Optimization of Clamping and Conveying Parameters for Spinach Orderly Harvesting with Low Damage by Simulation and Experiment

Abstract

The leaves of spinach are delicate and easily injured during harvesting. To reduce the spinach damage rate and increase the conveyance success rate, an orderly harvester was designed and manufactured, and the key conveying parameters of the harvester were optimized by simulation and experiments. The compression damage stress of spinach was determined by compression tests. Then, a finite element simulation model for spinach clamping was established, and the influence of different clamping heights on the spinach deformation and equivalent stress were simulated and analyzed. Finally, response surface Box–Behnken experiments were conducted to optimize the combinations of the twisting angle, clamping distance, and height difference. The results of the compression tests showed that the compression damage stresses of spinach leaves, stems, and their connection points were 8.04 × 10⁻² MPa, 7.85 × 10⁻² MPa, and 11.63 × 10⁻² MPa, respectively. The optimal clamping height of spinach for orderly conveyance was obtained to be 20 mm according to the finite element simulation. The response surface experimental results indicated that the significance order of factors affecting the extrusion force was the clamping distance, the height difference, and the twisting angle. The significance order of factors affecting the conveyance success rate was the clamping distance, the twisting angle, and the height difference. The optimal parameter combination was ae twisting angle of 60°, clamping distance of 24 mm, and a height difference of 20 cm. The experimental validation of the optimization results from the finite element simulation and response surface tests demonstrated that the extrusion force and conveyance success rate were 2.37 N and 94%, respectively, with a conveying damage rate of 3% for spinach, meeting the requirements for the low-damage and orderly harvesting of spinach.

1. Introduction

Spinach is widely cultivated in China [1,2,3,4,5], and the leaves of spinach are delicate and easily injured. Therefore, reducing the injury degree of spinach is a critical and important task in mechanical harvesting [6,7]. Currently, spinach harvesting in China predominantly relies on manual or semi-mechanized methods, which are inefficient and prone to causing leaf damage [8,9], and the orderly harvesting of spinach is a good way to improve the harvesting quality. In the process of the orderly harvesting of spinach, the design and performance of the clamping conveyor play a crucial role in reducing spinach damage and enhancing the harvesting efficiency. However, the existing machines for the orderly harvesting of spinach still face issues such as a high damage rate. Therefore, there is an urgent need to optimize the parameters of the orderly harvesting machines to reduce spinach harvesting damage and increase the success rate of harvesting [10].

The existing studies of leafy vegetable harvesters can be used for reference in the design and improvement of spinach harvesters [11,12]. Zou et al. analyzed the impacts of clamping and conveying parameters on spinach damage by utilizing the rheological properties of spinach, and constructed a test platform to validate their parameters’ feasibility [13]. Their research results provided a theoretical basis and technical reference for the design of low-damage mechanical harvesting for leafy vegetables. Jin et al. analyzed the elastic extrusion force and clamping distance during the harvesting of green leafy vegetables, resulting in an optimal harvesting parameter combination for a flexible conveying device with a conveyor roller speed of 80 r/min and a spring stiffness combination of 2.0 N/mm and 0.6 N/mm [5]. Yin et al. designed an orthogonal experimental scheme and determined the optimal speed combination for walking, cutting, and conveying during the machine harvesting of Chinese little greens to be 0.12 m/s, 0.50 m/s, and 0.5 m/s, respectively [14]. The above harvesting machines for leafy vegetables have been studied with regard to the vegetables’ rheological characteristics and the determination of harvesting parameters. However, the influence of factors such as the clamping torsion angle, the clamping height for spinach, and the conveying device on the damage to and harvesting success rate of spinach still need to be further studied.

