Finite Element Simulation Parameter Calibration and Verification for Stem Cutting of Hydroponic Chinese Kale

Abstract

The finite element simulation is a valid way for the rapid development of the root-cutting mechanism for hydroponic Chinese kale. The stem of the hydroponic Chinese kale was simplified as a transverse isotropic elastic body, and axial compression, three-point bending, and shear tests were performed. The ANSYS/LS-DYNA19.2 software was adopted for stem shear simulation, and the regression equation of the maximum simulated shear force was established. The optimized mechanical parameters were determined by minimizing the deviation between the maximum shear force obtained from the simulation and test. The three-dimensional scanning method was employed to establish the geometric model of the hydroponic Chinese kale stem. The cutting finite element simulation model and test platform were constructed. Displacement, deformation, and force measured from simulation and test were compared. Through measurement and simulation calibration, an axial elastic modulus of 6.22 MPa, axial Poisson’s ratio of 0.46, radial elastic modulus of 3.56 MPa, radial Poisson’s ratio of 0.44, radial shear modulus of 0.8 MPa, and a failure strain of 0.08 were determined. During the cutting simulation and test, the resulting maximum displacement deviations of the marking points on the end of the stem were 0.68 mm along the X-axis and 2.83 mm along the Y-axis, while the maximum deviations of the cutting and clamping force were 0.49 N and 0.77 N, respectively. The deformation and force variation laws of the kale stem in the cutting simulation and test process were basically consistent. It showed that the mechanical parameters calibrated by the simulation were accurate and effective, and the stem cutting simulation results with the finite element method were in good agreement with that of the cutting test. The study provided a reference for the rapid optimization design of the root-cutting mechanism for hydroponic Chinese kale harvest.

1. Introduction

Hydroponic Chinese kale is one of the clean, short-growth cycles, and high-value leaf vegetables widely planted in the southern China facility enterprise [1,2,3]. Currently, fresh hydroponic Chinese kales are harvested by being grabbed out of the pipeline and root cut using the manual method, which leads to high labor intensity and cost problems [4,5,6]. Previous studies on mechanical harvesting for hydroponic Chinese kales mainly focused on the grabbing mechanism [7,8,9,10]. There are few research reports on the root-cutting mechanisms for hydroponic Chinese kale. Simulation of the root–stem cutting process is an effective way for evaluating cutting force and stem deformation without carrying out physical prototype cutting tests. It could provide the basis for the development of root-cutting mechanisms with the advantage of low cutting resistance and high efficiency.

The finite element method (FEM) and discrete element method (DEM) are both important numerical simulation tools for analyzing the dynamic characteristics in the crop stem cutting process. DEM employs a viscoelastic particle combination to simulate the geometric model of the stem. The intrinsic material parameters, such as density, Poisson’s ratio, elastic modulus, and shear modulus etc., and the interparticle contact mechanical parameters, including normal contact stiffness, tangential contact stiffness, critical normal stress, critical tangential stress, and so on, should be determined firstly through experiments and simulation calibration. Zhang et al. [11], Zhang et al. [12], Zhao et al. [13], and Jiang et al. [14] individually developed stem discrete element simulation models for banana, cotton, and wheat, and validated the effectiveness of these models using shear tests. It was primarily used for simulating crop stem crushing, throwing motions, and other related problems. FEM utilizes a gridding unit body to accurately replicate the geometric model of the stem. The mechanical characteristic parameters, including density, elastic modulus, Poisson’s ratio, and yield strength, need to be determined through experiments and simulation validations. Xiong et al. [15], Liu [16], and Ren et al. [17], respectively, constructed the stem finite element models for rapeseed bud, watercress, and sisal, and discussed the influence of the cutting process parameters on cutting force and deformation. The method was mainly applied for optimizing the structure and operational parameters of the cutting device. Compared to DEM, FEM requires less material characteristic parameters and offers the advantage of a simpler model and higher simulation efficiency.

