Bohong Li, Hua Li, Xindan Qi, Xi Chen, ,Yunlong Ma, Yongjian Wang

(1. Key Laboratory of Intelligent Agricultural Equipment in Jiangsu Province, Nanjing Agricultural University, Nanjing, 210031, China; 2. Nanjing Tech University, Nanjing, 211816, China; 3. Huzhou Traffic Technician College, 313000, Huzhou, China)

Abstract： Improving the precision of mechanized seeding is the key breakthrough in vegetable planting, which can save cost and increase the efficiency of seeding. In order to improve the seeding performance of seed metering device, the computational fluid dynamics and discrete element method (CFD-DEM) coupling simulation technology was adopted to simulate the single factor performance of the seed metering device. Also, the movement characteristics of seeds under different suction nozzle structure and operation parameters were analyzed. In order to explore the best combination of parameters, the central composite design (CCD) was carried out by factoring the cone angle of suction nozzle, the angular velocity of seed plate, and the negative pressure and considering their effect on the two responses of the qualified index and the miss index. The variance analysis of the experimental results showed that the negative pressure had the most impact on the qualified index and the miss index, followed by cone angle of suction nozzle, and angular velocity of the seed plate. A parameterized mathematical model was then established to determine the parameter optimization region. Parameter optimization indicated that the qualified index of seeding was greater than 95% and the miss index was less than 2.5% at a cone angle of 50°, negative pressure in the range of 4.87-5.64 kPa, and an angular velocity in the range of 1.67-1.95 rad/s. The bench verification experiment further verified the accuracy of the parameter optimization results. The results of simulation and parameter optimization in this paper can provide reference for the development of seed metering device in the future.

Keywords: bench verification experiment; CFD-DEM; parameter optimization; seed metering device

0 Introduction

Vegetables are one of the essential foods in people’s daily diet, which can provide a variety of vitamins and minerals for the human body. In addition to their own nutrients, vegetables also have various benefits in weight control, beauty, and prevention of cancer[1-2]. China has a wide range of planting areas, but most farms are small and scattered because they are owned and ran by individual farmers. Manual or semi-mechanical seeding is the main method of vegetable seeding[3-4]. Therefore, the small and precise seeder has a broad application for Chinese farmers.For the precision seeder, seed metering device is the core component where it’s seeding performance is directly associated with the quality and efficiency of seeding[5-6]. According to seed metering device working principle, it can be divided into mechanical, pneumatic and other forms of seed metering devices including magnetic vibration type, electrostatic type, seed belt type and so on[7-8]. For the mechanical seed metering device, its function is to meter seeds according to the agronomic requirements based on the mechanical and physical principles. Although the mechanical seed metering device is simple in structure, it has strict requirements for seed size and cannot adapt to high speed operation with a forward speed of greater than 7 km/h[9]. The pneumatic seed metering device uses airflow to complete the whole process of seeding, and this kind of seed metering device has the advantages of less damage to seeds, strong versatility, high seeding precision, coupled with suitability for high-speed operation and it is therefore widely used in crop seeding[10-11]. The research object of this study is the mechanical-pneumatic combined seed metering device, which not only preserves the structural characteristics of the mechanical seed metering device, but also combines the characteristics of precision seeding of the pneumatic seed metering device[12-13].

Many researchers have conducted studies on the seeding performance of the seed metering device.Kamgar et al.[14]designed a new controlled seed metering unit, and a field with four different levels of wheat stubble coverage (10%, 30%, 40% and 50%) was selected for evaluation of the fabricated seed metering unit (FSMU). Moreover, the dynamic tests were conducted to compare the seeding performance of FSMU and common seed metering unit (CSMU) at three forward speeds of 4, 6 and 8 km/h for direct seeding of wheat. The evaluation of FSMU found that the increase in forward speed of grain drill and stubble coverage did not have a significant effect on the seeding rate of the grain drill, and the use of FSMU can reduce the variation coefficient of seeding by about 50%. Liao et al.[15]developed a novel prototype of pneumatic precision centralized seed metering device, which can sow six rows at a time, and the influence of positive pressure, negative pressure, and rotating speed on the seeding performance was investigated. The results from lab experiments showed that when the rotating speed was 16 r/min, positive pressure was 200 Pa, and negative pressure was -1 600 Pa, the best seeding parameters in one row had a qualified index (Iqs) of 92.48% and a miss-seeding index (Imiss) of 2.55%. It was observed that under similar conditions of rotating speed, positive pressure, and negative pressure, theIqsof six rows was above 86.5%, stability coefficient of variation (CV) of each row was below 4.6%, and the consistencyCVwas below 0.9%. The bench test results for multifunctional smart seed metering device used for two different kinds of soyabean and maize seeds found that in the range of 4-5 km/h, the shaft speeds were 43.05 r/min, 39.96 r/min and 40.25 r/min, and this gave higher seeding performance[16].

