Optimization of the Fluted Force-Feed Seeder Meter with the Helical Roller Using the Discrete Element Method and Response Surface Analysis

: The seed metering process of a ﬂuted force-feed seeder was simulated using the Discrete Element Method and its parameters optimized using the Box–Behnken Design of Experiments and the Response Surface Method. The rotational speed of the feed roller, the lead (helix) angle of the ﬂutes, and the number of ﬂutes were the independent variables, while the response value was the seeding uniformity index. Two regression models were investigated, and the following conclusions drawn. For the ﬂute lead angle between 0 and 10 degrees, and the number of ﬂutes between 10 and 14, it was found that the number of ﬂutes and the lead angle inﬂuenced the seeding performance the most, with the order of importance being the (i) number of ﬂutes, (ii) lead angle and (iii) roller speed. For the ﬂute lead angle between 5 and 15 degrees, and the number of ﬂutes between 12 and 16, it was found that the roller speed and the number of ﬂutes inﬂuenced the seeding performance the most, with the order of importance being the (i) roller speed, (ii) number of ﬂutes and (iii) ﬂute lead angle. The two regression models were then minimized for the seeding uniformity index and the corresponding optima veriﬁed experimentally on a conveyor belt test stand ﬁtted with an image recognition system.


Introduction
Wheat is cultivated annually on over 220 million hectares worldwide, accounting for about 30% of the world's grain planting area, exceeding that of corn, rice, and soybean [1]. Wheat is mainly drill sown, which ensures a high yield and high sowing productivity [2,3]. The design and performance of drill seeders play an important role in seed utilization and crop yield [4], with the seed meter being their key component. Due to their simplicity, small size and stable indexing, most seed-metering devices are of the fluted force-feed type, with either straight or helical flutes [5][6][7]. Fluted rollers are commonly sold as standalone, generic components, separate from the rest of the seed-metering device [8].
In the case of straight-flute rollers, the seed flow is pulsated [9]. By contrast, helicalflute rollers can maintain a near continuous seed flow, with reduced pulsation, thus providing uniform and stable seeding [10]. Extensive research has been conducted on the optimization of the fluted force-feed seed-metering devices and on the effect of the parameters affecting their sowing performance. Yu et al. added an elastic scrapper to a straight-flute roller, which eliminated the driving layer and force sowing [11]. Zhang et al. optimized the size of the straight-flute rollers through simulation [12]. Singh et al. designed and optimized a fluted force-feed seeder for cotton sowing [13]. Liu et al. analyzed the influence of the working length of the feed roller on the seed flow uniformity and found that the longer the working length of the feed roller, the better the seeding performance [14].
Most wheat seeders use fluted seed-metering rollers, and research into how to improve their performance and optimize their parameters remains of interest to engineers and researchers. In the reports published so far [14,15], the influence of only one parameter at a time has been investigated. This paper moves the research forward and reports on the use of the Discrete Element Method (DEM) and Response Surface Analysis (RSA) for the optimization of three separate parameters of the helical-flute rollers used in force-feed wheat seeding, namely the rotational speed of the roller, flute lead (helix) angle and number of flutes.

Design and Operation of the Fluted Force-Feed Seed Metering Devices
The main components of a force-feed seeder with a helical-flute roller are shown in Figure 1. These include a feed cup, feed roller, cutoff block, feed shaft, seed-cleaning brush, and check ring. The feed roller assembles with the feed shaft through a positioning sleeve, which locates axially the feed roller along the feed shaft. The end face of the seed protection arc plate contacts the seed-cleaning brush, and the arc surface contacts the helical feed roller.