Finite element simulation can effectively show the mechanical interactions between agricultural implements and leafy vegetables during the harvesting process [15,16,17,18,19,20], and it is therefore widely utilized in the design and optimization of agricultural machinery. Kang Wu et al. conducted a finite element simulation analysis on a clamping device for watermelon grafting, optimizing the grafting speed and the contact material thickness of the clamping device during watermelon grafting. The reliability of the simulation model was verified by comparing the simulation results with experimental results, indicating that finite element simulation not only provides theoretical support for design but also effectively enhances the performance of the equipment [21]. Meanwhile, Box–Behnken experiments have been widely employed to determine the optimal parameter combinations for mechanical equipment. Xiong et al. designed and analyzed the core components of a harvester by integrating the material characteristics of rapeseed stems and leaves, conducted single-factor and response surface optimization tests, and identified the optimal machine parameters of a forward speed of 0.42 m/s, conveyor belt speed of 0.89 m/s, and gripping distance of 11.43 mm for low-loss harvesting [22].

To improve the harvesting quality for spinach, an experimental platform for the low-damage clamping and conveying of spinach in an orderly manner is designed in this paper. Finite element simulation is employed to determine the clamping height of spinach. Through Box–Behnken experiments, the parameter combinations of the twisting angle, clamping distance, and height difference are optimized to reduce the damage rate during the orderly conveying of spinach and improve the success rate of conveying.

2. Materials and Methods

2.1. Experimental Material

Spinach is a common leafy green vegetable widely cultivated in both open fields and greenhouse facilities. The experimental material in this study is Spinacia oleracea L., for which the average plant height is 26.29 cm with a standard deviation of 2.39, the average leaf spread is 20.48 cm with a standard deviation of 4.31, and the average weight is 20.92 g with a standard deviation of 3.40. Due to the delicate nature of spinach leaves, they are prone to being damaged during the harvesting process.

2.2. Design and Structure of Test Platform

The scheme of the spinach orderly harvesting test platform is depicted in Figure 1. It mainly consists of a rack, a conveyor belt, and a clamping and conveying mechanism.

The spinach clamping and conveying mechanism is a core component affecting the orderly harvesting effect, primarily responsible for clamping, twisting, and conveying spinach. Factors such as the twisting angle, clamping gap, and conveying height difference will influence spinach damage and the success rate of conveying. Specifically, to ensure orderly conveying and effective dumping of spinach during the harvesting process, the twisting angle θ ranges from 0 to 60° according to the results of pre-experiments. The clamping distance L is set between 20 and 26 mm, as the spinach will be damaged when the clamping distance is less than 20 mm, and the clamping stability will decline when the clamping distance exceeds 26 mm. To ensure stable conveying of spinach after the conveyor belt twists and elevates at its end, the conveying height difference H is selected within the range of 0 to 40 cm. The above parameters can be manually adjusted, and the conveying speed is set at 0.25 m/s.

2.3. Experimental Methods

2.3.1. Measurement of Spinach Compression Damage

To determine the force value for spinach damage under compression, a series of compression tests on spinach were conducted, as shown in Figure 2. The testing device used was a texture analyzer (TA.XTC-16, manufactured by Baosheng Industrial Development Co., Ltd., Shanghai, China). During the tests, spinach was placed on a polyurethane conveyor belt. A piece of polyurethane conveyor belt (13 mm × 2.4 mm) was affixed to the surface of the texture analyzer probe. The probe compressed the spinach at a speed of 2 mm/s, with the initial trigger force set at 0.1 N, incrementally increasing by 0.1 N until the spinach was damaged, at which point the force was recorded as the damage force value. This procedure was repeated 30 times each for the stems, the leaves, and their connections.