For achieving consistent results with the physical cutting test, it is imperative to precisely define the mechanical property parameters of the stem in the finite element simulation. As some parameters are difficult to obtain through mechanical performance tests, scholars normally utilize the calibration method of combining finite element simulation and experimental verification. Jiang et al. [18] calibrated the strain rate, yield stress, and Poisson’s ratio of forage rape stems using a shear simulation and stem-breaking test. Wang et al. [19] simulated the cutting process of wild chrysanthemum stems and verified the yield stress, failure strain, strain rate, and other parameters using a shear test. Huang et al. [20] used a three-point bending simulation and test to calibrate the anisotropic Poisson’s ratio of phloem and the isotropic Poisson’s ratio of xylem for industrial hemp stems. Si et al. [21] calibrated the rolling friction coefficient, the Poisson’s ratio of phloem, and the Poisson’s ratio of xylem for ramie stems using a three-point bending simulation and test. The above studies show that the calibration of the mechanical characteristic parameters related to crop stem cutting using the finite element simulation method possesses high accuracy.

The accurate determination of the mechanical parameters associated with the cutting of Chinese kale stems is a prerequisite for simulating the cutting mode and mechanism using the finite element method. Therefore, the primary objectives of this study were to construct the constitutive mechanical model of the kale stem through theoretical analysis and to determine the finite element model parameters of the kale stem using a static test measurement and shear simulation calibration. To further validate the effectiveness of the finite element simulation method in the study of the cutting force and deformation law of the hydroponic Chinese kale stem, a cutting test platform for the kale stem was constructed, and the cutting simulations and experimental results were compared. The study would provide a parameter basis for the simulation design of the hydroponic Chinese kale stem cutting device.

2. Materials and Methods

2.1. Materials

Mature Lvbao hydroponic Chinese kales with a growth period of 45 days were selected. Based on the harvest standard [22] issued by the Ministry of Agriculture of the People’s Republic of China, stem samples were cut between 3 and 4 leaves upward from the root of the hydroponic Chinese kale, as shown in Figure 1. Since the stem shape of the hydroponic Chinese kale is approximately cylindrical, it was assumed to be an elastic body with transverse isotropy. The constitutive stress–strain relationships were established by Formulas (1) to (8) [23,24].

$$\left\{\epsilon \right\}=\left\{S\right\}\left\{\sigma \right\}$$

(1)

$$\{S\}=\left[\begin{array}{cccccc}\frac{1}{E_x}& -\frac{{\mu }_{yx}}{E_y}& -\frac{{\mu }_{zx}}{E_z}& 0& 0& 0\\ -\frac{{\mu }_{xy}}{E_x}& \frac{1}{E_y}& -\frac{{\mu }_{zy}}{E_z}& 0& 0& 0\\ -\frac{{\mu }_{xz}}{E_x}& -\frac{{\mu }_{yz}}{E_y}& \frac{1}{E_z}& 0& 0& 0\\ 0& 0& 0& \frac{1}{G_{yz}}& 0& 0\\ 0& 0& 0& 0& \frac{1}{G_{xz}}& 0\\ 0& 0& 0& 0& 0& \frac{1}{G_{xy}}\end{array}\right]$$

(2)

$$\frac{{\mu }_{xy}}{E_x}=\frac{{\mu }_{yx}}{E_y}$$

(3)

$$\frac{{\mu }_{zx}}{E_z}=\frac{{\mu }_{xz}}{E_x}$$

(4)

$$\frac{{\mu }_{zy}}{E_z}=\frac{{\mu }_{yz}}{E_y}$$

(5)

$$E_x=E_y$$

(6)

$${\mu }_{yz}={\mu }_{xz}$$

(7)

$$G_{yz}=G_{xz}$$

(8)

where {ε} is the strain matrix, {S} is the flexibility matrix, {σ} is the stress matrix, E_x and E_y are the radial elastic modulus, E_z is the axial elastic modulus, μ_yz and μ_xz are the radial Poisson’s ratios, μ_xy is the axial Poisson’s ratios, G_yz and G_xz are the radial shear modulus, and G_xy is the axial shear modulus. The axial shear modulus (G_xy) could be calculated with the following Formula (9).

$$G_{xy}=\frac{E_x}{2(1+{\mu }_{xy})}$$

(9)

The above equations show that the root stem of hydroponic Chinese kale possesses five independent intrinsic mechanical parameters, including axial elastic modulus (E_z), axial Poisson’s ratio (μ_xy), radial elastic modulus (E_y), radial Poisson’s ratio (μ_yz), and radial shear modulus (G_yz).

