Maize grain modelling for the DEM simulation of sowing process
-
摘要:
为实现基于离散元法的玉米播种过程数字化重现，改善播种机械的性能，需要构建相应的玉米颗粒群体模型。该研究对东北地区常见的玉米品种的颗粒形状、尺寸分布进行统计分析，提出了一种通用的玉米颗粒形状分类方法；在此基础上，基于球填充构建了相应的玉米颗粒群体离散元法建模方法，并以吉平1和平安11两个品种玉米为研究对象，通过堆积试验和筛分试验对填充球数目进行了优化。仿真结果表明，当马齿形、球锥形和类球形玉米颗粒模型的填充球数目分别为10～14、18和1时，玉米颗粒离散元法模型群体特性与实际玉米颗粒群体特性相一致，初步证明了所提玉米颗粒群体建模方法的有效性；最后，基于所建立的玉米颗粒群体模型进行了内窝孔排种器排种过程仿真，对其排种轮转速进行了优化，仿真优化结果与试验结果一致，进一步验证了本文所提出的玉米颗粒群体建模方法的有效性。研究结果可为播种机械数字化设计提供一定参考。
Abstract:The discrete element method is widely used in the analysis and improvement of agriculture machinery performance. To realize digital reproduction of maize seeding process based on discrete element method and improve seeding performance of seeding machinery, the corresponding maize grain assembly model needs to be constructed. In this paper, maize grain shape and size distribution of 10 common varieties in Northeast China were statistically analyzed, and a general shape classification method of maize grains was proposed. That is, the actual assembly of maize grains could be considered as a collection of horse-tooth, spherical-cone, and spheroid maize grains. On this basis, the corresponding assembly modelling of maize grains was constructed based on the sphere filling method and discrete element method. Namely, a single maize grain model was used as a template, the main size was randomly generated according to a normal distribution, the other feature sizes were calculated from the main size to generate each maize seed model, and this was repeated; In addition, the corresponding number of maize seeds was generated according to the percentage of quantity, so that the characteristics of generated maize grain assembly model should be closer to the actual maize grain. The number of filling spheres was optimized through the stacking test and sieve test with the two varieties of maize. The results showed that when the number of filling spheres in the maize grain model was 10-14, 18, and 1 for horse-tooth, spherical-cone, and spheroid maize grain models respectively, the population characteristics of the maize grain discrete element method model were consistent with those of the actual maize grains, which preliminarily proved the validity of the proposed maize grain assembly modelling method. Further, a discrete element method simulation of the seed discharging process of the inner nest hole rower was carried out based on the established maize grain assembly model, and the rotation speed of the seed discharging wheel was optimized, and the optimization result (30 r/min) was consistent with the experimental one, which further demonstrated the validity of the proposed maize grain assembly modelling method. Finally, with the increase of the rotational speed of the seed discharge wheel, the single grain rate was the first to rise and then fall, the double grain rate was the first to fall and then rise, and when the rotational speed was 30 r/min, the single grain rate reached a maximum of 88%, and the double grain rate was the minimum of 11%. Cavity rate was the first to fall rapidly after the basic stability in the vicinity of 1%. This is because when the row of seed wheel speed gradually increased, the particles