Calibration and Experimental Verification of Finite Element Parameters for Alfalfa Conditioning Model

Abstract

Conditioning is an important step in harvesting alfalfa hay, as squeezing and bending alfalfa stems can break down the stem fibers and accelerate the drying rate of alfalfa. The quality of alfalfa hay is directly affected by the conditioning effect. The finite element method (FEM) can quantitatively analyze the interaction relationship between alfalfa and conditioning rollers, which is of great significance for improving conditioning effects and optimizing conditioning systems. The accuracy of material engineering parameters directly affects the simulation results. Due to the small diameter and thin stem wall of alfalfa, some of its material parameters are difficult to measure or have low measurement accuracy. Based on this background, this study proposed a method for calibrating the finite element parameters of thin-walled plant stems. By conducting radial tensile, shear, bending, and radial compression tests on alfalfa stems and combining with the constitutive relationship of the material, the range of engineering parameters for the stems was preliminarily obtained. By conducting a Plackett–Burman experiment, the parameters that affect the maximum shearing force of stems were determined, including Poisson’s ratio in the isotropic plane, radial elastic modulus, and the sliding friction coefficient between the alfalfa stem and steel plate. By conducting the steepest ascent experiment and Box–Behnken experiment, the optimal values of Poisson’s ratio, radial elastic modulus, and sliding friction coefficient were obtained to be 0.42, 28.66 MPa, and 0.60, respectively. Finally, the double-shear experiment, radial compression experiment, and conditioning experiment were used to evaluate the accuracy of the parameters. The results showed that the average relative error between the maximum shear and the measured value was 0.88%, and the average relative error between the maximum radial contact force and the measured value was 2.13%. In the conditioning experiment, the load curve showed the same trend as the measured curve, and the simulation results could demonstrate the stress process and failure mode of alfalfa stems. The modeling and calibration method can effectively predict the stress and failure of alfalfa during conditioning.

1. Introduction

Alfalfa is a perennial legume forage with rich nutritional value, widely planted worldwide, covering an area of approximately 32 million hectares worldwide [1,2,3,4]. Alfalfa is rich in crude protein and various vitamins, making it an important feed for dairy cows [5,6,7]. According to feeding needs, alfalfa can be made into silage or hay. Conditioning is one of the core procedures for harvesting alfalfa hay, which involves using conditioning rollers to compress and bend the cut alfalfa to achieve the goal of destroying the fibers in the alfalfa stem [8]. The water evaporation rate of alfalfa leaves is faster than that of stems, and physically destroying stem fibers can accelerate the water evaporation rate in stems [9,10,11]. By shortening the difference in water evaporation rate between stems and leaves, the dry matter loss of alfalfa during field drying can be reduced [12,13,14,15]. Many studies have shown that conditioning can accelerate the crop drying rate, reduce bundling energy consumption, and increase bale density [16,17,18,19]. The conditioning roller is the core component of the lawn mower conditioning mechanism, consisting of a seamless steel roller, connecting steel plates, shafts, and the profile. The profile of the conditioning roller is made of polyurethane (PU) or rubber. When harvesting alfalfa hay, the upper and lower conditioning rollers rotate in opposite directions to complete the squeezing and bending of alfalfa, as shown in Figure 1. In conditioning, alfalfa is compressed, bent, and rubbed, resulting in elastic deformation, plastic deformation, and failure. The effectiveness can be judged by the degree of stem damage and leaf shedding after conditioning. Due to the higher content of crude protein in leaves under the same weight, it is necessary to reduce the shedding of alfalfa leaves while increasing the degree of stem damage. The speed and gap of the conditioning roller, the planting density of alfalfa, and the shape of the profile have important effects on the conditioning effect of alfalfa [20]. At present, research on alfalfa conditioning is mostly conducted through physical experiments, which quantitatively analyze the influence of different factors on the modulation effect through statistical summary of macroscopic experimental results [21,22]. This type of experimental method is relatively expensive, affected by the season, and cannot reveal the deformation and failure mechanism of alfalfa under the action of mechanical parts. The finite element method (FEM) has significant advantages in simulating the interaction between flexible crops and elastic or rigid mechanical components [23,24,25,26]. Zhao et al. [27] established material mechanics models for the fruit, leaves, flowers, fruit calyxes (flower calyx), fruit stems, and branches of Chinese wolfberry. The separation mechanism of the goji berry picking process was determined through the finite element method and separation experiment, providing a basis for optimizing the lycium barbarum picking method. The detachment mechanism of the lycium barbarum picking process was determined through the finite element method and experiment, providing a basis for optimizing the lycium barbarum picking method. Stopa Roman et al. [28] proposed a method for determining the surface pressure of carrot root at the contact surface with various shaped loading elements by using the finite element method and analyzed the contours of stresses formed by three loading elements: flat surface, cylindrical surface, and flat bars. Govilas J. et al. [29] analyzed the influence of plant fiber geometry on its transverse behavior using the finite element method and proposed an analysis model considering the elliptical cross-section. Compared with traditional models, the new model has improved the accuracy of identifying the transverse elastic modulus by 93%. Petrů M. et al. [30] applied the finite element method to analyze the mechanical behavior of Jatropha curcas L. seeds under linear compression loading and proposed an empirical equation for seed compression deformation. The research provides a reference for the optimization design of pressing machines. Wang et al. [31] applied the finite element method to calibrate the model of the wild chrysanthemum stem cutting, and the maximum error between the simulation results and the test results was 7.8%. Regarding the stem lodging of quinoa, Wang N. et al. [32] applied crop lodging mode (GCLM) and the finite element method to analyze the effects of the irrigation threshold, nitrogen fertilizer rate, and plant density on the lodging rate of quinoa. The research results indicated that the irrigation threshold and planting density were the main factors affecting the lodging of quinoa, and the optimal planting conditions were obtained based on local planting conditions. Li M. et al. [33] used the finite element method to establish the root–soil interaction model and analyzed the resistance force on a stubble cutting tool. The research results can provide a reference for the design and optimization of tillage tools. Santos F. L. et al. [34] used the stochastic finite element method to analyze the natural frequency of macaw palm and analyzed the influence of fruit origin and fruit maturity on the natural frequency. The research served as a base of knowledge for the design and development of macaw palm harvesting machinery. Kabas O. et al. [35] conducted a peach sample drop-test simulation using the finite element method and determined the optimal material parameter combination. Fourcaud et al. [36] used the finite element method to study the relationship between tree shape and growth stress. Moore J. R. et al. [37] studied the natural frequencies of Douglas fir trees. Santos F. L. et al. [38] analyzed the natural frequencies and mode shapes of coffee fruit-stem systems, and studied the stress generated by mechanical vibration during coffee harvesting based on the linear theory of elasticity. Liu H. et al. [39] proposed an extended finite element model that can predict the cracking susceptibility of tomato pericarp.