2.2. Mechanical Parameters Measurement Test

The mechanical parameter measurement test was carried out based on the GB/T 15777-2017 standard [25]. The universal testing machine (accuracy of 0.001 N, test force range of 0 to 500 N) was used for the measurement tests. In total, 8 root stems with an average length of 15 mm and diameter of 12 mm were selected. A flat press head with a diameter of 50 mm was utilized to apply axial pressure on the stems. The compression process was conducted at a speed of 2 mm/s, resulting in a displacement of 7 mm. E_z was calculated according to the following Formula (10).

$$E_z=\frac{{\sigma }_z}{{\epsilon }_z}$$

(10)

where σ_z is the maximum stress during the elastic deformation stage, MPa, and ε_z is the corresponding maximum strain.

In total, 8 Chinese kale root stems with an average diameter of 12 mm and length of 15 mm were selected. A flat press head with a diameter of 30 mm was used to exert pressure along the axis of the stems at a speed of 2 mm/s. At a loading displacement of 4 mm, the pressure application was halted for a duration of 60 s, and a vernier caliper with an accuracy of 0.01 mm was utilized to measure both the radial deformation (∆d, mm) and axial deformation (∆l, mm) of the stem sample. For acquiring reliable radial and axial dimensions of the stem samples, an approach of averaging measurements from three distinct orientations was employed. The Poisson’s ratio μ_xy was determined by employing Formula (11).

$${\mu }_{xy}=\frac{\Delta l\times d}{\Delta d\times l}$$

(11)

where d (mm) and l (mm) represent the diameter and length of the stem sample, respectively, and ∆d (mm) and ∆l (mm) represent the radial and axial deformation of the stem sample, respectively.

As the length of the root stem samples of the obtained Chinese kale is less than 45 mm, it is difficult to clamp both ends of those samples to conduct torsion tests. The three-point bending test was conducted in accordance with the standard GB/T 11546.2-2022 [26], and the experimental platform is illustrated in Figure 2. In total, 8 samples of Chinese kale root stems, having an average diameter of 12 mm and length of 40 mm, were positioned on the supporting frame with a span of 30 mm. The compression probe had a diameter of 2 mm, while the compression speed and loading displacement were set at 2 mm/s and 11 mm, respectively. E_y was determined using Formula (12).

$$E_y=\frac{L^3}{48I}(\frac{F_x}{\Delta \delta })$$

(12)

where L is the span between the two end supports, mm; I is the sample’s moment of inertia, mm⁴; F_x is the maximum force F_x experienced by the sample during the linear elastic deformation stage, N; and Δδ is the deformation amount, mm.

The shear test was conducted in accordance with the shear strength testing standard of GB.1937.2009 to obtain the maximum shear force during the shearing process, as shown in Figure 3. The shearing tool had dimensions of 150 mm length, 20 mm width, and 2 mm thickness, with a blade angle of 10°. It was made of stainless steel with a density of 7900 kg/m³, elastic modulus of 206 GPa, and Poisson’s ratio of 0.3. In total, 8 samples of Chinese kale root stems were used, each having an average diameter of 12 mm and a mean length of 30 mm. The shear speed was set at 2 mm/s while maintaining a shear displacement of 20 mm.