Agriculture 2023, 13, x FOR PEER REVIEW 2 of 16 straight-flute rollers through simulation [12]. Singh et al. designed and optimized a fluted force-feed seeder for cotton sowing [13]. Liu et al. analyzed the influence of the working length of the feed roller on the seed flow uniformity and found that the longer the working length of the feed roller, the better the seeding performance [14]. Most wheat seeders use fluted seed-metering rollers, and research into how to improve their performance and optimize their parameters remains of interest to engineers and researchers. In the reports published so far [14,15], the influence of only one parameter at a time has been investigated. This paper moves the research forward and reports on the use of the Discrete Element Method (DEM) and Response Surface Analysis (RSA) for the optimization of three separate parameters of the helical-flute rollers used in force-feed wheat seeding, namely the rotational speed of the roller, flute lead (helix) angle and number of flutes.

Design and Operation of the Fluted Force-Feed Seed Metering Devices
The main components of a force-feed seeder with a helical-flute roller are shown in Figure 1. These include a feed cup, feed roller, cutoff block, feed shaft, seed-cleaning brush, and check ring. The feed roller assembles with the feed shaft through a positioning sleeve, which locates axially the feed roller along the feed shaft. The end face of the seed protection arc plate contacts the seed-cleaning brush, and the arc surface contacts the helical feed roller. During operation, the feed shaft rotates the fluted roller together with the check ring. The cutoff block and the check ring prevent the seeds from escaping through the sides of the feed roller [16]. The seeds stored in the feed cup fill the flutes due to gravity. With the rotation of the feed roller, the seeds in the flute enter the seed-cleaning area, while the seed-cleaning brush removes the extra seeds. Those remaining in the flute enter the seed-protection area through the seed-cleaning area. After passing the seed-protection area, the seeds enter the seed-delivery area, where they fall via gravity into the seed bed through the seed delivery pipe. The seeding rate can be adjusted by changing the position of the feed roller along the feed shaft.
The overall goal of optimizing the seed-metering operation is to improve the uniformity of the seeds falling into the seed bed, as they are discharged by the seed-metering device and During operation, the feed shaft rotates the fluted roller together with the check ring. The cutoff block and the check ring prevent the seeds from escaping through the sides of the feed roller [16]. The seeds stored in the feed cup fill the flutes due to gravity. With the rotation of the feed roller, the seeds in the flute enter the seed-cleaning area, while the seed-cleaning brush removes the extra seeds. Those remaining in the flute enter the seed-protection area through the seed-cleaning area. After passing the seed-protection area, the seeds enter the seed-delivery area, where they fall via gravity into the seed bed through the seed delivery pipe. The seeding rate can be adjusted by changing the position of the feed roller along the feed shaft.
The overall goal of optimizing the seed-metering operation is to improve the uniformity of the seeds falling into the seed bed, as they are discharged by the seed-metering device and are delivered into the furrow opener or seed ditch, through the seed delivery pipe. The seed delivery pipe must have sufficient flexibility to accommodate the required opener lifting, ground profiling and row spacing adjustment. Commonly, seed delivery pipes are metal-coil pipes, steel pipes, corrugated pipes, folded pipes, etc., and their total length is determined by the planter design. The total length, adjustment setting, and inner wall geometry of the seed delivery pipe interfere with the seed flow; these effects, however, will not be accounted for in the present research.
