1. Introduction

2. Mathematical model of reseeding link of air-suction precision tray seeder

2.1. Mathematical model of seeds in a “suspended” state

The forces on the seeds in the “suspended” state are shown in Figure 7. The seeds in the “suspended” state are subjected to the fluid buoyancy force M, the fluid resistance to the seeds’ bypassing F and the seeds’ own gravity G. The magnitudes of these forces are [17]:

$$\mathrm{M}=\frac{m_s}{{\rho }_s}{\rho }_{a}g$$

(1)

$$F=\frac{1}{2}{\rho }_a{C}_d{S}_s{v}_t{}^2$$

(2)

$$\mathrm{G}=m_s\mathrm{g}$$

(3)

Where: ρ_a -- fluid density, kg/m³;

C_d -- resistance coefficient between seed and air, dimensionless;

S_s -- the projected area of seed in motion direction, m²;

v_t -- relative velocity between seed and air, m/s;

ρ_s -- seed density, kg/m³;

m_s -- seed weight, kg;

g -- the acceleration of gravity, m/s²;

Figure 7. Seed stress analysis.

Figure 7. Seed stress analysis.

The stress equilibrium equation of seeds in a “suspended” state is:

$$F+M=G$$

(4)

$$F_Z+\frac{m_s}{{\rho }_s}{\rho }_{a}g=m_{s}g$$

(5)

At this time, the critical velocity of the seed is:

$$v_t=\sqrt{\frac{2cos\beta mg\left({\rho }_s-{\rho }_a\right)}{C_d{S}_s{\rho }_s{\rho }_a}}\left(0\le \beta <90°\right)$$

(6)

The precision tray seeder designed in this paper is mainly applicable to hole tray seeding of small grain-size seeds. Therefore, the more common small-grained seed, kale seed (Jingfeng No. 1) [18], was selected as the object of study, and because of its approximate spherical shape, the drag coefficient at critical speed was obtained as:

$$C_d=\frac{4gd\left({\rho }_s-{\rho }_a\right)}{3{\rho }_a{v}_t{}^2}$$

(7)

To determine the critical velocity of the seeds, the calculation using the table look-up method requires eliminating the v_t² term and using the factorless quantity C_dR_e².

$$R_e=\frac{v_{t}d{\rho }_a}{\eta }$$

(8)

Where: d -- seed diameter, mm;

η -- the dynamic viscosity of the fluid;

By substituting equation (7) into equation (6), we get:

$$C_d{R}_e{}^2=\frac{4g{d}^3{\rho }_a\left({\rho }_s-{\rho }_a\right)}{3{\eta }^2}$$

(9)

The equivalent diameter of kale seeds is 1.97 mm, the fluid density of air ρ_a is 1.23 kg/m³, g is taken as 9.8 m/s², the dynamic viscosity of air η is 18.4×10^-6 pa·s; the seed (mass) density of kale seeds ρ_s is 0.742×10³ kg/m², which gives C_dR_e² as 2.7×10⁵, and from the literature [19] the sphere of R_e and The maximum suspension speed v_t of single kale seeds is 3.7 m/s, which means that the kale seeds are in the range of needle suction nozzle, and the speed of “suspension” is 3.7 m/s.