The reliability of the finite element method depends on the model size, material parameters, load, and boundary conditions, and requires a comparison between experimental data and simulation data to verify the simulation results [40,41]. The methods for obtaining material parameters include direct measurement and batch calibration [40]. Unlike the discrete element method (DEM), which requires inputting microscopic parameters of particles, the finite element method generally directly uses macroscopic parameters of materials for simulation, and some of these parameters can usually be measured through experiments. However, when the geometry of the research object is too complex to produce standard material parameter test specimens, or when the properties of the material are too complex (such as macroscopic isotropic materials and anisotropic materials) to measure some material parameters or the measurement accuracy is low, the reliability of the simulation results will be reduced. At this point, it is necessary to calibrate parameters based on certain volume properties of the material. In the finite element method, the stress–strain behavior of materials is usually used as the indicator [26,42,43]. By adjusting the material parameters, the simulation results are made to be close to the measured results. When there are many material parameters that affect the simulation results, there may be more than one parameter combination that matches the simulation results with the measurement results. Therefore, in order to ensure that the calibrated parameters have sufficient accuracy in another application, it is necessary to conduct application validation tests to verify the calibration results [41,43].

At present, there are problems with uneven stem damage and significant nutrient loss in the conditioning process of alfalfa. Due to the complex interaction between alfalfa and conditioning rollers, it is difficult to directly quantify, which limits the design and optimization of conditioning mechanisms and main operating components. The use of FEM to simulate the conditioning process of alfalfa can provide a visual method for understanding the damage law of alfalfa and the interaction relationship between alfalfa and conditioning rollers. However, due to the thin stem of alfalfa, it is difficult to measure material parameters, such as the radial elastic modulus and Poisson’s ratio. Based on the above background, this study aims to establish a finite element parameter calibration method for thin-walled plant stems represented by alfalfa, and effectively predict the stress and damage of alfalfa during the conditioning process. The double-shear test and stem radial compression test were used to calibrate the finite element parameters. Finally, the calibration results were verified through conditioning experiments. The research results can provide a reference and parameter basis for conducting simulation studies on alfalfa conditioning, improving the quality of alfalfa conditioning, and optimizing the structure of conditioning rollers.

2. Materials and Methods

2.1. Materials

The alfalfa collection site was located at the alfalfa planting base in Wuji County, Hebei Province, China. The variety was “Zhongmu 5”, which was successfully bred by the Chinese Academy of Agricultural Sciences in 2014. This variety of alfalfa exhibits good salt tolerance and is suitable for planting in the Huang Huai Hai region of China. The collected alfalfa was free from pests, diseases, and obvious mechanical damage. Alfalfa was collected in its natural state and stored in Ziploc bags. Mechanical parameters were measured in the afternoon on the same day. The moisture content of the selected alfalfa samples was all greater than 70%.