With increasing complexity of research, however, a new computational model is needed to simulate the fluid-particle system, and the CFD-DEM coupling method emerges as a prime candidate. The shape, material properties and particle size distribution of particles can be considered to describe the movement of particles and their interaction with the flow field in this novel method. Gas-solid flow in an inside-filling air-blowing maize precision seed metering device was simulated using CFD-DEM method, and it was found that the optimal parameters of lower located lateral hole with a width of 1.5 mm and average arc length of 10 mm had good working performance. The verification of the optimized results through laboratory experiments found that the qualified rate of seed metering device was greater than 93% when the working pressure was above 5.5 kPa with a working speed lower than 10 km/h[17]. Jia et al.[18-19]designed an agitated seed metering device with horizontal seed filling. It was found that the optimal parameter combination among different working conditions was determined by the results of Fluent-EDEM simulation and the angle, position, and number of agitating plates were 30°, 24.4 mm, and 13, respectively. Additionally, the diameter of convex spoon was 11.0 mm. Given the optimal parameter combination coupled with a seeding speed of 12 km/h, the qualified, multiple, and missing seeding indexes were 93.1%, 2.1% and 4.8%, respectively. The objective of this study was to improve the seeding performance of seed metering device, and it can provide reference for the development of the same type of seed metering device in the future. Since the seeds would be subjected to the interaction of gas phase and solid phase in the actual working process, the CFD-DEM coupling simulation technology was adopted to simulate the working process of the seed metering device. The single factor effects coupled with the interaction effects of the factors on the qualified index of seeding and the miss index were studied in this paper, and the parameterized mathematical model was then established to determine the parameter optimization region.

1 Materials and methods

1.1 Structure and working principles of seed metering device

As is shown in Figure 1, the seed metering device is mainly composed of suction nozzles, a seed box, a stirring wheel, a seed plate, a positive pressure tube, airflow passages, a motor, a negative pressure tube, and an air chamber shell. The working process includes seeds filling, seeds carrying, seeds throwing, and idle stroke.

(a) Structure of seed metering device

(b) Division of working area

The seeds in the seed box are in a flowing state driven by the stirring wheel when the seed metering device is working. In addition, the negative pressure airflow produced by the blower is connected to the negative pressure tube, and the seeds are adsorbed to the suction nozzle under the action of internal and external differential pressure of negative pressure chamber. This marks the completion of the seed filling process (In seed-filling zone Ⅰ). Next, the seeds rotate counterclockwise in sync with the seed plate under the action of suction nozzle, thereby completing the seeds carrying process (In seed-carrying zone Ⅱ). When the seed plate rotates to the seed-throwing zone, the seeds fall from the suction nozzle under the action of gravity and positive pressure airflow, thereby completing the seed throwing process (In seed-throwing zone Ⅲ). Then the seed plate rotates to the idle stroke zone (Ⅳ), ready to repeat the next cycle. In Figure 1(b), the thickness of the seed layer has been indicated. The distance from the lowest to the highest of the seed in the seed-filling zone is defined as the thickness of the seed layer (h).

1.2 Flow field modeling and mesh generation

The internal flow field of seed meter mainly consists of air chamber, airflow passage, and suction nozzle.In the working process of seed metering device, change in the structure and size of the suction nozzle will significantly affect the distribution of airflow field near the suction nozzle, especially the formation of the vortex region[20-21]. The formation of the vortex zone greatly reduced the adsorption performance of the suction nozzle, resulting in a decrease in the seeding performance[22]. To avoid mutual influence, the free flow layer is divided into two zones, positive pressure zone and negative pressure zone. The structure of the suction nozzle is illustrated in Figure 2. It consisted of the leada(mm), diameterb(mm), cone anglec(°), and top end of suction nozzle (I).

Fig. 2 Structure of the suction nozzle

The flow field of the seed meter is modeled using SOLIDWORKS, as shown in Figure 3. It consisted of the air chamber, airflow passage, free flow layer in the positive pressure zone, suction nozzle, and free flow layer in the negative pressure zone. The dimensions for main parts of the seed metering device under simulations are presented in Table 1.

In this paper, the mesh division tool (MeshTool) of ANSYS Workbench 17.0 was used to mesh the flow field model of the seed meter. Due to the complexity of the flow field model, the adaptable tetrahedral mesh was used for mesh division. In order to improve the accuracy of numerical calculation, the local mesh refinement technique of the flow field model at the suction nozzle was used[23]. When meshing in MeshTool, the mesh refinement command (Refinement) was added to refine the flow field model at the nozzle. Also, the edge of the flow field model whose size changed at the suction nozzle was selected, after which the mesh was generated, as shown in Figure 4.