2.3. Simulation Calibration Test

The radial Poisson’s ratio μ_yz, radial shear modulus G_yz, and failure strain were calibrated using the finite element simulation of the shearing process. Solidworks2019 was used to establish simplified models of the Chinese kale root stem with a diameter of 12 mm and length of 30 mm, a shearing supporting frame with a span of 30 mm, and a shear tool with a length of 150 mm, width of 20 mm, thickness of 2 mm, and cutting blade angle of 10°. The assembling simulation model was imported into the Explicit Dynamic module (LS-DYNA) in Ansys Workbench 19.0, as shown in Figure 4. The supporting frame was fixedly constrained, the cutting speed was set to 2 mm/s, and the simulation time lasted for 10 s.

According to the mechanical characteristic parameters of similar crop stems [27,28,29,30], and following the principles of the Box-Behnken central composite test, the ranges for the radial Poisson’s ratio (X₁), radial shear modulus (X₂), and failure strain (X₃) of the kale stem were determined as 0.3–0.5, 0.4–0.8 MPa, and 0.06–0.08, respectively, with three levels designated as high, medium, and low. The test coding is shown in

Table 1. Central composite design factor coding.

Factor Level	X1	X2	X3
−1	0.3	0.4	0.06
0	0.4	0.6	0.07
1	0.5	0.8	0.08

.

2.4. Cutting FEM Simulation and Test Validation

For further verifying the accuracy of the calibrated mechanical parameters and confirming the rationality and effectiveness of the FEM, a cutting validation simulation and test were carried out. In total, 5 mature hydroponic Lvbao Chinese kales were selected, and tests were conducted at speeds of 600 mm/s, 700 mm/s, 800 mm/s, 900 mm/s, and 1000 mm/s, respectively. To facilitate the observation of the cutting process, the root below the third leaf of the Chinese kale test sample was cut off and the leaves on the stem were removed.

2.4.1. Cutting Simulation Model and Method

The 3D scanning method was employed to establish a geometric model possessing high consistency with the actual morphological characteristics of Chinese kale. The scanning test platform is shown in Figure 5. A handheld Einstar 3D scanner (Xianlin 3D Technology Co., Ltd., Hangzhou, China) with a point distance of 0.1~3 mm and a maximum scanning speed of 14 fps was selected for collecting the point cloud data of the hydroponic Chinese kale with the top leaves reserved. The point cloud data was tracked, spliced, and trimmed through the EXStar v1.0.6.0 software installed in the Dell Precision T3660 graphic workstation. The data points in the region of the hydroponic Chinese kale stem were retained, and the encapsulation process, such as filtering and smoothing, was carried out. To minimize the influence of the intricate or irregular shapes at the stem, and petiole fracture on the finite element grid division, the encapsulated model was further optimized and smoothed, as shown in Figure 6.

The assembly model, consisting of a cutting tool, two-finger holder, and kale stem, was established with solidworks2019 software and was imported into the Explicit Dynamic module (LS-DYNA) in Ansys Workbench 19.0. The fixed constraint was set between the lower holder and the kale stem, and an initial clamping force of 15 N on the kale stem was exerted from the upper holder. The cutting simulation model was constructed, as shown in Figure 7.

To reduce the calculation time, the initial distance between the blade of the cutting tool and the axis of the kale stem was defined as 6.4 mm, and the simulation time was set as 2 s. Marking point A was set at the end of the kale stem model, and the X-axis and Y-axis coordinates of point A were recorded during the cutting simulation process.

2.4.2. Cutting Test Platform and Method

The cutting test platform is illustrated in Figure 8. The cutting tool is 150 mm long, 20 mm wide, and 2 mm thick, and the cutting blade angle is 10°, which is driven by an MTP-100 electric slide table (Dongguan Meitemei Co., Ltd., Dongguan, China) with a speed range of 0–1000 mm/s. A JLBS-M2 strain force sensor (Bengbu Sensor System Engineering Co., Ltd., Bengbu, China) with a measuring range of 0–500 N and a maximum sampling frequency of 2000 Hz is installed between the cutting tool and the electric slide table. The root area of the kale stem is clamped by a PGE-50-26 electric two-finger holder (Huiteng Industry Co., Ltd., Shanghai, China) with a maximum clamping force of 50 N. A film clamping force sensor with a measuring range of 0–100 N and a maximum sampling frequency of 2000 Hz is attached inside the lower finger of the electric two-finger holder to measure the clamping force on the lower side of the kale stem. The initial clamping force of the electric two-finger holder is set to 15 N during the cutting test.