The geometry of a helical-flute feed roller is shown in Figure 2. The roller is provided with an axial hole which fits the hexagonal feed shaft. By changing the number of flutes n f , their depth b and radius r, the volume of one single flute will change. Additionally, by modifying the lead angle of the flute helix and the rotational speed of the roller, the flow uniformity of the seeds delivered by the meter can be adjusted. For an outer radius of the roller R = 30 mm, the values of the flute radius r and flute depth b correlate with the number of flutes n f , as shown in Table 1. In this study, the rotation speed ω of the roller was taken as between 30 and 50 RPM, consistent with the recommendations of the Chinese Academy of Agricultural Mechanization Sciences [17]. The lead angle of the flute β was taken as between 0 and 15 degrees, while the working length of the feed roller was kept constant at h = 30 mm. are delivered into the furrow opener or seed ditch, through the seed delivery pipe. The seed delivery pipe must have sufficient flexibility to accommodate the required opener lifting, ground profiling and row spacing adjustment. Commonly, seed delivery pipes are metal-coil pipes, steel pipes, corrugated pipes, folded pipes, etc., and their total length is determined by the planter design. The total length, adjustment setting, and inner wall geometry of the seed delivery pipe interfere with the seed flow; these effects, however, will not be accounted for in the present research. The geometry of a helical-flute feed roller is shown in Figure 2. The roller is provided with an axial hole which fits the hexagonal feed shaft. By changing the number of flutes nf, their depth b and radius r, the volume of one single flute will change. Additionally, by modifying the lead angle of the flute helix and the rotational speed of the roller, the flow uniformity of the seeds delivered by the meter can be adjusted. For an outer radius of the roller R = 30 mm, the values of the flute radius r and flute depth b correlate with the number of flutes nf, as shown in Table 1. In this study, the rotation speed ω of the roller was taken as between 30 and 50 RPM, consistent with the recommendations of the Chinese Academy of Agricultural Mechanization Sciences [17]. The lead angle of the flute β was taken as between 0 and 15 degrees, while the working length of the feed roller was kept constant at h = 30 mm.  The parametric equations for the flute helix (see Figure 3) as a function of the feedroller length H, lead angle β, lead L, and roller radius R are: where θ is the polar angle in radians. As they are transported by the fluted force-feed seeder meter, the wheat seeds go through three stages: seed filling, seed clearing and seed protecting [18]. Simplified force analyses of these three stages are shown in Figure 4. Before the seeds enter the flute of the feed roller  The parametric equations for the flute helix (see Figure 3) as a function of the feed-roller length H, lead angle β, lead L, and roller radius R are: where θ is the polar angle in radians. moving from the seed cup, they are acted upon by their own weight G and by the resultant force F due to the contact with the seeds above.
(a) (b)   As they are transported by the fluted force-feed seeder meter, the wheat seeds go through three stages: seed filling, seed clearing and seed protecting [18]. Simplified force analyses of these three stages are shown in Figure 4. Before the seeds enter the flute of the feed roller moving from the seed cup, they are acted upon by their own weight G and by the resultant force F due to the contact with the seeds above. moving from the seed cup, they are acted upon by their own weight G and by the resultant force F due to the contact with the seeds above.
(a) (b)   After the flutes are filled with wheat seeds, and as the roller rotates, excess seeds are removed by the seed-cleaning brush ( Figure 4b). The acting forces are gravitational force G, flute contact force F m and seed-cleaning brush force F n . After the seed clearing, the remainder seeds will rotate together with the roller, and their centroids will project below the edge of the flute.
In the seed-protection stage (Figure 4c), the seeds move on a circular path together with the feed roller. Due to the space limitation, the seeds remain stationary relative to the flute, and their movement and speed are the same as those of the roller. At this stage, the seeds are acted upon by gravity G and by the contact force with the flute F m . Also shown in Figure 4c, marked with F c , the centripetal force upon one seed caused by the rotation of the feed roller.

Simulation of the Seed-Metering Process
The Discrete Element Method simulation software EDEM 2018 [19,20] was used to simulate the fluted force-feed seeder seed-metering process. The wheat grains were treated as discrete elements, and their constrained motion by the meter was solved by applying Newton's Second Law. The shape and size of the wheat grains affect the pulsation of the fluted force-feed seeder. In this paper, the dimensions of the wheat variety Dingxi 35 cultivated in China's Gansu Province were measured and analyzed statistically. Their measured lengths, widths and thicknesses ranged between 6.02 and 7.10 mm, 2.53 and 3.89 mm, and 2.67 and 3.43 mm, respectively. As the width and thickness were very close values, the shape of one wheat grain was approximated with an ellipsoid with the long and short axes equal to 6.50 mm and 3.20 mm, respectively ( Figure 5a). In addition, the mass of 1000 seeds was measured to be 41.5 g. Each wheat grain was assumed to be made of a homogeneous, linear elastic material [21]. Their ellipsoidal shape was approximated with spherical particles, as shown in Figure 5a [22,23]. A three-dimensional model of the seeder was created in Pro/E 5.0 and imported into the EDEM software (see Figure 5b). To facilitate the computer simulation and reduce the CPU time, the parts of the fluted force-feed seeder that do not contact the wheat grains were removed from the simulation. After the flutes are filled with wheat seeds, and as the roller rotates, excess seeds are removed by the seed-cleaning brush ( Figure 4b). The acting forces are gravitational force G, flute contact force Fm and seed-cleaning brush force Fn. After the seed clearing, the remainder seeds will rotate together with the roller, and their centroids will project below the edge of the flute.
