Seed-Filling Characteristics of a Centralized Seed-Metering Device for Rapeseed Caused by Vibration

: Sowing quality is directly inﬂuenced by the seed-ﬁlling characteristics of a centralized seed-metering device, and vigorous seed-motion status deteriorates seeding performance resulting from ﬁeld surface roughness, seeder vibration, etc. However, the relationship between vibration and seed-ﬁlling properties remains unclear. This study measured the vibration characteristics of a seed-metering device, examined unmeasurable seed-motion characteristics based on DEM simulation, and used bench tests to determine the seed-ﬁlling characteristics under vibration conditions. The frequency distribution of the rapeseed seeder was 0–180 Hz. The simulation results revealed that the vibration mainly changed the level of seed in the seed-ﬁlling area; moreover, it signiﬁcantly increased the seed-ﬁlling angle, ranging from 56.00 ◦ –59.00 ◦ to 69.78 ◦ –91.40 ◦ , which affected the seed-ﬁlling performance. A vibration frequency of 10–40 Hz resulted in a target seed rate within 88.67–99.44%, but when there is no vibration, the target seed rate reached 100%. The bench test results demonstrated that the seed-ﬁlling angle under vibration will increase with an increase in longitudinal distance, and will change between 15.49 ◦ –102 ◦ . The seed-ﬁlling performance affected by longitudinal distance was larger than that affected by lateral distance. By adjusting the longitudinal distance to range from 0–20 mm, the target seed rate could be maintained above 91%. The ﬁndings help to improve our knowledge of seed-ﬁlling characteristics under vibration conditions, and should be conducive to improving seeding performance by adjusting the seed layer height to reduce the impact of vibration on ﬁeld operations.


Introduction
Rape is one of the most important oil crops in China [1,2]. The yield of rape in Sichuan Province has been the largest in China over the years, but its mechanized sowing ratio is less than 30%. An important factor is that most of the fields in Sichuan are steep and mountainous and have small farmland [3], with more than 60% of the sloped fields in the hilly areas of rapeseed cultivation having an angle larger than 6 • . The commonly used large-scale planter cannot operate, and most of the fields are sown manually. Therefore, sowing equipment suitable for small field operations have come into being, including the centralized metering device for rapeseed [4] and pneumatic rapeseed planters [5][6][7].
device. The seeder is connected to the tractor by a three-point hitch. The rotary tillage device is driven by a tractor, and the centralized seed-metering device is mounted on the rotary tillage device. The processes of seedbed preparation, fertilization, and seeding are accomplished synchronously. The vibration of the centralized seed-metering device mainly comes from the tractor, rotary tillage device, and seedbed surface conditions.  (4) ditching opening device, (5) double disc opener, (6) seed tube, (7) pesticide tank, (8) installation position of accelerometer, (9) centralized seed-metering device, (10) seed box, and (11) fertilizer discharging device. Figure 2 shows the centralized seed-metering device, which is a key component of the rapeseed seeder. It mainly consists of a seed-metering wheel, a regulating plate of seed layer, a seed-protecting plate, and a shell. The seed-metering wheel is a fundamental component to ensure that six rows of model-holes have 1-3 seeds simultaneously [33], with an involute-type model-hole of 3.5 mm and 2.6 mm in length and depth, respectively ( Figure 3). The inclination angle of the regulating plate of seed layer is 60° (Figure 4a). The seed layer height was adjusted by the longitudinal (l) and lateral distances (h) (Figure 4b).

Structure of Centralized Seed-Metering Device
ditching opening device, (5) double disc opener, (6) seed tube, (7) pesticide tank, (8) installation position of accelerometer, (9) centralized seed-metering device, (10) seed box, and (11) fertilizer discharging device. Figure 2 shows the centralized seed-metering device, which is a key component of the rapeseed seeder. It mainly consists of a seed-metering wheel, a regulating plate of seed layer, a seed-protecting plate, and a shell. The seed-metering wheel is a fundamental component to ensure that six rows of model-holes have 1-3 seeds simultaneously [33], with an involute-type model-hole of 3.5 mm and 2.6 mm in length and depth, respectively ( Figure 3). The inclination angle of the regulating plate of seed layer is 60 • (Figure 4a). The seed layer height was adjusted by the longitudinal (l) and lateral distances (h) (Figure 4b).

