Kinematic Analysis of the Vibration Harvesting Process of Lycium barbarum L. Fruit

Abstract

The traditional shrub fruits harvesting method is manual picking, while the efficiency is low, which seriously restricts the development of Lycium barbarum L. industry. In order to mechanize the harvesting process of Lycium barbarum L. and improve the correct picking rate while reducing the damage rate of Lycium barbarum L. harvesting, it is very important to analyze the kinematic model of the fruit-bearing branch during vibration harvesting. Through the measurement and analysis of the natural characteristics and physical parameters of the branches, a simplified model of Lycium barbarum L. shrub fruit-bearing branch was built by Solidworks 2023 software, and the appropriate material properties were selected. Through modal analysis and harmonious response analysis, the response characteristics data of fruit-bearing branches of Lycium barbarum L. shrub were obtained. In Qinghai Nuomuhong Farm, the field vibration harvesting kinematic model feature analysis test was carried out, and the acceleration data of the vibration harvesting process were collected by using the acceleration sensor, and through the analysis of the frequency spectrum characteristics of the data, it was concluded that when the excitation frequency was maintained between 8 and 14 Hz, the Lycium barbarum L. fell off well and the picking rate can reach 97.56%, the efficiency can reach 6.88 pieces of fruit per second, and the branch damage was acceptable, which theoretically met the needs of harvesting.

1. Introduction

Lycium barbarum L. is a shrub with adventitious inflorescence which produces delicious fruit [1,2]. The fruit is not only nutritious, but also has high medicinal value [3,4,5]. With the large-scale standardized production of Lycium barbarum L. and the continuous improvement of planting management, the output increased year by year, and the demand for agricultural mechanization operation technology also increased [6]. The traditional harvesting method is manual picking, which has low efficiency, and it seriously restricts the development of the Lycium barbarum L. industry [7]. With the reduction in agricultural labor intensity and the promotion of rational use of resources in agricultural production [8], the development of mechanized harvesting technology of Lycium barbarum L. is the key to increase the yield of Lycium barbarum L. and reduce the labor demand [9,10,11].

At present, there are various types of Lycium barbarum L. harvesting machines, and the main working methods are divided into vibration type, air suction type, comb brush type, etc. [12,13,14,15,16]. Among these various types of mechanized harvesting methods, vibration harvesting presents the highest efficiency [6]. The efficiency of vibration harvesting is strongly correlated with response frequency [12]. Liu’s team built an eccentric mechanism to vibrate the branch and pick fruits, the output rotate speed was set to 160 r/min, which equals to 2.7 Hz [13]. Sargent’s team used a self-propelled blueberry harvester with full branch coverage tines and their output frequency was 7 Hz [17]. Fu’s team used an eccentric shaker to harvest a raspberry tree by vibrating the main trunk and the best frequency range was 15 Hz to 19 Hz [18]. Ding’s team used a reciprocating vibration generator to vibrate the trunk of a mulberry tree and the best frequency was set to 28 Hz [19]. Gao’s team used a well-designed eccentric harvester to vibrate the main trunk of a Camellia oleifera tree and the best vibration frequency was 15 Hz [20]. As we can see from these results of the existing studies, we can see that when we are about to harvest fruits by vibrating the branch, it needs lower frequency, and it needs higher when we vibrate the trunk. So, when it comes to low cost as high frequency damages the tree, we need to choose the branch as the vibration target, the existing studies of other kinds of berry picking shows that the frequency is around 5 Hz to 10 Hz. Based on the research results above, it is important to design a highly efficient harvesting machine with optimized resonance frequency by using methods of kinematic analysis.

The harvesting mechanism of the vibrating Lycium barbarum L. harvester is to apply a specific parameter of vibration excitation to the fruit-bearing branches, and the Lycium barbarum L. branches will vibrate in response, and then drive the fruit to reciprocate at a certain frequency. According to Newton’s second law, when the acceleration of the fruit reaches a certain value, the resultant force on the fruit will exceed its binding force, and the fruit will detach from the branch, thus completing the picking of the Lycium barbarum L. However, the Lycium barbarum L. flowers and fruits grow at the same time, so in the process of vibrating harvesting, while picking ripe fruits, it also caused picking of unripe fruits and flowers, which affected the yield. It is also easy to cause damage to the fruit in the process of mechanized harvesting. Based on these conditions, to improve the ripe fruit picking rate of the existing vibrating Lycium barbarum L. harvesting machine on the market and reduce the rate of unripe fruit picking and damage, it is necessary to research the physical size of Lycium barbarum L. plants and the kinematic characteristic parameters in the vibration process to lay a theoretical foundation for the design of a new generation of high-efficiency, low-loss, and intelligent Lycium barbarum L. harvesting machine.