According to the length of alfalfa, we divided it evenly into three parts: upper, middle, and lower, as shown in Figure 2. The lower stem had fewer lateral branches, while the middle stem had an average of 3–6 lateral branches. The upper stem had the highest number of lateral branches. The tensile strength and shear strength of the lower stem were higher than those of the middle and upper stems [44]. Due to the fact that the lower stem of alfalfa had the least branching and was closest to a cylinder, the material parameters of this study were taken from the lower stem.

2.2. Constitutive Relationship of Alfalfa Stem Material

The cross-section of alfalfa stems is approximately circular in shape. From a microscopic perspective, the stem consists of the epidermis, cortex, phloem, vascular bundle, thin-walled lignified cells, and pith, from the outside to the inside [11,19,45], as shown in Figure 3. Unlike plant stems with well-developed xylem, the epidermis, cortex, phloem, and parenchyma cell of alfalfa are difficult to separate to measure the material parameters separately. Fresh alfalfa pith is cotton-like, with a loose structure and irregular shape, gradually wilting with a decrease in moisture content. Its mechanical properties can be ignored compared with other structures [44]. Therefore, some studies have simplified the alfalfa stem model, such as Tao Chen’s [44] study on the shear characteristics of alfalfa stems and Yanhua Ma’s [46] study on the compression characteristics of alfalfa stems. We simplified the alfalfa stem model by referring to the methods in [44,46], and the alfalfa stem model was set as a thin-walled circular tube structure.

Alfalfa stems belong to transversely orthotropic material, and the material engineering elastic parameters satisfy the following equation [44,47,48]:

$$\left\{\begin{array}{c}{E}_X=E_Y\\ G_{XZ}=G_{YZ}\\ {\mu }_{XZ}={\mu }_{YZ}\\ G_{XY}={\displaystyle \frac{E_X}{2(1+{\mu }_{XY})}}\end{array}\right.$$

(1)

where E_X and E_Y are the radial elastic modulus (MPa), G_XZ and G_YZ are the anisotropic shear modulus (MPa), G_XY is the isotropic shear modulus (MPa), while μ_XZ and μ_YZ are the anisotropic Poisson’s ratio.

2.3. Theoretical Methods for Determining Material Parameters

The outer diameter (D/mm), inner diameter (d/mm), and wall thickness (h/mm) of the stem were measured using a vernier caliper. The average outer diameter of alfalfa stems was 2.53 mm, and the average inner diameter was 1.88 mm. The calculation equation for the cross-sectional area (S/mm²) of the stem is as follows:

$$S=\pi \times \left({\displaystyle \frac{D^2-d^2}{4}}\right)$$

(2)

The axial elastic modulus, E_Z, and tensile strength, σ, of the stem can be calculated using Equation (3):

$$\left\{\begin{array}{c}{E}_z={\displaystyle \frac{\delta }{\xi }}={\displaystyle \frac{F\cdot l}{S\cdot \Delta l}}\\ \sigma ={\displaystyle \frac{F_{max}}{S}}\end{array}\right.$$

(3)

where δ and $\xi$ are the changes in stress and strain during the elastic stage, respectively. F_max is the peak tensile force. By conducting a three-point bending test on alfalfa stems and using Equation (4), the anisotropic out-of-plane shear modulus, G_XZ, of stems can be determined [26]:

$$\left\{\begin{array}{c}U={\displaystyle \frac{\mathsf{\Delta }p\cdot L}{4(f-\frac{f_1\cdot L}{3a})}}\\ G_{XZ}={\displaystyle \frac{2U}{\frac{\pi }{4}(D^2-d^2)}}=2.564{\displaystyle \frac{U}{D^2-d^2}}\end{array}\right.$$

(4)

where U is the shear stiffness (N), ΔP is the incremental load in the elastic phase (N), L is the span (mm), f is the incremental mid-span deflection (mm), f₁ is the incremental deflection at the free end (mm), and a is the free end extension length (mm).

2.4. Mechanical Testing of Alfalfa Stems

The alfalfa stems were subjected to tensile, shear, bending, and compression tests using the Instron Universal Testing Machine (range: 500 N; accuracy: 0.0001) (INSTRON CORPORATION, Boston, MA, USA) and matching fixtures, as shown in Figure 4. The relevant parameters of the sample are shown in

Table 1. Relevant parameters of the sample.