Structure of Centralized Seed-Metering Device
device. The seeder is connected to the tractor by a three-point hitch. The rotary tillage device is driven by a tractor, and the centralized seed-metering device is mounted on the rotary tillage device. The processes of seedbed preparation, fertilization, and seeding are accomplished synchronously. The vibration of the centralized seed-metering device mainly comes from the tractor, rotary tillage device, and seedbed surface conditions.  (4) ditching opening device, (5) double disc opener, (6) seed tube, (7) pesticide tank, (8) installation position of accelerometer, (9) centralized seed-metering device, (10) seed box, and (11) fertilizer discharging device. Figure 2 shows the centralized seed-metering device, which is a key component of the rapeseed seeder. It mainly consists of a seed-metering wheel, a regulating plate of seed layer, a seed-protecting plate, and a shell. The seed-metering wheel is a fundamental component to ensure that six rows of model-holes have 1-3 seeds simultaneously [33], with an involute-type model-hole of 3.5 mm and 2.6 mm in length and depth, respectively ( Figure 3). The inclination angle of the regulating plate of seed layer is 60° (Figure 4a). The seed layer height was adjusted by the longitudinal (l) and lateral distances (h) (Figure 4b).   (2) seed-protecting plate, (3) rear motherboard, (4) connecting plate, (5) panel for unloading seeds, (6) front motherboard, (7) base, (8) regulating plate of seed layer, (9) seed-metering wheel, (10) bearing end-cap, (11) drive sprocket, (12) shaft, (13) electric motor.  (8) regulating plate of seed layer, (9) seed-metering wheel, (10) bearing end-cap, (11) drive sprocket, (12) shaft, (13) electric motor.

Structure of Centralized Seed-Metering Device
(a) (b) (c)

Conditions of Vibration Test
The vibration test of the rapeseed seeder was conducted at the agricultural demonstration base of Sichuan Agricultural University, Ya'an City, Sichuan Province, China, in 2021. The soil was red loam and the previous crop was rape. The soil moisture content, firmness, and bulk density were 32.75%, 767.78 kPa, and 1290 kg m −3 , respectively (the samples were taken from a depth of 0-10 cm below the ground). The rapeseed seeder was powered by a M704-KQ tractor (Kubota Co., Ltd., Osaka, Japan).

Methods of Field Vibration Test
To assess the vibration characteristics under different working conditions, the effects of engine speed, PTO speed, and tractor forward speed on the vibration of the rapeseed seeder were carried out. The PTO speeds were 540 rpm and 720 rpm , respectively. The engine speeds were tested at 750 rpm (idling speed), 1600 rpm (65% of rated speed), and   (8) regulating plate of seed layer, (9) seed-metering wheel, (10) bearing end-cap, (11) drive sprocket, (12) shaft, (13) electric motor.

Conditions of Vibration Test
The vibration test of the rapeseed seeder was conducted at the agricultural demonstration base of Sichuan Agricultural University, Ya'an City, Sichuan Province, China, in 2021. The soil was red loam and the previous crop was rape. The soil moisture content, firmness, and bulk density were 32.75%, 767.78 kPa, and 1290 kg m −3 , respectively (the samples were taken from a depth of 0-10 cm below the ground). The rapeseed seeder was powered by a M704-KQ tractor (Kubota Co., Ltd., Osaka, Japan).

Methods of Field Vibration Test
To assess the vibration characteristics under different working conditions, the effects of engine speed, PTO speed, and tractor forward speed on the vibration of the rapeseed seeder were carried out. The PTO speeds were 540 rpm and 720 rpm , respectively. The engine speeds were tested at 750 rpm (idling speed), 1600 rpm (65% of rated speed), and

Conditions of Vibration Test
The vibration test of the rapeseed seeder was conducted at the agricultural demonstration base of Sichuan Agricultural University, Ya'an City, Sichuan Province, China, in 2021. The soil was red loam and the previous crop was rape. The soil moisture content, firmness, and bulk density were 32.75%, 767.78 kPa, and 1290 kg m −3 , respectively (the samples were taken from a depth of 0-10 cm below the ground). The rapeseed seeder was powered by a M704-KQ tractor (Kubota Co., Ltd., Osaka, Japan).

Methods of Field Vibration Test
To assess the vibration characteristics under different working conditions, the effects of engine speed, PTO speed, and tractor forward speed on the vibration of the rapeseed seeder were carried out. The PTO speeds were 540 rpm and 720 rpm, respectively. The engine speeds were tested at 750 rpm (idling speed), 1600 rpm (65% of rated speed), and 2500 rpm (rated speed) using tractor forward gear (I-IV). In the experiment, the speed of the tractor engine was controlled by adjusting the manual throttle. Figure 5a shows the vibration field experiment of the rapeseed seeder. CA-YD-103 piezoelectric acceleration sensor (Lianneng Electronic Technology Co., Ltd., Yangzhou, China) was mounted on the seed-metering device (Figure 5b), and uT3604FS (16 bit) data collector (uTekl Electronic Technology Co., Ltd., Wuhan, China) was applied to detect vibration signals from the seeder. The sampling mode of the collector was continuous sampling at 512 Hz. The sampling time was 15 s with three replicates. 2500 rpm (rated speed) using tractor forward gear (I-IV). In the experiment, the speed of the tractor engine was controlled by adjusting the manual throttle. Figure 5a shows the vibration field experiment of the rapeseed seeder. CA-YD-103 piezoelectric acceleration sensor (Lianneng Electronic Technology Co., Ltd., Jiangsu, China) was mounted on the seed-metering device (Figure 5b), and uT3604FS (16bit) data collector (uTekl Electronic Technology Co., Ltd., Wuhan, China) was applied to detect vibration signals from the seeder. The sampling mode of the collector was continuous sampling at 512 Hz. The sampling time was 15 s with three replicates.

