Performance Parameters Optimization of a Three-Row Pneumatic Precision Metering Device for Brassica chinensis

Abstract

To improve the problem of low seeding efficiency facing the single-row planting mode traditionally used in China, this study aimed to design a novel three-row pneumatic precision metering device. The working principle and main structure were introduced in the paper. The three main factors affecting the seeding performance comprised of vacuum pressure, angular velocity of the metering tray, and taper angle of the sucking hole. A Box-Behnken experiment design having the qualified index and missed seeding index as the experimental index was used, and the results indicated that optimal performance of the metering device was achieved when the vacuum pressure was 2.16 kPa, the angular velocity of the metering tray was 29.43 rpm, and the taper angle of the sucking hole was 61.51°. The qualified index of the inner, middle, and outer ring was 95.12%, 94.68% and 94.24% respectively, while the missed seeding index of the inner, middle, and outer ring was 3.67%, 3.12% and 2.58% respectively under the optimal combination of parameters. The bench test results were basically consistent with the optimized results. This paper can provide support for the design of a three-row pneumatic precision metering device for Brassica chinensis.

1. Introduction

Brassica chinensis, also known as Chinese cabbage, has become a popular and cheap vegetable in Asia owing to advantages such as being easy to grow, high yield, disease resistance, as well as being nutritious and delicious [1]. However, the traditional manual sowing method which is labor-intensive and time-consuming is still widely used in most areas to plant Brassica chinensis.

Precise seeding, soil moistening, even spacing and similar seeding depth provide suitable living conditions and sufficient nutrients for seed development, reduce costs and increase crop yields [2]. The small three-axis size of Brassica chinensis seeds coupled with their spherical shape, makes them very suitable for high-speed and precise seeding proposed by the agricultural requirements in China. Since the 1950s, Datta et al. [3] developed the concept of precision sowing, which was the precise positioning of individual seeds in the soil to maintain uniform plant in spacing. Although there are two types of metering devices: mechanical and pneumatic, pneumatic metering devices are used by more farmers and agricultural companies because of high precision, low requirements for seed shape, minor damage to seeds, and high-speed seeding [4].

Many experts and scholars worldwide have carried out a lot of investigation on the design of the pneumatic metering device. Affected by site factors and scientific research funding, they mainly improved the seeding ability of pneumatic precision metering devices in the laboratory to gain credible information and further conduct experiments in the field, omitting tedious steps and reducing costs. Zhang et al. [5] analyzed the effect of inlet tube size and eyelet shape on airflow velocity using basic principles of ANSYS fluid simulation. Singh et al. [6] designed a cotton metering device to achieve precision in spacing by optimizing the running speed of the metering tray, vacuum pressure and the entry shape of the suction hole. Liu et al. [7] designed a combined cotton metering device. After optimization, the optimal combination that achieved the lowest missed seeding index (0.59%) was as below: a vacuum pressure of 2.67 kPa, a slot width of 2.83 mm, and an angular velocity of 20 r/min. The seed motion features were obtained by CFD-DEM coupling simulations, demonstrating that the size of the seed tube and drop height had a notable effect on seed distribution position [8]. Field tests were carried out using different techniques under conditions different from those used in the laboratory. The results showed that seed spacing uniformity was at a 95% confidence level in the laboratory and the field over a speed range of 3 to 4.5 km/h [9]. Gao et al. [10] investigated a new quantitative seed discharging system using the CFD-DEM gas-solid coupling method. The results showed that a suitable nozzle convergence angle of roughly 70° and a seed discharging angle of around 45° were required for a good seed discharging system. A pneumatic metering device was developed with the double-row metering tray, and an orthogonal experiment was optimized to obtain the optimal parameter combination The optimal combination of parameters was as given below: a sucking hole diameter of 4.5 mm, a vacuum pressure of 4.5 kPa, and a forward speed of 10 km/h. Under the condition, the missed rate was not more than 1%, the multiple seeding index was not more than 3%, and the qualified rate was more than 97%, which met the design requirements [11]. Xue et al. [12] developed and modeled a precision soybean metering device to plant at high-speed working conditions. The test showed that the optimum seed holder angle was 61.9°, the length of the second setting tray was 5.18 mm, and its qualified index was 99.59%. The seed throwing device of the rice metering device was studied, and the seed throwing path was assessed scientifically and systematically. The result indicated that the optimum sucking hole of the metering tray improved the seeding performance of the rice pneumatic metering device on hilly terrain [13]. A pneumatic maize precision metering device that rotated synchronously with the vacuum pressure chamber without relative motion was developed and compared with the Kverneland metering device. The findings revealed that the synchronous rotating maize metering device required less vacuum pressure [14]. The sowing parameters were studied and monitored at different sowing speeds and planting spacing. The results indicated that the parameter monitoring changes of relative error of sowing volume, qualified index, and missed seeding index was the same for three different sensors at five-speed and three spacing gradient levels [15].

