Analysis and Optimized Design of Rigid–Flexible Coupling Characteristics of Crab Apple Picking Machines and Crab Apple Trees

Abstract

In recent years, with the gradual expansion of the planting area for Chinese crab apple trees, the traditional method of picking crab apples has become inadequate due to its large workload, low efficiency, and high cost. To address this issue, this paper presents the design of a trunk-type vibration picker specifically for crab apple picking. The design process began with a modal analysis and a harmonic response analysis of a crab apple tree using Ansys Workbench. Through these analyses, the optimal excitation frequency for the crab apple tree was determined to be 12.7 Hz. Subsequently, the picker was designed, and its key components underwent modal and stress analyses. A comparison revealed no resonance between the picker and the key components, ensuring the feasibility of the picker. To further evaluate the performance of the picker, a rigid–flexible coupling analysis was conducted using Adams. This analysis determined the acceleration response curves of the lateral branch points of the crab apple tree at various excitation frequencies: 9.7 Hz, 12.7 Hz, 15.7 Hz, and 18.7 Hz. Finally, field trials were carried out to validate the reliability of the data obtained from Adams. The results showed that the lateral branch point acceleration increased with higher excitation frequencies. However, when the optimal excitation frequency of 12.7 Hz was reached, the lateral branch point acceleration decreased. This indicated that the most effective vibration frequency for picking crab apples was 12.7 Hz.

1. Introduction

Crab apple, also known as wenlinguo, lingo, or flower red fruit [1], is a small tree belonging to the genus Apple in the family Rosaceae. It has loose flesh with a sweet and sour flavor, but it is not suitable for long-term storage. After a short period of storage, the flesh becomes sandy, which gives the fruit its name. Its Latin name is Malus asiatica. The crab apple fruit possesses various medicinal properties, including the ability to generate fluids to quench thirst, eliminate food stagnation, astringe essence to stop dysentery, and expel worms while improving eye health. It is rich in vitamins, iron, zinc, calcium, and other trace elements [2,3], with particularly high levels of antioxidant factors and zinc [4]. Therefore, crab apple is renowned as a premium green fruit that combines pharmacological benefits, healthcare advantages, and nutritional value [5]. Crab apples are predominantly found in the northeastern region of China and Inner Mongolia, where they are highly regarded as local fruits [6]. The government has provided significant support for the cultivation and processing of crab apple orchards, which has contributed to the economic development of these regions [7]. Additionally, the cultivation and processing of crab apples have been industrialized and expanded in northeastern China and Inner Mongolia to meet market demand and improve economic benefits [8].

In recent years, the crab apple plantation industry has experienced rapid growth due to the promulgation of the policy of returning farmland to forests and the increasing support for the forest fruit picking project. This has led to an increase in the types of crab apple trees, planting areas, and yields, resulting in heightened enthusiasm among fruit farmers for the industry [9,10]. The popularity of crab apple products, such as dried crab apples and crab apple paste, has also expanded, creating a craze for crab apples in many places. One region particularly suitable for crab apple tree cultivation is Xing’anmeng in the Inner Mongolia Autonomous Region. Situated in the eastern part of Inner Mongolia within the Daxing’anling region, Xing’anmeng benefits from a hilly terrain, fertile land, and significant temperature variations between day and night. These factors create an ideal environment for the growth of crab apple trees and the accumulation of sugar in the fruits [11,12]. However, China’s crab apple picking primarily relies on manual labor, leading to a high demand for manpower within a short period of time. The seasonal and labor-intensive nature of crab apple picking not only results in significant wastage of human resources but also falls short of achieving optimal results [13,14]. To address this issue, it is crucial to improve the level of mechanized crab apple fruit picking, which has become an inevitable trend for the development of the crab apple industry in Inner Mongolia [15]. The limited mechanization and automation of crab apple picking, particularly in the Inner Mongolia Autonomous Region, along with other factors, have significantly hindered the industry’s development. Therefore, enhancing the mechanized picking capabilities of crab apple fruits is essential to foster the growth of the industry in Inner Mongolia.

