2BG-2型玉米垄作免耕播种机播种深度数学模型的仿真与验证.pdf

第 31 卷 第 9 期 农 业 工 程 学 报 Vol.31 No.9 2015 年 5 月 Transactions of the Chinese Society of Agricultural Engineering May 2015 19 Simulation and validation of seeding depth mathematical model of 2BG-2 type corn ridge planting no-till planter Lin Jing1, Qian Wei1, Li Baofa1, Liu Yanfen1,2 (1. College of Engineering, Shenyang Agricultural University, Shenyang 110866, China; 2. College of Mechanical and Electrical Engineering, Qingdao Agricultural University, Qingdao 266109, China) Abstract: No-till planter works in the condition that the ground is covered with residual and straw, so it is important to keep its residue cutting quality and to maintain the stability of seeding depth. Based on 2BG-2 type corn ridge planting no-till planter, complete machine design and forces model of the planter unit were studied. Mathematical model of change of the seeding depth was established, and according to this model, computer simulations were conducted to study the related factors affecting seeding depth stability. Theoretical analysis showed that: in order to keep the seeding depth stability, the spring constant should be increased appropriately, and configuration location of the parts, on the basis of ensuring the necessary mass of system, should have reasonable layout to increase the rotary inertia. Field tests showed that: trends of the theoretical angles over time were similar with the measured ones; the average relative error (ARE) were 7.86%, 6.98% and 8.07% for mass of 70, 110 and 150 kg, respectively; Determination coefficient (R2) were 0.9707, 0.9692 and 0.9697 for mass of 70, 110 and 150kg, respectively. The ARE were 7.45%, 7.91% and 8.73% for spring constant of 16, 20 and 25 N/mm, respectively; the R2 were 0.9767, 0.9720 and 0.9603 for spring constant of 16, 20 and 25 N/mm. This study provides valuable information for the development and improvement of no-till planter in the Northeast ridge zone in China. Key words: mathematical model; seeds; stability; ridge-till; no-till planter; seeding depth doi：10.11975/j.issn.1002-6819.2015.09.004 CLC number: S223.2 Document code: A Article ID: 1002-6819(2015)-09-0019-06 Lin Jing, Qian Wei, Li Baofa, et al. Simulation and validation of seeding depth mathematical model of 2BG-2 type corn ridge planting no-till planterJ. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2015, 31(9): 1924. (in English with Chinese abstract) 林 静，钱 巍，李宝筏，等. 2BG-2型玉米垄作免耕播种机播种深度数学模型的仿真与验证J. 农业工程学报，2015， 31(9)：1924. 0 Introduction Conservation tillage has been implemented in the Northeast area of China for 20 years. Compared with the traditional planting patterns, it has many advantages, such as water conservation, high spike rate, drought and cold resistance, strong anti-freezing and anti-reversibility effect, etc1-6. Corn no-till planter works in the field with bad conditions that the ground is covered with residue and straw7-8. Thus, the seeding depth stability of no-till planter is affected. In order to control the seeding depth, many studies have been conducted over the several past decades9. Most of the foreign no-till planters use double disc furrow opener with deep rubber wheel censored by its sides, and some adopt the methods of post repression wheel or setting deep limit circle on disc furrow opener. Meanwhile, adding loading equipments, such as a spring, so the parallel four linkage profiling mechanism is common. Germany Amazone Company and France Kuhn Company adopt Received date: 2014-10-17 Revised date: 2015-04-10 Foundation item: Special Fund for Agro-scientific Research in the Public Interest (201503116); National Natural Science Foundation of China (1275318) Biography: Lin Jing, professor, research on dry farming mechanization and intelligence. Shenyang, College of Engineering, Shenyang Agricultural University, 110866, China. Email: synydxlj69 spring loading devices; America JohnDeere Company uses air bags instead of the spring, while America Greet Plains Company adopts air cylinder in place of air bags; Denmark Krerne Land Company fixes a hydraulic cylinder on the lower hanging point of no-till planter, so that it can increase down pressure to control working depth of residue-cutting and seeding furrow opener. Researchers in University of Manitoba in Canada found that, compared to the hydraulic system, the spring-loaded parallel linkage system has better performance10. The