DEM Simulation Model
Seed movement characteristics under vibration conditions were analyzed using DEM software EDEM 2018 (DEM Solutions Limited, Edinburgh, UK). The geometric model of the centralized seed-metering device was simplified into two parts: the shell and the seed-metering wheel. The shell and seed-metering wheel were made of aluminum alloy and engineering plastic ABS (acrylonitrile butadiene styrene copolymer), respectively. In the simulation, the Hertz-Mindlin (no-slip) model was chosen as the particle contact model with a hard-sphere model. The simulation parameters are shown in Table 1. 8.96 × 10 8 Coefficient of restitution between rapeseed and rapeseed 0.60 Coefficient of static friction between rapeseed and rapeseed 0.50 Coefficient of rolling friction between rapeseed and rapeseed 0.01 Coefficient of restitution between rapeseed and aluminum alloy 0.60 Coefficient of static friction between rapeseed and aluminum alloy 0.30 Coefficient of rolling friction between rapeseed and aluminum alloy 0.01

DEM Simulation Model
Seed movement characteristics under vibration conditions were analyzed using DEM software EDEM 2018 (DEM Solutions Limited, Edinburgh, UK). The geometric model of the centralized seed-metering device was simplified into two parts: the shell and the seed-metering wheel. The shell and seed-metering wheel were made of aluminum alloy and engineering plastic ABS (acrylonitrile butadiene styrene copolymer), respectively. In the simulation, the Hertz-Mindlin (no-slip) model was chosen as the particle contact model with a hard-sphere model. The simulation parameters are shown in Table 1.

Simulation Test Method
In the simulation, three frequency ranges were selected based on the vibration signal of the rapeseed seeder-including a low frequency of 0-60 Hz, a medium frequency of 70-110 Hz, and a high frequency of 120-180 Hz, with an interval of 10 Hz-in connection with a vibration acceleration of 14 m s −2 , 23 m s −2 , and 33 m s −2 , respectively. The vertical displacement was calculated according to the vibration frequency and vibration acceleration. The inclination angle of the regulating plate of seed layer, longitudinal distance, lateral distance, and rotational speed of the seed-metering wheel were 60 • , 15 mm, 46 mm, and 20 rpm, respectively. The seed-filling quantity of 30 model-holes (6 rows) was measured using DEM software's post-processing modules. The vertical displacement was calculated as Equation (1).
The rate of a single seed, rate of double seeds, rate of triple seeds, target seed rate, missing rate of seed filling, and multiple rates of seed filling were calculated based on standard ISO-7256/2, 1984 [34]. An total of 1-3 seeds per ridge was the qualified level of seed filling according to agronomic requirements. The number of retained seeds, the initial seed-filling angle, seed-filling angle, and seed speed were extracted. The evaluation indexes were given as follows. (1) where D is the vertical displacement (mm); a is the vibration acceleration (m s −2 ); f is the vibration frequency (Hz); P 1 , P 2 , and P 3 are the rate of single seed, double seeds and triple seeds, respectively (%); N 1 , N 2 , and N 3 are the quantities of single seed, double seeds and triple seeds, respectively; Q, M, and L are the target seed rate (1-3 seeds per model-hole), missing rate of seed filling (0 seeds per model-hole), and multiple rates of seed filling (>3 seeds per model-hole), respectively (%); n 1 , n 2 , and n 3 are the number of qualified model-holes for seed filling, missing model-holes for seed filling, and multiple model-holes for seed filling; and N is the total number of sample model-holes (180).