This research aims to design a three-row pneumatic precision metering device for Brassica chinensis to improve the seeding efficiency. The influence of experimental factors such as vacuum pressure, the angular velocity of the metering tray, and the taper angle of the sucking hole on the seeding performance of the metering device was analyzed.

2. Materials and Methods

2.1. Working Principle of the Experiment Bench

The structure of the experiment bench mainly consisted of a metering device, fan, motor, conveyor belt, motor governor, and a conveyor belt frequency modulator, as shown in Figure 1. The appropriate vacuum pressure was adjusted by the wind pressure regulator to adsorb the seeds so that the seeds were stably adsorbed on the metering tray. The conveyor belt frequency modulator adjusted the speed of the conveyor belt, so that there was a corresponding speed gap between the conveyor belt and the metering device in order to simulate the actual operation of the seeder in the field.

No. 3 in Figure 1 is a three-row pneumatic precision metering device for Brassica chinensis, which is the core component of the whole experimental bench. The metering device consisted mainly of the front housing, rear housing, metering tray, diversion tube, seed box, outer seed-cleaning device, inner seed-cleaning device, retaining tray, sprocket wheel, transmission shaft, and seed stirring wheel, as shown in Figure 2.

The metering tray was the key part of the metering device. The seeds were detached from the population by gravity, centrifugal force, airflow, and disturbance of the seed stirring wheel. The vacuum pressure generated by the fan absorbed the seeds into the sucking hole, after which the seeds were rotated simultaneously with the metering tray to the seed cleaning zone. This was mainly done by the seed cleaning device and the high-speed airflow to ensure that there was only one seed in each hole. The single seed then passed smoothly through the seed carrying zone by adsorption force of the sucking hole into the seed-discharging zone, where it lost adsorption force instantly and entered the division tube for a three-row narrow spacing sowing operation.

2.2. Determination of the Main Parameters of the Sucking Hole

The metering tray determined the structural dimensions of the metering device. The size of the metering tray influenced the position of the holes, the linear velocity of the holes, the speed of the metering tray, the number of sucking holes, the inertial forces on the holes, and the vacuum pressure generated by the fan. Less contact time between the holes and the seed-filling zone coupled with shorter seed-filling time, led to insufficient seed-filling. Going by the Agricultural Machinery Design Manual, the diameter of the metering tray ranged between 80–240 mm, and the center linear velocity of the sucking hole was not more than 0.35 m/s. It was determined that the angular velocity of the metering tray was less than or equal to 41.79 rpm. The planter is called high-speed seeding when its forward speed is bigger than 6 km/h, and the plant spacing of the seeds is 4–5 cm. Therefore, the minimum value of sucking holes on the metering tray was calculated using Equation (2), whereby Z ≥ 59.8. This paper set the number of sucking holes in the inner, middle, and outer ring as 60. Taking into account various factors, the diameter of the metering tray was given as 220 mm, the thickness was 1 mm, and the diameter of the sucking hole circle of the outer ring, middle ring, and inner ring was 194 mm, 182 mm, and 170 mm, respectively.

$$V_C=2\pi nr$$

(1)

$$Z=\frac{60V_m}{nl}$$

(2)

where V_C is the center linear speed of the sucking hole, in m/s; n is the angular velocity of the metering tray, in rpm; r is the radius of the metering tray, in m; Z is the number of sucking holes; V_m is the speed of the planter, in m/s; l is the spacing of the seeds, in mm.

The triaxial dimensions of the seeds were small. The range of triaxial dimensions was measured several times using a vernier caliper, as shown in

Table 1. Measured dimensions of Brassica chinensis seeds.