3. Simulation experiments and results analysis of the reseeding device

4. Simulation experiments and results analysis of the seed vibration device

5. Conclusions

6. Acknowledgments

References

1. Karayel, D.; Barut, Z.B.; zmerzi, A. Mathematical modelling of vacuum pressure on a precision seeder. Biosyst Eng 2004, 87, 437–444. [Google Scholar] [CrossRef]
2. Arzu, Y.; Adnan, D. Optimisation of the seed spacing uniformity performance of a vacuum-type precision seeder using response surface methodology. Biosyst Eng 2007, 97, 347–356. [Google Scholar]
3. Gaikwad, B.B.; Sirohi, N.P.S. Design of a low-cost pneumatic seeder for nursery plug trays. Biosyst Eng 2008, 99, 322–329. [Google Scholar] [CrossRef]
4. Singh, R.C.; Singh, G.; Saraswat, D.C. Optimization of design and operational parameters of a pneumatic seed metering device for planting cottonseeds. Biosyst Eng 2005, 92, 429–438. [Google Scholar] [CrossRef]
5. Zheng, G.; Liu, J.; Nie, X.B.; Li, B.M.; Wang, C.D. Application of plant seedling technology and equipment for plant vegetable. Agricultural Engineering Technology 2019, 39, 60–65. [Google Scholar]
6. Yang, Q.Z.; Xu, L.; Shi, X.Y.; Ahamd, I.; Mao, H.P.; Hu, J.P.; Han, L.H. Design of seedlings separation device with reciprocating movement seedling cups and its controlling system of the full-automatic plug seedling transplanter. Comput Electron Agr 2018, 147, 131–145. [Google Scholar] [CrossRef]
7. Qin, G.M.; Zhao, Y.; Xiao, H.R.; Jin, Y.; Wu, Y.D.; Li, Q. Development and performance test of 2BSL-320 drum suction type vegetable precision sowing machine. Journal of Chinese Agricultural Mechanization 2015, 36, 68–71. [Google Scholar]
8. Yu, J.J.; Liao, Y.T.; C, S.; Yang, S.; Liao, Q.X. Simulation analysis and match experiment on negative and positive pressures of pneumatic precision metering device for rapeseed. Int J Agr Biol Eng 2014, 7, 1–12. [Google Scholar]
9. Arzu, Y.; Adnan, D. Measurement of seed spacing uniformity performance of a precision metering unit as function of the number of holes on vacuum plate. Measurement 2014, 10, 128–135. [Google Scholar]
10. Liu, H.T. Study on Mechanical-Electron-Magnetismco-Simulation of Electromagnetic Vibrated Seed-Metering Device. Master’s thesis, Guangxi University, Guangxi, China, 2013. [Google Scholar]
11. Luo, X.; Hu, B.; Dong, C.W. Simulation experimental study on the adsorption properties of suction nozzle of the air-suction precision tray seeder. Journal of Hebei Agricultural University 2011, 34, 111–113+118. [Google Scholar] [CrossRef]
12. Chen, J.; Li, Y.M.; Wang, X.Q.; Zhao, Z. Finite Element Analysis for the Sucking Nozzle Air Field of Air-suction Seeder. Transactions of the Chinese Society for Agricultural Machinery 2007, 09, 59–62. [Google Scholar]
13. Chen, J.; Zhou, H.; Zhao, Z.; Li, Y.M.; Gong, Z.Q. Analysis of Rice Seeds Motion on Vibrating Plate Using EDEM. Transactions of the Chinese Society for Agricultural Machinery 2011, 42, 79–83+100. [Google Scholar]
14. Yazgi, A.; Degirmencioglu, A. Optimisationof the seed spacing seeder using response surface methodology. Biosyst Eng 2007, 97, 347–356. [Google Scholar] [CrossRef]
15. Zhao, Z.; Li, Y.M.; Chen, J.; Xu, L.Z. Influence of seeds spatial distribution on suction performance of precision vacuum seeder. Journal of Jiangsu University (Natural Science Edition) 2009, 30, 559–563. [Google Scholar]
16. Zhao, Z.; Li, Y.M.; Liang, Z.W.; Gong, Z.Q. DEM simulation and physical testing of rice seed impact against a grain loss sensor. Biosyst Eng 2013, 116, 410–419. [Google Scholar]
17. Zhang, Z.L.; Wang, J.L.; Cheng, H.Q.; Zhang, W.Z. ; Airflow Simulation and Optimization Design for Vegetable Pneumatic Seed Supply Device-Based on ANSYS/FOTRAN. Journal of Agricultural Mechanization Research 2011, 33, 43–45. [Google Scholar]
18. Li, Q.C. Mechanism Analysis and Experimental Study on Scoop Type Precision Seed Metering Device for Small Size Vegetable Seeds. Master’s thesis, Northeast Agricultural University, Heilongjiang, China, 2020. [Google Scholar]
19. Zhou, Z.E. Physical Properties of Bio-Materials. Beijing: agriculture press: Beijing, China, 1994; pp. 1–100. [Google Scholar]
20. Chen, J.; Zhou, H.; Zhao, Z.; Li, Y.M.; Gong, Z.Q. Analysis of Rice Seeds Motion on Vibrating Plate Using EDEM. Transactions of the Chinese Society for Agricultural Machinery 2011, 42, 79–83+100. [Google Scholar]
21. Tang, J.; Yan, H.R.; Yang, H. Design and Simulation of a Novel Electromagnetic Vibration Feeder. Journal of Xihua University(Natural Science Edition) 2009, 28, 12–16+24. [Google Scholar]
22. Yang, W.W. Research on Cylinder Precision tomato Seeder Based On The Pneumatic Suspension Seed Supply. Master’s thesis, Shihezi University, Xinjiang, China, 2014. [Google Scholar]
23. Zhang, S.P.; Chen, J.; Li, Y.M. Analysis of seeds “Boiling” motion on vibrational air-suction tray seeder. Transactions of the Chinese Society of Agricultural Engineering 2008, 07, 20–24. [Google Scholar]
24. Gong, Z.Q.; Chen, J.; Li, Y.M. Seed Force in Airflow Field of Vacuum Tray Precision Seeder Device during Suction Process of Seeds. Transactions of the Chinese Society for Agricultural Machinery 2014, 45, 92–97+117. [Google Scholar]