In the seed-protection stage (Figure 4c), the seeds move on a circular path together with the feed roller. Due to the space limitation, the seeds remain stationary relative to the flute, and their movement and speed are the same as those of the roller. At this stage, the seeds are acted upon by gravity G and by the contact force with the flute Fm. Also shown in Figure 4c, marked with Fc, the centripetal force upon one seed caused by the rotation of the feed roller.

Simulation of the Seed-Metering Process
The Discrete Element Method simulation software EDEM 2018 [19,20] was used to simulate the fluted force-feed seeder seed-metering process. The wheat grains were treated as discrete elements, and their constrained motion by the meter was solved by applying Newton's Second Law. The shape and size of the wheat grains affect the pulsation of the fluted force-feed seeder. In this paper, the dimensions of the wheat variety Dingxi 35 cultivated in China's Gansu Province were measured and analyzed statistically. Their measured lengths, widths and thicknesses ranged between 6.02 and 7.10 mm, 2.53 and 3.89 mm, and 2.67 and 3.43 mm, respectively. As the width and thickness were very close values, the shape of one wheat grain was approximated with an ellipsoid with the long and short axes equal to 6.50 mm and 3.20 mm, respectively (Figure 5a). In addition, the mass of 1000 seeds was measured to be 41.5 g. Each wheat grain was assumed to be made of a homogeneous, linear elastic material [21]. Their ellipsoidal shape was approximated with spherical particles, as shown in Figure 5a [22,23]. A three-dimensional model of the seeder was created in Pro/E 5.0 and imported into the EDEM software (see Figure 5b). To facilitate the computer simulation and reduce the CPU time, the parts of the fluted force-feed seeder that do not contact the wheat grains were removed from the simulation. Since the normal and tangential dissipative forces between wheat grains are small, the Hertz-Mindlin non-sliding contact model was employed to analyze their movement inside the fluted force-feed seeder [24]. The main external forces acting on the wheat grains were gravity and the contact forces with the feed roller. The physical parameters and contact parameters of each material in the DEM simulation are summarized in Tables 2 and 3 [18,[25][26][27][28][29], with the fluted force-feed seeder cup and the seed-cleaning brush being assumed to be made of high-density plastic. Since the normal and tangential dissipative forces between wheat grains are small, the Hertz-Mindlin non-sliding contact model was employed to analyze their movement inside the fluted force-feed seeder [24]. The main external forces acting on the wheat grains were gravity and the contact forces with the feed roller. The physical parameters and contact parameters of each material in the DEM simulation are summarized in  Tables 2 and 3 [18,[25][26][27][28][29], with the fluted force-feed seeder cup and the seed-cleaning brush being assumed to be made of high-density plastic.  In order to prevent the wheat grains from being counted repeatedly when extracting the simulation data, a control volume was defined around the fluted force-feed seeder (see Figure 5). The lower boundary of this control volume was chosen such that all the wheat grains exiting the meter were captured.