Fig. 3 Physical model of flow field in seed meter1.Airflow passage 2.Air chamber3.Free flow layer in the negative pressure zone 4.Suction nozzle5.Free flow layer in the positive pressure zone

Fig. 4 Flow field model for mesh division using local mesh refinement techniqueⅠ.Static region Ⅱ.Dynamic region

Tab. 1 Dimensions for main parts of the seed metering device under simulations

Since the suction nozzle and airflow passage are in motion, and the air chamber and free flow layer are at rest, the simple transformation coordinate system method cannot solve the relative motion of the dynamic and static region. The sliding mesh method (moving mesh) was adopted in this study, and the contact surface of the dynamic and static region was defined as the interface surface (interface). The static coordinate system was used for both the dynamic and static regions. In the calculation process, the region where the dynamic region and the static region are connected is the internal region, and the region that is not connected is defined as the wall region. The number of grids in the calculation region of the flow field model is about 1.1 million, and the minimum size of the mesh model is 0.6 mm. When the diameter of the suction nozzle (b) is 1.3 mm and the lead (a) is 3 mm, the results of the mesh division of the flow field model of the seed meter is shown in Figure 4.

1.3 Fluid flow equations

Numerical simulation is the process of solving the basic conservation equation of hydrodynamics, including mass conservation equation (continuity equation), momentum conservation equation (Navier-Stokes equation) and energy conservation equation[24].

The fluid medium of numerical simulation is air, assuming that the flow field meets the following conditions: (1) The working temperature is constant at 25 ℃, and the atmospheric pressure is constant at 1.01×105Pa. (2) The flow velocity is low when the seed metering device is working, and Mach number is less than 0.3, so it is defined as an incompressible gas. (3) The form of air flow is turbulent. (4) The positive and negative pressure chambers are sealed and have no influence on each other.

For numerical simulation of flow field model using ANSYS Fluent 17.0, the equation in formula(1)-(3) should be satisfied.

Mass conservation equation (continuity equation)

(1)

Where,ρis the fluid density, in kg/m3;tis the time, in s;uiis the mean velocity component, in m/s.

Momentum conservation equation (Navier-Stokes equation)

(2)

Where,ujis the mean velocity component, in m/s;pis the static pressure, in Pa;xi,xjis each coordinate component, in m;τijis the stress tensor, in m;gi,Fiare the gravitational volume force and external volume force in theidirection, in N;μis the viscosity coefficient.

Energy conservation equation

(3)

Where,Tis the temperature, in K;keffis the effective thermal conductivity;Jj′is the diffusion flux of componentj′;hj′is the enthalpy of componentj′;Shis the chemical reaction heat.

When the diameter of the suction nozzle is 1.3 mm and the lead is 3 mm, and given the appropriate operating parameters (Negative pressure: 4 000 Pa; Positive pressure: 500 Pa; Angular velocity: 2 rad/s), select one of the nozzles to obtain simulation diagram of the flow field as shown in Figure 5.

Fig. 5 Flow field simulation of seed meter

1.4 Particle contact model

At present, the hard-sphere model and the soft-sphere model are commonly used in the discrete element modelling[25-26]. The hard-sphere model assumes that collision of the element is instantaneous, the energy loss during the collision is expressed by the recovery coefficient, and the particle contact force and the details of the particle surface deformation are completely ignored. When the particles move faster and the concentration of particles is low, the hard-sphere model is commonly used to depict the contact model between particles. The soft-sphere model can ignore the amount of deformation on the particle surface, and the contact force between particles can be calculated according to the normal overlap and tangential displacement. In addition, the soft-sphere model can simulate the collision of two or more particles at the same time and the whole calculation process is simpler than that of the hard-sphere model[27-28]. When simulating the movement of seeds inside the seed metering device, the collision between seeds will cause plastic deformation on the surface of the seeds, and the concentration of seed particles accumulated in the filling-zone is high. Therefore, the hard-sphere model cannot describe the internal physical mechanism of the particle system, and as such, the soft-sphere model was used in this paper.

As shown in Figure 6, the particles come into contact by external force or inertia.Cis the contact point between particleiand particlej, and the dashed line in the figure is the position of particleiat the moment of contact between the two particles.

Fig. 6 Soft sphere model of two particles in contact with each other

After the particles collide, the relative movement between the two particles will occur. Meanwhile, the surface of the particles is deformed, and the contact force is generated. The surface deformation of the two particles can be ignored in the soft-sphere model, and the contact force between the particles can be obtained by calculating the normal overlapαand tangential displacementδ[29].

The soft-sphere model does not introduce any force, and the matching relation of particles is determined by adding a coupler between the two particles in contact with each other. In addition, the spring constantkand damping coefficientcare introduced. This is shown in Figure 7. (Mathematical relations adopted by Wang et al.[29]are presented in formula (4)-(8)).

