrinsic parameters were set to be the same as the silicone rubber material. The collision restitution coefficient, static friction coefficient, and rolling friction coefficient were set to 0.
As shown in Figure 12, a semicircular hollow pipe with a diameter of 320 mm was added to the EDEM software. In the pipe, two particles were generated at the bottom and 60 mm from the base point in the vertical direction. The intrinsic parameters of the pipe did not have a significant effect on the experimental process, so the pipe intrinsic parameters were set to be the same as the silicone rubber material. The collision restitution coefficient, static friction coefficient, and rolling friction coefficient were set to 0.  Table 3 presents the design scheme and results of the simulation experiment, where the collision restitution coefficient (Ex2) was considered as a factor and the highest rising heights were adopted as indexes.  Table 3 presents the design scheme and results of the simulation experiment, where the collision restitution coefficient (Ex 2 ) was considered as a factor and the highest rising heights were adopted as indexes. A rectangular body (500 mm in length, 500 mm in width, and 10 mm in height) was added in the EDEM software, and its intrinsic parameters were set to be the same as those of the silicone rubber material. A multi-sphere combination method was used to generate three combined particles to simulate the bonded fresh goji berries under real test conditions, as illustrated in Figure 13. The collision restitution coefficient of fresh goji berry-silicone rubber material was taken to be the calibrated value of 0.195, and the rolling friction coefficient was taken to be 0. Appl  A rectangular body (500 mm in length, 500 mm in width, and 10 mm in height) was added in the EDEM software, and its intrinsic parameters were set to be the same as those of the silicone rubber material. A multi-sphere combination method was used to generate three combined particles to simulate the bonded fresh goji berries under real test conditions, as illustrated in Figure 13. The collision restitution coefficient of fresh goji berrysilicone rubber material was taken to be the calibrated value of 0.195, and the rolling friction coefficient was taken to be 0. θ Figure 13. Simulation experiment for calibrating the static friction coefficient of fresh goji berrysilicone rubber material.
In the simulation experiment, one side of the plate was always attached to the ground, and the other side was slowly raised at a speed of 2°/s. When the particles started to slide, the slope inclination (θ) was read by the post-processing module. Table 4 presents In the simulation experiment, one side of the plate was always attached to the ground, and the other side was slowly raised at a speed of 2 • /s. When the particles started to slide, the slope inclination (θ) was read by the post-processing module. Table 4 presents the design scheme and results of the simulation experiment.

Simulation Experiment for Rolling Friction Coefficient of Fresh Goji Berry-Silicone Rubber Material
A plate with an inclined angle of 30 • and a horizontally placed plate were added in the EDEM software, with the bottom end of the inclined plate touching the horizontally placed plate ( Figure 14). The intrinsic parameters of the two plates were set in the software to be the same as those of the silicone rubber material. In setting the simulation parameters, the collision restitution coefficient and the static friction coefficient of fresh goji berry-silicone rubber material were taken as the calibrated values above, that is, Ex 1 = 0.195, µ s1 = 0.377. Appl A plate with an inclined angle of 30° and a horizontally placed plate were added in the EDEM software, with the bottom end of the inclined plate touching the horizontally placed plate (Figure 14). The intrinsic parameters of the two plates were set in the software to be the same as those of the silicone rubber material. In setting the simulation parameters, the collision restitution coefficient and the static friction coefficient of fresh goji berrysilicone rubber material were taken as the calibrated values above, that is, Ex1 = 0.195, μs1 = 0.377. α Y Figure 14. Simulation experiment for calibrating the rolling friction coefficient of fresh goji berrysilicone rubber material. A fresh goji berry particle was generated at a distance of S = 30 mm along the inclined flat surface, and the particle rolled down the sloping surface with an initial velocity of 0. When the particle was stationary, the rolling distance (Y) of the particle on the horizontally placed plate was measured. Table 5 presents the design scheme and results of the simulation experiment.  A fresh goji berry particle was generated at a distance of S = 30 mm along the inclined flat surface, and the particle rolled down the sloping surface with an initial velocity of 0. When the particle was stationary, the rolling distance (Y) of the particle on the horizontally placed plate was measured. Table 5 presents the design scheme and results of the simulation experiment.