Currently, there are three methods of vibratory picking for crab apple harvesting: branch vibratory picking, canopy vibratory picking, and trunk vibratory picking. The principle behind vibratory picking involves the clamping mechanism of the picking machine generating an excitation force through an excitation device [16]. This force is then transmitted to the branches and trunks of the fruit tree, causing vibration. As a result of this vibration, when the inertial force of the fruit exceeds the binding force of the fruit stalk, the fruit breaks free from the stalk and falls off [17]. Branch vibratory picking requires picking each branch individually, which can be time-consuming and inefficient, requiring a significant amount of human resources [18,19,20,21,22]. On the other hand, canopy vibratory picking involves directly vibrating the crown of the tree, increasing the chances of contact between the shaking rod and the fruit [23,24,25,26,27,28,29,30]. However, this method also poses a higher risk of fruit damage and potential harm to the fruit tree itself. In contrast, trunk vibratory picking utilizes an excitation device to generate an excitation force that is transmitted to the tree trunk [31]. Although this method requires the largest excitation force among the three, it significantly reduces the time required for the harvesting operation compared to the other methods. Trunk vibratory picking is particularly suitable for fruits with relatively thick trunks, larger fruit masses, and good fruit-fall [32,33,34].

2. Materials and Methods

2.1. Characterization of Vibrational Mechanics of Crab Apple Trees

2.1.1. Tree Morphology Analysis

For the purpose of our study, we selected 4- to 5-year-old crab apple trees and conducted a sampling of their physical attributes. The attributes measured include the length and diameter of branches at all levels of the crab apple tree. The results of this sampling are presented in

Table 1. Measurement of main dimensions of crab apple trees.

Measurement Target	Range
Tree height/m	4.00–5.00
Primary branch diameter/m	0.16–0.25
Minimum branch height/m	0.50–1.10
Secondary branch height/m	1.90–2.50
Secondary branch diameter/m	0.10–0.16
Height of tertiary branches/m	0.90–2.00
Tertiary branch diameter/m	0.02–0.06

, which provides a range of the main dimensions of the crab apple trees.

Based on the above data, a 3D solid model was created in Solid Works [35], as shown in Figure 1.

2.1.2. Harmonic Response Analysis for Modal Analysis of Crab Apple Trees

In this study, we conducted a modal analysis and a harmonic response analysis of a crab apple tree using Ansys Workbench 2021 R1. The material properties of the tree were selected based on its physical characteristics, with a density of 600 kg/m³, modulus of elasticity of 10 GPa, and Poisson ratio of 0.38. Since the three-dimensional model of the tree consists of irregular shapes, we set the mesh precision to 5 mm to ensure accurate representation. Considering the actual conditions, we constrained only the root of the tree, while treating the branch part as a free end without any additional constraints. Therefore, when defining the boundary conditions for the tree, we fixed only the root end of the tree.

To determine the optimal excitation frequency of the vibratory crab apple picker, a two-step analysis process was proposed. Firstly, the modal analysis method in Ansys Workbench was utilized to determine the tenth-order intrinsic frequency of the crab apple tree. This analysis involves setting the necessary conditions and running the modal simulation function in the modal analysis module. Figure 2 illustrates the meshing and boundary conditions used in this analysis. Once the modal analysis of the crab apple tree was completed, the next step involved analyzing the effect of different magnitudes of excitation force applied to the tree at various heights. This analysis aims to derive the optimum excitation frequency for the vibratory crab apple picker. In Ansys Workbench’s Multiple Systems-Mechanical interface, the Harmonic Response option was selected for harmonic response analysis. Since the modal analysis already provided insights into the tenth-order mode of the crab apple tree, the physical data, mesh delineation, and boundary condition settings from the modal analysis could be utilized in the harmonic response analysis. The frequency range in the harmonic response analysis corresponded to the frequency range of the tenth-order mode [36].

By following this two-step analysis process, we can determine the optimal excitation frequency for the vibratory crab apple picker, taking into account the modal characteristics of the crab apple tree and its response to different magnitudes of excitation force.

The harmonic response analysis will investigate the clamping height ranging from 150 mm to 270 mm. For each 30 mm increment in height, excitation forces of 2000 N, 2500 N, 3000 N, 3500 N, and 4000 N will be applied to the trunk of the crab apple tree. The direction of the excitation force is the same as the direction of the clamping mechanism of the vibratory crab apple picker. By varying the height and excitation force, the optimal excitation frequency of the tree can be determined [37].

2.2. Vibratory Picker Structural Design

2.2.1. Design Concept

The structural design of the vibrating crab apple picker plays a crucial role in addressing the challenges and complexities encountered during field operations. In this paper, a trunk vibration method is proposed, utilizing the excitation force generated by an eccentric block. This method achieves an impressive fruit drop rate of over 80%, making it the most effective picking technique available. To ensure smooth navigation across diverse terrains and maximize the picking efficiency, the picker incorporates an all-in-one design that integrates autonomous drive, trunk vibration, fruit harvesting, and boxing functionalities. This comprehensive unit comprises various components, including a clamping device, a driving device, and a vibration device. To minimize potential damage to the fruit tree, rubber pads can be installed on the clamping device, providing a cushioning effect [38,39,40,41].