A selection of five simulation frames of the metering process are shown in Figure 6. At time t = 5 s, seeds have just finished filling the flutes and the feed roller starts rotating. At t = 5.05 s, the process of seed cleaning has been completed, the first flute has passed the seed-cleaning brush, and the seed protecting has started. When the simulation reaches t = 5.1 s, under the effect of gravity, centrifugal force and pressure from other seeds, the seeds in the flute are transferred into the seeding area and the seed speed begins to increase. At time t = 5.15 s of the simulation, the first seed reaches the outlet of the fluted force-feed seeder and falls into the seed-delivery pipe. To make the seeding process continuous, the seed counting started at t = 5 s and the seeds were counted as they exited the control volume every 0.05 s. The counted seeds served to calculate the uniformity index CI of the seed metering using the following equation [30,31]: where x i is the number of seeds per each sample (in the simulation experiment, the number of seeds per sample is the seeds discharged by the feed roller rotating for 5 cycles), N is the number of samples, x is the average seed count, and σ is the standard deviation of the seed count.  In order to prevent the wheat grains from being counted repeatedly when extracting the simulation data, a control volume was defined around the fluted force-feed seeder (see Figure 5). The lower boundary of this control volume was chosen such that all the wheat grains exiting the meter were captured.
A selection of five simulation frames of the metering process are shown in Figure 6. At time t = 5 s, seeds have just finished filling the flutes and the feed roller starts rotating. At t = 5.05 s, the process of seed cleaning has been completed, the first flute has passed the seedcleaning brush, and the seed protecting has started. When the simulation reaches t = 5.1 s, under the effect of gravity, centrifugal force and pressure from other seeds, the seeds in the flute are transferred into the seeding area and the seed speed begins to increase. At time t = 5.15 s of the simulation, the first seed reaches the outlet of the fluted force-feed seeder and falls into the seed-delivery pipe. To make the seeding process continuous, the seed counting started at t = 5 s and the seeds were counted as they exited the control volume every 0.05 s. The counted seeds served to calculate the uniformity index CI of the seed metering using the following equation [30,31]: where xi is the number of seeds per each sample (in the simulation experiment, the number of seeds per sample is the seeds discharged by the feed roller rotating for 5 cycles), N is the number of samples, ̄ is the average seed count, and σ is the standard deviation of the seed count.  The main factors affecting the performance of the fluted force-feed seed meter were the flute lead angle, the number of flutes and the rotation speed of the roller. A Box-Behnken [32] Design of Experiments was implemented, having as the independent variables the roller speed (ω), lead angle (β) and number of flutes (n f ), while the response value was the seed uniformity index CI in Equation (2). Two groups of three factors and three levels were selected [33]. The factor-level codes are shown in Table 4 [26]. A total of 34 groups of response tests were carried out, as shown in Table 5. Each group with the factor codes ω*, β* and n f * in Table 5 was simulated three times, and the average of the three values was taken as the test result. To save time, the 26 distinct DEM simulations in Table 5 were performed concomitantly on 13 different computers, i.e., two simulations per computer. The time required to perform one simulation was, on average, 95 h on a Windows 10 computer equipped with an Intel(R) Core (TM) i5-7500 CPU processor at 3.40 GHz.

Results and Discussion
With the help of Design-Expert 8.06 [34,35], the quadratic regression model of the seeding uniformity index for the first group of experiments was obtained as: An analysis of variance and significance test of the regression coefficient were carried out for the above model, and the results are summarized in Table 6. It can be seen that the p-value of the regression model is less than 0.01, indicating that the relationship between the regression equations and the experiment is extremely significant [36]. The linear terms β (lead angle) and n f (number of flutes) of the model have a very significant effect on the seeding uniformity index, while ω (rotation speed) has no significant effect. The quadric term has a negligible effect on the seeding uniformity index, while the interaction term β·n f has a significant effect, and the interaction items ω·β and ω·n f have no significant effect on the seeding uniformity index. According to the regression coefficient of each term, and of the respective p-value, the factors affecting the uniformity index of the seed metering were, in order of importance, the number of flutes (n f ), the lead angle (β) and the rotational speed of the roller (ω). Using Design-Expert 8.06 software, the regression Equation (3) was minimized, resulting in a minimum uniformity index CI of 1.23%. The corresponding optimum parameters were ω = 33.38 RPM, lead angle β = 9.91 • , and number of flutes n f = 14.