Simulation of the Angle of Repose
The AoR simulation experiment is the same as the physics experiment. A particle factory was set up on top of the hollow cylinder, and particles were generated at a rate of 0.2 kg/s for a total of 1 kg. Particles of different sizes were generated according to a normal distribution. In the simulator module, the Rayleigh time step was set to 20%, the simulation time was set to 30 s, the data writing time step was 0.5 s, and the grid cell size was two times the minimum particle radius.
After stabilization, the cylinder was lifted vertically upward at a speed of 0.005 m/s, and a stable pile of particles was formed on a horizontally placed silicone rubber plate, as illustrated in Figure 15. Eventually, the AoR image was processed, and the angle value was read by the same method as the physical experiment.

Central Composite Design Experiment
To determine the optimal value interval of each factor, we performed a steep cent search experiment. The experiment was carried out with the inter-particle stat tion and rolling friction coefficients as the factors, and the relative error between the ured AoR and the simulated AoR as the index. The relative error of AoR is calculat Equation (11).
where ε is the relative error of AoR between simulation and physical experiment (% the physical experiment value of AoR (°); γ is the simulation experiment value of A After extensive pre-simulation experiments, the inter-particle static friction cient was determined to range from 0.450 to 0.550, and the inter-particle rolling fr coefficient was determined to range from 0.030 to 0.040. The Design-Expert V12 sof (Stat-Ease Inc., Minneapolis, MN, USA) was used to design a central composite d experiment. Table 6 presents the scheme and results of the central composite desi periment. Table 6. Design scheme and results of central composite design experiment. (μs2 is the static f coefficient of fresh goji berry-fresh goji berry, and μr2 is the rolling friction coefficient of fre berry-fresh goji berry.)

Central Composite Design Experiment
To determine the optimal value interval of each factor, we performed a steepest ascent search experiment. The experiment was carried out with the inter-particle static friction and rolling friction coefficients as the factors, and the relative error between the measured AoR and the simulated AoR as the index. The relative error of AoR is calculated by Equation (11).
where ε is the relative error of AoR between simulation and physical experiment (%); β is the physical experiment value of AoR ( • ); γ is the simulation experiment value of AoR ( • ). After extensive pre-simulation experiments, the inter-particle static friction coefficient was determined to range from 0.450 to 0.550, and the inter-particle rolling friction coefficient was determined to range from 0.030 to 0.040. The Design-Expert V12 software (Stat-Ease Inc., Minneapolis, MN, USA) was used to design a central composite design experiment. Table 6 presents the scheme and results of the central composite design experiment.

Validation Tests
To verify that the above calibrated simulation parameters can be applied to the simulation of the grading machine, validation tests were performed. The geometric model of the grading machine is shown in Figure 16. The model was drawn at a 1:1 scale using SolidWorks 2019 software and saved in "-*.igs" format and imported into EDEM software.

Validation Tests
To verify that the above calibrated simulation parameters can be applied to the simulation of the grading machine, validation tests were performed.