Test Method	Average Moisture Content (%)	Sample Length (mm)	Average Diameter of Stem (mm)	Loading Speed (mm/min)
Tensile test	80.62	60	2.43	20
Shear test	76.91	60	2.92	20
Radial compression test	78.35	30	2.25	20
Bending test	76.13	60	3.03	5

.

The double-shear test was conducted using a shear box, and the calculation equation for shear strength is as follows [49]:

$${\tau }_S={\displaystyle \frac{F_{\tau max}}{2S_1}}$$

(5)

where τ_s is the shear strength (MPa), F_τmax is the maximum shearing force (N), and S₁ is the cross-sectional area of the stem after shearing (mm²). According to the relationship between material parameters, the Poisson’s ratio and stem elastic modulus satisfy the following relationship:

$${\mu }_{YZ}<{\displaystyle \frac{1}{\sqrt{2{\mu }_{XY}}}}\times {\displaystyle \frac{E_X}{E_Z}}$$

(6)

Due to limitations in experimental equipment, it was not possible to accurately measure the Poisson’s ratio of alfalfa stems. Referring to [16,17], the range of the isotropic plane Poisson’s ratio for alfalfa stems was set to 0.3 to 0.5. The anisotropic plane Poisson’s ratio could be calculated using Equation (6), which ranged from 0.01 to 0.03. The mechanical parameters of alfalfa stems are shown in

Table 2. Mechanical parameters of alfalfa stems.

Parameters	Values
EX	2 MPa~30 MPa
EY	2 MPa~30 MPa
EZ	550.72 MPa
GXY	0.67 MPa~11.53 MPa
GXZ	60.32 MPa
GYZ	60.32 MPa
μXY	0.3~0.5
μXZ	0.01~0.03

.

2.5. Contact Parameters of Alfalfa Stems

The mass and volume of alfalfa were measured using high-precision electronic scales and measuring cylinders (Ohaus Instruments (Shanghai) Co., Ltd., Shanghai, China), as shown in Figure 5. The average density of alfalfa stems was 637.72 kg/m³.

The experimental equipment for measuring the frictional coefficient included a slope meter, 45 steel plate, double-sided tape, and a digital angle meter, as shown in Figure 6.

The principle of measuring the friction coefficient is shown in Figure 7. When measuring the sliding friction coefficient, the axial direction of the stem was parallel to the XY plane in Figure 7a. The slope was slowly lifted until the stem slid down along the slope, and the angle at this point was recorded as φ₁. When measuring the rolling friction coefficient, the axial direction of the stem was perpendicular to the XY plane in Figure 7b. The slope was slowly lifted until the stem rolled along the slope, and the angle at this point was recorded as φ₂.

We calculated the sliding friction coefficient between alfalfa stems and 45 steel using Equation (7). The sliding friction coefficient ranged from 0.53 to 0.85, with an average sliding friction coefficient of 0.64.

$${\mu }_1=tan{\phi }_1$$

(7)

where μ₁ is the sliding friction coefficient, and φ₁ is the angle at which the alfalfa stem is about to slide on the measuring plane. According to the principle of conservation of energy, the stem satisfies Equation (8) during the rolling process:

$$W=E_p{-E}_k$$

(8)

where W is the work carried out by the frictional force of the stem, E_p is the initial gravitational potential energy of the stem, and E_k is the kinetic energy when the stem rolls to the end of the inclined plane. For the convenience of calculation, the experiment used the approximate energy conservation of the stem at the moment of rolling to calculate the rolling friction coefficient. When the alfalfa stem with a gravity of G reached a critical angle, φ₂, on the inclined plane, the stem would roll a small distance, S, when the inclined plane was raised slightly. Based on the stress situation of the stem on the plane, the following relationship could be obtained:

$$N=Gcos{\phi }_2$$

(9)

$$F={\mu }_{2}N$$

(10)

$$W=FS$$

(11)

$$E_p=GSsin{\phi }_2$$

(12)

where N is the normal force on the slope of the stem, and F is the rolling friction force. When the rolling distance S is small, the speed change of the stem can be ignored. Assuming that the kinetic energy, E_k, is 0 at this time, the rolling friction coefficient Equation (13) was obtained by combining Equations (8)–(12):

$${\mu }_2=tan{\phi }_2$$

(13)

where μ₂ is the rolling friction coefficient, and φ₂ is the angle at which the alfalfa stem is about to roll on the measuring plane. After multiple measurements, the rolling friction coefficient ranged from 0.12 to 0.18, with an average sliding friction coefficient of 0.15.

2.6. Finite Element Model Parameter Determination

We simplified the alfalfa stem into a thin-walled circular tube structure and established a double-shear model and radial compression model of the alfalfa stem using Solidworks (2020) software. The outer diameter of the valve stem was 2.5 mm, and the inner diameter was 1.9 mm. We imported the model into the Workbench LS-DYNA module and generated the mesh. The mesh size for the alfalfa stem was set to 0.3 mm, and the mesh size for the shear and compression device was set to 0.9 mm. The total number of elements in the shear model was 95,687, and the total number of elements in the compression model was 37,800, as shown in Figure 8.