Bench Test
In the bench test, the influence of vibration frequency, longitudinal distance, and lateral distance on seed filling and seeding performance was investigated with a rapeseed variety of Zhongshuang 11. The vibration frequencies ranged from 0 to 40 Hz, with an internal of 10 Hz. The longitudinal distances ranged from 0 mm to 20 mm, with an internal of 5 mm based on standard ISO-7256/2, 1984 [34]. The change in longitudinal distance represents the change in the level of seed in the seed-filling area. The lateral distances were 42 mm, 46 mm, and 50 mm, respectively (Table 2).  Figure 6 presents the seed-metering platform upon installation of a DH40200 type vibration exciter (Donghua Testing Technology Co., Ltd., Jiangsu, China) on the JPS-12 seed-meter performance test bench (Heilongjiang Academy of Agricultural Mechanization Engineering, China). A DH40200-type vibration exciter generated vibration signals from the bottom of the seed-metering device. The vibration signal was monitored by the uT3604FS (16-bit) data collector and the CA-YD-103 piezoelectric acceleration sensor. The seed-filling process was extracted using a high-speed camera system (FASTCAM Mini UX100; Photron Limited, Tokyo, Japan) and lasted 25 s, with a shooting speed of 250 frames per second. The direction of the images was from the back of the seed-metering device. The seed-filling angle on both sides of the seed-metering device was extracted. The evaluation indexes were calculated with 30 model-holes per row as samples (6 rows). Each treatment was repeated in triplicate.
lateral distance on seed filling and seeding performance was investigated with a rapeseed variety of Zhongshuang 11. The vibration frequencies ranged from 0 to 40 Hz, with an internal of 10 Hz. The longitudinal distances ranged from 0 mm to 20 mm, with an internal of 5 mm based on standard ISO-7256/2, 1984 [34]. The change in longitudinal distance represents the change in the level of seed in the seed-filling area. The lateral distances were 42 mm, 46 mm, and 50 mm, respectively ( Table 2).  Figure 6 presents the seed-metering platform upon installation of a DH40200 type vibration exciter (Donghua Testing Technology Co., Ltd., Jiangsu, China) on the JPS-12 seed-meter performance test bench (Heilongjiang Academy of Agricultural Mechanization Engineering, China). A DH40200-type vibration exciter generated vibration signals from the bottom of the seed-metering device. The vibration signal was monitored by the uT3604FS (16-bit) data collector and the CA-YD-103 piezoelectric acceleration sensor. The seed-filling process was extracted using a high-speed camera system (FASTCAM Mini UX100; Photron Limited, Tokyo, Japan) and lasted 25 s, with a shooting speed of 250 frames per second. The direction of the images was from the back of the seed-metering device. The seed-filling angle on both sides of the seed-metering device was extracted. The evaluation indexes were calculated with 30 model-holes per row as samples (6 rows). Each treatment was repeated in triplicate. Figure 6. Vibration seed-metering test bench: (1) computer for vibration measurement, (2) uT3604FS (16bit) data collector, (3) computer for high-speed camera, (4) host of high-speed camera, (5) JPS-12 seed-meter performance test bench, (6) exposure lamp, (7) high-speed camera, (8) DH40200 type vibration exciter, (9) CA-YD-103 piezoelectric acceleration sensor, (10) seed-metering device, and (11) mobile phone bracket. Figure 7 shows the time-domain signals at different engine speeds and PTO speeds. It is noticeable that the amplitude increased an increase in engine speed. Vibration acceleration at an engine speed of 2500 rpm was significantly larger than that at 850 rpm and 1600 rpm (Figure 7a). The engine speed significantly increased the vibration Figure 6. Vibration seed-metering test bench: (1) computer for vibration measurement, (2) uT3604FS (16 bit) data collector, (3) computer for high-speed camera, (4) host of high-speed camera, (5) JPS-12 seed-meter performance test bench, (6) exposure lamp, (7) high-speed camera, (8) DH40200 type vibration exciter, (9) CA-YD-103 piezoelectric acceleration sensor, (10) seed-metering device, and (11) mobile phone bracket. Figure 7 shows the time-domain signals at different engine speeds and PTO speeds. It is noticeable that the amplitude increased an increase in engine speed. Vibration acceleration at an engine speed of 2500 rpm was significantly larger than that at 850 rpm and 1600 rpm (Figure 7a). The engine speed significantly increased the vibration acceleration and amplitude of the seed-metering device. At an engine speed of 1600 rpm and a tractor forward speed of 3.86 km h −1 , the amplitude at a PTO speed of 540 rpm was significantly less than that at a PTO speed of 720 rpm, indicating that an increase in PTO speed resulted in an increase in vibration (Figure 7b).

Vibration Characteristics of a Rapeseed Seeder
The vibration frequencies of the first three-order peaks under various working conditions are shown in Table 3. No significant influence of forward speed on the first three−order vibration frequencies was observed under the same PTO and engine speeds. The first three−order main frequencies of seeder vibration were significantly affected by engine speed ( Table 4). The frequencies mainly included 0-60 Hz, 70-110 Hz, and 120-180 Hz for the rapeseed seeder. Through analyzing various frequency ranges, the maximum vibration accelerations were was calculated to be 14, 23, and 33 m s −2 , respectively. acceleration and amplitude of the seed-metering device. At an engine speed of 1600 rpm and a tractor forward speed of 3.86 km h −1 , the amplitude at a PTO speed of 540 rpm was significantly less than that at a PTO speed of 720 rpm, indicating that an increase in PTO speed resulted in an increase in vibration (Figure 7b). The vibration frequencies of the first three-order peaks under various working conditions are shown in Table 3. No significant influence of forward speed on the first three−order vibration frequencies was observed under the same PTO and engine speeds. The first three−order main frequencies of seeder vibration were significantly affected by engine speed (Table 4). The frequencies mainly included 0-60 Hz, 70-110 Hz, and 120-180 Hz for the rapeseed seeder. Through analyzing various frequency ranges, the maximum vibration accelerations were was calculated to be 14, 23, and 33 m s −2 , respectively.    Note: p < 0.01 (highly significant, **), p < 0.05 (significant, *); A means PTO speed, B means engine speed, and C means forward speed.