2.2.2. Overall Structure of Vibratory Picker

The vibrating crab apple picker’s components were modeled in Solid Works to establish their three-dimensional structure. Key components undergo modal analysis and harmonic response analysis using Ansys Workbench. Subsequently, the components are assembled and combined to form the overall structure. Figure 3 displays the three-dimensional representation of the complete structure of the vibratory crab apple picker. The main parameters of this picker are shown in

Table 2. Technical specifications of the vibrating crab apple picking mechanism.

Vibratory Picker Structure	Technical Indicators
Overall length, width, and height of the picker	1.80 m; 0.75 m; 1.20 m
Picker diesel engine output	6.60 KW
Vibration frequency adjustment range	0.00 Hz–38.00 Hz
Maximum angle of clamping mechanism	120.00°
Area opened by harvesting device	21.00 ${\mathrm{m}}^2$
Overall weight of the picker	300.00 kg

.

2.2.3. Vibratory Crab Apple Picker Excitation Device

Fruit picking operations need to be carried out outdoors. An inertial vibration device is used to generate centrifugal force by the circular motion of the eccentric block, which generates the vibration excitation force of the vibrating tree under the action of centrifugal force. Therefore, a vibration device with large excitation force, easy operation, and simple maintenance should be selected. The shapes of eccentric blocks are mainly fan-type and hammer-type blocks (semi-circular eccentric blocks are special fan-type eccentric blocks). In this section, it is shown that differences in their external structure, mass, and eccentricity lead to significant differences in the excitation force generated at the same excitation frequency.

Different eccentrics in operation: hammer eccentrics generate the highest excitation force; fan eccentrics are widely used and their excitation force is second only to that of hammer eccentrics; semi-circular eccentrics have all the characteristics of fan eccentrics since they are sector eccentrics with a 180° center of circle, and are easier to process than sector eccentrics with other degrees of centering, and their eccentrics generate a higher excitation force. Therefore, the semicircular eccentric block was selected for processing in this paper. At the same time, it is also possible to change the structure and number of eccentric blocks, or change the speed of the eccentric blocks, so as to change the size of the excitation force and to cope with different picking operations.

As shown in Figure 4, the single eccentric block generates a force Fx in the x-direction and a force Fy in the y-direction during rotation, which drives the excitation device to generate an excitation force, which is then transmitted to the trunk to vibrate it, where Fx is the longitudinal component of the excitation force and Fy is the transverse component.

In this paper, 45 steel was selected as the processing material. The density of the material is 7850 kg/m³. For the production of the eccentric block, multiple pieces of the same semicircular eccentric block were stacked and welded. The thickness of the eccentric block was determined as 90 mm. Additionally, the speed of the eccentric block was set at 750 r/min.

During the process of crab apple picking, different excitation forces and rotational speeds are utilized based on the specific fruit trees. Parameters such as the excitation force of the eccentric block can be calculated using the following formula:

$$F=m{\omega }^{2}r$$

(1)

In this equation, $F$ represents the excitation force; $m$ refers to the eccentric block mass; $\omega$ represents the angular velocity of the eccentric block; and $r$ represents the center of gravity.

The angular velocity relation of the eccentric block is given by:

$$\omega =\frac{2n\pi }{60}$$

(2)

In this equation, $n$ represents the eccentric wheel speed.

The mass relationship of the eccentric wheel is given by:

$$m=\rho V=\frac{\pi \rho h{R}_1^2}{2}$$

(3)

In this equation, $\rho$ represents the density of materials used for eccentric wheels; $h$ refers to the thickness of the eccentric wheel; and $R$ represents the angular velocity of the eccentric block.

The center of mass formula is:

$$r=\frac{4R}{3\pi }$$

(4)

From Equations (1)–(4), the excitation force is organized as:

$$F=\frac{\rho h{\pi }^2{n}^2{R}^3}{1350}$$

(5)

Simplifying (5) yields the following equation for the radius of the eccentric wheel:

$$R=\sqrt[3]{\frac{1350F}{\rho h{\pi }^2{n}^2}}$$

(6)

According to the given clamping height range of 150 mm to 270 mm and the excitation force range of 2000 N to 4000 N, Formula (6) can be used. Additionally, the radius of the eccentric wheel should be in the range of 111 mm to 190 mm. To determine the radius of the eccentric wheel, the middle value of 150 mm can be taken.

During the operation of the vibrating crab apple picker, the eccentric block plays a crucial role in generating the excitation force through high-speed rotation. Additionally, when selecting the eccentric shaft, it is important to consider reducing the friction caused by the rotation of the eccentric block. Therefore, the material chosen for the eccentric block support shaft is No. 45 steel.