1) Spring constant. If particleiand particlejare the same material and have the same particle size, the spring constantkcan be simplified as follows

(4)

Where,knis normal spring constant of the particle;Ris the radius of particle, in m;Eis the elastic modulus of the particle material;νis the Poisson’s ratio of the particle material;ktis tangential spring constant;Gis the shear modulus of the particle;αis the normal overlap, in m.

2) Damping coefficient

(5)

Where,cnis the normal damping coefficient;ctis the tangential damping coefficient.

3) Normal contact force

Fnij=(-knα3/2-cnvij·n)n

(6)

Where,Fnijis the resultant force of the elastic force and damping force acting on particleiby spring and normal damper, in N;vijis the velocity of particleirelative to particlej,vij=vi-vj, in m/s;nis the unit vector from the center of particleito the center of particlej.

4) Tangential contact force

(7)

Where,Ftijis the resultant force of the elastic force and damping force acting on particleiby spring and tangential damper, in N;μsis the static friction coefficient;ntis the tangential unit vector;vctis the slip velocity of the contact point, in m/s;Riis the radius of particlei, in m;ωiis the angular velocity of particlei, in rad/s;Rjis the radius of particlej, in m;ωjis the angular velocity of particlej, in rad/s.

5) Resultant force and resultant moment. When the particle concentration is high, the particleican come in contact with several particles at the same time, and the resultant force and moment acting on the particleiare shown as follows

(8)

Where,Fiis the resultant force of particlei;Tiis the resultant moment of particlei.

(a) Normal force

(b) Tangential force

1.5 Solver parameter settings

The standardk-εturbulence model and standard wall functions were used to solve the motion of gas phase in Fluent software. In the cell zone condition setting, other than the movement type of the suction nozzle and the air flow passage in the flow field model being set to Mesh Motion, the rest were fixed. The rotation-axis direction (1/-1) and rotation speed (rad/s) of the moving part of the flow field model were set.

In addition, the inlet and outlet of the flow field model were set as pressure-inlet and pressure-outlet in the boundary conditions setting. In the EDEM software, the soft-sphere model and Hertz-Mindlin (no slip) model were selected as particle model and particle contact model.

Moreover, linear rotation was applied for seed plate in EDEM software, and rotation speed (rad/s) was matched with the moving part of the flow field model in Fluent software, so as to realize the synchronous rotation of the gas-solid two-phase through the coupling interface. The main values of parameter used in CFD-DEM coupling simulation were listed in Table 2.

Since the time step size required by Fluent for convergence was much longer than EDEM in the coupling simulation, the time step sizes for Fluent and EDEM were set to 5×10-4s and 5×10-6s, respectively, and the total simulation time was set to 2.4 s.

Tab. 2 Computational parameters used in the coupling simulation

1.6 Experiment scheme and evaluation index

The main parameters affecting the seeding performance of the seed metering device are the cone angle of the suction nozzle, the angular velocity of the seed plate, and the negative pressure value[18-19, 30].Therefore, the three parameters were selected as the main experiment factors in this experiment. In the single factor experiment, when exploring the influence of one of the main experiment factors on the seeding performance, the values of the other two main factors were fixed at the center value. The remaining experimental factors that had little effect on seeding performance were the diameter of the suction nozzle, lead, angular velocity of stirring wheel, and thickness of seed layer, which were selected as 1.3 mm, 1 mm, 3 rad/s, and 35 mm, respectively. The values for the selected factors of remaining experimental factors remained fixed throughout the entire experiment. The experiment scheme is shown in Table 3.

Tab. 3 Single factor experiment scheme showing different values for cone angle, angular velocity, and negative pressure

In order to find the optimal parameter combination of influencing factors, Central composite design was used in the simulation.This method was chosen because it reduces the number of trials and avoids correlations between regression coefficients. The experiment factors and levels are shown in Table 4. In the simulation, suction nozzle models with different cone angles (CA=30°, 42°, 60°, 78°, 90°) were used to meet different experiment conditions, the structure of suction nozzle is shown in Figure 2.

Tab. 4 Central composite design experiment factors and levels

It is known from National Standard of P.R.C (GB/T 6973—2005 Testing Methods of Single Seed Drills (Precision Drills))[31]that the seeding performance of the seed metering device is evaluated by the qualified index, the multiple index, and the miss index of whose sum is 100%. The third item can be derived if the other two items are known, so the qualified index and the miss index can be selected as the evaluation index[32]. The suction nozzle that first passed through the seed box and rotated to the seed-throwing zone is marked as the first suction nozzle, and the adsorption ofzsuction nozzles are checked continuously. When one seed falls after it passes through the seed-throwing zone, the corresponding suction nozzle is effective for adsorption. No seed falling is regarded as the miss seeding, and two or more seeds falling at the same time are regarded as reseeding. These indexes can be calculated by the following

(9)

Where,R′ is the multiple index, in %;Mis the miss index, in %;Qis the qualified index, in %;zis the number of suction nozzles counted that pass through the seed-filling zone and the seed-throwing zone;n1is the number of suction nozzles counted when two or more seeds fall in the seed-throwing zone;n2is the number of suction nozzles counted when there is no seed in the seed-throwing zone.