2.3.2. Finite Element Model for Spinach Clamping Simulation

To determine the optimal clamping height for spinach during the conveying process, the stress distribution and transmission characteristics at various heights were analyzed by the finite element simulation. A simplified model of spinach transportation and compression was established in Ansys 2022 R1 (Ansys 2022 Workbench, Ansys Inc., Canonsburg, PA, USA), as shown in Figure 3. The material properties of spinach leaves are a density of 0.57 g/mm³, an elastic modulus of 2.14 MPa, and a Poisson’s ratio of 0.12 [23]. The conveyor belt material is polyurethane, simulated by the Mooney–Rivlin model, with a density of 1.18 g/cm³, material constant C10 of 0.62 MPa, material constant C01 of 0.15 MPa, and incompressibility parameter D1 of 1270 MPa. In the simulation models, Hex20 high-order hexahedral elements were selected for the contact conveyor belt, and the Sweep method was employed for meshing, which ensured the uniformity and accuracy of the mesh. For the spinach model, Tet10 high-order tetrahedral elements were used, with a mesh size set at 2 mm, and fine meshing was carried out through the Tetrahedrons method. This process resulted in a total of 100,037 nodes (Nodes) and 50,003 elements (Elements). Selecting spinach stems as the clamping points, the clamping heights were set at 10 mm, 20 mm, 30 mm, 40 mm, and 50 mm. Two steps were used in the FEA simulation, and the spinach model was placed between the conveyor belts and was free in all degrees-of-freedom (DOFs) in all steps. The belts were free in the z axis only and fixed in the other DOFs in the first step, and displacements of 10 mm, 20 mm, 30 mm, 40 mm, and 50 mm were defined in the z axis, respectively. Then, the belts were free in the x axis and fixed in the other DOFs in the second step, and we defined +/− 18.75 mm x axis displacements for the two belts, respectively, so that the belts were in contact with the spinach in the second step.

2.3.3. Box–Behnken Experimental Method

To optimize the parameters for the orderly conveyance of spinach, an experimental platform was developed, as shown in Figure 4. The extrusion force of the spinach harvesting mechanism was measured using a gripping force measurement system, which primarily included a thin-film pressure sensor (DF9-40, measuring range: 0–20 N, response: 0.2 N, Suzhou Leanstar Electronic Technology Co., Ltd., Suzhou, China), a signal conversion module (SCM-5, Suzhou Leanstar Electronic Technology Co., Ltd., Suzhou, China), a 16-channel data acquisition card (USB-1608GX-2AO, Measurement Computing Corporation, Norton, MA, USA), and a computer. The spinach position was manually adjusted to ensure the film pressure sensor was in contact with the spinach. When measuring the extrusion force of the spinach, two channels were used for data collection of the extrusion force for each spinach plant.

The selected experimental factors include the twisting angle X₁, clamping distance X₂, and height difference X₃, as shown in Figure 1. According to the results of preliminary experiments, the levels of these experimental factors were chosen as follows: a twisting angle ranging from 20 to 60°, a clamping distance between 20 and 26 mm, and a height difference for conveyance from 20 to 40 cm. Each factor could be manually adjusted, and the coding of factor levels in the tests is shown in

Table 1. Coding of factors levels in the Box–Behnken tests.

Level	Factors
	Twisting Angle X1 (°)	Clamping Distance X2 (mm)	Height Difference X3 (cm)
−1	20	20	20
0	40	23	30
1	60	26	40

.

The experimental indicators were the orderly conveying extrusion force and conveying success rate of spinach. During the experiment, a film pressure sensor was placed on each side of the conveyor belt, and they were all 25 mm from the upper edge (as shown in Figure 4). As the conveyor belt clamped the spinach, the film pressure sensor recorded the force value change curve throughout the conveying process, with the maximum value taken as the final extrusion force for orderly conveyance. This study conducted a Box–Behnken experiment [24] with a total of 17 groups, each repeated 10 times, using 10 spinach plants per trial. When measuring the extrusion force and conveyance success rate, the average of the 10 trials was taken as the result for each group. In the data analysis stage, to compare the differences among multiple groups and determine the statistical significance, we employed analysis of variance (ANOVA). ANOVA was used to assess whether there were significant differences in the measured variable among different experimental conditions or treatment groups. The specific steps involved calculating the sum of squares between groups and within groups, followed by determining the F-statistic. If the obtained F-value exceeded the critical value at a certain significance level, it indicated that there were significant differences among the groups.