Parameter	Range	Mean	Standard Error
Length (mm)	1.37–2.08	1.77	0.15
Width (mm)	1.33–1.91	1.68	0.13
Thickness (mm)	1.32–1.98	1.66	0.16
Thousand seed mass (g)	2.39–2.43	2.41	0.013

. According to Equations (3) and (4), the average equivalent diameter and the average spherical rate of the seeds were calculated [16], which was about 1.67 mm and 96%, respectively, so it was very suitable for narrow-row, narrow-distance, and dense planting mode.

$$D_S=\sqrt[3]{LW\mathrm{T}}$$

(3)

$$\mathsf{\Phi }=\frac{D_{\mathrm{s}}}{L}$$

(4)

$$d=(0.64-0.66)W$$

(5)

$$d+2tan\frac{{\theta }_1}{2}\ge W_{MAX}$$

(6)

The sucking hole structure is shown in Figure 3. Depending on Equation (5), the diameter range was found to be 1.07–1.1 mm. A larger taper angle requires a larger vacuum pressure, which in turn could easily cause the problem of missed seeding. Therefore, the taper angle was calculated from Equation (6) to be higher than 34°.

Where H is the thickness of the metering tray; d₁, d₂ and d₃ is the diameter of the sucking hole of the inner, middle and outer ring; θ₁, θ₂ and θ₃ are taper angle of the inner, middle ring and outer ring; D₁, D₂ and D₃ are entrance diameter of the sucking hole of the inner, middle ring and outer ring, respectively. L, W, and T are the average length, width, and thickness of the seeds (mm), respectively; D_s is the equivalent diameter of the seeds (mm), Φ is the average sphericity of the seeds (dimensionless).

2.3. Performance Test of the Metering Device

2.3.1. Test Materials and Equipment

The test material selected in this paper was the seeds of “Shanghai Ai Ji”. The 1000-seed weight was 2.52 g, the angle of repose was 24.1°, the average moisture content was 5.67%, and the density was 0.918 g/cm³. In consideration of cost and site factors, bench tests were used instead of a field test in this study. A self-built test bench was utilized to study the seeding performance of a three-row pneumatic precision metering device for Brassica chinensis. The test equipment mainly consisted of the metering device, conveyor belt, variable frequency motor, vacuum tube, positive pressure tube, u-manometer, conveyor belt frequency modulator, wind pressure detection system, fan and fan frequency regulator. The relative movement between the metering device and the conveyor belt was used to simulate the movement of the planter in the field. The velocity of the conveyor belt was changed by adjusting the frequency converter to simulate the different field driving states of the planter [17], as shown in Figure 4.

2.3.2. Test Method and Index

The three-row pneumatic precision metering device developed can achieve high-speed, narrow-row, and narrow-distance seeding. In accordance with the agronomic requirements of planting Brassica chinensis, the row spacing was about 100 mm, and the seed spacing was about 40–50 mm. Considering the analysis of the previous experiment, the vacuum pressure, the angular velocity of the metering tray and the taper angle of the sucking hole were chosen as experimental factors [18,19]. The appropriate vacuum pressure ensured that the seeds were adsorbed stably in the sucking holes and reduced multiple seeds in one hole. The metering device used a single metering tray with three rows of holes, which required relatively high vacuum pressure than single and double rows of holes. From theoretical analysis, the critical minimum vacuum pressure required to adsorb one seed was calculated to be 342.41 Pa. Taking into account the pressure loss, the vacuum pressure range was determined to be 0.5–3.5 kPa. According to the pre-experiment, it was found that missed seeding occurred seriously when the angular velocity exceeded 40 rpm. When the angular velocity was less than 10 rpm, it was difficult for the seeds to be adsorbed in the sucking holes due to the poor mobility of the seeds. For the determination of optimal angular velocity, angular velocity ranging from 10–40 rpm was selected from the pre-experiment.

Going by the theoretical calculation, the taper angle was bigger than 34°. The taper angle was the major factor that affected the adsorption effect. The adjustable range of the taper angle was selected to be 45–75° in combination with the pre-experiment. Three metering trays with different taper angles were machined to study the influence of the above three factors on the sowing ability and determine the optimum parameters. An experiment using Box-Behnken design was conducted, and the experimental design is shown in

Table 2. Levels of experimental factors.

Level	Factor
	X1/kPa	X2/rpm	X3/°
−1	0.5	10	45
0	2	25	60
1	3.5	40	75

Note: X₁ is vacuum pressure; X₂ is angular velocity of the metering tray; X₃ is taper angle of the sucking hole.

.