1.7 Parameter optimization and bench verification experiment

In consideration for further improvement of the seed metering device seeding performance, the qualified index was defined in the range of 95%-100%, and the miss index was equal to the multiple index in the defined range of 0%-2.5%. Combining the boundary conditions of cone angle, angular velocity, and negative pressure value as well as target range (95%≤Q≤100%, 0%≤M≤2.5%) for parameter optimization using Design-Expert 8.0.6 optimization module.

In order to verify the accuracy of the parameter optimization results, the bench verification experiment was carried outaccording to the National Standard of P.R.C (GB/T 6973—2005 Testing Methods of Single Seed Drills (Precision Drills))[31]by the self-built bench. The experiment selected the median value of the range of parameter optimization, and experiment was repeated three times to verify whether the experiment results achieved the objective of parameter optimization.

2 Results and discussion

2.1 Single factor experiment

2.1.1 Effect of angular velocity of seed plate on seeding performance

Figure 8 presents the relationship between angular velocity of seed plate and seeding performance at a cone angle of 60° and negative pressure of 4 kPa. The qualified index (Q) reached the maximum value (Qmax=89.67%) when the angular velocity was 1.73 rad/s and minimum value (Qmin=71.20%) when the angular velocity was 2.5 rad/s. When the angular velocity increased from 1.5 rad/s to 2.5 rad/s, the qualified index first increased and then decreased. The miss index (M) reached the minimum value (Mmin=9.64%) when angular velocity was 1.67 rad/s and maximum value (Mmax=27.54%) when the angular velocity was 2.5 rad/s. With the increase of angular velocity from 1.5 rad/s to 2.5 rad/s, the miss index first decreased and then increased. When the angular velocity of the seed plate was slow, the suction nozzle stayed in the seed-filling zone for a relatively longer time, and the phenomenon where one suction nozzle adsorbed multiple seeds could be easily observed. When the angular velocity of the seed plate was high, the time of the suction nozzle passing through the seed-filling zone became shorter, hence increasing the miss index. From Figure 8, it can also be observed that when the angular velocity was in the range of 1.55-1.79 rad/s, the qualified index of seeding was high (Q≥85%) and the miss index was low (M≤10%).

2.1.2 Effect of cone angle on seeding performance

Figure 9 describes the relationship between cone angle of suction nozzle and seeding performance at the angular velocity of 2 rad/s and negative pressure of 4 kPa.With an increase in the cone angle, the qualified index (Q) first increased and then decreased while the miss index (M) first decreased and then increased. When the cone angle was 90°, the qualified index reached the minimum (Qmin=48.68%), and the miss index reached the maximum (Mmax=50.99%), which indicated that the seeding performance was the worst under this condition. When the cone angle was large, the contact part between the seed and the inner wall of the suction nozzle was small, and it was therefore not conducive for the adsorption of the seed. When the cone angle was small, the cross-sectional area (A) at the top of the suction nozzle was small. According to the pressure equation (P=F/A), the adsorption force (F) generated by the suction nozzle was relatively small, so the seeding performance decreased at this time. From Figure 9, it can also be seen that the qualified index of seeding was high (Q≥85%) and the miss index was low (M≤10%) when the cone angle was in the range of 36.07°-56.79°.

Fig. 8 Effect of angular velocity on seeding performance at a cone angle of 60° and a negative pressure of 4 kPa

Fig. 9 Effect of cone angle on seeding performance at an angular velocity of 2 rad/s and a negative pressure of 4 kPa

2.1.3 Effect of negative pressure on seeding performance

Figure 10 shows the effect of negative pressure on the seeding performanceat an angular velocity of 2 rad/s and a cone angle of 60°. It can be observed that with increase in negative pressure, the qualified index (Q) first increased and then decreased while the miss index (M) first decreased and then increased. When the negative pressure was 5.3 kPa, the seeding performance was better than other cases under a variety of negative pressure values. However, when the negative pressure was 2 kPa, the seeding performance was poor. When the negative pressure was low, the impact of adsorption force on the seeds was lower, and the probability of the seeds being adsorbed decreased. Consequently, the miss index was high and the qualified index was low. When the negative pressure was large, because of the large pressure difference between the inside and outside of the suction nozzle, it became easier to adsorb many seeds at the same time, so the qualified index increased at first and then decreased. From Figure 10, it can also be seen that when the negative pressure was in the range of 4.2-6 kPa, the qualified index of seeding was high (Q≥85%) and the miss index was low (M≤10%).