2.3.4. Validation Test Method

To verify the finite element simulation results for the spinach clamping height and the optimal parameter combination obtained from the Box–Behnken experiment for spinach clamping, a validation test was conducted. The validation test indicators selected were the ordered conveying extrusion force of spinach, the conveying success rate, and the conveying damage rate. The optimal spinach clamping height from the finite element simulation and the optimal parameter combination derived from the Box–Behnken experiment were used as the conditions for the validation test. During the test, spinach was clamped and conveyed by the conveyor belt, and the force value curve during the conveying process was recorded by a thin-film pressure sensor, with the maximum value being taken as the final ordered conveying extrusion force. Finally, staining spinach by fuchsin staining was employed to determine whether the spinach had been damaged [25]. The experiment was repeated 100 times, and the mean absolute deviation (MAD) was used as the validation criterion for the results of the ordered conveyance extrusion force test; the formula for its calculation is:

$$MAD={\displaystyle \frac{1}{n}}{{\displaystyle \sum }}_{i=1}^n\left|x_i-\mu \right|$$

(1)

$n$ represents the number of trials, set at 100; $x_i$ denotes the i-th data point; and $\mu$ stands for the expected value of the orderly conveyance extrusion force.

The formula for calculating the conveyance success rate is as follows:

$$S={\displaystyle \frac{S_1}{n}}\times 100\%$$

(2)

where $S$ represents the conveyance success rate, $S_1$ denotes the number of successful conveyances, and $n$ signifies the number of trials.

The formula for calculating the damage rate is as follows:

$$D={\displaystyle \frac{D_1}{n}}\times 100\%$$

(3)

where $D$ represents the conveyance damage rate, $D_1$ denotes the number of delivery damage occurrences, and $n$ signifies the number of trials conducted.

3. Results and Discussion

3.1. Mechanical Characteristics of Spinach Extrusion Injury

Figure 5 illustrates an example of the force–displacement curve recorded by the texture analyzer during the compression of spinach, for which the compression position was the spinach stem. The force curve could be divided into two regions: the elastic deformation region (I) and the plastic deformation region (II). The spinach stem was continuously compressed until the specified trigger force value was reached. During this period, the compressive force showed a pattern of first rising, then falling, and rising again, which was similar to the compression variation of wheat stems [26]. At point $a$, the spinach stem reaches its elastic limit, transitioning from elastic to plastic deformation, and the spinach stem was damaged.

The statistical results of the extrusion damage force for the stem, stem leaf connection, and leaf are shown in Figure 6. The average extrusion damage force for the spinach stems, stem leaf connection, and leaf were 2.64 N, 2.51 N, and 3.84 N, respectively. The average extrusion damage forces for spinach stems and the connection were similar but lower than that for spinach leaves. This was because spinach leaves have more stomata and cellular spaces, which could buffer external forces [27]. The size of the polyurethane conveyor belt that compressed the spinach was 13 mm × 2.4 mm in the spinach compression tests; hence, the minimum stresses which caused damage to spinach stem, stem–leaf connection, and leaf were calculated as 8.04 × 10⁻² MPa, 7.85 × 10⁻² MPa, and 11.63 × 10⁻² MPa, respectively. Since the growth of different leaves on the same spinach plant varies, and the conveyor belt clamps both leaves and stems simultaneously, the smallest value among the three tested areas (7.85 × 10⁻² MPa) was chosen as the compressive damage value for the entire spinach plant.

3.2. Finite Element Simulation Results of Spinach Clamping Height

Figure 7 illustrates the total deformation and equivalent stress of spinach at a clamping height of 20 mm. Figure 7a presents the simulation results under total deformation, where the maximum deformation was approximately 18.55 mm and the minimum was about 0.18 mm. The deformation primarily occurred in the area between the two conveyor belts and stems upward, showing a significant deformation gradient. Figure 7b displayed the distribution of the equivalent stress, with a maximum value of approximately 6.23 × 10⁻² MPa and a minimum of about 0.69 × 10⁻² MPa. The stresses were observed in the root and stem sections. The conveyor belt initially contacted the spinach stem, causing a deformation and bending moment to be applied to the root. Consequently, a significant stress concentration was exhibited in the spinach root. Some stress was also generated at the stem due to the contact with the conveyor belt.