The performance test of the metering device was duplicated three times under each group of data, and the mean was used as the experimental result. Going by “GB/T6973-2005 Testing Methods of Single Seed (Precision Drills)”, the missed seeding index and the qualified index were selected as the evaluation index [20,21], and the calculation equations were as follows:

$$M=\frac{N_1}{N}\times 100\%$$

(7)

$$Q=\frac{N_2}{N}\times 100\%$$

(8)

where M is missed seeding index; Q is the qualified index; N₁ is the number of missed seeding; N₂ is the qualified number; N is the theoretical seeding numbers. The theoretical spacing is x (40–50 mm), and the distance between adjacent seeds on the conveyor belt is L. When 0.5x < L < 1.5x, it is qualified, and where L > 1.5x [22], it is missed seeding.

3. Results and Discussion

3.1. Test Results

A three-factor, a three-level experiment was conducted using the Box-Behnken design method of Design-Expert 13 Software. The qualified index and missed seeding index were considered as the performance indexes. The test results are shown in

Table 3. Test results.

NO.	Experimental Factors			Results
	X1	X2	X3	Y1/%	Y2/%	Y3/%	Y4/%	Y5/%	Y6/%
1	−1	−1	0	82.88	13.21	84.02	13.12	83.33	13.31
2	1	−1	0	83.21	4.86	90.56	4.13	89.98	3.96
3	−1	1	0	83.56	5.56	86.32	2.84	86.68	2.68
4	1	1	0	86.65	2.26	83.37	3.36	82.84	3.42
5	−1	0	−1	85.12	3.56	98.64	0.37	98.43	0.41
6	1	0	−1	82.45	2.68	85.46	4.33	87.41	4.56
7	−1	0	1	83.45	12.89	98.13	0.82	98.11	0.75
8	1	0	1	90.32	4.24	98.73	0.94	98.25	1.03
9	0	−1	−1	92.85	4.98	83.32	5.68	83.45	5.43
10	0	1	−1	91.21	2.12	97.96	0.35	98.14	0.29
11	0	−1	1	89.12	10.12	92.56	5.11	93.01	5.36
12	0	1	1	96.12	3.12	84.12	3.89	84.33	3.95
13	0	0	0	98.25	0.46	82.56	12.65	82.69	12.35
14	0	0	0	98.46	0.82	88.91	12.43	89.46	12.37
15	0	0	0	97.38	1.2	95.82	3.53	96.38	3.61
16	0	0	0	98.25	0.24	90.68	2.63	91.46	2.57
17	0	0	0	98.12	0.21	97.45	0.51	96.69	0.48

Note: Y₁ is the inner ring qualified index; Y₂ is the inner ring missed seeding index; Y₃ is the middle ring qualified index; Y₄ is the middle ring missed seeding index; Y₅ is the outer ring qualified ring index; Y₆ is the outer ring missed seeding index.

.

3.2. Variance Analysis and Model Establishment

The variance analysis of the qualified index and missed seeding index of the inner ring is shown in

Table 4. Variance Analysis result of inner ring seed-metering performance test.

Performance Index	Source	Sum of Square	df	Mean Square	F Value	p Value
inner ring qualified index	Model	641.89	9	71.32	121.43	<0.0001 **
	X1	7.26	1	7.26	12.36	0.0098 **
	X2	11.23	1	11.23	19.13	0.0033 **
	X3	6.81	1	6.81	11.59	0.0114 *
	X1X2	1.90	1	1.90	3.24	0.1148
	X1X3	22.75	1	22.75	38.74	0.0004 **
	X2X3	18.66	1	18.66	31.77	0.0008 **
	X12	464.52	1	464.52	790.89	<0.0001 **
	X22	51.98	1	51.98	88.50	<0.0001 **
	X32	21.38	1	21.38	36.41	0.0005 **
	Residual	4.11	7	0.5873
	Lack of fit	3.42	3	1.14	6.58	0.0502
	Pure Error	0.6931	4	0.1733
	Cor Total	646.01	16
inner ring missed seeding index	Model	268.44	9	29.83	50.80	<0.0001 **
	X1	56.07	1	56.07	95.51	<0.0001 **
	X2	50.55	1	50.55	86.10	<0.0001 **
	X3	36.25	1	36.25	61.75	0.0001 **
	X1X2	6.38	1	6.38	10.86	0.0132 *
	X1X3	15.09	1	15.09	25.71	0.0014 **
	X2X3	4.28	1	4.28	7.30	0.0306 *
	X12	46.47	1	46.47	79.14	<0.0001 **
	X22	27.69	1	27.69	47.16	0.0002 **
	X32	15.76	1	15.76	26.84	0.0013 **
	Residual	4.11	7	0.5871
	Lack of fit	3.40	3	1.13	6.40	0.0524
	Pure Error	0.7087	4	0.1772
	Cor Total	272.55	16

Note: * represents significant difference (0.01 < p < 0.05), ** represents extremely significant difference (p < 0.01).