Fig. 10 Effect of negative pressure on seeding performance at an angular velocity of 2 rad/s and a cone angle of 60°

2.2 Central composite design experiment

2.2.1 Regression mathematical model

The design scheme and results of the simulation are shown in Table 5. Among them, 9 center point runs and 1 block were included in the CCD. Through the multiple regression analyses of the experiment results by Design-Expert 8.0.6, the regression model between qualified indexQ, miss indexM, and various factors were obtained.

1) Establishment and significance test of qualified indexQregression model. The qualified indexQwas derived using Design-Expert 8.0.6. Through the multiple regression fitting of the simulation data, the regression model for the influence of cone angle, angular velocity, and negative pressure value on the qualified indexQof the seeding is described as follows

Q=-121.84+1.74x1+108.46x2+29.03x3+

0.24x1x2+0.17x1x3+1.17x2x3-0.03x12-

35.63x22-3.89x32

(10)

Where,Qis the qualified index, in %;x1is the cone angle of the suction nozzle, in(°);x2is the angular velocity of the seed plate, in rad/s;x3is the negative pressure value, in kPa.

Tab. 5 Design scheme and results of the simulation experiment

The variance analysis and the significance test of the regression coefficient were performed on the regression model, and the results are shown in Table 6. In the qualified indexQregression model, the value of variance analysis isF=38.22, and the corresponding value of significance test isP<0.001, which shows that the fitting degree of the model is highly significant. In the item (lack of fit) of Table 6, the value of variance analysis isF=2.72, and the corresponding value of significance test isP=0.100 8, which shows that the impact of this item is not significant. It also shows that there are no other significant influencing factors. The coefficient of determination (R2) of the model is 0.963 6, and the coefficients of determination is close to 1, indicating that the model can accurately fit the relationship between experiment factors and experiment results. ThePvalue corresponding to the interaction term of the cone angle and the angular velocity (x1x2) and thePvalue corresponding to the interaction term of the angular velocity and the negative pressure (x2x3) are all greater than 0.05, which indicates that these two interaction terms have no significant effect on the qualified index.

Tab. 6 Variance analysis of regression equation

The closer the residual divergence point is to a straight line, the higher the fitting degree of the regression model[33]. The distribution position of the residual point derived from Design-Expert software was close to a straight line, which indicated that the fitting regression model of each factor was good. Based on theFvalue from the variance analysis of the regression model, it can be concluded that the factors affecting the qualified index of seeding, in the order of most significant to least significant are negative pressure, cone angle and angular velocity. The re-fit regression model excluding non-significant factors is as follows

Q=-158.66+2.20x1+126.63x2+31.30x3+

0.17x1x3-0.03x12-35.43x22-3.88x32

(11)

2) Establishment and significance test of miss indexMregression mode. Through the multivariate regression fitting of the simulation data, the regression model for the effect of cone angle, angular velocity, and negative pressure value on the miss indexMis described as follows

M=173.78-1.03x1-103.99x2-18.32x3-

0.30x1x2-0.19x1x3-2.54x2x3+

0.03x12+36.63x22+3.03x32

(12)

The variance analysis and the significance test of the regression coefficient were performed on the regression model, and the results are shown in Table 6. In the miss indexMregression model, the value of variance analysis wasF=33.37, and the corresponding value of significance test wasP<0.001, which shows that the fitting degree of the model is highly significant. In the item (lack of fit) of Table 6, the value of variance analysis wasF=3.39, and the corresponding value of significance test wasP=0.061 2, which shows that the impact of this item was not significant. It also shows that there are no other significant influencing factors. In the qualified indexQregression model, the value of variance analysis wasF=38.22, and the corresponding value of significance test wasP<0.001, which shows that the fitting degree of the model is highly significant. In the item (lack of fit) of Table 6, the value of variance analysis wasF=2.72, and the corresponding value of significance test wasP=0.100 8, which shows that the impact of this item was not significant. It also shows that there are no other significant influencing factors. The coefficient of determination (R2) of the model was 0.958 5, and the coefficients of determination was close to 1, indicating that the model is highly fitted with the experimental data. ThePvalue corresponding to the interaction term of the cone angle and the angular velocity (x1x2), and thePvalue corresponding to the interaction term of the angular velocity and the negative pressure (x2x3) are all greater than 0.05, which indicates that these two interaction terms have no significant effect on the qualified index. This also indicates that the two interaction terms have no significant effect on the miss index.

The distribution position of the residual point derived from Design-Expert software was close to a straight line, indicating that the fitting regression model of each factor was good. Based on the valueFof the variance analysis of the regression model, it can be concluded that the factors affecting the miss index of seeding, in the order of most significant to least significant are negative pressure, cone angle and angular velocity. The re-fit regression model excluding non-significant factors is as follows

M=229.52-1.63x1-131.65x2-23.34x3-

0.19x1x3+0.03x12+36.45x22+3.02x32

(13)

2.2.2 Influence of each factor on the qualified index of seeding

The effects of cone angle, angular velocity, and negative pressure on the qualified index (Q) was obtained by processing the data through Design-Expert 8.0.6, and its response surface is shown in Figure 11.