The relationship between the maximum stress on the spinach and the clamping heights is shown in Figure 8. The maximum stresses, corresponding to each factor in the figure, are all derived from the results of the finite element simulation. When the conveyor belt position was 20 mm above the root, the stress generated by the compression of the spinach reached its maximum, but it was still lower than the damage strength of the spinach, which was 7.85 × 10⁻² MPa. Therefore, variations in the clamping height of the spinach did not cause spinach damage. As the clamping height of the spinach exceeded 20 mm, the maximum compressive stress decreased. This was due to the stems part becoming more dispersed in terms of space distribution when the contact height increased, while the inward compressive stroke of the conveyor belt was unchanged, resulting in a reduction in the compressive stress. When the stress on the spinach was increased, the interaction force between the conveyor belt and spinach also increased correspondingly [28]; thus, the spinach could be clamped more effectively, which increased the success rate of conveyance. Therefore, a clamping height of 20 mm for spinach was chosen.

3.3. Box–Behnken Experimental Results and Discussion

3.3.1. Experimental Results

Table 2. Results of the Box–Behnken experiment.

Test Groups	Experimental Factors			Experiment Index
	Twisting Angle, X1/°	Clamping Distance, X2/mm	Height Difference, X3/cm	Extrusion Force, Y1/N (Mean Value)	Conveyance Success Rate, Y2 (%)
1	40	20	20	3.65	93
2	20	20	30	3.72	93
3	60	26	30	2.46	80
4	20	26	30	1.72	70
5	40	23	30	2.55	90
6	40	23	30	2.79	87
7	60	20	30	3.27	93
8	20	23	40	2.22	83
9	40	26	40	1.75	70
10	40	23	30	2.76	93
11	60	23	20	2.56	93
12	40	23	30	2.68	90
13	40	23	30	2.68	90
14	20	23	20	2.4	87
15	60	23	40	2.53	90
16	40	20	40	3.26	93
17	40	26	20	2.12	83

gives the results of the Box-Behnken tests (17 groups). A quadratic polynomial model for the three factors and extrusion force $Y_1$ was established using Design-Expert, as shown in Equation (4), with the model’s $R^2$ being 0.98.

$$\begin{gathered} Y_1=2.69+0.0950x_1-0.7312x_2-0.1213x_3+0.2975x_1{x}_2+0.0372x_1{x}_3+0.0050x_2{x}_3-0.0835x_1^2 \\ +0.1840x_2^2-0.1810x_3^2 \end{gathered}$$

(4)

where $Y_1$ is the extrusion force, and $x_1,x_2, x_3$ are the twisting angle, clamping distance, and height difference, respectively.

The analysis of variance of the quadratic model (

Table 3. Analysis of variance for extrusion force.

Source	Extrusion Force
	Sum of Squares	Degree of Freedom	F Value	p Value
Model	5.12	9	47.92	<0.0001 **
X1	0.0722	1	6.08	0.0431 *
X2	4.28	1	360.11	<0.0001 **
X3	0.1176	1	9.90	0.0162 *
X1X2	0.3540	1	29.80	0.0009 **
X1X3	0.0056	1	0.4735	0.5135
X2X3	0.0001	1	0.0084	0.9295
X12	0.0294	1	2.47	0.1599
X22	0.1426	1	12.00	0.0105 *
X32	0.1379	1	11.61	0.0113 *
Residual	0.0832	7
Lack of hit	0.0485	3	1.86	0.2765
Pure error	0.0347	4
Cor total	5.21	16

Notes: * indicates a significant effect (0.01 < p < 0.05), and ** indicates an extremely significant effect (p < 0.01).