.

According to Table 4, the regression model was extremely significant because p in the inner ring qualified index was less than 0.01. Further, it can be seen that the p of the regression terms X₁, X₂, X₃, X₁X₃, X₂X₃, X₁², X₂² and X₃² are all less than 0.05, which has a significant effect. The regression equation was strongly fitted due to the p in the misfit item being larger than 0.05, demonstrating that the non-existence of other factors affected the performance indicators. The p of X₁X₂ term in the model was 0.1148, demonstrating that the term had no significant effect on the inner ring qualified index. The R² value of 0.9907 indicated that the model fitted well with the data. The regression model of the inner ring qualified index obtained after removing insignificant factors was shown in Equation (9). It can be seen that the major and minor factors influencing the inner ring qualified index were X₂ > X₁ > X₃. As can also be seen from Table 4, the regression model was extremely significant for the inner ring missed seeding index. Further, it can be seen that the p of the regression terms X₁, X₂, X₃, X₁X₃, X₁X₂, X₂X₃, X₁², X₂² and X₃² are all less than 0.05, which has a significant effect. The regression model of the inner ring missed seeding index obtained was shown in Equation (10). The major and minor factors influencing the inner ring missed seeding index were X₁ > X₂ > X₃. The R² value of 0.9849 indicated that the model fitted well with the data.

$$\begin{array}{l}{Y}_1=98.09+0.9525X_1+1.19X_2+0.9225X_3+2.38X_1{X}_3\\ +2.16X_2{X}_3-10.5X_1{}^2-3.51X_2{}^2-2.25X_3{}^2\end{array}$$

(9)

$$\begin{array}{l}{Y}_2=29.32-3.89X_1-0.57X_2-0.61X_3+0.06X_1{X}_2\\ +0.09X_1{X}_3-0.01X_2{X}_3+1.48X_1{}^2+0.01X_2{}^2+0.01X_3{}^2\end{array}$$

(10)

The variance analysis of the qualified index and missed seeding index of the middle ring is shown in

Table 5. Variance Analysis result of middle ring seed-metering performance test.

Performance Index	Source	Sum of Square	df	Mean Square	F Value	p Value
Middle ring qualified index	Model	618.60	9	68.73	131.05	<0.0001 **
	X1	6.86	1	6.86	13.09	0.0085 **
	X2	11.50	1	11.50	21.92	0.0023 **
	X3	6.55	1	6.55	12.49	0.0095 **
	X1X2	0.5184	1	0.5184	0.9884	0.3533
	X1X3	18.62	1	18.62	35.50	0.0006 **
	X2X3	19.32	1	19.32	36.83	0.0005 **
	X12	431.30	1	431.30	822.32	<0.0001 **
	X22	66.73	1	66.73	127.23	<0.0001 **
	X32	20.54	1	20.54	39.16	0.0004 **
	Residual	3.67	7	0.5245
	Lack of fit	2.57	3	0.8579	3.13	0.1499
	Pure Error	1.10	4	0.2745
	Cor Total	622.27	16
Middle ring missed seeding index	Model	289.83	9	32.20	228.06	<0.0001 **
	X1	40.41	1	40.41	286.18	<0.0001 **
	X2	66.01	1	66.01	467.48	<0.0001 **
	X3	39.52	1	39.52	279.85	<0.0001 **
	X1X2	8.76	1	8.76	62.05	0.0001 **
	X1X3	16.08	1	16.08	113.88	<0.0001 **
	X2X3	10.30	1	10.30	72.97	<0.0001 **
	X12	37.60	1	37.60	266.31	<0.0001 **
	X22	30.21	1	30.21	213.93	<0.0001 **
	X32	29.53	1	29.53	209.16	<0.0001 **
	Residual	0.9884	7	0.1412
	Lack of fit	0.7009	3	0.2336	3.25	0.1423
	Pure Error	0.2875	4	0.0719
	Cor Total	290.82	16

Note: ** represents extremely significant difference (p < 0.01).