Seed Speed at Different Frequencies
The direction of seed motion in the seed-metering device is shown in Figure 8a. We extracted the speed of the last 6 seeds in the same columns. When it came to vibration, the speed fluctuated in the X, Y, and Z directions (Figure 8b-d). There was no obvious trend of speed change in the X and Y directions because the vibration mainly occurred in the Z direction. The speed change in the Z direction was exactly proportional to the vertical displacement, and the speed change at 10 Hz was more intense than at other frequencies, which was related to the greatest vertical displacement.  Table 5 shows that the target seed rate increased with an increase in vibration frequency at 10-40 Hz, while the missing rate of seed filling decreased. The vertical displacement decreased with an increase in vibration frequency. As the vertical displacement was too slight to affect seed-filling performance, the vibration frequency had no significant effect on the target seed rate, as evidenced by the target seed rate of  Table 5 shows that the target seed rate increased with an increase in vibration frequency at 10-40 Hz, while the missing rate of seed filling decreased. The vertical displacement decreased with an increase in vibration frequency. As the vertical displacement was too slight to affect seed-filling performance, the vibration frequency had no significant effect on the target seed rate, as evidenced by the target seed rate of 100% at 50-180 Hz. The vibration frequency had a significant effect on the rate of single seed and double seeds. There was no missing rate of seed filling and no multiple rates of seed filling at 70-110 Hz and 120-180 Hz. The rate of single seed decreased when frequency increased, while the rate of double seeds increased. The distribution of the rate of single seed and double seeds was affected by the missing rate of seed filling at 0-60 Hz, but the rate of single seed was lower, and the rate of double seeds was larger.

Effect of Vibration on Retained Seeds and Seed Bounce
Figure 9a presents seed retention after bouncing. At 10-60 Hz, the number of retained seeds was less than 20, and decreased with increasing vibration frequency. In contrast, the quantity of retained seeds increased dramatically at 70 Hz (Figure 9b). The number of retained seeds reached a maximum of 95 at 80 Hz, and then decreased at 90-180 Hz. The number of retained seeds was 0 at 0 Hz because the seeds in the model-hole did not leave the model-hole if they were vibration-free. The seeds filled in the model-hole dropped out of the model-hole and settled in the zone between the seed-metering wheel and the back motherboard at medium frequencies, thereby resulting in more retained seeds. The vibration made the number of retained seeds range from 0-95. In the simulation, the excessive number of retained seeds did not have a great impact on the seed-filling performance, but it is likely to be detrimental to seed-filling performance under real sowing conditions. Agriculture 2022, 5, x FOR PEER REVIEW 12 of 21 (a) (b)  Figure 10a shows that the seed-filling angle θ and the initial seed-filling angle varied between 56° and 59° at 0-180 Hz (Figure 10b), indicating that the initial seed status was relatively stable without vibrations. No significant differences in seed-filling angle were observed at 20-180 Hz, ranging from 80° to 87° (Figure 10b). However, the fluctuation range of seed-filling angle under vibration was larger than that without vibration. The seed-filling angle differed significantly at 0 Hz and 10 Hz, with a minimum value of 69.78° at 0 Hz and a maximum value of 91.4° at 10 Hz. The seed-metering device's largest vertical displacement occurred at 10 Hz, causing seeds to bounce back into the seed-filling area and increasing the seed-filling angle. The vibration significantly increased the seed-filling angle to 69.78°-91.40°.   Figure 10a shows that the seed-filling angle θ and the initial seed-filling angle varied between 56 • and 59 • at 0-180 Hz (Figure 10b), indicating that the initial seed status was relatively stable without vibrations. No significant differences in seed-filling angle were observed at 20-180 Hz, ranging from 80 • to 87 • (Figure 10b). However, the fluctuation range of seed-filling angle under vibration was larger than that without vibration. The seed-filling angle differed significantly at 0 Hz and 10 Hz, with a minimum value of 69.78 • at 0 Hz and a maximum value of 91.4 • at 10 Hz. The seed-metering device's largest vertical displacement occurred at 10 Hz, causing seeds to bounce back into the seed-filling area and increasing the seed-filling angle. The vibration significantly increased the seed-filling angle to 69.78 • -91.40 • .  Figure 10a shows that the seed-filling angle θ and the initial seed-filling angle varied between 56° and 59° at 0-180 Hz (Figure 10b), indicating that the initial seed status was relatively stable without vibrations. No significant differences in seed-filling angle were observed at 20-180 Hz, ranging from 80° to 87° (Figure 10b). However, the fluctuation range of seed-filling angle under vibration was larger than that without vibration. The seed-filling angle differed significantly at 0 Hz and 10 Hz, with a minimum value of 69.78° at 0 Hz and a maximum value of 91.4° at 10 Hz. The seed-metering device's largest vertical displacement occurred at 10 Hz, causing seeds to bounce back into the seed-filling area and increasing the seed-filling angle. The vibration significantly increased the seed-filling angle to 69.78°-91.40°.  It is worth noting that the increase in the seed-filling angle corresponds to an increase in the level of seed in the seed-filling area. As a result, it may be concluded that the vibration alters the level of seed in the seed-filling area. The vibration's impact on seedfilling performance can, therefore, be solved by altering the level of seed in the seed-filling area. Next, in the bench test, the level of seed in the seed-filling area can be varied by altering the longitudinal distance.