in the row of seed wheel under the perturbation of the centrifugal inertia force gradually increased, when the rotation speed of the seed discharging wheel was less than 30 r/min, the single particles could reliably rotated with the row of seed wheels, while more than the particles fell back to the bottom of the seed chamber due to the size limitations of the holes, the role of their gravity, and other factors. However, when the rotational speed of the seed discharge wheel was greater than 30 r/min, the centrifugal inertial force dominating the maize seed made it difficult for the excess particles to fall back to the bottom of the seed chamber and rotate with the seed discharge wheel's nest hole, which led to a decrease in the single grain rate. The results of this paper can provide a certain reference for the digital design of maize-seeding machinery.
-
Keywords:
- maize /
- discrete element method /
- sow seeds /
- assembly modelling /
- inner nest hole rower
-
0. 引 言
玉米是中国第一大粮食生产作物[1-2]，产量占粮食总产量的30%，种植面积占粮食种植总面积的26%，依据《“十四五”全国粮食生产能力提升建设规划》，到2025年，力争粮食产能达到7×1011 kg以上，其中玉米是重中之重。在国内耕地面积不断减少的情况下，提高玉米的总产量只能依靠提高单位面积上的产量来实现[3]，播种过程是影响玉米产量的关键环节[4-5]。因此，有必要对播种机械的播种性能进行改进。传统的优化过程难以观察到播种过程中玉米颗粒与机械部件接触过程及运动形式，进而难以达到预期优化目的。离散元法（discrete element method，DEM）作为一种专业处理多颗粒系统的数值分析方法[6-8]，其应用领域遍布工业、食品制药[9-12]、农业[13]以及采矿业[14-17]等。玉米播种过程为典型的玉米颗粒系统与播种机械部件之间相互作用过程，因而基于DEM开展玉米播种机械数字化设计是可行的，但前提是精确建立玉米颗粒DEM分析模型。
为了精确建立玉米颗粒DEM分析模型，首先需研究玉米颗粒的几何形状。玉米颗粒的几何形状复杂，不同的学者将其分为不同的种类[18-21]。因此，需构建一种通用的玉米颗粒形状分类方法；其次，选取合适的颗粒特征尺寸，目前多数学者选择颗粒三轴尺寸作为特征尺寸[22-24]，这样不能很好的体现玉米颗粒形状特征；再者，不同的学者采用球充填方法建立了玉米颗粒模型[21, 25-26]，这些模型填充球的排布方式和数目各不相同，填充球的数目越多，DEM计算时间越长，但是并不一定改善颗粒模型的建模精度[27]。然而在实际应用中，当填充球数目处于合适范围时，模型精度与计算时间均趋于合理[28]。目前合理的填充球排布方式和数目还没有定论；最后，关于所建颗粒模型的有效性验证方法多为料仓和堆积试验等[29-31]，这些方法可以体现颗粒群体效果，但不能反映单个颗粒形状、尺寸对模型精度的影响，因此，验证方法还有待进一步改进。
针对上述问题，本文以东北地区常见的两玉米品种为例，对玉米颗粒的几何形状、特征尺寸分布以及特征尺寸之间的相关性进行测试研究；在此基础上，提出一种玉米颗粒分类方法及相应的玉米颗粒群体建模方法；最后，通过堆积和筛分试验验证其群体特性，通过排种试验反映单个颗粒形状、尺寸对模型精度的影响，并体现其实际应用效果。
1. 玉米颗粒形状和特征尺寸分析
1.1 形状分析
如图1所示，实际玉米果穗的Ⅰ处的颗粒形状主要为球锥形，其上部为楔形，下部形状近似为半球形，且宽度与厚度尺寸相差较小。Ⅱ处的颗粒形状主要为马齿形，其正面与侧面的投影为梯形，且宽度尺寸明显大于厚度尺寸。Ⅲ处的颗粒主要为类球形，包括部分球锥形颗粒，类球形颗粒表面圆滑，形状近似球形。Ⅳ处的颗粒主要为不规则形。鉴于此，选取10个品种玉米，从每个品种中随机选取
1000 粒颗粒，统计每种形状颗粒的数量百分比，结果显示马齿形、球锥形、类球形以及不规则形颗粒数量百分比分别约为70%、8%、13%和9%，可见前三种形状的玉米颗粒总占90%以上。因此，本文把玉米颗粒分为马齿形、球锥形和类球形。![]()
图 1 玉米果穗及颗粒特征尺寸示意图注：W1为上底，(mm)；W2为下底，(mm)；H1、H2为高度，(mm)；T1、T2、T为厚度，(mm)；L为长，(mm)；W为宽，(mm)。Figure 1. Schematic diagram of maize ear and characteristic dimensions of maize grainNote: W1 is the upper bottom, (mm); W2 is the lower bottom, (mm); H1, H2 are the height, (mm); T1, T2, and T are the thickness, mm; L is the length, (mm); W is the width, (mm).1.2 尺寸分析
马齿形、球锥形和类球形玉米颗粒特征尺寸如图1所示，马齿形和球锥形玉米颗粒特征尺寸包括上底、下底、高度和厚度，类球形颗粒特征尺寸包括长、宽和厚。从吉平1和平安11中各随机挑选每一种形状颗粒100粒，作为试验样本，用精度为0.01 mm的数显卡尺测量对应的特征尺寸，结果显示玉米颗粒特征尺寸均近似服从正态分布，如图2所示；其次，通过特征尺寸相关性分析发现，对于马齿形和球锥形玉米颗粒，其它特征尺寸与上底之间存在强相关性，类球形玉米颗粒的长、宽与厚之间存在强相关性，函数关系如式（1），通过试验测量计算所得，系数见表1，决定系数R2≥0.87，标准差σ＜0.90。
![]()
图 2 不同品种玉米颗粒特征尺寸分布图Figure 2. Distributions of characteristic sizes of maize seeds of different varieties表 1 玉米颗粒特征尺寸函数待定系数Table 1. Function undetermined coefficient of characteristic sizes of maize grains品种
Variety形状
Shapea (k) b (l) c (m) d (n) e f g h i j 吉平1