Plackett–Burman Experiment

Due to the Plackett–Burman experiment and the steepest ascent method being preliminary screening of the experimental data, in order to reduce the simulation time, the above two experiments only used the results of shearing tests as experimental indicators. In the Box–Behnken experiment, in order to improve the accuracy of parameter values, shearing test results and compression test results were used as experimental indicators.

Based on physical experiment data, the Plackett–Burman experiment design was carried out using Design Expert 10 software. The experiment selected Poisson’s ratio in the isotropic plane, Poisson’s ratio in the anisotropic plane, radial elastic modulus, sliding friction coefficient, and rolling friction coefficient as influencing factors, as shown in

Table 3. Test parameters of the Plackett–Burman test.

Simulation Parameters	Level
	−1	+1
Poisson’s ratio in the isotropic plane, X1	0.3	0.5
Poisson’s ratio in the anisotropic plane, X2	0.01	0.03
Radial elastic modulus, X3	2	30
Sliding friction coefficient between alfalfa stem and steel plate, X4	0.3	0.8
Rolling friction coefficient between alfalfa stem and steel plate, X5	0	0.3

. The results of the Plackett–Burman test are shown in

Table 4. Design and results of the Plackett–Burman test.

Test Number	X1	X2	X3	X4	X5	Shearing Force/N
1	−1	1	1	1	−1	28.15
2	1	−1	1	1	−1	33.86
3	1	1	1	−1	1	30.52
4	−1	−1	−1	1	−1	5.85
5	1	−1	−1	−1	1	5.94
6	−1	1	−1	1	1	7.35
7	1	1	1	−1	−1	30.55
8	−1	−1	1	−1	1	27.40
9	1	1	−1	1	1	10.12
10	−1	−1	−1	−1	−1	4.17
11	1	1	−1	−1	−1	5.52
12	1	−1	1	1	1	33.15

.

A significance analysis was conducted on the experimental results, as shown in

Table 5. Variance analysis of the Plackett–Burman test results.

Source	Sum of Squares	df	F	p	Significance
Model	1785.81	5	166.30	<0.0001	**
X1	20.54	1	9.56	0.0213	*
X2	0.28	1	0.13	0.7294
X3	1744.36	1	812.20	<0.0001	**
X4	17.23	1	8.02	0.0299	*
X5	3.39	1	1.58	0.2556
Residual	12.89	6
Cor. Total	1798.69	11

Note: * represents a significant value (p < 0.05) and ** represents a highly significant value (p < 0.01).

. The Lenth method was used to determine the significant impact in the Plackett–Burman experiment [23,24]. The Pareto plot of the standardized effect of factors is shown in Figure 9. The results indicated that Poisson’s ratio X₁, radial elastic modulus X₃, and sliding friction coefficient X₄ had a significant impact on the shearing force. The regression model for Y was obtained, as follows:

$$Y=18.55+1.31X_1+0.15X_2+12.06X_3+1.20X_4+0.53X_5$$

(14)

2.7. Steepest Ascent Method

After determining the three main influencing parameters, the steepest ascent experiment was conducted. The parameter values were determined based on the standardization effect, as shown in Table 5. Equation (15) was used to calculate the relative error between the simulation results and the experimental results, and the relative error was used as the objective function of the experiment. The average maximum shearing force obtained after five shear tests was 28.83 N.

$$\eta ={\displaystyle \frac{|F_s-F_c|}{F_c}}\times 100\%$$

(15)

where η is the relative error, F_S is the simulated contact force, and F_C is the average force obtained from testing. The experimental results are shown in

Table 6. Design and results of the steepest ascent experiment.

Number	X1	X3	X4	Shearing Force/N	Relative Error/%
1	0.30	2.00	0.3	6.21	74.74
2	0.34	7.60	0.4	9.70	60.54
3	0.38	13.20	0.5	16.56	32.63
4	0.42	18.80	0.6	19.80	19.45
5	0.46	24.40	0.7	24.86	13.26
6	0.50	30.00	0.8	33.23	15.95

. The relative error of the shearing force initially decreased and then increased. The minimum relative error was observed in the fifth experiment.

2.8. Box–Behnken Test

During the conditioning process, alfalfa was radially compressed and bent. In order to ensure the reliability of the simulation, the relative error of radial contact force was added as an additional parameter indicator in the Box–Behnken experiment. The average maximum radial contact force obtained from five radial compression tests was 31.03 N. The parameters of the 5th experimental group in the steepest ascent experiment were used as the middle level (0), and the adjacent two experimental groups were used as the high level (+1) and low level (−1), respectively. The parameters are shown in

Table 7. Factors and levels of the orthogonal test.