main structure of the planter in domestic is suspending pattern, and repression wheel and parallel four linkage system with a spring-loaded down force device are usually used in order to control seeding depth. For the purpose of keeping residue cutting quality and maintaining stability of seeding depth, average weight of the no-till planters that have been promoted in the Northeast area of China in recent years are over 1 t, which flattens the ridge-shape, enhances the ditch bottom firmness11-12, and increases fuel consumption and manufacturing cost. So it is not a reasonable option. Based on 2BG-2 type corn ridge planting no-till planter13, this paper studied complete machine design and forces model of the planter unit, and established mathematical model of change of the seeding depth. In addition, the purpose of this paper was to investigate the 农业工程学报 2015 年 20 effect of different parameters on seeding depth so as to provide a theoretical information for the design of no-till planter in the Northeast ridge zone in China. 1 Material and methods 1.1 Structure of 2BG-2 type corn ridge planting no-till planter The prototype passes through the performance test conducted by China Agricultural Machinery Test Center in May 2008. As is shown in Fig.1, the whole mass of the planter is 465 kg, and the planter is driven by tractor with power more than 18.3 kW. The fan, residue cutting disc, ridge cleaning and side deep fertilizing device, fertilizer box and land wheel transmission system are installed on the front frame of the planter, and the mass of them is 325 kg. In addition, it is suspended behind the tractor by way of position-control hydraulics, so that part of the tractor weight can be transferred to it. The unit of the planter links with the front frame via parallel four linkage mechanism with down pressure spring, and its mass is 70 kg. In addition, each of the unit bears down pressure 2 278.5 N, which is larger than the required pressure 2 224 N (500 lb)14. 1.Universal joint 2.Frame 3.Fan 4.Fertilizer box 5.Seed box 6.Soil covering and repression device 7.Land wheel mechanism 8.Ridge cleaning device 9. Double disc fertilizing furrow opener 10. Residue cutting device Fig.1 General structure of 2BG-2 type corn ridge planting no-till planter The planter was tested in many places in Liaoning Province, and it turned out that it can reach the requirements of residue cutting and seeding depth stability. The main technical parameters are shown in Table 1. Table 1 Main technical parameters of 2BG-2 type corn ridge planting no-till planter Technical parameters Value Total weigh /kg 465 Supporting power /kW 18.3 Size( lengthwidthheight )/mmmmmm 155017001290 Working rows 2 Adaptive row spacing /mm 500-650 Working velocity /(kmh-1) 5 Seed covering depth /mm 40 Fertilizer covering depth /mm 68 1.2 Structure of planter unit and forces model The main unit working parts structure of 2BG-2 type corn ridge planting no-till planter is shown in Fig.2. 1.Repression wheel 2.Rear frame 3.Seed box and fertilizer apparatus 4. Parallel four linkage mechanism 5.Seeding furrow opener 6. Seed pressure wheel 7.Soil covering device Fig.2 Structure of planter unit Through the analysis of the force on unit of 2BG-2 type corn ridge planting no-till planter, its force condition could be obtained, intensity of each component of the planter could be checked and configuration location layout could also be obtained. Forces on seed pressure wheel and soil covering device are small through analysis of the actual working condition of planter, therefore, they can be consolidated through horizontal and vertical resistance on seeding furrow opener (Rx and Rz ) being respectively multiplied by a coefficient that is 1.1-1.215. When the planter unit is in normal working conditions, the parallel four linkage mechanism should be in a horizontal position. Rod BD（the lower rod）bears pulling force, while rod AC （the upper rod）is under pressure16-17.The simplified force model is shown in Fig 3. Note: 1.Repression wheel; 2.Seeding furrow opener; X and Z are coordinate axes; A, C, B, and D are end of rod AC and BD; FAx, FAz are horizontal and vertical force on the upper rod, N; FBx, FBz are horizontal and vertical force on the lower rod, N; is angle between the horizontal direction and pressure spring, 14; is the angle that traction angle swings upward, rad; F is force on the pressure