) showed that the model of regression equation was extremely significant (p < 0.0001), and the lack-of-fit of the regression equation was insignificant (p = 0.2765), indicating a good fit of the model to the data. Furthermore, this model could be utilized to identify the optimal combination of factors and their order of significance [29]. The order of significance for the single factors was as follows: (i) the clamping distance, (ii) the height difference, and (iii) the twisting angle; the p values of the factors were <0.0001, 0.0162, and 0.0431, respectively. The clamping distance had a remarkable influence on the extrusion force. The order of significance of the double factors was: (i) the twisting angle and clamping distance, (ii) the twisting angle and height difference, and (iii) the clamping distance and height difference; the p values were 0.0009, 0.5135, and 0.9295, respectively. The twisting angle and clamping distance were the most notable of the double factors.

A quadratic polynomial model relating three factors to the conveyance success rate $Y_2$ was established using Design-Expert, as shown in Equation (5), with the model’s $R^2$ value being 0.97.

$$Y_2=90.00+2.88x_1-8.62x_2-2.50x_3+2.50x_1{x}_2-0.2500x_1{x}_3-3.25x_2{x}_3-1.25x_1^2-4.75x_2^2-0.5000x_3^2$$

(5)

where $Y_2$ is the conveyance success rate, and $x_1,x_2,x_3$ are the twisting angle, clamping distance, and height difference, respectively.

The analysis of variance of the quadratic model (

Table 4. Analysis of variance for conveyance success rate.

Source	Conveyance Success Rate
	Sum of Squares	Degree of Freedom	F Value	p Value
Model	886.19	9	27.85	0.0001 **
X1	66.13	1	18.70	0.0035 **
X2	595.12	1	168.32	<0.0001 **
X3	50.00	1	14.14	0.0071 **
X1X2	25.00	1	7.07	0.0325 *
X1X3	0.2500	1	0.0707	0.7980
X2X3	42.25	1	11.95	0.0106 *
X12	6.58	1	1.86	0.2148
X22	95.00	1	26.87	0.0013 **
X32	1.05	1	0.2977	0.6023
Residual	24.75	7
Lack of hit	6.75	3	0.5000	0.7022
Pure error	18.00	4
Cor total	910.94	16

Notes: * indicates a significant effect (0.01 < p < 0.05), and ** indicates an extremely significant effect (p < 0.01).

) showed that the model of regression equation was extremely significant (p = 0.0001), and that the lack of fit of the regression equation was insignificant (p = 0.7022), indicating a good fit of the model to the data. Furthermore, this model can be utilized to identify the optimal combination of factors and their order of significance. The order of significance for the single factors is as follows: (i) the clamping distance, (ii) the twisting angle, and (iii) the height difference; the p values of the factors were <0.0001, 0.0035, and 0.0071, respectively. The clamping distance had a remarkable influence on the extrusion force. The order of significance of the double factors was: (i) the clamping distance and height difference, (ii) the twisting angle and clamping distance, and (iii) the twisting angle and height difference; the p values were 0.0106, 0.0325, and 0.7980, respectively. The twisting angle and clamping distance were the most notable of the double factors.

3.3.2. Two-Factor Interaction Response Surface Analysis

Figure 9 indicates the interaction effect of the twisting angle (X₁) and clamping distance (X₂) on the extrusion force (Y₁). When X₁ was constant, Y₁ decreased as X₂ increased. This was due to the stress dispersion leading to a reduced extrusion force, as measured by the thin-film sensor, as X₂ increased. When X₂ exceeded 23 cm, Y₁ increased with the increase in X₁. An increase in X₁ caused additional gravitational force on one side of the conveyor belt from the spinach, resulting in an increased extrusion force.

Figure 10 indicates the interaction effect of the twisting angle (X₁) and height difference (X₃) on the extrusion force (Y₁). When X₁ was constant, Y₁ initially increased and then decreased as X₃ decreased. When X₃ was relatively large, reducing X₃ optimized the stability of the conveyor belt. However, further reduction of X₃ may cause looseness between the conveyor belt and spinach, leading to a decrease in Y₁. When X₃ was fixed, Y₁ first increased and then decreased as X₁ decreased. With the increase in X₁, the gravity gradually exerted force on one side of the conveyor belt, causing Y₁ to gradually increase. As the twisting angle further increased, the force on one side of the conveyor belt became uneven, and Y₁ no longer concentrated in the area where the film sensor was in contact, finally leading to a decrease in Y₁.