1) Interaction between the cone angle and the angular velocity. When the negative pressure was 4 kPa, the response surface figure of the interaction between the cone angle and the angular velocity of the qualified index (Q) of seeding is shown in Figure 11 (a). The interaction relationship between cone angle and angular velocity was analyzed as the negative pressure was at the central value of 4 kPa. It can be seen from the figure that when the cone angle was constant, the qualified index of seeding first increased and then decreased with the increase in angular velocity. When the angular velocity was low (AV: The range of 1.5-1.8 rad/s), the filling time of the suction nozzle in the seed-filling zone was long. As a result, it became easier to adsorb the seeds, so the qualified index was good. When the angular velocity was constant, the qualified index of the seeding first increased and then decreased with the increase of cone angle. When the cone angle increased from 51° to 90°, the adsorption capacity of the suction nozzle decreased, and as a result the qualified index decreased significantly. Overall, it is determined from the figure that the qualified index of seeding was high (87.05%≤Q≤91.55%) when the cone angle was in the range of 45°-60° and the angular velocity was in the range of 1.6-2.0 rad/s.

2) Interaction between the cone angle and the negative pressure. When the angular velocity was 2 rad/s, the response surface figure of the interaction between the cone angle and the negative pressure of the qualified index (Q) of seeding is shown in Figure 11 (b). The interaction relationship between cone angle and negative pressure was analyzed as the angular velocity was at the central value of 2 rad/s. When the cone angle was constant, the qualified index of seeding first increased and then decreased with the increase in negative pressure. When the negative pressure increased from 5.2 kPa to 6 kPa, the adsorption force of the suction nozzle on the seeds was large enough to cause the phenomenon of simultaneous adsorption of multiple seeds, and the qualified index showed a downward trend. When the negative pressure was constant, the qualified index of seeding first increased and then decreased with the increase of the cone angle. Overall, it is determined from the figure that the qualified index of seeding was high (85.90%≤Q≤94.93%) when the cone angle was in the range of 40°-62° and negative pressure was in the range of 4.0-5.5 kPa.

3) Interaction between the negative pressure and the angular velocity. When the cone angle was 60°, the response surface figure of the interaction between the negative pressure and the angular velocity of the qualified index (Q) of seeding is shown in Figure 11 (c). The interaction relationship between negative pressure and angular velocity was analyzed as the cone angle was at the central value of 60°. When the negative pressure was constant, and the angular velocity was in the range of 1.5-1.83 rad/s. Also, the residence time of the suction nozzle in the seed-filling zone was shortened with the increase of the angular velocity, and the phenomenon of adsorption of multiple seeds by one suction nozzle was significantly reduced. As such, the multiple index decreased and the qualified index increased. When the negative pressure was constant, and angular velocity was in the range of 1.83-2.5 rad/s, further increase in the angular velocity caused the filling time of the suction nozzle in the seed-filling zone to be too short. As a result, the miss index increased and the qualified index decreased. To sum up, it is determined from the figure that the qualified index of seeding was high (85.75%≤Q≤95.46%) when the negative pressure was in the range of 4.0-6.0 kPa and the angular velocity was in the range of 1.5-2.0 rad/s.

(a) Q(x1, x2, 0)

(b) Q(x1, 0, x3)

(c) Q(0, x2, x3)

2.2.3 Influence of each factor on the miss index of seeding

When the negative pressure was 4 kPa, the response surface figure of the interaction between the cone angle and the angular velocity of the miss index (M) is shown in Figure 12 (a). The interaction relationship between cone angle and angular velocity was analyzed as the negative pressure was at the central value of 4 kPa. It is determined from the figure that the miss index of seeding was low (7.11%≤M≤9.97%) when the cone angle was in the range of 45°-53° and the angular velocity was in the range of 1.6-2.0 rad/s. When the angular velocity was 2 rad/s, the response surface figure of the interaction between the cone angle and the negative pressure of the miss index (M) is shown in Figure 12 (b). The interaction relationship between cone angle and negative pressure was analyzed as the angular velocity was at the central value of 2 rad/s. It is determined from the figure that the miss index of seeding was low (2.66%≤M≤8.97%) when the cone angle was in the range of 42°-68° and the negative pressure was in the range of 5.2-6.0 kPa. When in this intersection area (CA: The range of 42°-68°;NP: The range of 5.2-6.0 kPa), the negative pressure was large enough to ensure that the suction nozzle could adsorb the seeds, and the reasonable range of cone angle ensured sufficient contact between the seeds and the inner wall of the suction nozzle, as a result, the miss index was low in this intersection area. When the cone angle was 60°, the response surface diagram of the interaction between the negative pressure and the angular velocity of the miss index (M) is shown in Figure 12 (c). The interaction relationship between negative pressure and angular velocity was analyzed as the cone angle was at the central value of 60°. It is determined from the figure that the miss index of seeding was low (2.76%≤M≤9.23%) when the negative pressure was in the range of 4.6-6.0 kPa and the angular velocity was in the range of 1.6-2.1 rad/s. When in this intersection area (NP: The range of 4.6-6.0 kPa;AV: The range of 1.6-2.1 rad/s), the suitable angular velocity ensured that the suction nozzle stayed in the seed-filling zone for a relatively longer time, and that the suction nozzle could effectively adsorb seeds, so the miss index was low in this intersection area.