Jiping 1马齿形 0.97 -0.08 1.26 -0.12 1.34 -0.13 0.51 -0.05 0.56 -0.05 球锥形 0.97 -0.09 1.21 -0.11 1.29 -0.12 0.51 -0.04 0.58 -0.05 类球形 0.45 -0.03 0.43 -0.03 -- -- -- -- -- -- 平安11
Ping'an 11马齿形 0.92 -0.07 1.20 -0.11 1.29 -0.12 0.50 -0.04 0.54 -0.05 球锥形 1.03 -0.09 1.28 -0.13 1.37 -0.14 0.54 -0.05 0.62 -0.06 类球形 0.46 -0.03 0.42 -0.03 -- -- -- -- -- -- {W2=((a+bW1)W1)2H1=((c+dW1)W1)2H2=((e+fW1)W1)2T1=((g+hW1)W1)4T2=((i+jW1)W1)4L=((k+lT)T)4W=((m+nT)T)4 (1) 式中a、b、c、d、e、f、h、i、j、k、l、m、n为待定系数。
对于类球形玉米种子，通过式（2）计算试验样本中类球形玉米颗粒球形率（Φ），结果显示类球形颗粒的球形率分布在0.9附近，见表2，说明其形状近似球形。因此在建模时，为了在不损失建模精度同时，降低建模复杂度，提升DEM仿真计算效率，可将类球形玉米颗粒简化为球形，其形状误差可通过标定接触参数进行补偿；同时，选择马齿形与球锥形的上底以及类球形的厚度尺寸作为主尺寸，其他特征尺寸通过所建立尺寸之间的函数关系计算得到，这样得到的玉米颗粒模型与实际颗粒相接近。
表 2 不同品种类球形颗粒球形率Table 2. Sphericity ratio of spheroid maize of different varieties尺寸
Size吉平1 Jiping 1 平安11 Ping’an 11 平均值
Mean标准差
Standard deviation平均值
Mean标准差
Standard deviation长Length L/mm 9.57 0.77 9.81 0.75 宽Width W/mm 8.91 0.76 8.74 0.66 厚Thickness T/mm 7.81 0.79 7.82 0.73 球形率Sphericity ratio Φ 0.91 0.05 0.89 0.06 Φ=L(L⋅W⋅T)1/3 (2) 2. 玉米颗粒建模
单个玉米颗粒建模方法为：由于马齿形颗粒整体呈楔板状，所以其填充球主要沿高度方向对称分布两列，并且依据球数目不同建立8、10、14、20和25球模型；由于球锥形颗粒存在一个球形大端和棱台形中部，故在其球形大端填充1球，中部每一层呈正方形填充4球，依据层数不同建立14、18和22球模型；类球形颗粒近似球形，因此建立球模型，如图3所示。
玉米颗粒群体的建模方法：以上述单个玉米颗粒模型为模板，主尺寸按正态分布随机产生，由主尺寸计算得到其他特征尺寸，由此生成每个玉米颗粒模型，如此反复即可；此外，按马齿形、球锥形和类球形所占百分比生成相应数量的玉米颗粒，这样所生成的玉米颗粒群体模型和实际玉米颗粒群体特性较为接近。
3. 建模方法验证与分析
3.1 仿真及参数
3.1.1 堆积仿真
构建直径为62.5 mm、高度105 mm的圆筒容器模型，如图4a所示，在圆筒容器正下方放置一块镀锌钢板模型。
![]()
图 4 玉米颗粒模型验证过程注：α、β为休止角，(°)。Figure 4. Validation process of maize grain modelNote: α, β is angle of repose, (°).选用Hertz-Mindlin无滑动接触模型，泊松比、剪切模量以及玉米颗粒与镀锌钢板间的滚动摩擦系数等参数如表3[32-33]。仿真中，圆筒容器分别生成0.2 kg的马齿形、球锥形、类球形玉米颗粒模型，然后以0.1 m/s的速度向上移动圆筒容器，直到颗粒模型全部落在镀锌钢板上，形成锥形堆，测量静态休止角α和β，将平均值作为本次仿真结果，每组仿真重复3次。
表 3 仿真参数Table 3. Parameters used in the simulations参数
Parameter吉平1Jiping 1 平安11Ping’an 11 颗粒
Grain筛板
Sieve plate颗粒
Grain筛板
Sieve plate密度Density ρ/(kg/m3) 1276 7850 1306 7850 泊松比Poisson's ratio v 0.4 0.4 0.4 0.4 剪切模量
Shear modulus E /Pa1.37×108 7.92×1010 1.37×108 7.92×1010 碰撞恢复系数Coefficient of restitution e 0.7826 （颗粒-颗粒）0.7943 （颗粒-筛板）0.6526 （颗粒-颗粒）0.8236 （颗粒-筛板）静摩擦系数Coefficient of static friction μ 0.12（颗粒-颗粒） 0.3189 （颗粒-筛板）0.12（颗粒-颗粒） 0.3119 （颗粒-筛板）滚动摩擦系数Coefficient of rolling friction μr 0.02（颗粒-颗粒） 0.235（颗粒-筛板） 0.02（颗粒-颗粒） 0.235（颗粒-筛板） 马齿形体积Horse-tooth volume V马齿 /(mm3) 339.21 328.46 0.13 0.16 球锥形体积Spherical-cone volume V球锥 /(mm3) 346.93 348.99 0.17 0.15 类球形体积Spheroid volume V类球 /(mm3) 351.59 353.19 0.20 0.17 3.1.2 筛分仿真
构建倾角为6°、8°和10°的9 mm×9 mm方孔筛板模型，在其右上方分别生成马齿形、球锥形和类球形玉米颗粒模型各0.15 kg，仿真中玉米颗粒模型以自由落体的形式落到筛板上，玉米颗粒模型在筛板上自由向下滑动的同时，透过筛孔落入下方的接料盒中，如图4b所示。统计接料盒（A、B、C、D）中玉米颗粒的质量，通过式（3）计算透筛率以及透筛率沿筛板长度方向的分布情况，每组仿真重复3次，取其平均值作为最终仿真结果。
ξi=mim⋅100% (3) 式中i=A、B、C、D，mi分别为接料盒A、B、C和D中玉米颗粒（模型）的质量，m为仿真或试验中总玉米颗粒模型质量。
3.2 试验验证方法
3.2.1 堆积试验
试验器材尺寸和过程与3.1.1节一致，如图4c所示，将放置在镀锌钢板上的圆筒容器中分别装入0.2 kg的马齿形、球锥形、类球形以及玉米群体颗粒，以0.1 m/s的速度向上移动圆筒容器，直到颗粒模型全部落在镀锌钢板上，形成锥形堆，通过放置在其正前方的图像采集设备获得试验图片，然后通过Photoshop测量静态α角和β角，将平均值作为本次试验结果，每组试验重复3次。
3.2.2 筛分试验
试验器材尺寸和过程与3.1.2节一致，如图4d所示，称取两品种马齿形、球锥形和类球形玉米颗粒各0.15 kg，然后将其分别放在料盒中，然后自由落体的形式落到倾角分别为6°、8°和10°的9 mm×9 mm方孔筛板上，玉米颗粒在筛板上自由向下运动的同时，透过筛孔落入下方的接料盒中。统计接料盒中玉米颗粒的质量，计算透筛率以及透筛率沿筛板长度方向的分布情况，每组试验重复3次，取其平均值作为最终试验结果。
3.3 结果与分析
3.3.1 堆积过程对比分析