Discrete Element Simulation of the Grading Process
The geometric model of the grading machine is shown in Figure 16. The model was drawn at a 1:1 scale using SolidWorks 2019 software and saved in "-*.igs" format and imported into EDEM software. In the EDEM software, the goji berry-belt contact model was set as a Moving Plane model, the goji berry-goji berry contact model was a Liner Spring model, and the contact model of the goji berry with other components was a Hertz-Mindlin (no-slip) model [33]. In the simulator module, the Rayleigh time step was set to 20%. The simulation time and output frequency were 30 s and 0.01 s, respectively. The size of the grid cells was given as two times the minimum particle radius. The material properties and contact parameters in the simulation model were calibrated values, as shown in Table 7.  In the EDEM software, the goji berry-belt contact model was set as a Moving Plane model, the goji berry-goji berry contact model was a Liner Spring model, and the contact model of the goji berry with other components was a Hertz-Mindlin (no-slip) model [33]. In the simulator module, the Rayleigh time step was set to 20%. The simulation time and output frequency were 30 s and 0.01 s, respectively. The size of the grid cells was given as two times the minimum particle radius. The material properties and contact parameters in the simulation model were calibrated values, as shown in Table 7.  5. The experiment was prepared by randomly picking 20 kg of fresh goji berries at the goji berry planting base, which were cleaned, air-dried, and inspected for damage, as shown in Figure 17a. The prototype is shown in Figure 17b. The device started feeding after stable operation. The field experiment was carried out with continuous feeding, and the motor speed of the feeding conveyor was controlled by a frequency converter to adjust the feeding volume of fresh goji berries. The timing started when the goji berries reached the sieving unit, and the motor was switched off after 30 s. The graded goji berries were collected for manual measurement and the grading accuracy was calculated.

Evaluation Index
The grading accuracy was used to describe the accuracy of the machine when screening fresh goji berries. A larger value indicates a higher percentage of correctly graded goji berries. As shown in Figure 18, the red box shows the goji berries mixed with other sizes, and the more goji berries mixed with other sizes, the lower the grading accuracy. The grading accuracy can be calculated from Equation (12).
100% N (12) where N is the total mass of fresh goji berries entering the grading machine from the feeding device (kg); qi (i = 1, 2,…, 5) is the mass of fresh goji berries going out from the discharge device of each level (kg); N1 is the total mass of fresh goji berries meeting the specifications of each level after grading (kg); y is the grading accuracy of the machine (%).

Grading belt running direction
Goji berry discharge direction Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ  The prototype is shown in Figure 17b. The device started feeding after stable operation. The field experiment was carried out with continuous feeding, and the motor speed of the feeding conveyor was controlled by a frequency converter to adjust the feeding volume of fresh goji berries. The timing started when the goji berries reached the sieving unit, and the motor was switched off after 30 s. The graded goji berries were collected for manual measurement and the grading accuracy was calculated.

Evaluation Index
The grading accuracy was used to describe the accuracy of the machine when screening fresh goji berries. A larger value indicates a higher percentage of correctly graded goji berries. As shown in Figure 18, the red box shows the goji berries mixed with other sizes, and the more goji berries mixed with other sizes, the lower the grading accuracy. The grading accuracy can be calculated from Equation (12).
where N is the total mass of fresh goji berries entering the grading machine from the feeding device (kg); q i (i = 1, 2, . . . , 5) is the mass of fresh goji berries going out from the discharge device of each level (kg); N 1 is the total mass of fresh goji berries meeting the specifications of each level after grading (kg); y is the grading accuracy of the machine (%). The prototype is shown in Figure 17b. The device started feeding after stable operation. The field experiment was carried out with continuous feeding, and the motor speed of the feeding conveyor was controlled by a frequency converter to adjust the feeding volume of fresh goji berries. The timing started when the goji berries reached the sieving unit, and the motor was switched off after 30 s. The graded goji berries were collected for manual measurement and the grading accuracy was calculated.

Evaluation Index
The grading accuracy was used to describe the accuracy of the machine when screening fresh goji berries. A larger value indicates a higher percentage of correctly graded goji berries. As shown in Figure 18, the red box shows the goji berries mixed with other sizes, and the more goji berries mixed with other sizes, the lower the grading accuracy. The grading accuracy can be calculated from Equation (12).
100% N (12) where N is the total mass of fresh goji berries entering the grading machine from the feeding device (kg); qi (i = 1, 2,…, 5) is the mass of fresh goji berries going out from the discharge device of each level (kg); N1 is the total mass of fresh goji berries meeting the specifications of each level after grading (kg); y is the grading accuracy of the machine (%).