.

Table 5 shows that p in the middle ring qualified index was less than 0.01. It can be concluded that the model was extremely significant. The p in the misfit item is 0.1499, demonstrating that Equation (11) was strongly fitted. The p of the X₁X₂ term in the model was 0.3533, demonstrating that the term had no significant influence. The R² value was 0.9941. The response regression model of the middle ring qualified index obtained after removing insignificant factors was shown in Equation (11). It can be seen that the major and minor factors influencing the middle ring qualified index were X₂ > X₁ > X₃. As can also be seen from Table 5, the model was extremely significant for the middle ring missed seeding index. The response regression model of the middle ring missed seeding index obtained was shown in Equation (12). The major and minor factors influencing the middle ring missed seeding index were X₂ > X₁ > X₃. The R² value of 0.9966 indicated that the model fitted well with the data.

$$\begin{array}{l}{Y}_3=98.18+0.93X_1+1.2X_2+0.91X_3+2.16X_1{X}_3\\ +2.20X_2{X}_3-10.12X_1{}^2-3.98X_2{}^2-2.21X_3{}^2\end{array}$$

(11)

$$\begin{array}{l}{Y}_4=0.59-2.25X_1-2.87X_2+2.22X_3+1.48X_1{X}_2\\ -2.01X_1{X}_3-1.61X_2{X}_3+2.99X_1{}^2+2.68X_2{}^2+2.65X_3{}^2\end{array}$$

(12)

The variance analysis of the qualified index and missed seeding index of the outer ring is shown in

Table 6. Variance Analysis result of outer ring seed-metering performance test.

Performance Index	Source	Sum of Square	df	Mean Square	F Value	p Value
Outer ring qualified index	Model	600.93	9	66.77	187.92	<0.0001 **
	X1	3.37	1	3.37	9.48	0.0179 *
	X2	13.11	1	13.11	36.89	0.0005 **
	X3	2.45	1	2.45	6.90	0.0340 *
	X1X2	0.6320	1	0.6320	1.78	0.2241
	X1X3	31.47	1	31.47	88.58	<0.0001 **
	X2X3	17.94	1	17.94	50.48	0.0002 **
	X12	434.81	1	434.81	1223.72	<0.0001 **
	X22	50.83	1	50.83	143.06	<0.0001 **
	X32	14.76	1	14.76	41.53	0.0004 **
	Residual	2.49	7	0.3553
	Lack of fit	0.5209	3	0.1736	0.3532	0.7905
	Pure Error	1.97	4	0.4916
	Cor Total	603.42	16
Outer ring missed seeding index	Model	287.86	9	31.98	182.45	<0.0001 **
	X1	43.62	1	43.62	248.81	<0.0001 **
	X2	64.41	1	64.41	367.43	<0.0001 **
	X3	37.58	1	37.58	214.40	<0.0001 **
	X1X2	7.98	1	7.98	45.52	0.0003 **
	X1X3	16.85	1	16.85	96.12	<0.0001 **
	X2X3	8.91	1	8.91	50.83	0.0002 **
	X12	35.97	1	35.97	205.18	<0.0001 **
	X22	28.20	1	28.20	160.84	<0.0001 **
	X32	32.96	1	32.96	188.00	<0.0001 **
	Residual	1.23	7	0.1753
	Lack of fit	0.8735	3	0.2912	3.29	0.1399
	Pure Error	0.3537	4	0.0884
	Cor Total	289.09	16

Note: * represents significant difference (0.01 < p < 0.05), ** represents extremely significant difference (p < 0.01).

.

Table 6 shows that the model was extremely significant because p in the outer ring qualified index was less than 0.01. The p in the misfit item was 0.7905, demonstrating that Equation (13) was strongly fitted. The R² value of 0.9959 indicated that the model fitted well with the data. The response regression model of the outer ring qualified index obtained was shown in Equation (13). It was apparent that the major and minor factors influencing the outer ring qualified index were X₂ > X₁ > X₃. As seen in Table 6, p in the outer ring missed seeding index was less than 0.01. It can be concluded that the model is extremely significant. The response regression model of the outer ring missed seeding index obtained was shown in Equation (14). It was apparent that the major and minor factors influencing the outer ring missed seeding index were X₂ > X₁ > X₃. The R² value of 0.9958 indicated that the model fitted well with the data.