Using the same Equation (3), the response surface plots of the relationships among the various factors were created, and the strength of the interaction terms was evaluated based on the shape of these plots [37,38], i.e., ellipses indicate significant interaction between the two factors, while circles indicate the opposite. Figure 7a is a plot of the response surface (3) for the feed-roller speed between 30 and 50 RPM, and the flute lead angle between 0 and 10 • , while the number of flutes was held constant and equal to 12. It can be concluded that the influence of the lead angle on the uniformity index of the seed metering is more significant than the rotational speed, which is consistent with the analysis of variance results. With the increase in the rotational speed and in the lead angle, the uniformity index of the seed metering gradually decreases, the main reason being that the increase in the rotation speed reduces the distance between adjacent wheat grains. At the same time, with the increase in the lead angle, the distance between the wheat grains in the upper part and lower part of the flute will be reduced, thus decreasing the seeding uniformity index. Figure 7b is a plot of the response surface (3) for the feed-roller speed between 30 and 50 RPM, and the number of flutes between 10 and 14, while the flute lead angle was held fixed at 5 degrees. According to this plot, the seeding uniformity index is influenced more by the number of flutes than by the RPM of the feed roller, which is consistent with the analysis of variance results. When the rotation speed is held constant and the number of flutes changes from 10 to 14, the seeding uniformity index gradually decreases. With the increase in the rotating speed, the seeding uniformity index gradually decreases. When the rotation speed is held constant at 50 RPM, and the number of flutes is kept equal to 14, the seeding uniformity index remains essentially unchanged.    (3) for the flute lead angle between 0 and 10 degrees, and the number of flutes between 10 and 14, while the roller speed is maintained constant at 40 RPM. When the lead angle is constant, by increasing the number of flutes, the seeding uniformity gradually decreases, which is consistent with the analysis of variance results. The seeding uniformity remained virtually unchanged when the number of flutes was held equal to 10 and the lead angle varied between 0 to 10 degrees, and similarly when the lead angle was held constant at 10 degrees and the number of flutes varied between 10 and 14. Figure 7c also shows that the seeding uniformity index reached a minimum when the lead angle was equal to 10 degrees and the number of flutes was equal to 14.
Using the same Design-Expert 8.06 software, the quadratic regression model of the seeding uniformity index for the second set of experiments was obtained as: The results of the analysis of variance of the regression model in Equation (4) are gathered in Table 7. It can be seen that the p-value is less than 0.01, indicating that the relationship between the regression equations and the results of the virtual experiments is extremely significant. Among them, the linear term ω (rotation speed of the roller) has an extremely significant influence on the seeding uniformity index, while the quadric terms β (lead angle) and n f (the number of flutes) have a negligible effect. The quadratic terms ω 2 , β 2 , and n f 2 have a significant effect, and the interaction terms ω·β, ω·n f and β·n f have no significant effect on the seeding uniformity index. According to the regression coefficient and p-value of each factor in the model, the seeding uniformity index is influenced by ω (rotation speed), followed by n f (number of flutes) and then by β (flute lead angle). Using Design-Expert 8.06, Equation (4) was minimized, resulting in a minimum seeding uniformity index CI of 1%. The corresponding optimum parameters were lead angle = 10 degrees, number of flutes = 14, and rotational speed of the roller = 40 RPM. Figure 8a is a plot of the response surface (4) for the feed-roller speed ranging between 30 and 50 RPM, and the lead angle of the flute between 5 • and 15 • , while the number of flutes was held constant and equal to 14. As this plot shows, with the increase in the roller speed, the seeding uniformity index gradually decreases. When the lead angle varies from 5 • to 15 • , the seeding uniformity index decreases first and then increases, with a minimum value occurring around β = 10 • . This is because when the lead angle is small, pulsation occurs, while when the lead angle is large and the rotation speed is increased, the seeds are not saturated or caused to pile up. In addition, the inertial forces tend to bring out the seeds toward the edges, which reduces the seed-metering stability.   