In this study, a simplified model of the fruit-bearing branch was established based on measurements of the shape parameters. The modal analysis and the harmonious response analysis of the simplified modal were performed to obtain a range of frequencies suitable for vibration harvesting. Then, a vibration harvesting machine was designed and assembled to verify the simulation results. The vibration harvesting field test was performed using the harvesting machine and an acceleration sensor. Among these finding, the most efficient vibration frequency of Lycium barbarum L. fruits’ harvesting was provided. The flow chart of the study is shown in Figure 1. The whole study starts from the simulation analysis. We used the shape parameters and material parameters to establish a simplified model of the fruit-bearing branch, then we used modal analysis to gain the natural frequency range of the model, then we used harmonic response analysis to determine the frequency range with the highest corresponding acceleration, which will be used as the excitation frequency during the field tests. In the field tests we used a hand-held vibrating picking machine to stimulate the fruit-bearing branches, while collecting acceleration data using a triple-axis accelerometer. After processing of data using the FFT algorithm, the range of vibration frequencies are extracted, which can verify the simulation results, and the most suitable frequency range can be concluded.

2. Materials and Methods

2.1. Physical Tests of the Branches

Lycium barbarum L. belongs to the Solanaceae shrub, with a flowering period of June~July and a fruiting period of August~October. The fruit of Lycium barbarum L. is in the shape of an oval, the unripe Lycium barbarum L. is green or yellow while the ripe fruit is red, and only the red fruit can be picked when harvested, instead of the yellow and green fruit. In order to obtain the parameters of the kinematic simulation, the biomechanical properties and size of the branches and fruits of Lycium barbarum L. were measured.

In order to build an accurate simplified modal of the fruit-bearing branch, it was necessary to measure the parameters of the shrub. ‘Ningqi 1’ was selected as the experimental shrub of the study as it was the most widely cultivated type in Nuomuhong farm in Golmud City, Qinghai Province on 8 August 2023. A push–pull force gauge (type: HP; maximum testing force: 20 N; manufactured by HANDPI Co., Ltd., Leqing, China), a digital vernier caliper (type: SY04; maximum testing length: 150 mm; manufactured by SYNTEK Co., Ltd., Huzhou, China), and an electronic weight scale (type: FX5000I-JA; maximum testing weight: 5200 g; manufactured by A&D Co., Ltd., Tokyo, Japan) were used to perform the tests. The test results were recorded by test members. As is shown in Figure 2, 15 plants were randomly selected from the field, 4 branches were selected for each plant, and the parameters, such as the length of the fruit-bearing branches, the length of the fruit-bearing segments, the diameter of the thick ends and the thin ends, and 3 red fruits, 3 yellow, and 3 green fruits of Lycium barbarum L. were selected in the front, middle, and back of the fruit-bearing segment of each branch, and the fruit pedicle binding force, fruit stalk binding force, fruit size, fruit surface pressure tolerance, and other parameters were measured, respectively. We used a push–pull force gauge to measure the binding force between fruit and stalk, the fruit was placed in a clamp hooked on the gauge, then the tester pulled the fruit horizontally after setting the gauge to zero. We used a digital vernier caliper to measure the length and thickness of branches we needed. We used an electronic weight scale to measure the weight of all kinds of fruits.

2.2. Establishment of the Simplified 3D Branch Modal

The previous tests provided accurate parameters for the finite element modal (FEM) analysis tests. In this study, the fruit-bearing branches of Lycium barbarum L. shrubs were mainly used, and they were simplified into a segmented cylinder by scanning the hanging branch from the shrub and using variable diameter from the data we measured as being close to the actual shape. The shape parameters of the fruit-bearing branches are shown in

Table 1. The shape parameters of the fruit-bearing branch model.

Project	Longest	Shortest	Average
Thick End Diameter (mm)	1.13	0.82	4.32
Thin End Diameter (mm)	6.09	3.56	1.11
Length (mm)	902	371	552

based on the parameters obtained by the tests, and a 3D model of the fruit-bearing branch was established in SolidWorks software (2023; manufactured by Dassault Systèmes-SolidWorks Corporation, Waltham, MA, USA) based on the fruit-bearing branches shape, as shown in Figure 3.

