基于点云建模的核桃树振动参数优化与试验

doi:10.11707/j.1001-7488.LYKX20240671

Abstract

Abstract:

Objective: This study aims to investigate the forced-vibration responses of walnut trees with different sizes, and to address the problems of low efficiency and a low fruit removal rate in vibratory walnut harvesting. Method: A terrestrial 3D laser scanner was used to acquire point-cloud data of walnut trees. After preprocessing the tree point clouds, tree skeletons were extracted. Siemens NX was employed to perform 3D fitting and reconstruction, and 3D walnut-tree models with different size parameters were established. Material-property parameters were calibrated using measured frequency spectra, and the maximum relative error of resonance frequencies observed in both experiments and simulations was only 0.22%, ensuring the accuracy of the 3D models. ANSYS was used to conduct harmonic response analyses on the 3D model of walnut trees, to investigate the effects of excitation frequency, excitation force, and excitation height on vibration acceleration, and to analyze the displacement and acceleration responses of walnut trees with different sizes under different frequencies. In addition, suitable harvesting frequencies for walnut trees of different sizes were further determined by integrating the displacement and acceleration responses of fruiting branches with the whole-tree responses shown in harmonic-response contour plots. Result: The peak acceleration response decreased with increasing trunk diameter, tree height, and crown width. Higher trees and larger crowns exhibited weaker responses to high-frequency excitation, indicating that the geometric characteristics of the tree significantly affect its vibration characteristics. The vibration harvesting parameters of walnut trees were subjected to the response surface analysis and optimized to obtain an optimal parameter combination. Under the optimal excitation conditions, the walnut harvesting rate exceeded 90% for all tested trees, indicating that the optimised vibration parameters can provide guidance for parameter settings of vibratory walnut-harvesting devices. Conclusion: The walnut-tree modelling method described in this study enables reconstruction of fine lateral branches, and the reconstructed whole-tree models better capture realistic growth morphology. Walnut trees with different trunk diameters, heights, and crown widths show distinct vibration responses. The suitable excitation frequency range is 10–20 Hz, which can be further narrowed according to specific tree-structure parameters.

Key words: walnut harvesting, vibratory harvesting, finite element analysis, vibration response, response surface analysis, excitation frequency optimisation

CLC Number:

S225

Wangbin Cui,Hongping Zhou,Yang Zhang,Yanyan Wang,Linyun Xu,Gaoming Fan. Optimisation and Testing of Vibration Parameters of Walnut Trees Based on Point Cloud Modelling[J]. Scientia Silvae Sinicae, 2026, 62(2): 186-203.

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编号ID	根部直径 Basal diameter/cm	整树高度 Tree height/m	冠幅 Crown width/m
A₁	31.2	13.2	9.3
A₂	19.1	11.7	6.7
A₃	15.5	7.4	4.8
B₁	18.4	13.2	9.3
B₂	24.6	13.2	9.3
C₁	31.2	11.5	9.3
C₂	31.2	12.4	9.3
D₁	31.2	13.2	7.8
D₂	31.2	13.2	8.6

材料Material	弹性模量Elastic modulus/$ \text{MPa} $	密度Density/（kg·m^?3）	泊松比Poisson’ s ratio	阻尼比Damping ratio
核桃树Walnut tree	4 702	1 019	0.35	0.056

A₁	测试Test	阶次Mode order	1	2	3	4	5	6	7	8	9	10	11	12
	测试Test	频率Frequency	0.98	2.11	4.39	6.35	8.35	10.25	14.64	17.09	19.98	21.48	24.41	27.83
	仿真Simulation	阶次Mode order	2	5	10	16	22	28	42	50	57	61	69	77
	仿真Simulation	频率Frequency	0.98	2.11	4.39	6.36	8.35	10.24	14.65	17.07	19.98	21.46	24.42	27.85
A₂	测试Test	阶次Mode order	1	2	3	4	5	6	7
	测试Test	频率Frequency	1.01	8.61	12.21	14.16	20.02	21.16	23.93
	仿真Simulation	阶次Mode order	3	13	21	25	38	41	46
	仿真Simulation	频率Frequency	1.01	8.61	12.22	14.14	20.05	21.19	23.97
A₃	测试Test	阶次Mode order	1	2	3	4	5	6	7	8	9	10	11
	测试Test	频率Frequency	0.98	4.74	7.32	9.27	10.63	13.79	15.63	17.81	21.16	26.37	28.32
	仿真Simulation	阶次Mode order	2	5	8	11	13	15	19	23	28	35	38
	仿真Simulation	频率Frequency	0.98	4.74	7.32	9.25	10.63	13.79	15.64	17.83	21.16	26.33	28.31

树号 Tree number	编码 Code	振动频率 Vibration frequency (A)/Hz	激振力 Excitation force (B)/N	激振高度 Excitation height (C)/m
A₁	?1	10	3 000	0.4
	0	14	3 500	0.8
	1	18	4 000	1.2
A₂	?1	8	3 000	0.4
	0	12	3 500	0.8
	1	16	4 000	1.2
A₃	?1	7	3 000	0.4
	0	12	3 500	0.8
	1	17	4 000	1.2

树号Tree number	来源Source	平方和Sum of squares	自由度Degrees of freedom	均方和Mean square	F	P
A₁	模型Model	2.484E+06	9	2.649E+05	138.28	<0.000 1^**
	残差Residual	5 556.5	7	793.79
	失拟项Lack of fit	4 126.5	3	1375.5	3.85	0.113 0
	纯误差Pure error	1 430	4	357.5
	总和Total	2.489E+06	16
A₂	模型Model	2.311E+06	9	2.568E+05	15.02	<0.000 1^**
	残差Residual	1.197E+05	7	17 095.89
	失拟项Lack of fit	81 097.25	3	27 032.42	2.8	0.172 4
	纯误差Pure error	38 574	4	9 643.5
	总和Total	2.431E+06	16
A₃	模型Model	3.085E+06	9	3.428E+05	15.33	<0.000 1^**
	残差Residual	1.565E+05	7	22 357.61
	失拟项Lack of fit	74 973.25	3	24 991.08	1.23	0.409 3
	纯误差Pure error	81 530	4	20 382.5
	总和Total	3.241E+06	16

Optimisation and Testing of Vibration Parameters of Walnut Trees Based on Point Cloud Modelling

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树号Tree number	决定系数Coefficient of determination ($ {R}^{2} $)	校正系数Correction coefficient $ (R_{\text{Adj}}^{2}) $	预测系数Prediction coefficient $ (R_{\text{Pre}}^{2}) $	变异系数Coefficient of variation (%)	精密度Precision
A₁	0.997 8	0.994 9	0.972 6	2.36	58.807 5
A₂	0.950 8	0.887 5	0.441 4	10.41	13.219
A₃	0.951 7	0.889 6	0.590 6	12.51	12.754

树号 Tree number	激振频率 Excitation frequency/Hz	激振力 Excitation force/N	激振高度 Excitation height/m	响应值 Response level /(m·s^?2)
A₁	11.4	3 452.4	0.7	1 404.0
A₂	11.2	3 891.4	1.0	1 493.8
A₃	9.4	3 946.6	0.6	1 616.2

树号 Tree number	落果数 Number of fallen fruits	未脱落数 Number of retained fruits	核桃采收率 Walnut harvesting rate (%)
A₁	1 649	37	97.8
A₂	658	43	93.9
A₃	436	17	96.2