Figure 8b is the simulated response surface in Equation (4) for the feed-roller speed between 30 and 50 RPM, the number of flutes between 12 and 16, and a fixed lead angle equal to 10 • . The figure reveals that with the increase in the rotation speed, the seeding uniformity index gradually decreases and then increases again. When the number of flutes varies between 12 and 16, the seeding uniformity index first increases and then decreases, which is similar in effect to the feed-roller speed changing in the range from 30 to 50 RPM. The main reason for this behavior is that when the number of flutes increases, the seeds fill the flutes, which reduces the pulsation phenomenon and ensures the stability of the seed metering. When the number of flutes is too big, however, the flutes cannot be filled with seeds, which results in the pulsation phenomenon. Figure 8c is a plot of the simulated response surface in Equation (4) for the flute lead angle ranging between 5 degrees and 15 degrees, and the number of flutes ranging between 12 and 16, while the feed roller speed is maintained equal to 40 RPM. The figure shows that with the increase in the lead angle and the number of flutes, the seeding uniformity index decreases first and then increases, with the response surface assuming a concave shape, with a minimum occurring for the number of flutes equal to 14 and the lead angle equal to 10 • . This is similar to the trend observed in the first set of response surface experiments, when the number of flutes ranged between 10 and 14. The reason is that with the increase in the number of flutes, the distance between two adjacent flutes decreases, but when the number of flutes is big and the rotational speed increases, the flutes will not fully fill with seeds. When the seeding speed is increased, the seeding uniformity is first improved and then worsens.

Experimental Verification
To validate the proposed numerical simulation, experimental tests were performed using Dingxi 35 wheat seeds in the Laboratory of Dry Farming Agricultural Equipment Engineering of Gansu Province. A JPS-12 seed-metering performance test bench, manufactured by Heilongjiang Agricultural Equipment Technology Co. Ltd. (Harbin, China), was employed ( Figure 9). A speed control system was implemented to the test bench motor, which allowed the rotational speed of the feed roller to be modified according to the test plan. The helical-flute feed rollers were 3D printed out of high-toughness resin ( Figure 10).  (4) for the flute lead angle ranging between 5 degrees and 15 degrees, and the number of flutes ranging between 12 and 16, while the feed roller speed is maintained equal to 40 RPM. The figure shows that with the increase in the lead angle and the number of flutes, the seeding uniformity index decreases first and then increases, with the response surface assuming a concave shape, with a minimum occurring for the number of flutes equal to 14 and the lead angle equal to 10°. This is similar to the trend observed in the first set of response surface experiments, when the number of flutes ranged between 10 and 14. The reason is that with the increase in the number of flutes, the distance between two adjacent flutes decreases, but when the number of flutes is big and the rotational speed increases, the flutes will not fully fill with seeds. When the seeding speed is increased, the seeding uniformity is first improved and then worsens.

Experimental Verification
To validate the proposed numerical simulation, experimental tests were performed using Dingxi 35 wheat seeds in the Laboratory of Dry Farming Agricultural Equipment Engineering of Gansu Province. A JPS-12 seed-metering performance test bench, manufactured by Heilongjiang Agricultural Equipment Technology Co. Ltd. (Harbin, China), was employed (Figure 9). A speed control system was implemented to the test bench motor, which allowed the rotational speed of the feed roller to be modified according to the test plan. The helicalflute feed rollers were 3D printed out of high-toughness resin ( Figure 10).   . Experimental setup with: 1 test bench for the seed-metering device, 2 control deck, 3 fluted force-feed seeder metering device, 4 seed-sticking oil, 5 brush, and 6 oil nozzle. To prevent the seeds from splashing as they fell onto the conveyor belt of the test bench, an oil nozzle was installed in front of the seed-metering device. The nozzle allowed a layer of sticking oil with a width of about 100 mm to be applied to the conveyor belt To prevent the seeds from splashing as they fell onto the conveyor belt of the test bench, an oil nozzle was installed in front of the seed-metering device. The nozzle allowed a layer of sticking oil with a width of about 100 mm to be applied to the conveyor belt below the seed-metering port. The associated oil supply system allowed the quantity of the oil to be adjusted as needed. An oil brush installed in front of the oil nozzle allowed the thickness of the oil layer to be controlled by adjusting the height of the brush.