Effects of Vibration on Seed-Filling Performance
The established regression model of the target seed rate was significant (p < 0.01). The target seed rate was extremely significantly influenced by the frequency, longitudinal distance, and interaction of frequency and longitudinal distance (p < 0.01). The target seed rate was significantly influenced by the interaction of longitudinal distance and lateral distance (p < 0.05) ( Table 6). Note: p < 0.01 (highly significant, **), p < 0.05 (significant, *); A means frequency (Hz), B means longitudinal distance (mm), C means lateral distance (mm). Figure 11 presents the interaction surface between the longitudinal distance and the lateral distance under different frequencies. The target seed rate increased with an increase in longitudinal distance (Figure 11a,d), while no significant difference in the lateral distance on the target seed rate was observed. The target seed rate was at its maximum at a longitudinal distance of 20 mm due to the seeds' slight bounce at 10 Hz. The target seed rate achieved its minimum at a longitudinal distance of 20 mm and a vibration of 20-40 Hz (Figure 11g,j,m). The increase in vibration frequency increased the compressive force and contributed to the seeds filling the model-hole, resulting in repeated seed filling and reducing the target seed rate.
The established regression model of the missing rate of seed filling was significant (p < 0.01). The missing rate of seed filling was markedly affected by frequency, longitudinal distance, and the interaction of frequency and longitudinal distance (p < 0.01), and was significantly affected by lateral distance (p < 0.05) ( Table 6). Figure 11b,e shows that the missing rate of seed filling increased with decreasing longitudinal distance, whereas there was no significant difference in the lateral distance to the missing rate of seed filling. The seed layer height was insufficient at the longitudinal distance of 0 mm, causing a maximum missing rate of seed filling.  The established regression model of the missing rate of seed filling was significant (p < 0.01). The missing rate of seed filling was markedly affected by frequency, longitudinal distance, and the interaction of frequency and longitudinal distance (p < 0.01), and was significantly affected by lateral distance (p < 0.05) ( Table 6). Figure 11b,e shows that the missing rate of seed filling increased with decreasing longitudinal distance, whereas there was no significant difference in the lateral distance to the missing rate of seed filling. The seed layer height was insufficient at the longitudinal distance of 0 mm, causing a maximum missing rate of seed filling.
The established regression model of the multiple rates of seed filling was significant (p < 0.01). Table 6 shows that frequency, longitudinal distance, and the interaction of frequency and longitudinal distance significantly affected multiple rates of seed filling (p < 0.01). The interaction of longitudinal distance and lateral distance significantly affected multiple rates of seed filling (p < 0.05). The multiple rates of seed filling were at their maximum at a longitudinal distance of 20 mm and a lateral distance of 42 mm ( Figure  11c,f,i,l,o). A larger longitudinal distance caused a large seed layer height and sufficient compressive force, which contributed to the seeds being filled into the model-hole of seed-metering wheel. The vibration frequency had a significant influence on the seed-filling performance. The effects of longitudinal distance on seed-filling performance were greater than those of lateral distance, and longitudinal distance was a key parameter for improving seed-filling performance under vibration conditions.

Effect of Vibration on Seed-Filling Angle
The established regression model of the initial seed-filling angle was significant (p < 0.01). The variance analysis results indicated that the initial seed-filling angle was markedly influenced by longitudinal distance, lateral distance, and the interaction of longitudinal distance and lateral distance (p < 0.01) ( Table 7). Figure 12 presents the relationship between the initial seed-filling angle and the longitudinal and lateral distances. The longitudinal distance was positively and significantly correlated with the initial seed-filling angle, indicating that increasing longitudinal distance may increase the initial seed-filling angle. Table 7. Variance analysis of factors affecting initial seed-filling angle and seed-filling angle.  The established regression model of the multiple rates of seed filling was significant (p < 0.01). Table 6 shows that frequency, longitudinal distance, and the interaction of frequency and longitudinal distance significantly affected multiple rates of seed filling (p < 0.01). The interaction of longitudinal distance and lateral distance significantly affected multiple rates of seed filling (p < 0.05). The multiple rates of seed filling were at their maximum at a longitudinal distance of 20 mm and a lateral distance of 42 mm (Figure 11c,f,i,l,o). A larger longitudinal distance caused a large seed layer height and sufficient compressive force, which contributed to the seeds being filled into the model-hole of seed-metering wheel. The vibration frequency had a significant influence on the seed-filling performance. The effects of longitudinal distance on seed-filling performance were greater than those of lateral distance, and longitudinal distance was a key parameter for improving seed-filling performance under vibration conditions.