吉平1和平安11马齿形颗粒休止角试验值分别为25.68°、25.31°，球锥形颗粒休止角试验值分别为21.89°、22.06°。图5为玉米颗粒休止角仿真值。可以看出，当马齿形颗粒模型填充球数目分别为10和14时，仿真值与相应的试验值最为接近，相对误差为0.14%～2.7%。当球锥形颗粒模型填充球数目为18时，仿真值与相应的试验值最为接近，相对误差位于3.47%～4.18%。当利用球模型模拟类球形颗粒堆积过程时，休止角仿真值收敛于试验值标准差以内，相对误差分别为6.89%和9.42%。在此基础上，利用10-18-1（由10球马齿形颗粒模型、18球球锥形颗粒模型和球模型形成的玉米颗粒群体模型）和14-18-1（由14球马齿形颗粒模型、18球球锥形颗粒模型和球模型形成的玉米颗粒群体模型）颗粒模型模拟实际玉米颗粒的堆积过程，结果见表4。休止角的仿真值与试验值一致，相对误差均在5%以内，说明在颗粒与颗粒之间的相互作用方面，所建立的玉米种子群体模型与实际玉米种子群体一致，进一步验证了种子模型的有效性。
表 4 类球形颗粒和群体颗粒休止角仿真值与试验值对比Table 4. Comparison of the simulated results and experimental results of angle of repose for spheroid and maize assembly seeds品种
Variety颗粒类型
Particle type模型类型
Model type仿真
Simulation / (°)仿真标准差
Standard deviation of
simulation/ (°)试验
Experiment / (°)试验标准差
Standard deviation of
experiment / (°)相对误差
Relative error / %吉平 1
Jiping 1类球形颗粒 1 15.82 0.95 16.99 1.27 6.89 群体颗粒 10-18-1 27.15 0.21 26.53 0.92 2.29 14-18-1 25.98 0.20 26.53 0.92 2.07 平安 11
Ping’an 11类球形颗粒 1 15.97 0.71 17.63 1.76 9.42 群体颗粒 10-18-1 27.26 0.28 27.41 0.62 0.55 14-18-1 26.10 0.38 27.41 0.62 4.78 注：模型类型中1代表类球形颗粒模型，10-18-1和14-18-1分别代表由10球和14球马齿形颗粒模型、18球球锥形颗粒模型和球形颗粒模型形成的玉米颗粒群体模型。 Note: 1 - Spheroid，10-18-1 and 14-18-1 represent maize grain assembly model formed by horse-tooth with 10 filling spheres and 14 filling spheres, spherical-cone with 18 filling spheres, and spheroid with 1 filling sphere. 3.3.2 筛分过程对比分析
![]()
图 6 筛板倾角6°时不同填充球数目和接料盒下的玉米颗粒透筛率仿真值与试验值对比Figure 6. Comparison of simulated results and experimental results of transmissibility under inclination 6° of screen plate with different filling spheres and receiving boxes![]()
图 7 筛板倾角8°时不同填充球数目和接料盒下的玉米颗粒透筛率仿真值与试验值对比Figure 7. Comparison of simulated results and experimental results of transmissibility under inclination 8° of screen plate with different filling spheres and receiving boxes![]()
图 8 筛板倾角10°时不同填充球数目和接料盒下的玉米颗粒透筛率仿真值与试验值对比Figure 8. Comparison of simulated results and experimental results of percentage passing under inclination 10° of screen plate with different filling spheres and receiving boxes可以看出，当马齿形颗粒模型填充球数目为10和14时，仿真值与试验值（吉平1：74.95%～84.39%，平安11：77.91%～87.11%）最为接近，当球锥形颗粒模型填充球数目为18时，仿真值与试验值（吉平1：89.82%～91.17%，平安11：87.78%～89.50%）最为接近，并且透筛率仿真值与试验值沿筛板长度方向的分布规律相一致；其次，利用球模型仿真类球形颗粒的透筛过程，仿真值与试验值相接近，并且透筛率仿真值与试验值沿筛板长度方向的分布规律相一致（表5）；在此基础上，利用10-18-1和14-18-1颗粒模型仿真玉米群体颗粒的筛分过程，结果见表6。可以看出，透筛率以及透筛率沿筛板长度方向的分布规律与试验筛分过程相一致，进一步验证了上述结论的有效性。
表 5 类球形颗粒透筛率仿真值与试验值对比Table 5. Comparison of the simulated results and experimental results of transmissibility for spheroid grains筛板倾角
Inclination of
screen plate透筛率
Transmissibility吉平1 Jiping 1 平安11 Ping’an 11 仿真值
Simulation value/%试验值
Experimental value/%误差
Error/百分点仿真值
Simulation value/%试验值
Experimental value/%误差
Error/百分点6° A盒 43.15±1.48 45.85±6.91 2.70 39.53±2.52 40.10±6.34 0.57 B盒 15.00±0.76 16.56±4.88 1.56 20.34±3.51 25.23±6.14 4.89 C盒 1.70±1.31 0.43±0.50 1.27 3.03±0.46 0.79±0.39 2.24 D盒 0.62±0.37 0.00±0.00 0.62 1.75±0.32 0.00±0.00 1.75 总透筛率 60.47±1.12 62.84±4.27 2.37 64.65±1.34 66.12±6.13 1.47 8° A盒 33.77±2.45 36.15±3.30 2.38 30.87±1.70 35.61±6.02 4.74 B盒 19.22±2.83 23.19±6.63 3.97 23.16±0.27 24.16±6.21 1.00 C盒 3.41±0.33 2.20±1.77 1.21 4.91±1.08 1.32±0.82 3.59 D盒 2.62±0.57 0.39±0.42 2.23 3.68±1.02 0.12±0.12 3.56 总透筛率 59.02±1.35 61.93±6.32 2.91 62.62±0.10 61.22±3.75 1.40 10° A盒 29.56±3.85 33.29±4.08 3.73 23.84±1.82 22.37±8.98 1.47 B盒 20.41±3.88 23.18±1.29 2.77 19.61±1.75 23.17±7.36 3.56 C盒 5.91±0.94 1.23±1.28 4.68 8.33±2.01 9.58±5.32 1.25 D盒 4.61±0.34 0.28±0.29 4.33 8.81±0.87 2.72±2.13 6.09 总透筛率 60.49±1.04 57.98±6.22 2.51 60.59±2.07 57.84±7.06 2.75 注：表中值为平均值±标准差。 