Figure 11 illustrates the interaction effect of the clamping distance (X₂) and height difference (X₃) on the extrusion force (Y₁). When X₂ remained constant, Y₁ initially increased and then decreased as X₃ decreased. As X₃ decreased, the center of gravity of the spinach gradually leaned to one side of the conveyor belt, causing Y₁ to increase. However, with a continued decrease in X₃, the force applied on the spinach began to disperse, and some stress was no longer concentrated on the area in contact with the film sensor, leading to a reduction in Y₁. When X₃ was constant, Y₁ decreased as X₂ increased. As the conveyor belt gap widened, the stress exerted by the conveyor belt on the spinach decreased, leading to a decrease in Y₁. An increase in X₂ resulted in reduced stress from the conveyor belt on the spinach, which in turn lowered Y₁.

Figure 12 shows the interactive effect of the twisting angle (X₁) and clamping distance (X₂) on the conveyance success rate (Y₂). When X₁ was constant, Y₂ decreased as X₂ increased. An increase in X₂ lead to a reduction in the extrusion force of the conveyor belt on the spinach, thereby decreasing the stability of the conveyor belt. Conversely, when X₂ was constant, Y₂ increased as X₁ increased. The increase in X₁ enhanced the stability of the conveyor belt, reducing the spinach displacement or slippage due to angle deviation, thereby increasing Y₂.

Figure 13 illustrates the interaction effect of the twisting angle (X₁) and height difference (X₃) on the conveyance success rate (Y₂). When X₁ was constant, Y₂ increased as X₃ decreased. Reducing X₃ enhanced the stability of the conveyor belt, reduced slippage of the spinach, improved the stability of the conveyance, and thus increased Y₂. Conversely, when X₃ was constant, Y₂ decreased as X₁ decreased. The decrease in X₁ lead to the slippage of spinach, thereby reducing Y₂.

Figure 14 indicates the interaction effect of the clamping distance (X₂) and height difference (X₃) on the conveyance success rate (Y₂). When X₂ was constant, Y₂ increased as X₃ decreased. Reducing X₃ could optimize the relative positions of the conveyor belt, reduce the risk of spinach slipping and shifting, enhance the conveyor stability, and improve the conveyance success rate. When X₃ was constant, Y₂ increased as X₂ decreased. A reduction in X₂ could enhance the extrusion force of the conveyor belt on the spinach, reducing its wobble and shifting during conveyance, thereby improving Y₂.

3.4. Optimal Factor Combination

To obtain the optimal combination of factors that minimized the extrusion force and maximized the conveyance success rate, the optimization function of the Design-Expert 11 was applied, and the objective function and constraints are shown in Equation (6).

$$\left\{\begin{array}{c}min{X}_1=\left(X_1,X_2,X_3\right)\\ max{Y}_2=\left(X_1,X_2,X_3\right)\\ {20}^{\circ }\le X_1\le {60}^{\circ }\\ 20 \mathrm{mm}\le X_2\le 26 \mathrm{mm}\\ 0 \mathrm{cm}\le X_3\le 20 \mathrm{cm}\end{array}\right.$$

(6)

By utilizing the optimization function of the Design-Expert software, the optimal combination of factors for minimizing the orderly conveying extrusion force while maximizing the conveyance success rate was determined. The results indicated that the optimal combination for the maximum orderly conveying extrusion force was a twisting angle of 60°, a clamping distance of 24 mm, and a height difference of 20 cm. Under these conditions, the orderly conveying extrusion force was 2.49 N, with a delivery success rate of 92%.

