用于振动采收的有果有叶果树振动模型构建

Construction of the vibration model of the fruit trees with fruits and leaves for vibration harvesting

现有的果树振动有限元模型仅对果树的枝杆部分进行重建,忽略了果树的果实与树叶对果树固有频率的影响。该研究提出了一种将激光扫描技术与有限元法相结合,用空间6自由度梁单元构建果树空间振动模型。基于研究果实和树叶在树枝上的位置和质量分布规律,构建果树有果有叶、无果有叶、无果无叶振动模型。并对一棵小型实体银杏树分别处于有果有叶、无果有叶和无果无叶3种状态的频谱特性进行测试,并与构建的理论振动模型计算的各阶固有频率进行比对分析。结果表明,计算固有频率数量要多于实测所体现出来的固有频率数量,但实测固有频率均可在仿真频率中找到十分相近的值,且仿真模型的果树各枝振型幅值与实测的各枝加速度响应幅值相互的对应关系基本吻合;计算模型的最大相对误差为5.76%。该研究所述建模方法能够较准确有效地获取果树固有频率。

Most existing finite element models of a fruit tree used the trunk-branch model to simulating vibration response,ignoring the effects of fruit and leaves.But the fruitless and leafless model had many differences with the actual fruit tree and could not accurately calculate the vibration characteristics.In this study,a method for constructing a tree’s vibration model with fruits and leaves had been proposed.This method combined laser scanning technology and finite element calculation methods,having the ability to calculate the vibration characteristics of fruit trees based on the accurate shape of fruit trees.The first step in constructing the model with fruits and leaves was to extract the skeleton points and branch radius from the laser scanning point cloud information of the fruit tree.The next step was using the extracted fruit tree skeleton points as the nodes of the finite element model to construct a fruitless and leafless fruit tree model.Adding mass to the nodes based on the fruits and leaves natural laws with the assumption that some kind of fruit trees had the consistent distribution of fruits and leaves during the harvest period,the 6-degree-of-freedom beam element vibration model was constructed finally.A fruit-and-leaf vibration finite element model was applied to a fruit-leafed the ginkgo tree.A small laser scanner was used to scan the experimental ginkgo tree three times to obtain complete point cloud information.Through a statistic of 8 factors for the leaves and fruits distribution of the ginkgo tree,this study analyzed the number and quality of leaves and fruits on branches of unit length and based on the regular pattern above to build the ginkgo tree vibration model.The Ginkgo fruit distribution obtained from the analysis was that the average spacing of axillary buds was about 4.2 cm,an average of 6 fruits grow on each axillary bud,and the weight of each fruit was about 6 grams on branches with a diameter of less than 10 mm.The Ginkgo leaves distribution was that the average spacing of axillary buds was about 4 cm,an average of 5 leaves grow on each axillary bud,and the weight of each leaf was about 0.4 g on branches with a diameter of less than 12 mm.To verify the accuracy of the calculation results,the ginkgo trees were tested in three states of fruit-leaf,fruit-free,and trunk-branches.By comparing the three testing spectral curves,this study found that there were many differences at the number of natural frequencies and acceleration amplitude,which meant leaves and fruits significantly affected the spectral characteristics.Comparing the calculation results of the first 15 models and calculation results in 15-25 Hz with sample test results,this study found that the number of natural frequencies obtained from simulation results was more than the number of natural frequencies obtained from test results.The natural frequencies from test results could find very close values in the simulation results.The amplitude and the acceleration response of each branch in the tested spectrum curve were consistent with the simulation vibration mode shape.The corresponding maximum relative errors of natural frequencies in the three states of fruit-leaf,fruit-free,and trunk-branches were 5.76%,2.06%,and 1.98%Hz,respectively.The average relative errors of natural frequencies were 2.32%,0.82%,and 0.95%.By analyzing the calculation model’s accuracy,this study found that adding the leaves and fruits weight to the trunk-brank model could improve the calculation accuracy when the tree’s shape and analysis elements’quality of the trunk-brank model had not changed.The modeling method described in this study could obtain the natural frequencies of the fruit tree accurately and quickly.This study had a guiding significance for resonance method harvesting in practical applications.