An MV-CA016.10UC color industrial high-speed camera (Huaraytec Co., Ltd., Hangzhou, China) was selected to capture the cutting process, with a maximum resolution of 1440 × 1080 and a frame rate of 545 fps. Videos of the cutting process were imported into the motion analysis software MolysisV3.0. The coordinate system was established with the center of the two-finger holder as the origin (O), the kale stem axis as the X direction, and the vertical direction of the kale stem axis as the Y direction. The vertex at the end of the kale stem is defined as the marking point A′, which is consistent with the simulation marking point A. The width of aluminum profiles (40 mm) was used as the size calibration reference. The X and Y coordinates of the marking point A′ during the cutting process were tracked and recorded, as shown in Figure 9.

3. Results and Discussion

3.1. Mechanical Parameters Measurement Test Result

The E_z obtained from the eight tests were 5.72 MPa, 5.84 MPa, 6.48 MPa, 6.67 MPa, 6.11 MPa, 5.82 MPa, 6.34 MPa, and 6.81 MPa, respectively, with the average value of 6.22 MPa and variation coefficient of 0.066. The radial Poisson’s ratio μ_xy measured from the eight tests were 0.46, 0.47, 0.47, 0.45, 0.47, 0.43, 0.47, and 0.48, respectively, with an average value of 0.46 and variation coefficient of 0.0316. The E_y obtained from the eight tests were, respectively, 2.69 MPa, 2.98 MPa, 3.78 MPa, 3.81 MPa, 3.72 MPa, 3.84 MPa, 3.78 MPa, and 3.89 MPa, with an average value of 3.56 MPa and variation coefficient of 0.257. The shear force obtained in the test ranges from 9.8 N to 14.893 N, with an average value of 11.5 N, and a variation of 0.0965.

3.2. Simulation Calibration Test Result

The simulation calibration test results are presented in

Table 2. Simulation calibration test scheme and results.

No.	X1	X2	X3	Max Shear Force/N	Deviation/N
1	0.3	0.8	0.07	9.73	1.77
2	0.4	0.6	0.07	9.96	1.54
3	0.3	0.4	0.07	8.58	2.92
4	0.4	0.8	0.08	12.15	0.65
5	0.4	0.6	0.07	11.16	0.34
6	0.5	0.6	0.08	12.78	1.28
7	0.5	0.8	0.07	11.87	0.37
8	0.4	0.6	0.07	10.76	0.74
9	0.5	0.4	0.07	11.81	0.31
10	0.3	0.6	0.06	9.15	2.35
11	0.4	0.4	0.06	9.02	2.48
12	0.4	0.4	0.08	11.94	0.44
13	0.4	0.8	0.06	10.15	1.35
14	0.3	0.6	0.08	10.98	0.52
15	0.5	0.6	0.06	10.24	1.26
16	0.4	0.6	0.07	11.04	0.46
17	0.4	0.6	0.07	10.95	0.55

. The fitting analysis of the simulation test results of the maximum shear force was performed using Design-Expert 13. It was found that the quadratic polynomial fitting method was effective. The regression equation between the maximum shear force F and radial Poisson’s ratio X₁, radial shear modulus X₂, and failure strain X₃ is shown in Formula (13).

$$\begin{array}{l}F=-1.014+18.235X_1-18.828X_2-117.57X_3-13.625X_1{X}_2+177.5X_1{X}_3-\\ 115X_2{X}_3-15.2{X_1}^2-3.1125{X_2}^2+1655{X_3}^2\end{array}$$

(13)