Level	X1	X3 (MPa)	X4
−1	0.42	18.80	0.60
0	0.46	24.40	0.70
1	0.50	30.00	0.80

.

The results of the orthogonal experiment are shown in

Table 8. Orthogonal test results.

Number	X1	X3	X4	Shearing Force/N	Radial Contact Force/N	Relative Error of Shearing Force/%	Relative Error of Radial Contact Force/%
1	1	1	0	31.72	35.83	10.02	15.47
2	−1	−1	0	18.21	27.92	36.83	10.02
3	0	0	0	24.68	34.93	14.39	12.57
4	0	0	0	25.01	34.01	13.25	9.60
5	1	−1	0	18.99	28.03	34.13	9.67
6	0	−1	−1	20.53	31.85	28.79	2.64
7	0	1	1	35.61	37.31	23.52	20.24
8	1	0	−1	22.73	30.92	21.16	0.35
9	−1	0	1	22.13	31.68	23.23	2.09
10	1	0	1	24.02	33.26	16.68	7.19
11	0	1	−1	33.68	35.19	16.82	13.41
12	0	−1	1	21.02	25.37	27.10	18.24
13	0	0	0	26.01	34.02	9.78	9.64
14	0	0	0	25.15	33.01	12.76	6.38
15	−1	0	−1	22.93	30.65	20.46	1.22
16	0	0	0	24.82	33.02	13.91	6.41
17	−1	1	0	30.98	35.15	7.45	13.23

. Regression analysis was conducted on the experimental results to obtain regression model equations for shearing force (Y) and radial contact force (M), respectively:

$$\left\{\begin{array}{c}Y=0.40X_1+6.66X_3+0.36X_4-0.01X_1{X}_3+0.52X_1{X}_4+0.36X_3{X}_4-2.46X_1^2\\ +2.30X_3^2+0.28X_4^2+25.13\\ M=0.33X_1+3.79-0.12X_4+0.14X_1+0.33X_1{X}_4+2.15X_3{X}_4-1.43X_1^2-\\ 0.63X_3^2-0.74X_4^2+33.80\end{array}\right.$$

(16)

The variance analysis of the experimental results is shown in

Table 9. Analysis of variance of experimental results.

Source	Shearing Force					Radial Contact Force
	Sum of Square	df	F	p	Significance	Sum of Square	df	F	p	Significance
Model	403.9	9	143.83	<0.0001	**	148.67	9	11.32	0.0021	**
X1	1.29	1	4.13	0.0817	*	0.8712	1	0.5968	0.4651
X3	354.31	1	1135.54	<0.0001	**	114.84	1	78.66	<0.0001	**
X4	1.06	1	3.39	0.1081		0.1225	1	0.0839	0.7804
X1X3	0.0004	1	0.0013	0.9724		0.0812	1	0.0556	0.8203
X1X4	1.09	1	3.5	0.1036		0.429	1	0.2939	0.6046
X3X4	0.5184	1	1.66	0.2384		18.49	1	12.67	0.0092	**
X12	25.44	1	81.55	<0.0001		8.66	1	5.93	0.0451	*
X32	22.26	1	71.34	<0.0001		1.68	1	1.15	0.3191
X42	0.3225	1	1.03	0.3432		2.28	1	1.56	0.2512
Residual	2.18	7				10.22	7
Lack of fit	1.1	3	1.34	0.2837		7.62	3	3.9	0.7101
Pure Error	1.09	4				2.6	4
Cor. Total	406.08	16				158.89	16

Note: * represents a significant value (p < 0.05) and ** represents a highly significant value (p < 0.01).

. The significance levels of the quadratic regression models for maximum shearing force and maximum radial contact force were both p ≤ 0.01, indicating that the regression model was statistically significant. The p-values of lack of fit for both models were greater than 0.05, indicating good fitting results. The order of factors affecting the shearing force was: X₃ > X₁ > X₄ > X₁X₃ > X₁X₄ > X₃X₄. The order of factors affecting the radial contact force was: X₃ > X₁ > X₁X₃ > X₄ > X₁X₄ > X₃X₄. The experimental results are shown in Figure 10 and Figure 11.