Determination of Collision Restitution Coefficient of Fresh Goji Berry-Silicone Rubber Material
To clarify the relationship between the maximum rebound height and the collision restitution coefficient, we fitted the experimental data in Table 2 using Origin software (Version 2017). Figure 19a shows the fitting curve with the fitting equation expressed as Equation (13).
where X 1 is the collision restitution coefficient of fresh goji berry-silicone rubber material; Y 1 is the maximum rebound height of the goji berry after collision with the silicone rubber plate (mm).

Determination of Collision Restitution Coefficient of Fresh Goji Berry-Silicone Rubber Material
To clarify the relationship between the maximum rebound height and the collision restitution coefficient, we fitted the experimental data in Table 2 using Origin software (Version 2017). Figure 19a shows the fitting curve with the fitting equation expressed as Equation (13).
where X1 is the collision restitution coefficient of fresh goji berry-silicone rubber material; Y1 is the maximum rebound height of the goji berry after collision with the silicone rubber plate (mm). The coefficient of determination (R 2 ) of the curve was 0.9992, which was close to 1, indicating that the fitting equation was accurate and reliable. The average maximum rebound height of the physical experiment (11.5 mm) was substituted into the fitting Equation (13) to obtain X1 = 0.195. Three repetitions of the free-fall simulation experiment were performed using a collision restitution coefficient of 0.195, and Figure 19b shows the height-time curve of the particle motion. The maximum rebound heights of fresh goji berries were read by the post-processing module of the software as 11.587 mm, 11.696 mm, and 11.532 mm. The average value of 11.605 mm was taken, which had a relative error of 0.91% with the rebound height obtained from the physical experiment. This indicates that the calibrated simulation results are consistent with the physical experimental results, so the collision restitution coefficient of fresh goji berry-silicone rubber material was determined to be 0.195.

Determination of Collision Restitution Coefficient of Fresh Goji Berry-Fresh Goji Berry
To clarify the relationship between the maximum rising heights and the collision restitution coefficient, we fitted the experimental data in Table 3 with Origin software. Figure  20a shows the fitting curve with the fitting equation expressed as Equation (14). The coefficient of determination (R 2 ) of the curve was 0.9992, which was close to 1, indicating that the fitting equation was accurate and reliable. The average maximum rebound height of the physical experiment (11.5 mm) was substituted into the fitting Equation (13) to obtain X 1 = 0.195. Three repetitions of the free-fall simulation experiment were performed using a collision restitution coefficient of 0.195, and Figure 19b shows the height-time curve of the particle motion. The maximum rebound heights of fresh goji berries were read by the post-processing module of the software as 11.587 mm, 11.696 mm, and 11.532 mm. The average value of 11.605 mm was taken, which had a relative error of 0.91% with the rebound height obtained from the physical experiment. This indicates that the calibrated simulation results are consistent with the physical experimental results, so the collision restitution coefficient of fresh goji berry-silicone rubber material was determined to be 0.195.

Determination of Collision Restitution Coefficient of Fresh Goji Berry-Fresh Goji Berry
To clarify the relationship between the maximum rising heights and the collision restitution coefficient, we fitted the experimental data in Table 3 with Origin software. Figure 20a shows the fitting curve with the fitting equation expressed as Equation (14).
where X 2 is the collision restitution coefficient of fresh goji berry-fresh goji berry; Y 2 is the maximum rising height of fresh goji berry A (mm); Y 3 is the maximum rising height of fresh goji berry B (mm). where X2 is the collision restitution coefficient of fresh goji berry-fresh goji berry; Y2 is the maximum rising height of fresh goji berry A (mm); Y3 is the maximum rising height of fresh goji berry B (mm).
Simulation results of particle B Y 3 = −4.310X 2 2 +62.068X 2 +9.073 Adjust The coefficient of determination (R 2 ) of the two curves were 0.9687 and 0.9943, respectively. The measured values from the physical experiment were substituted into Equation (14) to obtain X2 = 0.158. Three repetitions of the suspension collision simulation experiment were performed using a collision restitution coefficient of 0.158, and Figure  20b shows the height-time curve of the motion of the two particles. The average value of Ha was 9.703 mm and the average value of Hb was 18.67 mm. The relative errors with the heights obtained from the physical experiment were 2.14% and 3.72%, respectively. This indicates that the calibrated simulation results are consistent with the physical experimental results, so the collision restitution coefficient of fresh goji berry-fresh goji berry was determined to be 0.158.