2.3. Modal Analysis and Harmonic Response Analysis

In order to carry out the kinematic experiment of vibrating Lycium barbarum L. harvesting, it is necessary to obtain the excitation frequency range, and which is generally determined by the natural frequency of the fruit-bearing branches. As mentioned in [21], when the plant vibrates freely, its displacement will change as time goes by in a sinusoidal manner; the vibration cycle length is related to the natural frequency of the system and has nothing to do with the setting of the initial conditions. The structure has an infinite number of natural frequencies in principle, and the fundamental frequency is the minimum natural frequency. When the natural frequency is consistent with the forced frequency, the resonance phenomenon of the system will occur to save energy and improve efficiency. The fruit-bearing branch was simplified as the main objective of the whole process of vibrating harvesting, so this analysis requires the construction of a FEM of the fruit-bearing branches of the Lycium barbarum L. shrub.

To obtain the natural frequency of the fruit-bearing branch of the Lycium barbarum L. shrub required for the experiment, using the modal analysis algorithm in the FEM analysis software is a mainstream approach. Firstly, the previously modeled Lycium barbarum L. shrub fruit-bearing branch was imported into Ansys Workbench 2022 software (2022 R1; manufactured by ANSYS, Inc, Canonsburg, PA, USA), and then the material property parameters were set for the model. Finally, the modal analysis function module and harmony response analysis function module of the software were used for simulation analysis to obtain the natural frequencies of the branch and the vibration response parameters at each excitation frequency. Referring to [22], the material parameters of the fruit-bearing branches of the Lycium barbarum L. shrub are shown in

Table 2. Material parameters of the fruit-bearing branches of the Lycium barbarum L. shrub.

Project	Value
Density (kg/m3)	1021.6
The Radial Elastic Moduli Ex and Ey (MPa)	65.49
The Axial Elastic Modulus Ez (MPa)	498.59
The Poisson’s Ratio uxy	0.3
The Poisson’s Ratio uyz	0.17
The Poisson’s Ratio uxz	0.17
The Axial Shear Modulus Gxy (MPa)	25.19
The Axial Shear Modulus Gyz and GxZ (MPa)	6.63

, where the branch material is defined as transversely isotropic.

The modal analysis function was invoked, and after importing the model of fruit-bearing branch into the geometric structure and setting the material property parameters, since the constraints of the fruit-bearing branches are mainly located at the junction between them and the branches of the upper level, a location constraint was added to its thick end. The Lycium barbarum L. shrub fruit-bearing branch is a small model, and the modal order to be solved is within 10, and the results obtained by using each modal solution algorithm are almost the same. The first 10-order natural frequencies of the fruit-bearing branch are solved by using the default Block Lanczos algorithm, which is widely used as a modal extraction algorithm. The sparse matrix solver is automatically employed in this method and it is less affected by the loss of orthogonality. The meshed branch model is shown in Figure 4.

After meshing, 7216 elements, 4807 elements, and 6747 elements were generated in the longest, shortest, average branch modal analysis process, and the grid was very small, which shows the sufficiency for the modal analysis of the branch.

The first 10-order natural frequencies’ range of the fruit-bearing branch were obtained through modal analysis. The next step is to use the harmonic response function to obtain the acceleration peaks and the displacement peaks of each order of vibration response. The same geometric structure and material property parameters were imported into the harmonic response analysis module and the same constraints were added, while the excitation force of 2 N was applied to the middle section of the branch model as shown in Figure 5. In order to find the peak vibration response, the output cluster result was selected. Since the modal shape is small, the frequency response below 5 Hz is not of reference value, so the swept frequency range was set to 5~20 Hz, while the damping ratio was set to 0.3 according to [23]. The results were then calculated.

2.4. Field Tests on the Kinetic Characteristics of Branches Using Vibration Harvesting Equipment

In the process of vibrational energy transference, the resonance frequency of fruit branches can be identified by looking for the peak displacement or acceleration amplitude of the fruit branches at different vibration frequencies, and the vibration motion characteristics of the fruit-bearing branches can be represented by the acceleration data measured by a piezoelectric triple-axis accelerometer during the actual harvesting process. By FFT transformation of the acceleration data measured by the sensor, the energy peak corresponding to each frequency component in the vibration harvesting process can be obtained to obtain the most suitable frequency for vibration harvesting.

The vibration harvesting equipment used in the field tests selected a hand-held vibrating picking machine, which is mainly composed of a motor, a transmission assembly, a vibration excitation claw, and a hand-held part, and is powered by a knapsack battery, and its overall model is shown in Figure 6.