(a) M(x1, x2, 0)

(b) M(x1, 0, x3)

(c) M(0, x2, x3)

2.3 Parameter optimization

2.3.1 Mathematical model

From the results obtained on the effect of interaction factors (CA&AV,CA&NP) on the seeding performance, it was found that when the cone angle was in the range of 45°-60° and 40°-62°, the qualified index of seeding was high (Q>85%). Also, when the cone angle was within the range of 45°-53° and 42°-68°, the miss index was low (M<10%). Therefore, the boundary condition of cone angle was fixed at 50°. The mathematical model of the non-linear programming is obtained and shown as follows

(14)

2.3.2 Optimization results

When the cone angle was 50°, Design-Expert 8.0.6 optimization module was used to optimize the parameters with the goal of a qualified index of greater than 95% and a miss index of less than 2.5%. The optimization results are shown in Figure 13. The intersection area in the figure is the parameter optimization region, that is, the negative pressure was in the range of 4.87-5.64 kPa and the angular velocity is in the range of 1.67-1.95 rad/s.

Fig. 13 Results of multi-index parameter optimization model

2.3.3 Bench verification experiment

The bench verification experiment was carried out when the cone angle was 50°, the negative pressure was 5.2 kPa, and angular velocity was 1.8 rad/s. Under the same parameter condition, the seeding performance of the seed metering device was simulated. The bench verification results are shown in Table 7. It can be observed from the experiment results that the qualified index is greater than 95% and the miss index is less than 2.5%, and the simulation results are basically the same as the experiment results, and the relative error is small, which indicates that the parameter optimization results are accurate.

Tab. 7 Bench verification results

3 Conclusions

In this paper, the single factor performance simulation was first performed on the seed metering device using the CFD-DEM coupling simulation technology. In order to find the best parameter combination, the CCD was carried out on cone angle of the suction nozzle, angular velocity of the seed plate, and negative pressure with qualified index and miss index as seeding performance indexes. The effects of various factors on seeding performance were analyzed, and the parameter optimization and the bench verification experiment were carried out, and the following main conclusions can be drawn.

1) From the results of the single factor experiment aimed at exploring the effect of angular velocity on seeding performance, it can be seen that when the angular velocity was 1.73 rad/s, the qualified index (Q) reached the maximum value (Qmax=89.67%), and when the angular velocity was 1.67 rad/s, the miss index (M) reached the minimum value (Mmin=9.64%). With respect to the effect of cone angle on seeding performance, it can be seen that when the cone angle was 50.18°, the qualified index (Q) reached the maximum value (Qmax=90.22%), and the minimum value of the miss index (Mmin=7.11%) was reached when the cone angle was 45.34°. From the results of the single factor experiment aimed at exploring the effect of negative pressure on seeding performance, it can be seen that when the negative pressure was 5.32 kPa, the qualified index (Q) reached the maximum value (Qmax=93.84%). When the negative pressure was 5.63 kPa, the miss index (M) reached the minimum value (Mmin=3.3%).

2) The CCD was used in the simulation, and the mathematical model between qualified index, miss index, angular velocity, cone angle, and negative pressure was established. The variance analysis of the experiment results was performed using Design-Expert 8.0.6. It was concluded that factors affecting the qualified index and the miss index of seeding in the order of most significant to least significant were negative pressure, cone angle, and angular velocity based on theFvalue of ANOVA {Fvalue:NP(118.33)>CA(83.27)>AV(13.02)}. In addition, the effects of the interaction of the factors on the qualified index and the miss index of seeding were studied.

3) The boundary conditions of cone angle, angular velocity and negative pressure value were combined in order to obtain a better parameter combination. The mathematical model of the non-linear programming was obtained. After optimizing using Design-Expert 8.0.6 optimization module, it was found that at a cone angle of 50°, negative pressure in the range of 4.87-5.64 kPa, and angular velocity in the range of 1.67-1.95 rad/s, the qualified index of seeding was greater than 95% and the miss index was less than 2.5%. The results obtained by the bench verification experiment were consistent with the results of the optimization, indicating that the optimization results were accurate.