Based on the results of the Box–Behnken experiment, the objective was to minimize the relative error of the maximum shearing force and radial contact force of alfalfa stem. The objective function and constraint conditions were set as follows:

$$\left\{\begin{array}{l}min{\eta }_{Y1}\left(X_1,X_3,X_4\right)\\ min{\eta }_{Y2}\left(X_1,X_3,X_4\right)\\ 0.42\le X_1\le 0.50\\ 18.80\mathrm{M}\mathrm{P}\mathrm{a}\le X_3\le 30.00\mathrm{M}\mathrm{P}\mathrm{a}\\ 0.60\le X_4\le 0.80\end{array}\right.$$

(17)

The optimal parameter combination was obtained through Design Expert 13 software: the isotropic plane Poisson’s ratio of the stem was 0.42, the radial elastic modulus was 28.66 MPa, and the sliding friction coefficient was 0.60.

2.9. Experimental Validation

In order to ensure the reliability and accuracy of model parameters, it was necessary to conduct simulation and physical experiments and compare the results. The validation experiment included shearing stems, radially compressing stems, and conditioning alfalfa, respectively.

2.9.1. Conditioning Experiment of Alfalfa

According to the technical requirements for conditioning alfalfa, an alfalfa conditioning experimental device was designed. The structural diagram is shown in Figure 12. The experimental device consisted of a conditioning mechanism, a gap and angle adjustment mechanism, and a transmission mechanism, and the feeding amount of alfalfa was controlled through a conveyor belt. The conditioning mechanism consisted of upper and lower conditioning rollers. The gap and angle adjustment mechanism consisted of adjustment bolts and sliding bearings. The transmission mechanism consisted of a variable frequency motor, multiple sprockets, and pulleys. The experimental device was controlled by a variable frequency motor for speed control. The speed of the upper and lower conditioning rollers was equal, but the direction was opposite. By meshing the upper and lower conditioning rollers, the alfalfa was compressed and bent to complete the conditioning process.

As shown in Figure 13, a pressure sensor was installed on the conditioning test device to obtain the load applied by the conditioning roller on the alfalfa stems. The S-type pressure sensor was manufactured by Bengbu High-Precision Sensor Co., Ltd., (Bengbu, China), with a range of 0~1000 kg. The pressure sensor was calibrated before the experiment. The upper end of the sensor was fixedly connected to the body frame, and the lower end was connected to the vertical sliding bearing through screw. According to the force relationship, it can be inferred that the load measured by the sensor was approximately half of the load on the alfalfa. Three-dimensional printing technology was used to produce profiles of the conditioning roller, with a length of 160 mm. The material of the profile was thermoplastic polyurethane (TPU). For the convenience of installation, bolts were used to connect the profiles to the steel rollers.

The alfalfa stems were cut into 150 mm specimens and arranged horizontally into 37 ± 2 mm-wide grass strips, as shown in Figure 14. The conditioning experiment was started with a conditioning roller speed of 650 rpm and a roller gap of 1.5 mm.

2.9.2. Conditioning Simulation of Alfalfa

The same method as in Section 2.5 was used to measure the friction coefficient between alfalfa stems and TPU, resulting in an average sliding friction coefficient of 0.75 and an average rolling friction coefficient of 0.13. A three-dimensional model of the alfalfa conditioning process was established using Solidworks (2020) software, and the model was imported into the Workbench LS-DYNA module. The length and width of the three-dimensional model of alfalfa stems were 150 mm and 37 mm, respectively. The material of the steel roller was set to structural steel, and the material of the profile was set to TPU. The mesh sizes of alfalfa stems and TPU profiles were 0.6 mm and 2.5 mm, respectively, resulting in a total of 2,821,194 elements, as shown in Figure 15. The speed and gap of the conditioning roller in the simulation process were the same as those in the experiment.

3. Results and Discussion

The shearing force curve obtained from the experiment was compared with the shearing force curve obtained from the simulation, as shown in Figure 14. The simulation experiment was repeated three times, and the maximum shearing forces were 28.41 N, 29.71 N, and 27.62 N, respectively. The average shearing force was 28.58 N, with an error of 0.88% compared to the measured results.

From Figure 16, the black line represents the simulation result, and the red line represents the experimental result. In order to prevent damage to the stem during the installation of the specimen, a shearing hole slightly larger than the diameter of the stem was selected for the shear experiment. Therefore, when the universal testing machine started loading, there was a horizontal stage in the test curve, as shown in Label A. As the load increased, the fibers of the stem gradually broke, causing fluctuations in the rising stage of the shearing force curve. This phenomenon could be reflected in both the simulation curve and the experimental curve, as shown in Label B. When the shearing force reached its maximum value, the alfalfa stem broke, and the shear force curve showed significant fluctuations and decreased.

Figure 17 shows the comparison of radial contact force curves. The radial contact force of the three simulation tests was 31.42 N, 28.55 N, 31.15 N, with an average radial contact force of 30.37 N, and an error of 2.13% compared to the measured results. The variation trend of the experimental curve was the same as that of the simulation curve.

