Empirical formula for the natural frequency of <i>Camellia oleifera</i> trunk using allometric growth

ZHANG Shiyi; TANG Lewei; WU Mingliang; LI Zhengchao; ZHANG Huiyu

doi:10.11975/j.issn.1002-6819.202403204

Volume 40 Issue 18

Sep. 2024

Turn off MathJax

Article Contents

Abstract

References

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

ZHANG Shiyi, TANG Lewei, WU Mingliang, et al. 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

Citation:

PDF (3182 KB)

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

1.
College of Mechanical and Electrical Engineering, Hunan Agricultural University, Changsha 410128, China
2.
Specialty Oil Crop (Camellia oleifera) Full Mechanization Research Center, Changsha 410128, China)

More Information

Received Date: March 26, 2024
Revised Date: June 05, 2024
Available Online: August 04, 2024

Graphical Abstract

Abstract

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.
- frequency,
- vibration,
- Camellia oleifera,
- allometric growth law,
- empirical formula,
- bifurcated basic unit

FullText(HTML)

References (31)

References

[1]	GAO L, JIN L, LIU Q, et al. Recent advances in the extraction, composition analysis and bioactivity of Camellia (Camellia oleifera Abel. ) oil[J]. Trends in Food Science & Technology, 2023, 143: 104211.
[2]	张立伟,王辽卫. 我国油茶产业的发展现状与展望[J]. 中国油脂,2021,46(6):6-9,27. ZHANG Liwei, WANG Liaowei. Prospect and development status of oil-tea camellia industry in China[J]. China Oils and Fats, 2021, 46(6): 6-9,27. (in Chinese with English abstract)
[3]	严茂林,付晓宇,陈畅,等. 大食物观下我国木本油料高质量发展的潜力挖掘、现实约束和对策建议[J]. 中国油脂,2024,49(6):11-17. YAN Maolin, FU Xiaoyu, CHEN Chang, et al. Potential exploration, realistic constraints and countermeasures for the high-quality development of woody oilseeds in China under the perspective of all-encompassing approach to food[J]. China Oils and Fats, 2024, 49(6): 11-17. (in Chinese with English abstract)
[4]	孟桂元,韩杰铖,詹兴国,等. 我国油茶产业分析与发展对策[J]. 中国油脂,2021,46(7):104-108,113. MENG Guiyuan, HAN Jiecheng, ZHAN Xingguo, et al. Industry analysis and development strategy of oil-tea camllia in China[J]. China Oils and Fats, 2021, 46(7): 104-108,113. (in Chinese with English abstract)
[5]	国家林草局和草原局国家发展和改革委员会财政部关于印发《加快油茶产业发展三年行动方案(2023—2025年)》的通知-国务院部门文件-中国政府网[EB/OL]. (2022-12-20)[2024-7-17]. https://www.gov.cn/zhengce/zhengceku/2023-01/10/content_5736075.htm
[6]	陈吉朋,汪亚东,周宏平. 油茶果采收机械与分选技术综述[J]. 林业工程学报,2024,9(4):12-24. CHEN Jipeng, WANG Yadong, ZHOU Hongping. Research on Camellia oleifera fruit harvesting machinery and sorting technology[J]. Journal of Forestry Engineering, 2024, 9(4): 12-24. (in Chinese with English abstract)
[7]	李正超,唐乐为,吴明亮,等. 偏移剪叉式油茶果收集装置设计与试验[J]. 农业工程学报,2024,40(3):62-71. doi: 10.11975/j.issn.1002-6819.202308174 LI Zhengchao, TANG Lewei, WU Mingliang, et al. Design and test of the fruit collecting device of Camellia oleifera with angular scissor mechanism[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2024, 40(3): 62-71. (in Chinese with English abstract) doi: 10.11975/j.issn.1002-6819.202308174
[8]	郑永军,江世界,陈炳太,等. 丘陵山区果园机械化技术与装备研究进展[J]. 农业机械学报,2020,51(11):1-20. doi: 10.6041/j.issn.1000-1298.2020.11.001 ZHENG Yongjun, JIANG Shijie, CHEN Bingtai, et al. Review on technology and equipment of mechanization in hilly orchard[J]. Transactions of the Chinese Society of Agricultural Machinery, 2020, 51(11): 1-20. (in Chinese with English abstract) doi: 10.6041/j.issn.1000-1298.2020.11.001
[9]	杜小强,李党伟,贺磊盈,等. 基于电子果实技术的机械振动采收过程果实运动分析[J]. 农业工程学报,2017,33(17):58-64. doi: 10.11975/j.issn.1002-6819.2017.17.008 DU Xiaoqiang, LI Dangwei, HE Leiying, et al. Fruit motion analysis in process of mechanical vibration harvesting based on electronic fruit technique[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2017, 33(17): 58-64. (in Chinese with English abstract) doi: 10.11975/j.issn.1002-6819.2017.17.008
[10]	崔王斌,周宏平,许林云,等. 我国林果机械振动式采收装备及理论研究进展[J]. 世界林业研究,2023,36(6):64-70. CUI Wangbin, ZHOU Hongping, XU Linyun, et al. Research progress in mechanically vibratory harvesting equipment of forest fruit and its theory in China[J]. World Forestry Research, 2023, 36(6): 64-70. (in Chinese with English abstract)
[11]	陈度,杜小强,王书茂,等. 振动式果品收获技术机理分析及研究进展[J]. 农业工程学报,2011,27(8):195-200. doi: 10.3969/j.issn.1002-6819.2011.08.033 CHEN Du, DU Xiaoqiang, WANG Shumao, et al. Mechanism of vibratory fruit harvest and review of current advance[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2011, 27(8): 195-200. (in Chinese with English abstract) doi: 10.3969/j.issn.1002-6819.2011.08.033
[12]	MURPHY K D, RUDNICKI M. A physics-based link model for tree vibrations[J]. American Journal of Botany, 2012, 99(12): 1918-1929. doi: 10.3732/ajb.1200141
[13]	LÁNG Z, CSORBA L. A two degree of freedom damped fruit tree model[J]. Agricultural Engineering International: CIGR Journal, 2015, 17(3): 335-341.