$$\begin{array}{l}{Y}_5=97.92+0.65X_1+1.28X_2+0.55X_3+2.8X_1{X}_3\\ +2.12X_2{X}_3-10.16X_1{}^2-3.47X_2{}^2-1.87X_3{}^2\end{array}$$

(13)

$$\begin{array}{l}{Y}_6=0.59-2.33X_1-2.84X_2+2.17X_3+\mathrm{.1.41}{X}_1{X}_2\\ -2.05X_1{X}_3-1.49X_2{X}_3+2.92X_1{}^2+2.59X_2{}^2+2.80X_3{}^2\end{array}$$

(14)

3.3. Influence of Reciprocal Factors on Performance Indicators

The dimension reduction method was used to reduce vacuum pressure, angular velocity, and taper angle to zero level [23,24]. The influence of the interaction between the other two factors was analyzed, and the response surface plots of the influence of the following groups of notable interaction on the inner ring qualified index, inner ring missed seeding index, middle ring qualified index, middle ring missed seeding index, outer ring qualified index and outer ring missed seeding index were obtained, as shown in Figure 5, Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10.

Figure 5a shows the response surface of the interaction between vacuum pressure and angular velocity on the inner ring qualified index. The result showed that the inner ring qualified index increased and subsequently decreased with the increase of the angular velocity when the taper angle was at zero level. When the angular velocity was low, the sucking hole stayed in the seed filling zone for a long time, and it was easy to adsorb multiple seeds. When the angular velocity increased, the sucking hole passed through the seed filling zone quickly, leading to decline of the seed filling qualified index. It was seen that the inner ring qualified index increased and subsequently decreased with increasing vacuum pressure. When the vacuum pressure was small, the adsorption force on the seed was also small, and the probability of the seed being adsorbed was reduced, so the qualified index was small. When the vacuum pressure was 1.4–2.6 kPa, and the angular velocity was 20–36 rpm, the inner ring the qualified index was relatively high. Figure 5b shows the inner ring qualified index increased and subsequently decreased with increase in the taper angle, and the inner ring qualified index increased and subsequently decreased with increase in the vacuum pressure. When the vacuum pressure was 1.6–2.4 kPa, and the taper angle was 53–70°, the inner ring qualified index was relatively high. As seen in Figure 5c, the qualified index increased and subsequently decreased while the angular velocity increased when the vacuum pressure was at zero level. If the angular velocity was low, the sucking hole stayed in the seed filling zone for a longer time, and it was easy to adsorb multiple seeds. Due to the increase in angular velocity, the sucking hole passed through the seed filling area quickly, resulting in a decrease in the seed filling qualified index. If the angular velocity was at zero level, the qualified index increased and subsequently decreased with the increase in taper angle. The qualified index of the inner ring was relatively high when taper angle was 58–72° and angular velocity was 24–35 rpm.

Figure 6a shows that the missed seeding index was relatively low for vacuum pressures of 1.8–3.1 kPa and angular velocity of 26–37 rpm. When the taper angle was at zero level, the missed seeding index decreased and subsequently increased with increase in angular velocity, while the missed seeding index increased and subsequently decreased with increase in vacuum pressure. Figure 6b shows the inner ring missed seeding index was relatively low for vacuum pressures of 2–2.8 kPa and taper angles of 48–61°. The missed seeding index decreased and subsequently increased with increase in taper angle, and the inner ring missed seeding index decreased and subsequently increased with increase in vacuum pressure. Figure 6c shows the missed seeding index was low for angular velocity ranging between 25–35 rpm and taper angle of 46–62°.

As shown in Figure 7a, the middle ring qualified index was relatively high when the vacuum pressure was 1.6–2.4 kPa and the angular velocity was 18–30 rpm. Figure 7b shows that the qualified index was relatively high when vacuum pressure was 1.7–2.5 kPa and taper angle was 55–70°. Figure 7c shows the middle ring qualified index was relatively high when taper angle was 58–70° and angular velocity was 23–34 rpm. As seen in Figure 8a, the middle ring missed seeding index was relatively low when vacuum pressure was at 1.8–2.9 kPa and angular velocity was at 27–38 rpm. Figure 8b shows that the missed seeding index was relatively low at a vacuum pressure of 1.9–2.5 kPa and taper angle of 52–58°. Figure 8c shows the missed seeding index was relatively low at a taper angle of 50–62° and angular velocity of 26–37 rpm.