As the fluted roller rotated, seeds were metered down onto the belt, forming a seed band ( Figure 11). The high-speed camera installed behind the seed-metering device was recording the seed band deposited on the conveyor belt [39]. The V1.2.1 computer vision software of the test bench (Figure 12), developed by Heilongjiang Agricultural Equipment Technology Co., Ltd., counted the seeds as they fell onto the conveyor belt and calculated their distribution. During testing, the belt speed of the stand was set at v = 1.06 m/s (or 3.8 km/h). As in the DEM simulations, the seeds were counted and their distribution calculated after the feed roller rotated for five turns. This corresponds to a distance S traveled by the conveyor belt equal to S = 60·5v/ω (5) where v is the speed of the belt in m/s and ω is the RPM of the feed roller. The sowing uniformity index CI can be calculated using Equation (2)  below the seed-metering port. The associated oil supply system allowed the quantity of the oil to be adjusted as needed. An oil brush installed in front of the oil nozzle allowed the thickness of the oil layer to be controlled by adjusting the height of the brush.
As the fluted roller rotated, seeds were metered down onto the belt, forming a seed band ( Figure 11). The high-speed camera installed behind the seed-metering device was recording the seed band deposited on the conveyor belt [39]. The V1.2.1 computer vision software of the test bench (Figure 12), developed by Heilongjiang Agricultural Equipment Technology Co. Ltd., counted the seeds as they fell onto the conveyor belt and calculated their distribution. During testing, the belt speed of the stand was set at v = 1.06 m/s (or 3.8 km/h). As in the DEM simulations, the seeds were counted and their distribution calculated after the feed roller rotated for five turns. This corresponds to a distance S traveled by the conveyor belt equal to 60 5 / where v is the speed of the belt in m/s and ω is the RPM of the feed roller. The sowing uniformity index CI can be calculated using Equation (2) by dividing the distance S in N subintervals and where xi is the number of seeds per subinterval.    The optimum solutions of the two parameter groups discussed earlier were tested on the stand, and the results obtained are listed in Table 8. It can be seen from the table that The optimum solutions of the two parameter groups discussed earlier were tested on the stand, and the results obtained are listed in Table 8. It can be seen from the table that the measured uniformity indexes are slightly larger than the simulation values. This can be attributed to the seed size variability, while in the DEM simulations, the seed sizes were all the same. However, the trends observed in the computer simulations and experimentally are, overall, consistent.

Conclusions and Discussion
The seed-metering process of a fluted force-feed seeder was simulated using the Discrete Element Method. Using the Box-Behnken experimental design principle, two groups of three factors and the three-level Response Surface Method were used to study and optimize the seed-metering performance parameters. Through significance tests of the quadratic regression models, it was found that when the lead angle is between 0 and 10 degrees and the number of flutes ranges between 10 and 14, the roller speed and the flute lead angle have the most impact (in this order) on the seeding performance, while the number of flutes has less impact. When the lead angle ranges between 5 degrees and 15 degrees and the number of flutes ranges between 12 and 16, the number of flutes and the roller speed have the most impact (in this order) on the seeding performance, while the lead angle has less impact.
It was confirmed experimentally that the optimum helical-flute feed rollers in the second group of DEM simulations is better than the optimum in the first group. Overall, it was confirmed through simulation and experimentally that when using helical-flute feed rollers, the seeding pulsation during metering is reduced compared with straight-flute rollers, resulting in better seeding performance.