Note: Values in the table are mean ± standard deviation. 表 6 玉米群体颗粒的透筛率仿真值与试验值对比Table 6. Comparison of the simulated results and experimental results of transmissibility for maize assembly grains透筛率
Transmissibility吉平1 Jiping 1 平安11 Ping’an 11 仿真值
Simulation value/%试验值
Experimental value/%误差
Error/百分点仿真值
Simulation value/ %试验值
Experimental value/%误差Error/百分点 10-18-1 14-18-1 10-18-1 14-18-1 A盒Box A 65.03 68.10 63.74 1.29/4.36 62.43 62.44 60.68 1.75/1.76 B盒Box B 14.26 14.09 16.48 2.22/2.39 13.15 15.67 15.74 2.59/0.07 C盒Box C 0.84 1.37 2.05 1.21/0.68 1.84 0.53 0.83 1.01/0.03 D盒Box D 0.10 0.23 0.24 0.14/0.01 0.12 0.18 0.04 0.08/0.14 总透筛率
Total transmissibility80.23 81.05 82.52 2.29/1.47 77.54 77.76 77.29 0.25/0.47 注：表中误差值的表示方法为10-18-1/14-18-1颗粒模型的误差值。 Note: The error values in the table represent error values for the 10-18-1/14-18-1 particle model. 透筛率沿筛板下降方向整体呈现递减趋势，这是因为筛分过程中，玉米种子模型研制筛板逐渐向下滚落，多数玉米种子在自身重力和种子间相互作用等复杂力系作用下，穿过A、B接料盒上方的筛孔，落入A、B接料盒，极少部分玉米种子落入C、D接料盒，因而透筛率呈递减趋势；其次，随着筛板倾角的增加，A处的透筛率有所下降，这是由于此时玉米种子沿筛板滚落运动明显，使得玉米种子在A处停留时间变小，透筛现象变弱；再者，与马齿形玉米种子相比，球锥形玉米种子在A处的透筛率较小，这是由于球锥形玉米种子存在较小的锥形小端，这会增加多个种子同时进入同一筛孔的可能性，反而使得玉米种子卡在筛孔，进而降低了透筛率。
4. 排种试验
如图9所示，以组合内窝孔排种器排种过程为例，基于EDEM软件，应用前文构建的玉米群体模型对排种器的工作过程进行DEM模拟。
在排种器排种过程中，排种盘转速是影响排种性能的一个重要工作参数[34]。因此以排种盘转速为变量，以单粒率、双粒率以及空穴率为评价指标，以吉平1玉米群体模型14-18-1为颗粒模型，通过DEM仿真获得排种器性能随排种轮转速的变化规律。其中，单粒率是指整个排种过程中内窝孔中出现单个玉米颗粒情况所占的数量百分比，双粒率是指整个排种过程中内窝孔中出现两个玉米颗粒情况所占的数量百分比，空穴率是指整个排种过程中内窝孔中出现空穴情况所占的数量百分比。仿真工况为：玉米颗粒模型为14-18-1，颗粒数量为
1000 ，内窝孔数目为18，排种轮转速范围为10～40 r/min，其他参数同表3，通过统计每次每个内窝孔排出种子的数目计算排种器性能。结果如图10所示，随着排种轮转速的增加，单粒率先上升后下降，双粒率先下降后上升，并且当转速为30 r/min时，单粒率达到最大为88%，双粒率最小为11%。空穴率先迅速下降后基本稳定在1%附近，这是由于当排种轮转速逐渐增加时，颗粒在排种轮的扰动下，其受离心惯性力逐渐增大，当排种轮转速小于30 r/min时，单个颗粒会可靠地随排种轮转动，而多于的颗粒则会由于窝孔的大小限制以及自身重力等因素的作用落回种室底部，但是当排种轮转速大于30 r/min时，玉米种子所受离心惯性力占主导作用，会使多余的颗粒难以落回种室底部，随排种轮窝孔转动，进而导致单粒率下降，双粒率上升。此外，上述排种器性能变化规律和最优排种轮转速与文献[35]的试验结果一致，进一步体现了本文所提出的玉米颗粒群体建模方法的有效性。通过该方法还可以分析得到排种器的其他最优工作参数和结构参数，进而为排种器的性能优化提供依据。
5. 结 论
1）通过对10多种玉米品种的颗粒形状分析，提出一种通用的玉米颗粒形状分类方法，即：可以将实际玉米颗粒群体视为马齿形、球锥形和类球形玉米颗粒的集合。
2）玉米颗粒的特征尺寸均近似服从正态分布；且马齿形和球锥形玉米颗粒其他特征尺寸与上底存在较强的相关性，类球形玉米颗粒长、宽和厚度存在强的相关性。在建立颗粒模型时，可选择马齿形与球锥形的上底以及类球形的厚度尺寸作为主尺寸，按正态分布随机生成，其他特征尺寸通过所建立尺寸之间的函数关系计算得到。
3）提出马齿型、球锥形与类球形3种玉米颗粒的单个颗粒和群体建模方法，得出马齿形和球锥形玉米颗粒模型的最优填充球数目分别为10～14和18。
4）基于所构建的玉米种子群体模型获得组合内窝孔排种器最优排种速度为30 r/min，与试验结果一致。
-
![]()
图 1 玉米果穗及颗粒特征尺寸示意图
注：W1为上底，(mm)；W2为下底，(mm)；H1、H2为高度，(mm)；T1、T2、T为厚度，(mm)；L为长，(mm)；W为宽，(mm)。
Figure 1. Schematic diagram of maize ear and characteristic dimensions of maize grain
Note: W1 is the upper bottom, (mm); W2 is the lower bottom, (mm); H1, H2 are the height, (mm); T1, T2, and T are the thickness, mm; L is the length, (mm); W is the width, (mm).
![]()
图 2 不同品种玉米颗粒特征尺寸分布图
Figure 2. Distributions of characteristic sizes of maize seeds of different varieties
![]()
图 4 玉米颗粒模型验证过程
注：α、β为休止角，(°)。
Figure 4. Validation process of maize grain model
Note: α, β is angle of repose, (°).