To obtain the motion characteristics data of branches during harvesting, a piezoelectric triple-axis accelerometer (type: BWT901CL; maximum testing acceleration: 16 G; manufactured by Wit-Motion Co., Ltd., Shenzhen, China) was selected, and the sampling frequency was set to 100 Hz, while the three-axis acceleration curves of a specific position of the branch during the vibration harvesting process were collected by the host computer software. The tests took place on 10 August. Four ‘Ningqi 1’ Lycium barbarum L. shrubs with similar growth were selected, then we chose 1 branch with a length of about 0.5 m from each plant. Before the start of vibration harvesting, the piezoelectric accelerometer was installed at 3/4 of the total length of the fruit-bearing branches where the fruits are dense, while the x-axis of the accelerometer was kept facing the gravity direction, and the excitation position was selected at 1/2 of the total length of the branches. The vibration harvesting started after the preparation was completed. The data collected by the accelerometer were transmitted to the host computer through Bluetooth, then the data were exported for processing. The setting of the accelerometer is shown in Figure 7.

3. Results

3.1. Physical Tests Results

The results of the physical tests are shown in

Table 3. Parts of the parameters of the Lycium barbarum L. shrubs.

Project	Range of the Value	Average Value
Length of the Fruit-Bearing branch (mm)	489~613	575
Length of the Fruit-Bearing Area (mm)	337~565	551.9
Thick End Diameter (mm)	3.864~6.445	4.32
Thin End Diameter (mm)	0.898~1.252	1.11
Weight of Red Fruit (g)	0.734~1.208	1.015
Weight of Yellow Fruit (g)	0.179~0.545	0.341
Weight of Green Fruit (g)	0.129~0.334	0.168
Binding Force of Red Fruit (N)	0.28~1.29	0.59
Binding Force of Yellow Fruit (N)	0.63~3.20	1.28
Binding Force of Green Fruit (N)	0.68~2.39	1.17

.

As can be seen from it, the length of fruit-bearing branches of Lycium barbarum L. shrubs is generally in the range from 489 mm to 613 mm, the length of fruit-bearing areas is from 337 mm to 565 mm, the thick end diameter is in the range from 3.864 mm to 6.446 mm, and the thin end diameter is in the range from 0.898 mm to 1.252 mm. The fruit is connected to the branch by a fruit stalk, and the length of the fruit stalk is about 20 mm long. The average weight of green fruits is 0.168 g, and the binding force between fruit stalk and branch is about 0.68~2.39 N. The average weight of yellow fruits is 0.341 g, and the binding force between the fruit stalk and the branch is about 0.63~3.20 N. The average weight of red fruit is 1.015 g, and its binding force is generally between 0.28 and 1.29 N. The fruits connect to the branch by a stalk and their movement can be seen as consistent with the branches, but with a certain delay when the branches are vibrating. For the sake of simple calculation, we assume that the binding area of the fruit-bearing branch is consistent with the movement of the fruit, so the approximate range of the acceleration peak during the vibration process can be roughly calculated by the following formula:

$$F_R<m_{R}a$$

(1)

$$F_Y>m_{Y}a$$

(2)

$$F_G>m_{G}a$$

(3)

where $F_R$ is the binding force of red fruits; $m_R$ is the weight of the red fruits; $F_Y$ is the binding force of yellow fruits; $m_Y$ is the weight of the yellow fruits; $F_G$ is the binding force of green fruits; $m_G$ is the binding force of green fruits; and $a$ is the total acceleration of the fruits.

After calculation, the suitable harvesting acceleration is between 581.3 $\mathrm{m}/{\mathrm{s}}^2$ and 3519.5 $\mathrm{m}/{\mathrm{s}}^2$.

3.2. Results of Modal Analysis and Harmonic Response Analysis

3.2.1. Results of Modal Analysis

The results of modal analysis are shown in

Table 4. The results of the modal analysis of the branch modal.

Rank	The Longest Branch’s Frequency (Hz)	The Shortest Branch’s Frequency (Hz)	The Average Branch’s Frequency (Hz)
1	0.58362	1.9946	0.99723
2	0.59644	2.0812	1.1198
3	0.99122	3.8342	2.8027
4	1.1347	4.2994	2.941
5	2.3156	9.0007	5.236
6	2.5706	10.012	5.5579
7	4.4582	17.43	9.424
8	4.6448	18.28	9.8064
9	6.9348	27.697	15.356
10	7.0448	27.959	16.045

. The results of this simulation analysis are obtained with the lowest 1.0 Hz and the highest 16.1 Hz of the first 10 natural frequencies of the fruit-bearing branch of the Lycium barbarum L. shrub. In order to determine the suitable frequency range for vibration harvesting, it is necessary to determine the characteristic parameters of movement response of various excitation frequencies through the results of harmonic response analysis.

