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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

Deduction and application of empirical formula for natural frequency of Camellia oleifera trunk based on allometric growth law

  • 摘要: 油茶产业发展是国家食用油安全的重要保障,而油茶果采收环节极大地限制油茶生产全程机械化发展。为克服油茶果人工采摘率低,提出采用振动式机械采摘方法,使其采摘率大幅提高。现有研究证明振动式采摘频率显著影响林果落果,构建油茶树动力学模型及计算主干自然频率,为油茶果振动式采摘装置设计及优化提供理论依据。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。代入油茶树参数,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%。最后,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: The development of the Camellia oleifera industry significantly guarantees the domestic safety of edible oil. The mechanized harvesting of Camellia oleifera greatly restricts the full mechanization development of Camellia oleifera industry. To overcome the shortcoming of low manual harvesting efficiency of Camellia oleifera fruit, the vibratory mechanized harvesting method is adopted with high harvesting efficiency. Existing studies have proved that the vibratory picking frequency directly affects the detachment of forest fruits. The establishment of the dynamics model of Camellia oleifera tree to calculate the trunk natural frequency, which will provide a theoretical basis for the design and optimization of vibratory harvesting machine for Camellia oleifera. According to the sympodial branching growth mode as well as the allometric growth law, an ideal fractal tree model of Camellia oleifera is investigated. The bifurcated basic unit is extracted from the fractal tree model. Based on the classic mass-spring analysis method, three dynamics models of the bifurcated basic unit for Camellia oleifera are deduced with point masses distributed at different locations. Consequently, the corresponding theoretical expressions of the first-order natural frequency are 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 are identified by measuring the morphological parameters of the tree. Subsequently, the branch density and flexural elastic modulus are measured by water immersion method and three-point bending test respectively. The theoretical values of the first-order natural frequency for the bifurcated basic unit with different branching angles are calculated by substituting the identified tree parameters. Then, a finite element simulation model of the bifurcated basic unit for Camellia oleifera is created and the simulation value of natural frequency is obtained. In comparison with the simulated value and the theoretical frequency value, it is proved that the dynamics model with point mass equally distributed at both rod ends is the closest to the simulated model, which shows an average error of 7.3%. Finally, on the basis of the mathematical formula of the first-order natural frequency of the cantilever beam with point mass at rod top, an empirical calculation formula for the bifurcated basic unit is derived using the parameter identification approach. The error between the theoretical natural frequency from the empirical formula and the simulated value is the smallest with the maximum error 0.41%. The validity and accuracy of the empirical formula are verified. The research results can provide theoretical guidelines for the setting of vibration parameters of Camellia oleifera fruit vibration picking device.

     

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