基于异速生长法则的油茶树主干自然频率经验公式推导及应用
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S718.42

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国家自然科学基金青年项目(52305020);国家资助博士后研究人员计划(GZC20230776);博士后科学基金面上项目(2023M741142)


Empirical formula for the natural frequency of Camellia oleifera trunk using allometric growth
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    摘要:

    为克服油茶果人工采摘率低,该研究根据油茶树体合轴分枝生长方式,结合树体异速生长法则,建立油茶分形树体理想模型,提取二分叉基本单元。基于经典质量-弹簧分析方法,建立3种不同质点分布的二分叉基本单元动力学模型,推导一阶自然频率计算表达式。以湖南省华鑫油茶品种为应用实例,通过测量油茶树形态学参数,辨识面积缩减系数和异速生长系数,采用水浸法和三点弯曲试验分别测量油茶树枝密度和弯曲弹性模量。计算不同分枝角度下二分叉基本单元的一阶自然频率理论值。创建二分叉基本单元ANSYS有限元仿真模型,通过模态分析得到自然频率仿真值,质量均分在刚性杆两端的动力学模型的自然频率ANSYS仿真值与理论计算值较接近,平均相对误差为7.3%。基于带端部质点的悬臂梁一阶自然频率计算公式,采用参数辨识方法推导二分叉基本单元一阶自然频率经验公式,自然频率的经验公式计算值与仿真值最大误差仅为0.41%,验证了经验计算公式的准确性。研究结果可为油茶果振动式采摘装置的激振参数设置供理论依据。

    Abstract:

    Camellia oleifera can significantly guarantee food safety in the edible oil industry. The manual harvesting of Camellia oleifera has greatly restricted the full mechanization of the Camellia oleifera industry. Vibratory mechanized harvesting has been adopted with the high harvesting efficiency of Camellia oleifera fruit. Existing studies have also proved that the vibratory picking frequency can directly dominate the detachment of forest fruits. There is a high demand to establish the dynamics model of the Camellia oleifera tree, in order to calculate the trunk's natural frequency. In this study, an ideal fractal tree model was investigated for the Camellia oleifera, according to the sympodial branching and allometric growth. The bifurcated basic unit was extracted from the fractal tree model. Three dynamics models were then deduced with the point masses at different locations using the classic mass-spring analysis. Consequently, the theoretical expressions of the first-order natural frequency were derived for three dynamics models. Taking Camellia oleifera (variety: Huaxin) in Hunan Province as an application example, the lateral branching ratio and the slenderness coefficient were identified to measure the morphological parameters of the tree. Subsequently, the branch density and flexural elastic modulus were measured by water immersion and a three-point bending test. The theoretical values of the first-order natural frequency were calculated for the bifurcated basic unit with different branching angles, in order to substitute the identified tree parameters. Then, a finite element simulation model of the bifurcated basic unit for Camellia oleifera was constructed to simulate the natural frequency. Compared with the simulated and theoretical frequency value, the dynamics model with point mass equally distributed at both rod ends was the closest to the simulated model, with an average error of 7.3%. Finally, the mathematical formula was obtained with the first-order natural frequency of the cantilever beam with point mass at the rod top. An empirical calculation formula was derived for the bifurcated basic unit using parameter identification. The smallest error was found between the theoretical natural frequency from the empirical formula and the simulated value, with a maximum error of 0.41%. The validity and accuracy of the empirical formula were verified. The finding can provide the theoretical guidelines to optimize the vibration parameters of fruit harvesting machines for Camellia oleifera.

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张诗怡,唐乐为,吴明亮,李正超,张慧宇.基于异速生长法则的油茶树主干自然频率经验公式推导及应用[J].农业工程学报,2024,40(18):32-41. DOI:10.11975/j. issn.1002-6819.202403204

ZHANG Shiyi, TANG Lewei, WU Mingliang, LI Zhengchao, ZHANG Huiyu. Empirical formula for the natural frequency of Camellia oleifera trunk using allometric growth[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE),2024,40(18):32-41. DOI:10.11975/j. issn.1002-6819.202403204

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  • 收稿日期:2024-03-27
  • 最后修改日期:2024-06-06
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  • 在线发布日期: 2024-09-11
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