3.2.2. Results of Harmonic Response Analysis

The acceleration response results of the harmonic response analysis are shown in Figure 8, from which it can be seen that there are two response peak points that are more suitable for harvesting, respectively: 6.6743 Hz and 11.78 Hz, among them, the frequency response peaks corresponding to the two peaks are very close, and the acceleration responses are both within the ideal range, so they can be used as vibration frequencies suitable for harvesting.

Through the above simulation analysis, the long branch needs higher power of excitation to harvest while the short branch can be harvested by using lower power or frequency. However, it can be concluded that the frequency suitable for vibration harvesting should be between 6.6 Hz and 14.8 Hz, because in the actual vibration harvesting process, it is difficult to maintain a stable frequency due to the influence of fruit shedding or other branch interference, so the vibration harvesting frequency between 6 Hz and 15 Hz can ensure efficient and low-loss harvesting.

3.3. Results of the Field Tests

The acceleration data were obtained through the tests and the data processing was carried out using Origin software (2022; manufactured by OriginLab Corporation, Northampton, MA, USA). The spectrogram was obtained through the fast Fourier transform (FFT). According to definition, power density, or spectrum, can be calculated using the following formula:

$$P_{xx}\left(e^{j\omega }\right)={\displaystyle \sum }_{m=-\infty }^{\infty }{r}_{xx}\left(m\right)e^{-j\omega m}$$

(4)

where $P_{xx}$ stands for power density; $r_{xx}\left(m\right)$ stands for the autocorrelation function of the input signal; and m stands for the abscissa of the discrete data point. Because the sample size of the input signal is finite, only certain methods can be used to estimate the power spectrum, so the power spectrum cannot be calculated using definitions. The mean square amplitude (MSA) image of the power is estimated from the amplitude of the fast Fourier transform data using the periodogram method of the following formula:

$$Amplitude={\displaystyle \frac{R{e}^2+I{m}^2}{n^2}}$$

(5)

where $Re$ and $Im$ stand for the real and imaginary parts of the transform data; $n$ is the length of the input sequence. According to [21], the vibration response trend in the triaxial direction is the same during the branch vibration process. The acceleration response of the sensor in the x-axis direction was selected, and the results are shown in Figure 9. The vibrating picking results are shown in

Table 5. The picking results.

Project	Picking Rate	Damage Rate	Efficiency (Piece/s)
Test 1	96.91	2.13	6.23
Test 2	96.63	2.33	6.53
Test 3	97.56	1.25	5.74
Test 4	91.14	2.78	6.88

.

Among them, the sampling frequency of the first and the second tests are 100 Hz, while the third and the last are 200 Hz. Figure 9a shows the spectrogram of the first Lycium barbarum L. shrub’s vibration response with peaks at 8.84 Hz and 10.47 Hz, and the peaks of the second branch shown in Figure 9b appear at 9.4 Hz and 13.6 Hz. The vibration response peaks of the third branch shown in Figure 9c appear at 11.6 Hz and 12.1 Hz, and the vibration response peaks of the last branch shown in Figure 9d appear at 11.8 Hz and 13.1 Hz. It can be seen from the analysis and the tests that the vibration responses of different Lycium barbarum L. branches have certain differences, and the main reasons for the differences are the different fruit distribution and different branch dimensions. The vibration response of the selected Lycium barbarum L. species, that is, the fruit-bearing branches of the ‘Ningqi 1’ shrub is generally similar, and the frequency range suitable for vibration harvesting should be between 8 and 14 Hz.

4. Conclusions

In this study, the parameters of the ‘Ningqi 1’ Lycium barbarum L. shrub were obtained by physical measurement tests. A 3D model of the Lycium barbarum L. fruit-bearing branch was established based on the tests of measurements of the parameters, and suitable acceleration for vibration harvesting was calculated by the tests. The kinematic analysis of the branch based on FEM was performed to obtain the resonance frequency range. The field tests show that when the vibration frequency reach between 8 Hz and 14 Hz, which is suitable for the picking of fruits from fruit-bearing branches, and for those branches whose size is too small or big, we need to turn down or up the output amplitude or force of the excitation picking device so it can ensure efficient and low-loss harvesting. Furthermore, a more efficient vibration harvester will be designed based on the obtained results and the used type mentioned above.