[14]	林欢,许林云,宣言,等. 基于集中质量的银杏树动力学建模研究[J]. 中国农机化学报,2019,40(11):81-88. LIN Huan, XU Linyun, XUAN Yan, et al. Study on kinetic modeling of Ginkgo tree based on concentrated mass[J]. Journal of Chinese Agricultural Mechanization, 2019, 40(11): 81-88. (in Chinese with English abstract)
[15]	ZHOU J, XU L, ZHANG A, et al. Finite element explicit dynamics simulation of motion and shedding of jujube fruits under forced vibration[J]. Computers and Electronics in Agriculture, 2022, 198: 107009. doi: 10.1016/j.compag.2022.107009
[16]	HOSHYARMANESH H, DASTGERDI H R, GHODSI M, et al. Numerical and experimental vibration analysis of olive tree for optimal mechanized harvesting efficiency and productivity[J]. Computers and Electronics in Agriculture, 2017, 132: 34-48. doi: 10.1016/j.compag.2016.11.014
[17]	DU X, HAN X, SHEN T, et al. Natural frequency identification model based on BP neural network for Camellia oleifera fruit harvesting[J]. Biosystems Engineering, 2024, 237: 38-49. doi: 10.1016/j.biosystemseng.2023.11.012
[18]	林欢,许林云,周宏平,等. 机械采收作业中银杏树频谱特性与振动响应关系研究(英文)[J]. 农业工程学报,2017,33(17):51-57. doi: 10.11975/j.issn.1002-6819.2017.17.007 LIN Huan, XU Linyun, ZHOU Hongping, et al. Relationship between frequency spectrum characteristics and vibration responses of Ginkgo biloba trees during mechanical harvesting operation[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2017, 33(17): 51-57. (in Chinese with English abstract) doi: 10.11975/j.issn.1002-6819.2017.17.007
[19]	WANG R, FANG D, WU C, et al. Dynamic response of Camellia oleifera fruit-branch based on mathematical model and high-speed photography[J]. Biosystems Engineering, 2024, 237: 232-241. doi: 10.1016/j.biosystemseng.2023.12.010
[20]	李斌,陆华忠,吕恩利,等. 荔枝树枝能量传递特性与去梗式振动采摘作业参数[J]. 农业工程学报,2018,34(8):18-25. doi: 10.11975/j.issn.1002-6819.2018.08.003 LI Bin, LU Huazhong, LYU Enli, et al. Characterizing energy transfer of litchi branches and working parameters of destemmed vibrational picking[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2018, 34(8): 18-25. (in Chinese with English abstract) doi: 10.11975/j.issn.1002-6819.2018.08.003
[21]	LANG Z. A one degree of freedom damped fruit tree model[J]. Transactions of the ASABE, 2008, 51(3): 823-829. doi: 10.13031/2013.24520
[22]	伍德林,赵恩龙,姜山,等. 基于能量传递规律的油茶树冠层振动参数优化与试验[J]. 农业机械学报,2022,53(8):23-33. doi: 10.6041/j.issn.1000-1298.2022.08.003 WU Dein, ZHAO Enlong, JIANG Shan, et al. Optimization and experiment of canopy vibration parameters of Camellia oleifera based on energy transfer characteristics[J]. Transactions of the Chinese Society of Agricultural Machinery, 2022, 53(8): 23-33. (in Chinese with English abstract) doi: 10.6041/j.issn.1000-1298.2022.08.003
[23]	翁凌云,许林云. Y型果树动力学模型假设与分析[J]. 农机化研究,2013,35(4):19-24. doi: 10.3969/j.issn.1003-188X.2013.04.004 WENG Lingyun, XU Linyun, et al. Analysis on mechanical model assumption of Y-trellis trees[J]. Journal of Agricultural Mechanization Research, 2013, 35(4): 19-24. (in Chinese with English abstract) doi: 10.3969/j.issn.1003-188X.2013.04.004
[24]	CASTRO-GARCIA S, BLANCO-ROLDAN G L, GIL-RIBES J A. Vibrational and operational parameters in mechanical cone harvesting of stone pine (Pinus pinea L. )[J]. Biosystems Engineering, 2012, 112(4): 352-358. doi: 10.1016/j.biosystemseng.2012.05.007
[25]	许林云,刘冠华,周杰,等. 用于振动采收的有果有叶果树振动模型构建[J]. 农业工程学报,2020,36(11):1-12. doi: 10.11975/j.issn.1002-6819.2020.11.001 XU Linyun, LIU Guanhua, ZHOU Jie, et al. Construction of the vibration model of the fruit trees with fruits and leaves for vibration harvesting[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2020, 36(11): 1-12. (in Chinese with English abstract) doi: 10.11975/j.issn.1002-6819.2020.11.001
[26]	黄强. 结合树木分枝方式构建树木骨架方法研究[D]. 保定:河北农业大学,2019. HUANG Qiang. Study on the Method of Constructing Tree Skeleton by Collecting Branches[D]. Baoding: Hebei Agricultural University, 2019. (in Chinese with English abstract)
[27]	RODRIGUEZ M, EMMANUEL D L, BRUNO M. A scaling law for the effects of architecture and allometry on tree vibration modes suggests a biological tuning to modal compartmentalization[J]. American Journal of Botany, 2008, 95(12): 1523-1537. doi: 10.3732/ajb.0800161
[28]	WANG J. Mechanical coffee harvesting[J]. American Society of Agricultural and Biological Engineers, 1965, 8(3): 400-402. doi: 10.13031/2013.40529
[29]	THECKES B, LANGRE D E, BOUTILLON X. Damping by branching: a bioinspiration from trees[J]. Bioinspiration Biomimetics, 2011, 6(4): 046010. doi: 10.1088/1748-3182/6/4/046010
[30]	陈志健. 面向机械振动采收的油茶树冠层识别与分析[D]. 合肥:安徽农业大学,2021. CHEN ZhiJian. Identification and Analysis of Camellia Oleifera Canopy for Mechanical Vibration Harvesting[D]. Hefei: Anhui Agricultural University, 2021. (in Chinese with English abstract)
[31]	TANG L, GOUTTEFARDE M, SUN H, et al. Dynamic modelling and vibration suppression of a single-link flexible manipulator with two cables[J]. Mechanism and Machine Theory, 2021, 162: 104347. doi: 10.1016/j.mechmachtheory.2021.104347