Since the eccentric block has a circular motion under the control of the motor, it generates periodic motion on the eccentric block support shaft, so here we calculate and analyze the journey of the support shaft of the eccentric wheel. The relation equation of the shaft diameter of the eccentric block support shaft of the crab apple picker is:

$$P=\frac{M\times n}{9550}$$

(7)

$$d\ge A\sqrt[3]{\frac{P}{n}}$$

(8)

In these equations, $M$ represents the motor starting torque; $A$ refers to the modern mechanical design manual fixed value; $P$ represents the diesel engine rated power; and $n$ refers to the rated motor speed.

The given values are as follows: $M$ = 92 Nm, $A$ = 118, $P$ = 6.6 kW, and $n$ = 750 r/min. By applying these values to Equation (8), the diameter of the eccentric wheel shaft is determined to be 25.108 mm.

According to modern mechanical design manuals [42], for shafts with d > 100 mm, the presence of one keyway increases the shaft diameter by 3%; the presence of two keyways increases the shaft diameter by 7%. For d < 100 mm shafts, one keyway increases the shaft diameter by 5% to 7%, and two keyways increase it by 10% to 15%. Additionally, the calculated shaft diameter should be selected as the standard diameter.

Then, according to the above calculation principle, the minimum diameter $d_{min}$ of the eccentric wheel support shaft is:

$$d_{min}=25.108\times \left(1+7\%\right)=26.865 \mathrm{m}\mathrm{m}$$

(9)

In this design, the minimum diameter of the eccentric block support shaft has been adjusted to 28 mm based on the specific requirements.

The eccentric block and eccentric shaft were designed using Solid Works 2021 3D software. The outer dimensions of the eccentric block are as follows: R = 150 mm, r = 30 mm, and r₀ = 30 mm. You can refer to Figure 5 for a visual representation of the design.

Then, the theoretical eccentricity of the eccentric block is:

$$r_e=0.4244\frac{R^3-r^3}{R^2+r^2-2{r_0}^2}=61.75 \mathrm{m}\mathrm{m}$$

(10)

The material chosen for the eccentric block is 45-gauge steel with density ρ = 7.85 × 10³ and thickness B = 95 mm; then, the mass of the eccentric block is:

$$m=\frac{\pi }{2}\left(R^2+r^2-2{r_0}^2\right)B\rho =26.93 \mathrm{k}\mathrm{g}$$

(11)

where $R$ represents the eccentric block radius; $r$ refers to the outer diameter of the small circle of the eccentric block; $r_0$ represents the eccentric shaft inner diameter; $B$ refers to the eccentric block thickness; and $\rho$ represents the eccentric block density.

2.2.4. Vibratory Crab Apple Picker Clamping Device

The clamping mechanism plays a crucial role in the crab apple picker as it is a critical component responsible for transferring vibration force from the vibrating mechanism to the fruit tree. Its primary objective is to minimize damage to the crab apple tree when clamping the trunk. In this paper, a translational clamping method is proposed as the most suitable option. This method comprises a fixed collet and a movable collet, which are driven by a cylinder. By operating the cylinder, the clamping device can be easily opened and closed, providing effective clamping of the fruit tree. According to the characteristics of the crab apple tree and the review of information, the vibration-type crab apple picker clamping mechanism, simulated through Solid Works design, is shown in Figure 6.

This clamping device changes the clamping range (0° to 120°) by pushing and pulling the hydraulic cylinder. The clamping force is reduced by installing rubber pads on the inside of the gripper.

The clamping force is calculated by the formula:

$$F_N\ge k_1{k}_2{k}_{3}G$$

(12)

where $F_N$ represents the clamping force; $k_1$ refers to the safety factor, taking the value 2.00; $k_2$ represents the work coefficient, taking the value 1.00; $k_3$ refers to the azimuthal coefficient, taking the value 1.25; and $G$ represents the mass of the object grasped. Then, the clamping force is 3000 N, in which the trunk can be tightened without causing large damage to the tree.