Variance analysis for the maximum shear force regression model is shown in

Table 3. ANOVA of central composite simulation test.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	21.03	9	2.34	9.50	0.0036
X1	8.53	1	8.53	34.66	0.0006
X2	0.8128	1	0.8128	3.30	0.1120
X3	10.79	1	10.79	43.85	0.0003
X1X2	0.2970	1	0.2970	1.21	0.3082
X1X3	0.1260	1	0.1260	0.5122	0.4974
X2X3	0.2116	1	0.2116	0.8600	0.3846
X12	0.0973	1	0.0973	0.3954	0.5494
X22	0.0653	1	0.0653	0.2653	0.6224
X32	0.1153	1	0.1153	0.4687	0.5156
Residual	1.72	7	0.2460
Lack of fit	0.8087	3	0.2696	1.18	0.4222
Pure error	0.9135	4	0.2284
Total	22.75	16

. The determination coefficient R2 of 0.9243 and p-value of 0.0036 indicated the good fitting effect of the model. The p-value of the lack of fit was 0.4222 and proved the reliability of the model. The p-value of radial Poisson’s ratio (X₁) and failure strain (X₃) were both less than 0.01, illustrating that the two parameters had an extremely significant influence on the maximum shear force during the stem cutting process. While the p-values of the radial shear modulus X₂ and interactions between the two parameters were all greater than 0.05. To ensure the precision of the model, all factors were retained in the regression equation.

The relative deviation δ of the maximum shear force obtained in the simulation test was adopted as the response analysis variable. The quadratic polynomial regression equation was established with Design-Expert 13 software, as shown in Formula (14).

$$\begin{array}{l}\delta =60.004-34.635X_1-140.135X_2-341.8X_3+308.125X_1{X}_2-1397.5X_1{X}_3+\\ 167.7X_2{X}_3-113.05{X_1}^2+98.175{X_2}^2+2570{X_3}^2\end{array}$$

(14)

The determination coefficient R2 of 0.9175 and the significance coefficient p-value of 0.0282 indicated that the deviation regression model fit well. The p-value of the lack of fit was 0.2205 and illustrated the reliability of the model. The p-value of the radial Poisson’s ratio (X₁) and failure strain (X₃) were both less than 0.05, proving that the two parameters had a significant influence on the deviation during the stem cutting process. And the p-values of other factors were all greater than 0.05.

The minimum extremum of Formula (14) was solved using the Design-Expert 13 software. The optimized radial Poisson’s ratio X₁, radial shear modulus X₂, and failure strain X₃ were 0.44, 0.8 MPa, and 0.08, respectively. Using the optimized parameters in the shear simulation, the obtained maximum shear force was 11.03 N, which was close to the actual measurement result of 11.5 N. It verified the feasibility of the mechanical parameter simulation calibration. The mechanical parameters of the simulation model were set as shown in

Table 4. Cutting simulation mechanical parameters.

Parameters	Value
Axial modulus of elasticity/MPa	6.22
Axial Poisson’s ratio	0.46
Axial shear modulus/MPa	1.65
Radial modulus of elasticity/MPa	3.56
Radial Poisson’s ratio	0.44
Radial shear modulus/MPa	0.8
Failure strain	0.08

.

3.3. Cutting FEM Simulation and Test Validation Result

The displacements of the marking points along the X and Y axes in both simulations and tests are illustrated in Figure 10 and Figure 11. At cutting speeds of 600 mm/s, 700 mm/s, 800 mm/s, 900 mm/s, and 1000 mm/s, respectively, the maximum X-axis displacements of the simulation marking point A were 2.04 mm, 2.57 mm, 2.84 mm, 2.93 mm, and 3.95 mm, and the corresponding maximum Y-axis displacements were 18.36 mm, 32.41 mm, 50.54 mm, 55.68 mm, and 66.71 mm. The maximum X-axis displacements for test marking point A’ under similar conditions were 2.07 mm, 2.17 mm, 2.75 mm, 2.9 mm, and 3.27 mm, and the respective maximum Y-axis displacements were 19.01 mm, 35.24 mm, 51.44 mm, 58.28 mm, and 68.83 mm. The displacements of the marking points along the X-axis and Y-axis directions increase with the cutting speed, as observed in both the simulation and test. The displacements along the Y-axis direction, which are consistent with the cutting tool insertion direction, exhibit a significantly greater magnitude compared to that in the X-axis direction.