![]()
图 6 筛板倾角6°时不同填充球数目和接料盒下的玉米颗粒透筛率仿真值与试验值对比
Figure 6. Comparison of simulated results and experimental results of transmissibility under inclination 6° of screen plate with different filling spheres and receiving boxes
![]()
图 7 筛板倾角8°时不同填充球数目和接料盒下的玉米颗粒透筛率仿真值与试验值对比
Figure 7. Comparison of simulated results and experimental results of transmissibility under inclination 8° of screen plate with different filling spheres and receiving boxes
![]()
图 8 筛板倾角10°时不同填充球数目和接料盒下的玉米颗粒透筛率仿真值与试验值对比
Figure 8. Comparison of simulated results and experimental results of percentage passing under inclination 10° of screen plate with different filling spheres and receiving boxes
表 1 玉米颗粒特征尺寸函数待定系数
Table 1 Function undetermined coefficient of characteristic sizes of maize grains
品种
Variety形状
Shapea (k) b (l) c (m) d (n) e f g h i j 吉平1
Jiping 1马齿形 0.97 -0.08 1.26 -0.12 1.34 -0.13 0.51 -0.05 0.56 -0.05 球锥形 0.97 -0.09 1.21 -0.11 1.29 -0.12 0.51 -0.04 0.58 -0.05 类球形 0.45 -0.03 0.43 -0.03 -- -- -- -- -- -- 平安11
Ping'an 11马齿形 0.92 -0.07 1.20 -0.11 1.29 -0.12 0.50 -0.04 0.54 -0.05 球锥形 1.03 -0.09 1.28 -0.13 1.37 -0.14 0.54 -0.05 0.62 -0.06 类球形 0.46 -0.03 0.42 -0.03 -- -- -- -- -- -- 
下载: 导出CSV
表 2 不同品种类球形颗粒球形率
Table 2 Sphericity ratio of spheroid maize of different varieties
尺寸
Size吉平1 Jiping 1 平安11 Ping’an 11 平均值
Mean标准差
Standard deviation平均值
Mean标准差
Standard deviation长Length L/mm 9.57 0.77 9.81 0.75 宽Width W/mm 8.91 0.76 8.74 0.66 厚Thickness T/mm 7.81 0.79 7.82 0.73 球形率Sphericity ratio Φ 0.91 0.05 0.89 0.06
下载: 导出CSV
表 3 仿真参数
Table 3 Parameters used in the simulations
参数
Parameter吉平1Jiping 1 平安11Ping’an 11 颗粒
Grain筛板
Sieve plate颗粒
Grain筛板
Sieve plate密度Density ρ/(kg/m3) 1276 7850 1306 7850 泊松比Poisson's ratio v 0.4 0.4 0.4 0.4 剪切模量
Shear modulus E /Pa1.37×108 7.92×1010 1.37×108 7.92×1010 碰撞恢复系数Coefficient of restitution e 0.7826 （颗粒-颗粒）0.7943 （颗粒-筛板）0.6526 （颗粒-颗粒）0.8236 （颗粒-筛板）静摩擦系数Coefficient of static friction μ 0.12（颗粒-颗粒） 0.3189 （颗粒-筛板）0.12（颗粒-颗粒） 0.3119 （颗粒-筛板）滚动摩擦系数Coefficient of rolling friction μr 0.02（颗粒-颗粒） 0.235（颗粒-筛板） 0.02（颗粒-颗粒） 0.235（颗粒-筛板） 马齿形体积Horse-tooth volume V马齿 /(mm3) 339.21 328.46 0.13 0.16 球锥形体积Spherical-cone volume V球锥 /(mm3) 346.93 348.99 0.17 0.15 类球形体积Spheroid volume V类球 /(mm3) 351.59 353.19 0.20 0.17
下载: 导出CSV
表 4 类球形颗粒和群体颗粒休止角仿真值与试验值对比
Table 4 Comparison of the simulated results and experimental results of angle of repose for spheroid and maize assembly seeds
品种
Variety颗粒类型
Particle type模型类型
Model type仿真
Simulation / (°)仿真标准差
Standard deviation of
simulation/ (°)试验
Experiment / (°)试验标准差
Standard deviation of
experiment / (°)相对误差
Relative error / %吉平 1
Jiping 1类球形颗粒 1 15.82 0.95 16.99 1.27 6.89 群体颗粒 10-18-1 27.15 0.21 26.53 0.92 2.29 14-18-1 25.98 0.20 26.53 0.92 2.07 平安 11
Ping’an 11类球形颗粒 1 15.97 0.71 17.63 1.76 9.42 群体颗粒 10-18-1 27.26 0.28 27.41 0.62 0.55 14-18-1 26.10 0.38 27.41 0.62 4.78 注：模型类型中1代表类球形颗粒模型，10-18-1和14-18-1分别代表由10球和14球马齿形颗粒模型、18球球锥形颗粒模型和球形颗粒模型形成的玉米颗粒群体模型。 Note: 1 - Spheroid，10-18-1 and 14-18-1 represent maize grain assembly model formed by horse-tooth with 10 filling spheres and 14 filling spheres, spherical-cone with 18 filling spheres, and spheroid with 1 filling sphere.
下载: 导出CSV
表 5 类球形颗粒透筛率仿真值与试验值对比
Table 5 Comparison of the simulated results and experimental results of transmissibility for spheroid grains
筛板倾角
Inclination of
screen plate透筛率
Transmissibility吉平1 Jiping 1 平安11 Ping’an 11 仿真值
Simulation value/%试验值
Experimental value/%误差
Error/百分点仿真值
Simulation value/%试验值
Experimental value/%误差
Error/百分点6° A盒 43.15±1.48 45.85±6.91 2.70 39.53±2.52 40.10±6.34 0.57 B盒 15.00±0.76 16.56±4.88 1.56 20.34±3.51 25.23±6.14 4.89 C盒 1.70±1.31 0.43±0.50 1.27 3.03±0.46 0.79±0.39 2.24 D盒 0.62±0.37 0.00±0.00 0.62 1.75±0.32 0.00±0.00 1.75 总透筛率 60.47±1.12 62.84±4.27 2.37 64.65±1.34 66.12±6.13 1.47 8° A盒 33.77±2.45 36.15±3.30 2.38 30.87±1.70 35.61±6.02 4.74 B盒 19.22±2.83 23.19±6.63 3.97 23.16±0.27 24.16±6.21 1.00 C盒 3.41±0.33 2.20±1.77 1.21 4.91±1.08 1.32±0.82 3.59 D盒 2.62±0.57 0.39±0.42 2.23 3.68±1.02 0.12±0.12 3.56 总透筛率 59.02±1.35 61.93±6.32 2.91 62.62±0.10 61.22±3.75 1.40 10° A盒 29.56±3.85 33.29±4.08 3.73 23.84±1.82 22.37±8.98 1.47 B盒 20.41±3.88 23.18±1.29 2.77 19.61±1.75 23.17±7.36 3.56 C盒 5.91±0.94 1.23±1.28 4.68 8.33±2.01 9.58±5.32 1.25 D盒 4.61±0.34 0.28±0.29 4.33 8.81±0.87 2.72±2.13 6.09 总透筛率 60.49±1.04 57.98±6.22 2.51 60.59±2.07 57.84±7.06 2.75 注：表中值为平均值±标准差。 Note: Values in the table are mean ± standard deviation.