spring, N; R is resistance on seeding furrow opener, N; Rx, Rz are the horizontal and vertical resistance on seeding furrow opener, N; N is counterforce on repression wheel, N; G is weight of planter unit, N; f is friction coefficients between soil and repression wheel; O1 is centroid coordinate of planter unit; O2 is the centroid coordinate of planter unit when the system is subjected to a disturbance force moment; h0 is seeding depth, m; h1 is distance between repression wheel center and the vertical rod, m; h2 is distance between planter unit centroid and the vertical rod, m; h3 is distance between seeding furrow opener center and the horizontal rod, m; h4 is distance between repression wheel center and the horizontal rod, m; L is horizontal rod length of parallel four linkage mechanism, m; H is vertical rod length of parallel four linkage mechanism, m. Fig.3 Forces on planter unit in longitudinal vertical plane As is shown in Fig.3, according to the equilibrium of force: 第 9 期 林 静等：2BG-2 型玉米垄作免耕播种机播种深度数学模型的仿真与验证 21 FBx-FAx-Fcos-Rx-fN=0 (1) Rz+N-Fsin-G+FBz-FAx=0 (2) In state of equilibrium = 0, let MB=0, then: FAxH=-G(h2+L)-FHcos+Rxh3-RzL+fNh4+N(h1+L) (3) The Eqs(1) and (2) could be converted into: FBx-FAx=Fcos+Rx+fN (4) G=Rz+N-Fsin+FBz-FAz (5) According to preliminary experiment, the value for each variable was: F 320 N, Rx 147 N, Rz 190 N, N 240 N, f 0.6, 14, h0 0.04 m, h1 0.89 m, h2 0.254 m, h3 0.32 m, h4 0.28 m, L 0.30 m, and H 0.15 m. According to Eqs (4) and (5) with data above, FAx, FBx, and G were 835.3, 1465.3, and 686 N, respectively. Therefore, the mass of the planter unit m was 70 kg. 1.3 Mathematical model of seeding depth change No-till planter unit works on the ridge, micro-relief in a field varies due to clumps of crop residue, traffic tracks, and undulating soil surface. Changes in the opener down-force affect the mean depth of seeding across the seeder by their effect on individual opener penetration. In order to study longitudinal stability of the planter unit, a mathematical model of the system with the second Lagrange equation was established. The Lagrange equation can be expressed as18-19: d (12) d j jj TT Qjk tqq = qj is generalized coordinates; j q Qj is generalized force; j is the jth generalized coordinate. As is shown in Fig.3, supposing that the planter moves forward with a uniform speed vm when the seeding furrow opener is in a stable depth, the centroid coordinate of planter unit is O1(x0, z0). When the system is subjected to a disturbance force moment Q, traction angle swings upward an angle , ditching depth becomes shallow, and centroid coordinates come into O2(x, z). There is a following relationship: () 0 0 cos1 sin m xxv tL zzL =+ =+ (7) Where: vm is initial velocity, m/s; is a generalized coordinate, rad. Centroid velocity is: d sin d d cos d m x xvL t z zL t =+ = I0 is system moment of inertia, kgm2. By taking the partial derivative of Eq.(9) with respect to and c2 is L(1.1Rz+N-G); c3 is L(G-Rz-N)+ 0.1Rxh3-0.1FHcos. The swing angle is the function of time t, and then by taking double integration of Eq.(15) with respect to t, the following equation can be obtained. 3 2 0 0.1(cos) (1.1) (1.1) 1 cos() zx x x R LR hFH LRfN LRfN t mLI + = + + + (16) The relevant data are as follows: m is 70kg, rotary inertia I0 is 48.2 kgm2. Then, the changes of with t shown in Fig.4 followed a curve of: =0.077(1-cos1.364t) (17) Fig.4 Change in swing angle with time 1.4 Simulating effects of parameters on seeding depth Eq.(16) is the mathematical model on change of the seeding 农业工程学报 2015 年 22 depth of 2BG-2 type corn ridge planting no-till planter, and from it, we can obtain that the swing angle is related to many parameters, such as m, I0, Rx, Rz, and k. Therefore, through computer simulations, influence of design parameters on traction angle can be studied, and valuable references for the design of no-till planter can be provided20-23. 1.5 Verification test for mathematical model 1.5.1 Field condition The prototype of the no-till planter unit was tested in an indoor clay soil bin located in the Agricultural Machinery Laboratory (414941.32N, 1233328.98E) at Shenyang Agricultural University. The soil bin was 40 m long, 1.8 m wide and 0.6 m deep. The volumetric moisture contents of soil were 12.52%, 14.24% and 17.18% at depths of 5, 10 and 15 cm, respectively. The soil firmnesses were 0.79, 1.05 and 1.14 MPa at depths of 5, 10 and 15 cm, respectively. 