In the optimal parameter combination, the torsion angle is at the upper boundary of the parameter range. If the parameter selection range is further increased, as the twisting angle increases, the belt spacing will gradually decrease, which will lead to an increase in the extrusion force of the conveyor belt on the spinach and further increase the harvest damage rate [30]. Therefore, to ensure orderly conveying and effective dumping, the torsion angle should be minimized as much as possible. The height difference is at the lower boundary of the parameter range, which does not affect the machine design, and so the value range of the height difference should be as small as possible.

3.5. Experimental Validation

Figure 15 presents a case of the extrusion force variation over time during the clamping process of spinach. The extrusion force for the spinach ranged from 0.62 N and 2.55 N during the clamping process. Curve a represents the force value change on the right side of the conveyor belt, while curve b indicates the force value change on the left side of the conveyor belt. During the clamping and conveying process, as the belt twists, the gravity exerted on the spinach is gradually applied more strongly to the a side of the conveyor belt (Figure 16); hence, the force value curve of side a gradually rose, and the force value curve of side b showed a downward trend.

Figure 17 presents the results of the validation tests. The mean force value of the extrusion force was approximately 2.37 N, with a standard deviation of about 0.06 N and a coefficient of variation of approximately 2.5%. These force values showed little difference from those obtained through the Box–Behnken experimental results. In the validation tests, spinach damage (Figure 18) occurred three times, and spinach detachment six times. The orderly conveying extrusion forces corresponding to the three instances of damage were 2.53 N, 2.45 N, and 2.46 N, indicating that the damage likely appeared when the extrusion force exceeded or closely matched the target force value. The extrusion forces corresponding to the instances of detachment were 2.25 N, 2.28 N, 2.26 N, 2.28 N, 2.24 N, and 2.28 N, suggesting that the stability of the clamping of the spinach was poor, and detachment was prone to occur when the extrusion force was less than the target force value [31].

The verification test results are 100 sets of irregular discrete data, which is a measurement error caused by the geometric characteristics of the spinach. The contact between the thin-film pressure sensor and spinach will change when spinach of different sizes and postures is fed, thus resulting in a certain measurement error. Therefore, the mean absolute deviation (MAD) is used to evaluate the reliability of the extrusion force results calculated by the Design-Expert software [32]. The mean absolute deviation (MAD) for the extrusion force between the verification experimental results and the target values calculated by the Design-Expert software was approximately 0.05, indicating a small MAD between the experimental and calculated values. Additionally, the conveying success rate stood at 94% with a conveying damage rate of 3%, ensuring a high success rate while achieving a low damage rate.

4. Conclusions

(1)

The average damage force values for the spinach stems, the connections of stems, and the leaves were 2.64 N, 2.51 N, and 3.84 N, respectively. The damage stress for the spinach stems was 8.04 × 10⁻² MPa, the extrusion damage stress at the connections of stems and leaves was 7.85 × 10⁻² MPa, and the extrusion damage stress for the spinach leaves was 11.63 × 10⁻² MPa. The damage force value for the entire spinach plant was determined to be the minimum value among the three measured parts (7.85 × 10⁻² MPa);

(2)

The finite element model for spinach and the clamping conveyor device was established. The spinach clamping height for orderly harvesting was determined by finite element simulation, and the solved clamping height was 20 mm. The maximum stress on the spinach under the extrusion force was 6.23 × 10⁻² MPa, which was less than the damage stress of spinach;

(3)

The Box–Behnken experimental results indicated that the order of significance of various factors was the clamping distance, the height difference, and the twisting angle. The significance order of the impact on the conveyance success rate was the clamping distance, the twisting angle, and the height difference. The optimal parameter combination was a twisting angle of 60°, clamping distance of 24 mm, and height difference of 20 cm;

(4)

Under the conditions of a clamping height of 20 mm, twisting angle of 60°, clamping distance of 24 mm, and height difference of 20 cm, a validation test was conducted. The average extrusion force of the test results was 2.37 N, with a conveying success rate of 94% and a conveying damage rate of 3%, achieving the orderly and low-damage harvesting of spinach.