下载: 导出CSV
表 6 玉米群体颗粒的透筛率仿真值与试验值对比
Table 6 Comparison of the simulated results and experimental results of transmissibility for maize assembly grains
透筛率
Transmissibility吉平1 Jiping 1 平安11 Ping’an 11 仿真值
Simulation value/%试验值
Experimental value/%误差
Error/百分点仿真值
Simulation value/ %试验值
Experimental value/%误差Error/百分点 10-18-1 14-18-1 10-18-1 14-18-1 A盒Box A 65.03 68.10 63.74 1.29/4.36 62.43 62.44 60.68 1.75/1.76 B盒Box B 14.26 14.09 16.48 2.22/2.39 13.15 15.67 15.74 2.59/0.07 C盒Box C 0.84 1.37 2.05 1.21/0.68 1.84 0.53 0.83 1.01/0.03 D盒Box D 0.10 0.23 0.24 0.14/0.01 0.12 0.18 0.04 0.08/0.14 总透筛率
Total transmissibility80.23 81.05 82.52 2.29/1.47 77.54 77.76 77.29 0.25/0.47 注：表中误差值的表示方法为10-18-1/14-18-1颗粒模型的误差值。 Note: The error values in the table represent error values for the 10-18-1/14-18-1 particle model.
下载: 导出CSV
-
[1] 史嵩,张东兴,杨丽,等. 气压组合孔式玉米精量排种器设计与试验[J]. 农业工程学报,2014,30(5):10-18. SHI Song, ZHANG Dongxing, YANG Li, et al. Design and experiment of pneumatic maize precision seed-metering device with combined holes[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2014, 30(5): 10-18 (in Chinese with English abstract)
[2] CHEN Z, YU J, XUE D, et al. An approach to and validation of maize-seed-assembly modelling based on the discrete element method[J]. Powder Technology, 2018, 328: 167-183. doi: 10.1016/j.powtec.2017.12.007
[3] 邵飞. 中国玉米经济:供给与需求分析 [D]. 杨凌:西北农林科技大学,2011. SHAO Fei. Corn Economy in China: Analysis on Supply and Demand [D]. Yangling: Northwest A&F University, 2011. (in Chinese with English abstract)
[4] 张昆,衣淑娟,刘海军,等. 气吸滚筒式玉米植质钵盘精密播种装置优化设计与试验[J]. 农业机械学报,2021,52(4):62-69. doi: 10.6041/j.issn.1000-1298.2021.04.006 ZHANG Kun, YI Shujuan, LIU Haijun, et al. Optimization design and test of suction derformance of air suction cylinder type precise seeding device for maize with plant material bowl-tray[J]. Transactions of the Chinese Society for Agricultural Machinery, 2021, 52(4): 62-69. (in Chinese with English abstract) doi: 10.6041/j.issn.1000-1298.2021.04.006
[5] 周龙. 基于离散元法的玉米种子建模及播种过程的仿真分析与试验研究 [D]. 长春:吉林大学,2021. ZHOU Long. DEM-based Modelling of Maize Seeds and the Simulation Analysis and Experimental Study of the Seed-sowing [D]. Changchun: Jilin University, 2021. (in Chinese with English abstract)
[6] CUNDALL P A, STRACK O D. A discrete numerical model for granular assemblies[J]. Geotechnique, 1979, 29(1): 47-65. doi: 10.1680/geot.1979.29.1.47
[7] BOAC J M, AMBROSE R P K, CASADA M E, et al. Applications of discrete element method in modeling of grain postharvest operations[J]. Food Engineering Reviews, 2014, 6(4): 128-149. doi: 10.1007/s12393-014-9090-y
[8] WHITTLES D N, KINGMAN S, LOWNDES I S, et al. An investigation into the parameters affecting mass flow rate of ore material through a microwave continuous feed system[J]. Advanced Powder Technology, 2005, 16(6): 585-609. doi: 10.1163/156855205774483370
[9] VAN ZEEBROECK M, TSKENS E, DINTWA E, et al. The discrete element method (DEM) to simulate fruit impact damage during transport and handling: Case study of vibration damage during apple bulk transport[J]. Postharvest Biology and Technology, 2006, 41(1): 92-100. doi: 10.1016/j.postharvbio.2006.02.006
[10] ANAND A, CURTIS J S, WASSGREN C R, et al. Predicting discharge dynamics from a rectangular hopper using the discrete element method (DEM)[J]. Chemical Engineering Science, 2008, 63(24): 5821-5830. doi: 10.1016/j.ces.2008.08.015
[11] COETZEE C J, ELS D N J, DYMOND G F. Discrete element parameter calibration and the modelling of dragline bucket filling[J]. Journal of Terramechanics, 2010, 47(1): 33-44. doi: 10.1016/j.jterra.2009.03.003
[12] KETTERHAGEN W R. Modeling the motion and orientation of various pharmaceutical tablet shapes in a film coating pan using DEM[J]. International Journal of Pharmaceutics, 2011, 409(1/2): 137-149. doi: 10.1016/j.ijpharm.2011.02.045
[13] SUN K, YU J, LIANG L, et al. A DEM-based general modelling method and experimental verification for wheat seeds[J]. Powder Technology, 2022, 401: 117353. doi: 10.1016/j.powtec.2022.117353
[14] LIU Z, WANG G, GUAN W, et al. Research on performance of a laboratory-scale SAG mill based on DEM-EMBD[J]. Powder Technology, 2022, 406: 117581. doi: 10.1016/j.powtec.2022.117581
[15] CHEN Z, XUE D, GUAN W, et al. Research on the disturbance behaviour of the track chassis to the sand-gravel pavement during the steering process of the electric shovel based on DEM[J]. Advanced Powder Technology, 2022, 33(9): 103731. doi: 10.1016/j.apt.2022.103731
[16] CHEN Z, WANG G, XUE D, et al. Simulation and optimization of crushing chamber of gyratory crusher based on the DEM and GA[J]. Powder Technology, 2021, 384: 36-50. doi: 10.1016/j.powtec.2021.02.003
[17] CHEN Z, XUE D, WANG G, et al. Simulation and optimization of the tracked chassis performance of electric shovel based on DEM-MBD[J]. Powder Technology, 2021, 390: 428-441. doi: 10.1016/j.powtec.2021.05.085