Determination of Static Friction Coefficient of Fresh Goji Berry-Silicone Rubber Material
To clarify the relationship between the critical sliding angle and the static friction coefficient, we fitted the experimental data in Table 4 with Origin software. Figure 21a shows the fitting curve with the fitting equation expressed as Equation (15 (15) where X3 is the static friction coefficient of fresh goji berry-silicone rubber material; Y4 is the angle between the silicone rubber plate and horizontal direction when the fresh goji berry sliding occurs (°). The coefficient of determination (R 2 ) of the two curves were 0.9687 and 0.9943, respectively. The measured values from the physical experiment were substituted into Equation (14) to obtain X 2 = 0.158. Three repetitions of the suspension collision simulation experiment were performed using a collision restitution coefficient of 0.158, and Figure 20b shows the height-time curve of the motion of the two particles. The average value of H a was 9.703 mm and the average value of H b was 18.67 mm. The relative errors with the heights obtained from the physical experiment were 2.14% and 3.72%, respectively. This indicates that the calibrated simulation results are consistent with the physical experimental results, so the collision restitution coefficient of fresh goji berry-fresh goji berry was determined to be 0.158.

Determination of Static Friction Coefficient of Fresh Goji Berry-Silicone Rubber Material
To clarify the relationship between the critical sliding angle and the static friction coefficient, we fitted the experimental data in Table 4 with Origin software. Figure 21a shows the fitting curve with the fitting equation expressed as Equation (15).
where X 3 is the static friction coefficient of fresh goji berry-silicone rubber material; Y 4 is the angle between the silicone rubber plate and horizontal direction when the fresh goji berry sliding occurs ( • ). The coefficient of determination (R 2 ) of the curve was 0.9918. We substituted the a erage inclination angle of the physical experiment (21.77°) into Equation (15) to obtain = 0.377. Three repetitions of the slope slip simulation experiment were performed using static friction coefficient of 0.377, and Figure 21b shows the velocity-time curve of t particle motion. The angles were read by the post-processing module of the software 21.146°, 21.025°, and 20.859°. The average value of 21.010° was taken, which had a relati error of 3.49% with the angle obtained from the physical experiment. This indicates th the calibrated simulation results are consistent with the physical experimental results, the static friction coefficient of fresh goji berry-silicone rubber material was determin to be 0.377.

Determination of Rolling Friction Coefficient of Fresh Goji Berry-Silicone Rubber Materia
To clarify the relationship between the horizontal rolling distance and the rolling fr tion coefficient, we fitted the experimental data in Table 5 with Origin software. Figu 22a shows the fitting curve with the fitting equation expressed as Equation (16).
where X4 is the rolling friction coefficient of fresh goji berry-silicone rubber material; Y5 the horizontal rolling distance of the goji berry (mm). The coefficient of determination (R 2 ) of the curve was 0.9948. The average rolling d tance of the physical experiment (237.2 mm) was substituted into Equation (16) to obta X4 = 0.063. Three repetitions of the slope rolling simulation experiment were perform using a rolling friction coefficient of 0.063, and Figure 22b shows the rolling distance-tim curve of the particle motion. The rolling distances were read by the post-processing mo ule of the software as 236.025 mm, 230.667 mm, and 233.159 mm. The average value 233.284 mm was taken, which had a relative error of 1.65% with the rolling distance o tained from the physical experiment. This indicates that the calibrated simulation resu are consistent with the physical experimental results, so the rolling friction coefficient fresh goji berry-silicone rubber material was determined to be 0.063. The coefficient of determination (R 2 ) of the curve was 0.9918. We substituted the average inclination angle of the physical experiment (21.77 • ) into Equation (15) to obtain X 3 = 0.377. Three repetitions of the slope slip simulation experiment were performed using a static friction coefficient of 0.377, and Figure 21b shows the velocity-time curve of the particle motion. The angles were read by the post-processing module of the software as 21.146 • , 21.025 • , and 20.859 • . The average value of 21.010 • was taken, which had a relative error of 3.49% with the angle obtained from the physical experiment. This indicates that the calibrated simulation results are consistent with the physical experimental results, so the static friction coefficient of fresh goji berry-silicone rubber material was determined to be 0.377.