2.2.5. Vibratory Crab Apple Picker Drive

The driving device serves as the power source for the entire crab apple picking mechanism. The motor drive, gasoline engine drive, and diesel engine drive methods are the main methods used for mechanical vibration. In this paper, the crab apple picking operation being studied takes place in a field environment with harsh conditions. The chosen picking method involves trunk vibration picking, resulting in a higher defoliation rate and requiring a larger excitation force. During the working process of crab apple picking, power loss occurs due to the driving power of the eccentric block and the friction loss power of the eccentric block. Based on the design of the eccentric block mentioned earlier, it has an eccentric distance of 61.75 mm and a mass of 26.93 kg. Additionally, the phase difference angle of the picker is 175°. Then, the effective driving power of the eccentric block of the vibrating crab apple picker is:

$$P=\frac{W_r}{T}=2m{r}_e{\omega }^{3}X\sin \phi =1345.20\mathrm{w}$$

(13)

where $m$ represents the eccentric block mass; $r_e$ refers to the eccentricity of the eccentric block; and $\phi$ represents the phase difference angle of the picker.

There is friction between the shaft diameters as the eccentric block rotates, so the work done by the eccentric block to overcome the friction is:

$$P_f=\mu m{\omega }^{2}rd=225.23 \mathrm{W}$$

(14)

The power required by the hydraulic motor is:

$$P_p=K\frac{P+P_f}{1000\eta }=1.2\frac{1345.2+225.2}{1000\times 0.92}=2.05 \mathrm{kW}$$

(15)

In this equation, $P_f$ represents the power required for hydraulic motors; $P_f$ refers to the eccentric block friction loss power; $F_f$ represents friction; $\mu$ refers to the coefficient of friction; $d$ represents the eccentric block shaft diameter; and $\eta$ represents the mechanical efficiency.

Therefore, this paper adopts the diesel engine drive, which can be better adapted to the field picking environment and has a relatively good stability and a high efficiency. By comparing different picker models, this paper chooses to use a CF186FS diesel engine to drive the picker, and at the same time chooses a BM2-50 hydraulic motor to drive the eccentric block. The shapes of the diesel engine and hydraulic motor are shown in Figure 7; the main parameters are shown in

Table 3. Main parameters of the diesel engine.

Model Number	Calibrated Power/kw	Number of Revolutions per Minute/RPM	Weights/kg	Engine Capacity/cc	Fuel Tank Volume/L
CF186FS	6.60	1800.00	48.00	418.00	5.50

and

Table 4. Main parameters of hydraulic motor.

Engine Capacitycc/r	50.00
Flux/LPM	Progression	38.00
	Intermittent	45.00
Number of revolutions per minute/RPM	Progression	750.00
	Intermittent	875.00
Stresses/bar	Progression	138.00
	Intermittent	155.00
Torsion/N·m	Progression	92.00
	Intermittent	105.00

.

2.2.6. Eccentric Block, Eccentric Block Support Shaft Finite Element Modeling and Analysis

Ansys Workbench 2021 R1 was utilized to perform a structural optimization of the vibratory crab apple picker, specifically focusing on the eccentric block and eccentric block support shaft models. These models underwent comprehensive analyses, including static and modal analyses, to determine the stresses, deformations, and intrinsic frequencies associated with these components.

The first step was to use Solid Works to establish the three-dimensional models of the eccentric block and the eccentric block support shaft. Then, in Ansys Workbench, the static structure module was opened, and No. 45 steel was selected as the material. The mesh accuracy was set to 2 mm, as shown in Figure 8. After successful mesh division, cylindrical constraints and a rotational load were added based on the actual situation of the eccentric block and eccentric shaft. A rotational load of 750 RPM was determined according to the design parameters of the linear motor. Once the finite element model was established, the static structure was analyzed using Ansys Workbench 2021 R1. Finally, the total deformation diagram and equivalent deformation diagrams of the eccentric block and eccentric block support shaft were obtained. These diagrams provide valuable information about the structural behavior. To ensure there is no resonance, the total deformation diagram and equivalent stress diagram of the support shaft were compared with the modal analysis of the crab apple tree.

2.3. Rigid–Flexible Coupling Model Analysis

The crab apple tree model was established in Solid Works with flexible processing. The clamping mechanism of the vibrating picker is rigidly and flexibly coupled. The material properties of the clamping mechanism were set to No. 45 steel, with a density of 7850 kg/m³, while the density of the crab apple tree is 600 kg/m³. According to the working principle of the picker, only the eccentric block drives the clamping device vibration. Therefore, during the process of adding constraints, a clamping force is applied to make the clamping mechanism on both sides of the mechanical claw move towards the center. A rotation vice was applied to the eccentric block from 0 s to 0.1 s after clamping the trunk. The value of the rotation vice is based on the excitation frequency mentioned above, and it was accelerated to the simulation value from 0.5 s to 0.6 s. Fixed constraints are applied between the body of the crab apple tree and the earth. The model is established as shown in Figure 9. For this simulation, four values of 9.7 Hz, 12.7 Hz, 15.7 Hz, and 18.7 Hz were selected and compared with the optimal excitation frequency of 12.7 Hz. The simulation time was set to 5 s, with 1000 steps to ensure higher accuracy [43,44,45,46].