[18] 崔涛,荆茂盛,张东兴,等. 玉米果穗离散元模型构建与脱粒仿真验证[J]. 农业工程学报,2023,39(24):33-46. CUI Tao, JING Maosheng, ZHANG Dongxing, et al. Construction of the discrete element model for maize ears and verification of threshing simulation[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2023, 39(24): 33-46. (in Chinese with English abstract)
[19] 王业成,高云鹏,台文硕,等. 夹持式玉米精密排种器设计与试验[J]. 农业机械学报,2019,50(9):40-46. WANG Yecheng, GAO Yunpeng, TAI Wenshuo, et al. Design and experiment of clamping maize precision seed-metering device[J]. Transactions of the Chinese Society for Agricultural Machinery, 2019, 50(9): 40-46. (in Chinese with English abstract)
[20] 张荣芳,周纪磊,刘虎,等. 玉米颗粒粘结模型离散元仿真参数标定方法研究[J]. 农业机械学报,2022,53(s1):69-77. ZHANG Rongfang, ZHOU Jilei, LIU Hu, et al. Determination of interspecific contact parameters of corn and simulation calibration of discrete element[J]. Transactions of the Chinese Society for Agricultural Machinery, 2022, 53(s1): 69-77. (in Chinese with English abstract)
[21] 陈玉龙,刘泽琪,韩杰,等. 气吸式排种器扁平种子吸附姿态调节机构设计与试验[J]. 农业工程学报,2022,38(23):1-11. CHEN Yulong, LIU Zeqi, HAN Jie, et al. Design and experiments of the flat seed-adsorbing posture adjustment mechanism for the air-suction metering device[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2022, 38(23): 1-11. (in Chinese with English abstract)
[22] 都鑫,刘彩玲,姜萌,等. 自扰动内充型孔轮式玉米精量排种器设计与试验[J]. 农业工程学报,2019,35(13):23-34. DU Xin, LIU Cailing, JIANG Meng, et al. Design and experiment of self-disturbance inner-filling cell wheel maize precision seed-metering device[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2019, 35(13): 23-34. (in Chinese with English abstract)
[23] 杨丽,李治民,张东兴,等. 离心式高速玉米精量排种器T形槽型孔设计与试验[J]. 农业工程学报,2024,40(7):50-60. YANG Li, LI Zhimin, ZHANG Dongxing, et al. Design and test of the T-shaped hole of centrifugal high-speed maize precision seed metering device[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2024, 40(7): 50-60. (in Chinese with English abstract).
[24] 董建鑫,高筱钧,张仕林,等. 高速播种机玉米姿控驱导式排种器设计与试验[J]. 农业机械学报,2022,53(11):108-119. DONG Jianxin, GAO Xiaojun, ZHANG Shilin, et al. Design and test of maize posture control and driving precision metering device for high-speed seeder[J]. Transactions of the Chinese Society for Agricultural Machinery, 2022, 53(11): 108-119. (in Chinese with English abstract)
[25] PASHA M, HARE C, GHADIRI M, et al. Effect of particle shape on flow in discrete element method simulation of a rotary batch seed coater[J]. Powder Technology, 2016, 296: 29-36. doi: 10.1016/j.powtec.2015.10.055
[26] PASHA M, HARE C, GHADIRI M, et al. Inter-particle coating variability in a rotary batch seed coater[J]. Chemical Engineering Research & Design, 2017, 120: 92-101.
[27] RADVILAITE U, RAMIREZ-GOMEZ A, KACIANAUSKAS R. Determining the shape of agricultural materials using spherical harmonics[J]. Computers and Electronics in Agriculture, 2016, 128: 160-171. doi: 10.1016/j.compag.2016.09.003
[28] WANG X, YU J, LV F, et al. A multi-sphere based modelling method for maize grain assemblies[J]. Advanced Powder Technology, 2017, 28(2): 584-595. doi: 10.1016/j.apt.2016.10.027
[29] GONZALEZ-MONTELLANO C, RAMIREZ A, GALLEGO E, et al. Validation and experimental calibration of 3D discrete element models for the simulation of the discharge flow in silos[J]. Chemical Engineering Science, 2011, 66(21): 5116-5126. doi: 10.1016/j.ces.2011.07.009
[30] TAO H, ZHONG W, JIN B. Comparison of construction method for DEM simulation of ellipsoidal particles[J]. Chinese Journal Of Chemical Engineering, 2013, 21(7): 800-807. doi: 10.1016/S1004-9541(13)60500-X
[31] MARKAUSKAS D, RAMIREZ-GOMEZ A, KACIANAUSKAS R, et al. Maize grain shape approaches for DEM modelling[J]. Computers and Electronics in Agriculture, 2015, 118: 247-258. doi: 10.1016/j.compag.2015.09.004
[32] ENGINEERS A S O A. Compression Test of Food Materials of Convex Shape [M]. USA, American Society of Agricultural and Biological Engineers, 2000.
[33] 崔涛,刘佳,杨丽,等. 基于高速摄像的玉米种子滚动摩擦特性试验与仿真[J]. 农业工程学报,2013,29(15):34-41. doi: 10.3969/j.issn.1002-6819.2013.15.005 CUI Tao, LIU Jia, YANG Li, et al. Experiment and simulation of rolling friction characteristic of corn seed based on high-speed photography[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2013, 29(15): 34-41. (in Chinese with English abstract) doi: 10.3969/j.issn.1002-6819.2013.15.005
[34] CHEN Z, XUE D, GUAN W, et al. Performance optimization of a spoon precision seed metering device based on a maize seed assembly model and discrete element method[J]. Processes, 2023, 11(11): 3076. doi: 10.3390/pr11113076
[35] 颜辉. 组合内窝孔玉米精密排种器优化设计新方法研究 [D]. 长春,吉林大学,2012. YAN Hui. A New Kind of Method for the Optimizated Design of Combination Inner-cell Corn Precision Seed Metering Device [D]. Changchun: Jilin University, 2012. (in Chinese with English abstract)
计量
- 文章访问数: 288
- HTML全文浏览量: 43
- PDF下载量: 133