1.5.2 Test procedure The horizontal and vertical resistance of soil (Rx and Rz) is determined in the field, which is difficult to control by person. Changing of I0 needs to reconfigure the location of each component, which is same as developing new planter, so a factorial experiment was designed with 3 spring constant settings (k1=16 N/mm, k2=20 N/mm, and k3=25 N/mm) and 3 mass settings (m1=70 kg, m2=110 kg, m3=150 kg). During the experiment, other parameters in the mathematic model were unchanged. The travel speed of the planter unit was kept constant at 1 m/s. Higher speeds were not used because of the excessive vibrations of the toolbar frame and planter unit. Each treatment was replicated three times. A tilt angle sensor was attached to rod AC to measure swing angle. Signals of swing angles were recorded with a data acquisition system at a sampling rate of 200 Hz. Each test run consisted of 10s of data recording. Compared the theoretical data (TD) with measured ones (MD) (mean value of the three data in each treatment), and then calculated average relative error (ARE) and determination coefficient (R2). 2 Results and analysis 2.1 Simulation results about effect of parameters on seeding depth 2.1.1 Effect of parameters on swing angle Simulation results showed that as the increase of the mass of system m, the traction angle decreased (Fig.5a), but it was not obvious, which indicated that it was not a preferred method to increase the weight of the planter to maintain seeding depth stability. With rotary inertia I0 increasing, the traction angle decreased (Fig.5b). Apparently, changing the configuration location of the parts to increase rotary inertia without changing the weight of the planter was more effective than changing m. With the vertical resistance Rz and the horizontal resistance Rx increasing, the traction angle increased obviously (Fig.5c and Fig.5d). Thus, it is necessary to develop new seeding furrow openers to reduce the soil resistance; with the spring constant k increasing, the traction angle decreases remarkably (Fig.5e). Consequently, it is conductive to increase the spring constant appropriately to keep the seeding depth stability. Note: and t are swing angle and time, respectively. Fig.5 Effect of different parameters on swing angle 2.1.2 Relationships between force on spring, arm of spring force and swing angle When k=16 N/mm, with increasing , the spring force F increased linearly (Fig.6a), which was favorable to keep stability of seeding depth. When k=16 N/mm, the arm of the spring force Lc and traction angle were well fitted with a conic curve (Fig.6b). 第 9 期 林 静等：2BG-2 型玉米垄作免耕播种机播种深度数学模型的仿真与验证 23 a. Relation of F and b. Relation of Lc and Note: Spring constant is 16 Nmm-1. Fig.6 Relationship of force on the spring, arm of spring force and swing angle 2.2 Comparison of theoretical and measured results It can be noted from Fig.7 that, the measured swing angle and the theoretical ones are slightly different. The difference in value between them was considered as test conditions with respect to soil compactness and field surface roughness. But trends of the theoretical angles over time were approximated as measured ones, as expected. In addition, the ARE were 7.86%, 6.98% and 8.07% for mass of 70, 110 and 150 kg, respectively; R2 were 0.9707, 0.9692 and 0.9697 for mass of 70, 110 and 150kg, respectively. The ARE were 7.45%, 7.91% and 8.73% for spring constant of 16, 20 and 25 N/mm, respectively; the R2 were 0.9767, 0.9720 and 0.9603 for spring constant of 16, 20 and 25 N/mm. When the planter works in the field, the swing angle is generally not more than 1024. That means the maximum deviation of swing angle were less than 0.807 and 0.873 for different mass and spring constant, respectively. Therefore, considering the influence of test conditions, the mathematical model can accurately reflect the variation of swing angle and can be used to predict and analysis the performance of no-till planter. Fig.7 Theoretical and measured curve of at different system masses or spring constant 3 Conclusions 1) Mathematical model of change of the seeding depth was established. According to theoretical analysis based on the model, the main parameters affecting seeding depth were structure of seeder and soil resistance characteristics. 2) As compared to increasing the mass of system, re