Effect of Vibration on Seed-Filling Angle
The established regression model of the initial seed-filling angle was significant (p < 0.01). The variance analysis results indicated that the initial seed-filling angle was markedly influenced by longitudinal distance, lateral distance, and the interaction of longitudinal distance and lateral distance (p < 0.01) ( Table 7). Figure 12 presents the relationship between the initial seed-filling angle and the longitudinal and lateral distances. The longitudinal distance was positively and significantly correlated with the initial seed-filling angle, indicating that increasing longitudinal distance may increase the initial seed-filling angle. Note: p < 0.01 (highly significant, **), p < 0.05 (significant, *); A means frequency (Hz), B means longitudinal distance (mm), and C means lateral distance (mm). The established regression model of the seed-filling angle was significant (p < 0.01). As shown in Table 7, the seed-filling angle was significantly influenced by frequency and longitudinal distance (p < 0.01), and markedly affected by lateral distance (p < 0.05). The seed-filling angle significantly increased with an increase in the longitudinal distance, with the minimum at a longitudinal distance of 0 mm and a lateral distance of 50 mm, and the largest at a longitudinal distance of 20 mm and a lateral distance of 42 mm (Figure 13a-e). The seed-filling angle affected by the longitudinal distance was greater than that affected by the lateral distance. The seed-filling angle at 20-40 Hz was significantly greater than that at 0-10 Hz. A larger frequency vibration increased the shaking and compressive force of the rapeseeds, resulting in an increase in the seed-filling angle. The established regression model of the seed-filling angle was significant (p < 0.01). As shown in Table 7, the seed-filling angle was significantly influenced by frequency and longitudinal distance (p < 0.01), and markedly affected by lateral distance (p < 0.05). The seed-filling angle significantly increased with an increase in the longitudinal distance, with the minimum at a longitudinal distance of 0 mm and a lateral distance of 50 mm, and the largest at a longitudinal distance of 20 mm and a lateral distance of 42 mm (Figure 13a-e). The seed-filling angle affected by the longitudinal distance was greater than that affected by the lateral distance. The seed-filling angle at 20-40 Hz was significantly greater than that at 0-10 Hz. A larger frequency vibration increased the shaking and compressive force of the rapeseeds, resulting in an increase in the seed-filling angle. Note: p < 0.01 (highly significant, **), p < 0.05 (significant, *); A means frequency (Hz), B means longitudinal distance (mm), and C means lateral distance (mm). The established regression model of the seed-filling angle was significant (p < 0.01). As shown in Table 7, the seed-filling angle was significantly influenced by frequency and longitudinal distance (p < 0.01), and markedly affected by lateral distance (p < 0.05). The seed-filling angle significantly increased with an increase in the longitudinal distance, with the minimum at a longitudinal distance of 0 mm and a lateral distance of 50 mm, and the largest at a longitudinal distance of 20 mm and a lateral distance of 42 mm (Figure 13a-e). The seed-filling angle affected by the longitudinal distance was greater than that affected by the lateral distance. The seed-filling angle at 20-40 Hz was significantly greater than that at 0-10 Hz. A larger frequency vibration increased the shaking and compressive force of the rapeseeds, resulting in an increase in the seed-filling angle.  Figure 14a shows the seed-filling situation at a longitudinal distance of 20 mm, a lateral distance of 50 mm, and a vibration frequency of 30 Hz. Though the larger seed-filling angle favored seed filling, the number of retained seeds after bounce increased significantly, resulting in an increased seed-damage ratio and multiple ratios of seed filling. As shown in Figure 14b, the seed-filling angle was large at a longitudinal  Figure 14a shows the seed-filling situation at a longitudinal distance of 20 mm, a lateral distance of 50 mm, and a vibration frequency of 30 Hz. Though the larger seed-filling angle favored seed filling, the number of retained seeds after bounce increased significantly, resulting in an increased seed-damage ratio and multiple ratios of seed filling. As shown in Figure 14b, the seed-filling angle was large at a longitudinal distance of 10 mm, a lateral distance of 50 mm, and a vibration frequency of 30 Hz. There were only a few retained seeds after the bounce, indicating that seed-filling performance was improved by optimizing the longitudinal distance. The phenomenon of seeds tilting to one side was observed at larger longitudinal and lateral distances and at higher frequencies of vibration (Figure 14a), which needed to be further investigated.  Figure 14a shows the seed-filling situation at a longitudinal distance of 20 mm, a lateral distance of 50 mm, and a vibration frequency of 30 Hz. Though the larger seed-filling angle favored seed filling, the number of retained seeds after bounce increased significantly, resulting in an increased seed-damage ratio and multiple ratios of seed filling. As shown in Figure 14b, the seed-filling angle was large at a longitudinal distance of 10 mm, a lateral distance of 50 mm, and a vibration frequency of 30 Hz. There were only a few retained seeds after the bounce, indicating that seed-filling performance was improved by optimizing the longitudinal distance. The phenomenon of seeds tilting to one side was observed at larger longitudinal and lateral distances and at higher frequencies of vibration (Figure 14a), which needed to be further investigated. The target seed rate was improved by adjusting various longitudinal distances under different vibration frequencies. The target seed rate was more than 91% with a longitudinal distance of 15-20 mm at 0 Hz, a longitudinal distance of 10-20 mm at 10 Hz, a longitudinal distance of 5 mm at 20 Hz, a longitudinal distance of 0-15 mm at 30 Hz, and a longitudinal distance of 5-10 mm at 40 Hz. The target seed rate was improved by adjusting various longitudinal distances under different vibration frequencies. The target seed rate was more than 91% with a longitudinal distance of 15-20 mm at 0 Hz, a longitudinal distance of 10-20 mm at 10 Hz, a longitudinal distance of 5 mm at 20 Hz, a longitudinal distance of 0-15 mm at 30 Hz, and a longitudinal distance of 5-10 mm at 40 Hz.