2.4. Harvesting Trial Design

2.4.1. Test Site and Equipment

The picking test took place at the planting base of crab apple trees in the Kerqin Right-Wing Qian Banner, Xing’an League, Inner Mongolia Autonomous Region. The test utilized the following equipment: an IEPE piezoelectric acceleration sensor, a DH5902N rugged data acquisition and analysis system, and a prototype vibratory crab apple picker. The purpose of the test was to validate the simulation data mentioned earlier and verify the feasibility of the vibratory crab apple picker based on its data. For a visual representation, please refer to Figure 10:

2.4.2. Purpose and Methodology of the Test

The purpose of this crab apple picking field test was to investigate the acceleration magnitude at the field side branch point under different excitation frequencies, which correspond to different rotational angles of the hydraulic motor throttle switch. Additionally, the test aimed to determine the changes in acceleration response curves at various vibration frequencies.

During the test, it was observed that when the inertial force experienced by the crab apple fruit exceeded the force of fruit stalk binding, the fruit would drop. This led to the conclusion that the inertia force of the crab apple fruit depended on its acceleration, which was represented by an acceleration response curve.

The excitation frequency of the vibrating crab apple picking mechanism served as the test factor for the crab apple fruit picking test. This frequency was determined by the rotational speed of the eccentric block, which was controlled by adjusting the rotational angle of the hydraulic motor throttle switch. In this particular test machine, the throttle switch angle was adjustable from 0° to 40°. Therefore, the excitation frequency of the field crab apple picking test was selected at throttle switch angles of 10°, 20°, 30°, and 40°.

In this experiment, the acceleration of the secondary branches of a crab apple tree was measured. Accelerometers were placed at the points of the lateral branches of the tree, while the excitation device of a vibratory crab apple picker induced vibrations.

The acceleration sensor was positioned 100 mm from the root of the secondary branch, and the angle between the secondary branch and the primary branch was 37°. To ensure the stability of the sensor during vibration and to prevent displacement, the sensor was reinforced using the tape fixing method. During the tree picking test, it should be noted that the clamping mechanism of the vibratory fruit picker did not have an up and down adjustment function at the time of the experiment. Therefore, a fixed clamping height was used. The measured clamping height of the vibratory fruit picker (the height of the center line of the clamping mechanism from the ground) was 210 mm. For a visual representation, please refer to Figure 11.

In this picker, the hydraulic control is operated using a throttle switch knob. The maximum rotation range of the switch knob is 0°–40°. In the Adams rigid–flexible coupling analysis mentioned earlier, the measured rotation angles were 10°, 20°, 30°, and 40°, corresponding to frequencies of 9.7 Hz, 12.7 Hz, 15.7 Hz, and 18.7 Hz, respectively. The acceleration data were recorded through the acceleration sensor and transmitted to the DHDAS dynamic signal acquisition and analysis system for acceleration response analysis. Please refer to Figure 12 for a visual representation of the mentioned details.

3. Results

3.1. Results of Harmonic Response Analysis for Modal Analysis of Sargassum Trees

Figure 13 shows the tenth-order modes in the modal analysis of the crab apple tree. According to

Table 5. Modal natural frequency of the flexible body of a crab apple tree.

Ordinal Number	1	2	3	4	5	6	7	8	9	10
Ansys	12.52	13.15	18.27	19.30	24.19	25.73	35.98	36.30	37.00	38.10

, the first-order modes to tenth-order modes are 12.52 to 38.10 Hz.

Based on the data obtained from the modal analysis of the tree, it was determined that the tenth-order intrinsic frequency of the tree body is 38.1 Hz. To ensure that the modal superposition of harmonic analysis does not result in the loss of modes, it is necessary for the modal frequency range to be wider than the harmonic frequency range by a factor of 1.5. Therefore, the frequency range for the harmonic response analysis was set at 0 Hz to 25.4 Hz. This range allows for a comprehensive analysis of the harmonic response of the tree. The final results of the harmonic response analysis can be found in Figure 14.

Based on the analysis conducted within the frequency range of 0 Hz to 25.4 Hz, it was observed that the acceleration of the test point reaches a maximum when the frequency reaches 12.7 Hz. This indicates that the vibration response of the system is at its peak during this frequency. Considering the objective of achieving fruit drop and aiming to enhance the harvesting efficiency by increasing the acceleration of the fruit tree, it is recommended to operate at or around the optimal harvesting frequency of approximately 12.7 Hz. By utilizing this optimal frequency, it is expected that the fruit tree will experience a higher acceleration, leading to improved harvesting efficiency.