By adjusting the pretension mechanism of the conditioning test device, the maximum load in the physical test was close to the maximum load in the simulation. Figure 18 shows the stress distribution of alfalfa during conditioning and the stem damage after conditioning. There were two obvious stress concentrations during the conditioning process: (1) stress concentration caused by the compression of alfalfa due to the clearance of the profile and (2) during the meshing process, bending the alfalfa resulted in stress concentration. Figure 18b shows a comparison of fiber damage in alfalfa after conditioning. It can be seen that the damage caused by conditioning the roller on alfalfa was in the same direction as the spiral of the roller teeth. The simulated alfalfa damage form was the same as the experimental results.

The comparison results between the load curve of the conditioning simulation and the load curve of the conditioning experiment are shown in Figure 16. The maximum load measured by the sensor in the modulation experiment was 171.61 N. According to the force relationship, the maximum load applied by the modulation roller on alfalfa was about 349.65 N. The maximum load in the conditioning simulation was 355.61 N, which differed from the measured result by 5.96 N, accounting for 1.68% of the measured result. The experimental curve and simulation curve both had a double-peak shape. Every time the roller teeth squeezed the alfalfa stem, a wave peak was generated, and as the contact area between the roller teeth and the stem changed, the load showed a pattern of first increasing and then decreasing, which is the reason for the formation of the wave peak.

From Figure 19a, compared with the experimental curve, the difference between the two peaks in the simulation curve was more significant. There are two reasons for the difference between experimental and simulation results. The first reason is that the testing accuracy of the sensor is relatively low. The second reason is that the width of the roller teeth is smaller than the width of the roller groove, and the test device adopts chain transmission, which causes a small relative displacement between the roller teeth and the roller groove during the conditioning process, reducing the difference between the two peaks of the test curve. In addition, the steel rollers, shafts, and other structures in the conditioning system are not rigid and will deform to some extent during the conditioning process. However, these parts are set as rigid bodies in the simulation, which is also one of the reasons for the difference between the simulation results and the experimental results [41]. The data-collecting time interval between the values of the simulation curve and the experimental curve was set to be the same, as shown in Figure 19b. The two curves had the same variation pattern, which verifies the accuracy of the finite element model of alfalfa stems.

According to Section 2.6, the basic FEM parameters (X₁, X₃, and X₄) were calibrated. We continuously adjusted the basic FEM parameters in the simulation experiments to obtain the same maximum shear force and maximum radial contact force as in the actual experiments [26]. The main influencing parameters determined based on the steepest ascent experiment were different from those determined in [26]. This difference may be determined by the mechanical properties of the research object itself. The structure and mechanical properties of stems from different plants varied, resulting in different main parameters that affected the material properties. The BB test results were used to fit the response surfaces of the shearing force and the radial contact force, and the FEM parameters were optimized [41,42,43].

In the conditioning experiment, the stress process of alfalfa was relatively complex, and the FEM parameters were verified by adding pressure sensors [3]. The variation trend of the simulation curve was consistent with the experimental results, which verifies the accuracy of the FEM parameters. However, there are still some shortcomings in this study. One of the key focuses of future research is to combine the multi-layered structure of alfalfa to achieve alfalfa modeling that is closer to the actual structure.

4. Conclusions

In this study, the finite element method (FEM) was conducted on the stress and failure behavior of alfalfa stems during the conditioning process. A calibration method of FEM parameters for thin-walled plant stems was proposed. Finally, the calibration parameters were validated through the shearing test, radial compression test, and conditioning test. The main conclusions are as follows:

(1)

Based on the constitutive relationship of alfalfa stem material, we conducted shear tests, radial compression tests, axial tensile tests, and bending tests. The initial range of engineering constant values for alfalfa stem materials was obtained.

(2)

Through the Plackett–Burman experiment, it was determined that the Poisson’s ratio in the isotropic plane, radial elastic modulus, and sliding friction coefficient were the main factors affecting the maximum shear force of the stem. By conducting the steepest ascent experiment and Box–Behnken experiment, the optimal values of the Poisson’s ratio, radial elastic modulus, and sliding friction coefficient were obtained to be 0.42, 28.66 MPa, and 0.60, respectively.

(3)

In the parameter verification experiment, the average maximum shear force obtained from simulation was 28.58 N, with a relative error of 0.88% compared to the measured results. The average maximum radial contact obtained from the simulation was 30.37 N, with a relative error of 2.13% compared to the measured results. The simulation curve was close to the experimental curve, which can reflect the stress and failure characteristics of the stem during the loading process.

(4)

In the conditioning experiment, there were certain differences between the simulation curve and the experimental curve due to external factors, such as sensor accuracy and the test bench, but the trend of curve changes was the same. During the conditioning process, stress concentration occurred when alfalfa was compressed and bent, resulting in damage along the spiral line of the conditioning roller teeth.