[1]	Zhang Xin, Yang Jianhua, Wang Weizhou, Jing Tianjun, Zhang Man. Construction and application of evaluation indexes for ruralmicro-energy-grid[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2020, 36(6): 196-205. DOI: 10.11975/j.issn.1002-6819.2020.06.023
[2]	Li Ming, Zhou Changji, Ding Xiaoming, Wei Xiaoming, Huang Shangyong, He Yanping. Heat insulation and storage performances of polystyrene-brick composite wall in Chinese solar greenhouse[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2016, 32(1): 200-205. DOI: 10.11975/j.issn.1002-6819.2016.01.028
[3]	Yuan Xiaoqing, Kong Qingxin, Li Qifeng, Li Lin, Li Daoliang. Evaluation method for application of internet of things for aquaculture[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2015, 31(4): 258-265. DOI: 10.3969/j.issn.1002-6819.2015.04.036
[4]	Qi Fei, Zhou Xinqun, Bao Shunshu, Ding Xiaoming, Wei Xiaoming, Lian Qinglong. Expression and evaluation method of integrated modes for protected horticulture engineering[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2013, 29(8): 195-202.
[5]	Wang Defu. Experimental study of particle-evaluation equipment for roughage[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2007, 23(2): 128-131.
[6]	Cao Shun′ai, Wu Cifang, Yu Wanjun. Method for environmental evaluation of land abroad and its application at Hangzhou City[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2006, 22(10): 263-266.
[7]	Wang Ailing, Zhao Gengxing, Li Zhanjun. Integrated evaluation method for project post-evaluation of land consolidation benefits[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2006, 22(4): 58-61.
[8]	Fan Jinmei, Wang Lei, Xue Yongsen. Evaluation of the benefit of land consolidation and rehabilitation[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2005, 21(13): 116-118.
[9]	Kong Xiaoling, Jiang Deyun, Wei Shan, Yang Haidong. Comparative study on muscle tenderness evaluating methods[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2003, 19(4): 216-219.
[10]	ZHAO Geng-xing, LI Yu-huan, Li Qiang. Quantitative and Automatic Evaluation Methods Supported by GIS of Agricultural Land[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 1999, 15(3): 219-223.