3.2. Eccentric Block and Eccentric Block Support Shaft Modal Analysis and Stress Analysis Results

The results of the total deformation and equivalent stress analysis are shown in Figure 15, and the data are shown in

Table 6. Main parameters of the cycloidal hydraulic motor.

Part Name	$\mathbf{Total} \mathbf{Deformation} \mathit{\delta }/\times {10}^{-4}$		$\mathbf{Constant} \mathbf{Force} \mathit{\sigma }/\mathbf{MPa}$
	Minimum Value	Maximum Values	Minimum Value	Maximum Values
Biasing block	0	777.94	5.80 × 10−2	3.13 × 102
Eccentric block support shaft	0	1.15	1.40 × 10−2	9.05 × 10−1

.

Based on the modal analysis conducted on the eccentric block and the eccentric block support shaft, the objective is to prevent the excitation frequency of the eccentric block and the eccentric shaft from coinciding with their own modal frequency. This is done to avoid resonance during operation and ensure the normal functioning of the vibrating crab apple picker. To achieve this, the sixth-order mode is designed, taking into consideration the modal frequencies of the eccentric block and the eccentric shaft. By ensuring that the excitation frequency does not match the modal frequency, resonance can be prevented. The analysis process for the modal analysis of the eccentric block and the eccentric block support shaft is similar to the previous analysis. The results of this analysis can be found in

Table 7. Modal analysis of key components of a crab apple picker.

Order	Biasing Block	Eccentric Block Support Shaft
1	1020.70	4114.50
2	2041.90	4182.70
3	2073.00	9121.70
4	3571.60	10738.00
5	4160.20	10863.00
6	5838.60	15552.00

.

Based on the information provided, it is stated that the vibration frequency of the eccentric block and the eccentric block support shaft is 12.7 Hz at 750 RPM. It is mentioned that this frequency is much smaller than the intrinsic frequency of the eccentric block and the eccentric block support shaft. Based on this comparison, it is concluded that no resonance will occur during the normal picking work, as the vibration frequency is significantly lower than the intrinsic frequency of the components.

3.3. Adams Rigid–Flexible Coupling Analysis Results

The upper middle part of the secondary trunk branches was taken as the measurement point and the simulation results are shown in Figure 16, Figure 17, Figure 18 and Figure 19.

The provided information describes the behavior of the clamping mechanism and its interaction with the trunk in the rigid–flexible coupling model. It states that there is no relative sliding between the clamping mechanism and the trunk, resulting in no displacement in the y-direction. In this context, the focus is on exploring the acceleration of the crab apple tree in the x-direction. A curve is derived from the simulation results, and the average acceleration data are presented in

Table 8. Adams rigid–flexible coupling analysis of lateral branch point acceleration response curve numerical values.

Clamping Height/mm	Excitation Frequency/Hz	Average Acceleration/mm/s2
150.00	9.70	31.10
	12.70	54.10
	15.70	51.30
	18.70	50.10
180.00	9.70	32.30
	12.70	60.20
	15.70	56.40
	18.70	44.60
210.00	9.70	46.30
	12.70	76.70
	15.70	60.10
	18.70	56.50
240.00	9.70	70.90
	12.70	108.90
	15.70	95.40
	18.70	48.20
270.00	9.70	100.10
	12.70	116.40
	15.70	110.00
	18.70	97.60

. Analyzing the vibration curve, several observations can be made: When the clamping height increases under the same excitation frequency, the acceleration of the lateral branch gradually increases. When the excitation frequency increases under the same clamping height, the acceleration also increases. The acceleration of the lateral branch reaches a maximum when the excitation frequency reaches the optimal value of 12.7 Hz. Beyond 12.7 Hz, the acceleration of the lateral branches gradually decreases with further increases in the excitation frequency. These observations suggest that the behavior of the lateral branches of the tree is influenced by both the clamping height and the excitation frequency. The acceleration increases with higher clamping heights and within a certain range of excitation frequencies, but it starts to decrease once the excitation frequency exceeds the optimal value of 12.7 Hz.

3.4. Field Trials

To ensure the representativeness of the data analysis, the acceleration response curve recorded by the acceleration sensor during the test was extracted specifically from the 20 s mark to the 40 s mark. This time interval was chosen as it is deemed more representative for data analysis. The robust data acquisition and analysis system focused on analyzing the acceleration response curve in the direction of the clamping mechanism during the vibration process. For visual reference, please refer to Figure 20, and for detailed numerical data, please consult

Table 9. Walking speed test results.