Determination of Rolling Friction Coefficient of Fresh Goji Berry-Silicone Rubber Material
To clarify the relationship between the horizontal rolling distance and the rolling friction coefficient, we fitted the experimental data in Table 5 with Origin software. Figure 22a shows the fitting curve with the fitting equation expressed as Equation (16).
where X 4 is the rolling friction coefficient of fresh goji berry-silicone rubber material; Y 5 is the horizontal rolling distance of the goji berry (mm). The coefficient of determination (R 2 ) of the curve was 0.9948. The average rolling distance of the physical experiment (237.2 mm) was substituted into Equation (16) to obtain X 4 = 0.063. Three repetitions of the slope rolling simulation experiment were performed using a rolling friction coefficient of 0.063, and Figure 22b shows the rolling distancetime curve of the particle motion. The rolling distances were read by the post-processing module of the software as 236.025 mm, 230.667 mm, and 233.159 mm. The average value of 233.284 mm was taken, which had a relative error of 1.65% with the rolling distance obtained from the physical experiment. This indicates that the calibrated simulation results are consistent with the physical experimental results, so the rolling friction coefficient of fresh goji berry-silicone rubber material was determined to be 0.063.

Determination of Static and Rolling Friction Coefficients of Fresh Goji Berry-Fresh Goji Berry
The ANOVA of the regression model for the central composite design experiment is shown in Table 8. The overall fitting degree of the regression model was p < 0.0001, the lack of fit term was p = 0.0684, and the coefficient of determination (R 2 ) was 0.9845. The regression model was significant, the lack of fit term was not significant, and the coefficient of determination was close to 1, indicating a good fit of the regression model. All factors that have a significant effect on the index have been taken into account, and we obtained well-fitted and analytically meaningful regression: Equation (17)  The AoR value obtained from the physical experiment was used as the target value (31.27°), and the optimization module of Design-Expert software was used to make the simulation results closest to the target value. The regression model was optimally solved with the constrained objectives (Equation (18)).

Determination of Static and Rolling Friction Coefficients of Fresh Goji Berry-Fresh Goji Berry
The ANOVA of the regression model for the central composite design experiment is shown in Table 8. The overall fitting degree of the regression model was p < 0.0001, the lack of fit term was p = 0.0684, and the coefficient of determination (R 2 ) was 0.9845. The regression model was significant, the lack of fit term was not significant, and the coefficient of determination was close to 1, indicating a good fit of the regression model. All factors that have a significant effect on the index have been taken into account, and we obtained well-fitted and analytically meaningful regression: Equation (17). The AoR value obtained from the physical experiment was used as the target value (31.27 • ), and the optimization module of Design-Expert software was used to make the simulation results closest to the target value. The regression model was optimally solved with the constrained objectives (Equation (18)). Finally, we obtained the fresh goji berry-fresh goji berry static friction and rolling friction coefficients as 0.454 and 0.037.

Validation Tests
To verify the accuracy of the calibrated discrete element simulation parameters, field experiments and simulation tests of the machine were conducted. We performed three simulations for the parameters determined in Table 7, and the simulation process is shown in Figure 23. Eventually, we obtained an average grading accuracy of 95.67% for the model. Finally, we obtained the fresh goji berry-fresh goji berry static friction and rol friction coefficients as 0.454 and 0.037.