Under different cutting speeds, the maximum displacement deviations of the marking points in the test and simulation along the X-axis were 0.03 mm, 0.4 mm, 0.09 mm, 0.03 mm, and 0.68 mm, respectively, and the maximum displacement deviations along the Y-axis were 0.85 mm, 2.83 mm, 0.9 mm, 2.6 mm, and 2.12 mm, respectively. The reason for the relatively greater displacement in the deviation of marking points along the Y-axis is that the cutting force imposed on the kale stem was mainly along the Y-axis, which resulted in a larger displacement along the Y-axis than that observed along the X-axis.

The overall deformation of the kale stem obtained by both the simulation and test at a cutting speed of 1000 mm/s and a cutting depth of 6mm, is illustrated in Figure 12. The deformation cloud map generated by the simulation had a good consistency with the image captured in the cutting test. It indicates that the deformation of the kale stem in the actual cutting process could be effectively reflected by the finite element simulation.

The simulation stress contour for the stem with a cutting depth of 6mm is shown in Figure 13. It indicates that the internal stress of Chinese kale stems during cutting is primarily localized in the contact area between the root and the cutting tool, while minimal internal stress is observed in the edible areas. This suggests that clamping and cutting at the root of the kale stem would not lead to the quality degradation of its edible areas.

Under different cutting speeds, both the cutting and clamping force obtained by the simulation and test demonstrated an initial increase, followed by a peak value and subsequent decrease, as shown in Figure 14. Taking the cutting speed of 1000 mm/s as an example, the variation trends of the cutting and clamping force obtained by the simulation and test were in good agreement. It was observed that the fluctuations of the clamping and cutting force in the simulation were more obvious than those measured from the cutting test.

As shown in Figure 15, with the increase of cutting speed from 600 mm/s to 1000 mm/s, the peak cutting and clamping force obtained by the simulation and test illustrated a decreasing trend, accompanied by a gradual reduction of the time taken to reach those peak forces with values of 0.017 s, 0.015 s, 0.013 s, 0.011 s, and 0.008 s, respectively. The simulation cutting and clamping peak force ranges were from 3.11 N to 4.39 N and from 21.99 N to 23.24 N. While the test cutting and clamping peak force ranged from 3.60 N to 4.47 N and from 22.24 N to 24.01 N. The maximum deviations between the test and simulation for the cutting and clamping peak force were 0.49 N and 0.77 N. It indicates that the finite element simulation can effectively reveal variations of cutting and clamping forces during the cutting process.

4. Conclusions

For precisely determining the finite element simulation parameters, the hydroponic Chinese kale root stem was simplified as a transverse isotropic elastic body, and its axial elastic modulus, axial Poisson’s ratio, radial elastic modulus, and maximum shear force were measured using tests. A shearing finite element simulation test for kale stem was carried out. By minimizing the maximum shear force deviation between the simulation and test, the optimized radial shear modulus, radial Poisson’s ratio, and failure strain were 0.8 MPa, 0.44, and 0.08, respectively.

The finite element simulation and test comparison of cutting the Chinese stem using the cantilever clamping method was conducted. The maximum displacement deviations between the simulation and test of the marking point along the X-axis and Y-axis were 0.68 mm and 2.83 mm, respectively. The deformation images of Chinese kale stems observed from the simulation and test exhibit a high level of consistency. The maximum cutting and clamping peak force deviation between the test and simulation were 0.49 N and 0.77 N, respectively. It verified the accuracy of the calibrated simulation parameters and the effectiveness of the finite element simulation method.

The calibrated mechanical parameters of the study will be applied in future root-cutting mechanism simulation designs for hydroponic Chinese kale. The applicability of the simulation calibration and experimental method for other varieties of hydroponic leafy vegetables with similar root-cutting function requirements would also be further verified.