As seen in Figure 9a, the outer ring qualified index was relatively high when vacuum pressure was 1.7–2.5 kPa and angular velocity was 18–35 rpm. Figure 9b shows the outer ring qualified index was relatively high at the vacuum pressure of 1.6–2.5 kPa and the taper angle of 50–72°. Figure 9c shows the outer ring qualified index was relatively high when the taper angle was 59–71° and the angular velocity was 25–33 rpm. As seen in Figure 10a, the outer ring missed seeding index was relatively low when taper angle was at zero level, vacuum pressure was 1.8–3 kPa, and angular velocity was 27–39 rpm. Figure 10b shows the outer ring missed seeding index was low at vacuum pressure of 2.2–2.7 kPa and taper angle of 53–60°. Figure 10c shows the outer ring missed seeding index was relatively low at taper angle of 51–62° and angular velocity of 27–38 rpm.

3.4. Parameters Optimization and Experimental Verification

The above three experimental factors were optimized to be well matched to get the best seeding operation parameters and improve the qualified index [25]. Depending on the above regression equations and the boundary conditions of each factor to find the solution for the largest qualified index and the smallest missed seeding index, the parametric models were constructed. The objective function and constraint conditions were shown the Equation (15). The constraint conditions were solved using Design-Expert 13 Software. The optimum parameters were identified as vacuum pressure of 2.16 kPa, angular velocity of 29.43 rpm, and taper angle of 61.51 °. Under these conditions, the inner ring qualified index was 95.12%, the missed seeding index was 3.67%, the middle ring qualified index was 94.68%, the missed seeding index was 3.12%, the outer ring qualified index was 94.24%, and the missed seeding index was 2.58%. Parameter optimization zone is shown in Figure 11.

$$\left\{\begin{array}{l}min\left(Y_1,Y_3,Y_5\right)\\ max\left(Y_2,Y_4,Y_6\right)\\ s.t.\left\{\begin{array}{l}0.5 kPa\le X_1\le 3.5 kPa\\ 10 rpm\le X_2\le 40 rpm\\ X_3=60°\end{array}\right.\end{array}\right.$$

(15)

In an attempt to evaluate the sowing performance of the optimized metering device, the seeding performance tests were carried out using a self-built test bench with the parameters (vacuum pressure of 2 kPa, angular velocity of 23 rpm, and taper angle of 61°) in the optimized zone. The average values of five repeat tests were noted and compared with the optimized values, as shown in

Table 7. Comparison of the optimized value and actual value.

Type	Position	Optimized Value	Actual Value
Qualified index/%	Inner ring	95.12	95.05
	Middle ring	94.68	93.98
	Outer ring	94.24	92.73
Missed seeding index/%	Inner ring	3.67	4.12
	Middle ring	3.12	3.56
	Outer ring	2.58	2.86

. It was demonstrated that the actual results were similar to the optimized results under the optimum combination of parameters.

3.5. Future Study Direction

A novel three-row pneumatic precision metering device for Brassica chinensis was tested using the self-built test bench and ignoring the vibration problem of the metering device itself, so there was a certain error in the experimental data. To further improve the performance of the metering device, follow-up studies were conducted on the collision of the seeds in the seed tube, the momentary force of the seeds leaving the seed-discharging port, and a single metering tray for four-row or five-row.

4. Conclusions

This paper showed a novel three-row pneumatic precision metering device for Brassica chinensis to improve the low seeding performance at high-speed working conditions. Its structure and principle were briefly described. Through theoretical analysis, it was determined that the diameter of the sucking hole was 1.67 mm, and the value range of the taper angle of the sucking hole was higher than 34°. Depending on the self-built test bench, the experiment of the Box-Behnken design was conducted with vacuum pressure, angular velocity of the metering tray, and taper angle of the sucking hole as the experimental factors, and qualified index and missed seeding index as the performance indexes.

The optimum parameters were identified as vacuum pressure of 2.16 kPa, angular velocity of 29.43 rpm, and taper angle of 61.51°. The performance was optimum under the parameters. The verification test was performed on the parameter combination in the optimized zone. The result indicated that the qualified index of the inner ring was 95.05%, the missed seeding index of the inner ring was 4.12%, the qualified index of the middle ring was 93.98%, the missed seeding index of the middle ring was 3.56%, the qualified index of the outer ring was 92.73%, and the missed seeding index of the outer ring was 2.86%, which were basically identical to the optimized results and met the national standards.