Discussion
The theoretical study found that the centralized seed-metering device's vibration frequencies were concentrated at 0-180 Hz when combined with the outcomes of the field tests. Low frequencies of 0-60 Hz had a vibration acceleration of 14 m s −2 , with a vibration acceleration of 23 m s −2 at 70-110 Hz and a vibration acceleration of 33 m s −2 at 120-180 Hz, and the vibration mainly came from the engine. This agrees with the vibration test findings reported by Liao et al. [21].
The seeds' motion was introduced using the discrete element method (DEM) simulation. Many academics have embraced this strategy since it can faithfully and correctly simulate the research process [35]. The results of the simulation test demonstrate that vibration will weaken the seeding performance (seeding uniformity), which is in line with the findings of Kuş [29] and Zhai [30] et al. Vibration also alters the seed layer height, which has a significant effect on seed-sowing quality [36][37][38][39].
The regulating plate of the seed layer was utilized in the bench test to mitigate the effects of vibration on seed layer height. It was discovered that adjusting the seed layer height in reverse can lessen the effects of vibration; as such, the higher the vibration, the lower the seed layer height needs to be. Hence, it is suggested that the seed-filling method should be altered in the follow-up study to ensure that the seed layer height is always high and has superior seed-filling performance under any vibration conditions.

Conclusions
The seed-filling and motion characteristics of the centralized seed-metering system of rapeseed under various vibration frequencies were investigated using DEM simulation and bench tests. The number of retained seeds, seed-filling indexes, seed-filling angle, and seed speed were analyzed. Conclusions can be drawn as follows: (1) The field vibration tests revealed that vibration acceleration in the vertical direction increased with an increase in the engine and PTO speeds, and the vibration frequencies of the centralized seed-metering system were concentrated at 0-180 Hz. Low frequencies of 0-60 Hz had a vibration acceleration of 14 m s −2 , with a vibration acceleration of 23 m s −2 at 70-110 Hz and a vibration acceleration of 33 m s −2 at 120-180 Hz. (2) The simulation results indicated that a vibration frequency of 10-40 Hz resulted in a target seed rate within 88.67-99.44% and significantly increased the seed-filling angle, ranging from 56.00 • -59.00 • to 69.78 • -91.40 • when the speed of the seed-metering wheel was 20 rpm. Vibration significantly increased the change in seed speed and made the number of retained seeds range from 0-95. Vibration mainly changes the level of seed in the seed-filling area, which affects the seed-filling performance. (3) The bench test demonstrated that vibration had a significant impact on the target seed rate, the missing rate of seed filling, the multiple ratios of seed filling, the seed-filling angle, and the number of retained seeds when the speed of the seed-metering wheel was 20 rpm. Longitudinal distance had a significantly greater influence on seed-filling performance than lateral distance at 10-40 Hz. At 10 Hz, the increase in longitudinal distance resulted in an increase in the target seed rate. At 20-40 Hz, the increase in longitudinal distance increased the multiple rates of seed filling while decreasing the target seed rate. By adjusting the longitudinal distance, the target seed rate can be maintained above 91%.
The results should be conducive to clarifying the mechanism of seed movement under vibration conditions, and then, optimizing the structure of the seed-metering device to reduce the impact of vibration on field operation. The seed damage and multiple rates of seed filling under the impact of the external environment, including the interaction between vibration and inclination, will be further investigated.
Funding: This research was funded by the National Natural Science Foundation of China (31901413).

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.

Data Availability Statement:
The data presented in this study are available upon request from the authors.

Conflicts of Interest:
The authors declare no conflict of interest.

Nomenclature
Initial seed-filling angle (θ 1 ) The included angle between the highest point and lowest point of the seed layer and the central axis of the seed-metering wheel under the condition of no vibration.
Seed-filling angle (θ 2 ) The included angle between the highest point and lowest point of the seed layer and the central axis of the seed-metering wheel under the condition of vibration. Longitudinal distance (h) The vertical distance between the bottom of the regulating plate of seed layer and the central axis of the seed-metering wheel.
Lateral distance (l) The lateral distance between the obtuse angle point of the regulating plate of seed layer and the central axis of the seed-metering wheel.
Retained seeds (I) The seeds that should have been discharged from the seed-metering device but left due to vibration. Target seed rate (Q) The proportion of 1-3 seeds per model-hole. Missing rate of seed filling (M) The proportion of 0 seeds per model-hole Multiple rates of seed filling (L) The proportion of more than 3 seeds per model-hole.