Angle of Rotation/°	Average Acceleration/mm/s2
10°	26.00
20°	94.00
30°	68.00
40°	43.00

.

Based on the data presented in Figure 20 and Table 9, it is evident that the side branch acceleration increases as the excitation frequency (represented by the angle of the throttle switch knob) increases under the same clamping position. However, once the excitation frequency surpasses the optimal value, the side branch acceleration starts to decrease with further increases in the excitation frequency. This observation aligns with the conclusion drawn from the previous Adams rigid–flexible coupling analysis.

4. Discussion

Crab apples are fruits that are distributed in Northeast China and Inner Mongolia. They are rich in nutrients and have a significant impact on the local economy. Additionally, they can be used to make various crab apple products. The aim of this study was to investigate a trunk-type vibratory picker specifically designed for crab apples. This picker was developed to address the current challenges faced during crab apple picking, such as high damage degree and low picking efficiency and fruit drop rate.

To achieve this goal, our team conducted a comprehensive analysis of test results and compared them to industry standards. We also evaluated existing pickers to gain valuable insights into the practicality of the baguette picker. Additionally, we conducted a preliminary study on the design, processing, and construction of various parts of the equipment, which laid a solid foundation for crab apple picking operations in Northeast China and Inner Mongolia.

In this paper, the design of the picking machine was compared with manual picking operations, first of all to study the tree, to determine the optimal excitation frequency of 12.7Hz for the picking of crab apple, and to study the mechanization of crab apple picking methods. We conclude that due to the thick trunk of the crab apple tree, the excitation force should be larger, which at the same time can greatly reduce the time of selecting the method of vibrating the tree trunk of the crab apple tree. There are three ways to choose vibration mode: the branches, crown, and trunk and in this paper we choose the trunk vibration mode.

In the design of the picking machine, we addressed the shortcomings of traditional excitation devices. We improved the excitation device by selecting a semicircular eccentric block capable of producing a larger excitation force. This choice resulted in a better picking effect, enhancing the overall performance of the fruit picker.

Furthermore, we introduced a method to assess the magnitude of the fruit stalk binding force by analyzing the acceleration of the lateral branching point of the crab apple tree. This approach allowed for a more accurate determination of the force required to overcome the fruit stalk binding, making crab apple picking more scientific. By utilizing acceleration sensors to collect the acceleration data, we were able to obtain precise measurements of the force needed to overcome the fruit stalk binding. Field trials and simulation tests validated the potential of this picker in terms of improved picking efficiency and sustainability, especially in high-density planting environments with dusty soil, such as a crab apple orchard.

In conclusion, the study of crab apple pickers effectively addressed the issues of labor waste and reduced the loss of crab apples, resulting in an improved yield during the picking process. The feasibility and practicality of this optimization approach were verified through the study. The findings highlight the potential of the picker to increase the picking efficiency and simplify operations.

5. Conclusions

The results of the study demonstrate that the vibratory picker has significant advantages in crab apple picking operations. Based on our analysis, the following main conclusions can be drawn:

• The optimal excitation frequency for picking crab apples is 12.7 Hz; the closer to 12.7 Hz, the better the picking effect.
• When considering the same excitation frequency, the acceleration of lateral branches gradually increases with the increase in clamping height.
• At the same clamping height, the acceleration increases with the increase in excitation frequency. The acceleration of the lateral branches of crab apple trees reaches its maximum when the excitation frequency reaches the optimal value of 12.7 Hz. However, beyond 12.7 Hz, the acceleration of the lateral branches gradually decreases with further increases in the excitation frequency.

6. Future Perspectives

Based on the related research and experiments conducted, this paper proposes several expectations for future work:

• Although this paper analyzes the physical properties of the tree, there is still room for improvement in terms of accuracy and comprehensiveness. To address this, future research should employ more advanced equipment and software to measure and model the tree, taking into account factors such as the varying density of different parts of the trunk and the displacement of the tree’s heel during the vibration process.
• The clamping mechanism of the vibration-type crab apple picker used in this test lacks an up and down adjustment function. To enhance the efficiency of crab apple picking, it is essential to continue research and development in this area and conduct an in-depth study on clamping height. Accurately measuring the mechanical characteristics of the crab apple tree will greatly contribute to the improvement of the picking process.
• The tests conducted in this study did not include verification of the rate of fruit drop and defoliation. To gain a comprehensive understanding, it is recommended to conduct further tests during the fruit ripening season specifically focused on evaluating the rate of fruit drop and defoliation. This additional research will provide valuable insights into the impact of the picker on fruit retention and tree health.