Validation Tests
To verify the accuracy of the calibrated discrete element simulation parameters, f experiments and simulation tests of the machine were conducted. We performed th simulations for the parameters determined in Table 7, and the simulation process is sho in Figure 23. Eventually, we obtained an average grading accuracy of 95.67% for model. Mass Moreover, the result of the field tests is shown in Figure 24, and the average grad accuracy of the field tests was 94.43%. The error of the grading accuracy between sim tion and field experiments was 1.31%. The results show that the calibrated discrete ment simulation model is applicable to the discrete element simulation of fresh goji ries.
Ⅰ Ⅲ Ⅱ Ⅳ Moreover, the result of the field tests is shown in Figure 24, and the average grading accuracy of the field tests was 94.43%. The error of the grading accuracy between simulation and field experiments was 1.31%. The results show that the calibrated discrete element simulation model is applicable to the discrete element simulation of fresh goji berries. Finally, we obtained the fresh goji berry-fresh goji berry static friction and friction coefficients as 0.454 and 0.037.

Validation Tests
To verify the accuracy of the calibrated discrete element simulation paramete experiments and simulation tests of the machine were conducted. We perform simulations for the parameters determined in Table 7, and the simulation process i in Figure 23. Eventually, we obtained an average grading accuracy of 95.67% model. Moreover, the result of the field tests is shown in Figure 24, and the average accuracy of the field tests was 94.43%. The error of the grading accuracy between tion and field experiments was 1.31%. The results show that the calibrated disc ment simulation model is applicable to the discrete element simulation of fresh ries.

Discussion
One crucial step to ensure the accuracy of the model is inputting accurate simulation parameters. Through Newton's second law, Newton's third law, and Hertz-Mindlin contact theory, we can know that the main parameters affecting the accuracy of the model are the intrinsic parameters and the contact parameters. In this paper, we took fresh goji berry as the research object, and the discrete element parameter acquisition models were established on the basis of creating a simulation model of fresh goji berries. We used a method that combines physical and simulation experiments, where all discrete element modeling parameters were obtained sequentially. However, it should be noted that due to the wide variety of fresh goji berries and the wide distribution of physical properties, the shape and volume of the particles vary greatly among the different varieties. In this paper, only the Ningqi No.5. mature fresh goji berry, which is widely planted in China, is the subject of study. The discrete element modeling parameters need to be recalibrated if the experimental subject changes.

Conclusions
(1) For the accurate and non-destructive grading of fresh goji berries, we designed a variable gap-type fresh goji berry grading machine. The key component of the machine, the grading belt, was made of silicone rubber material. (2) Intrinsic parameters such as the triaxial size, density, Poisson's ratio, elastic modulus, and shear modulus of fresh goji berries were determined by physical experiments. By free-fall, suspension collision, slope slip, and slope rolling experiments, the collision restitution, static friction, and rolling friction coefficients of fresh goji berry-silicone rubber material were determined to be 0.196, 0.340, and 0.057, respectively. The collision restitution coefficient of fresh goji berry-fresh goji berry was 0.150. (3) We used the SFM-CMVS technique to extract the outline of the goji berry, and we obtained the dense point cloud and fitted model of the goji berry. The model was meshed to obtain a 3D model of the fresh goji berry, which was used in EDEM. A discrete element simulation particle model of fresh goji berry was established by using the multi-sphere particle aggregation method. (4) By simulation, the collision restitution, static friction, and rolling friction coefficients of fresh goji berry-silicone rubber material were calibrated to 0.195, 0.377, and 0.063, respectively; the collision restitution coefficient of fresh goji berry-fresh goji berry was calibrated to 0.158. We designed the steepest ascent search and central composite design experiments to calibrate the static friction and rolling friction coefficients of fresh goji berry-fresh goji berry to 0.454 and 0.037. (5) Validation tests were conducted on the calibrated discrete element parameters, and the results showed that the grading accuracy obtained from the simulation model matched that under real test conditions.
This study aims to determine the discrete element parameters required in the model for the mechanized grading process of fresh goji berries, and to provide a DEM simulation model of fresh goji berries to fill the gaps in the study of parameters and models of fresh goji berries. Meanwhile, the study provides the theoretical basis for the design and optimization of the variable gap-type fresh goji berry grading machine.

Patents
One Chinese invention patent applied for: CN112317325A.