Alfalfa Stalk Crushing Simulation Test and Parameter Optimization Method

Abstract

To investigate the impact of different cutter structures on the crushing effect of forage stalks at various rotational speeds, this study designed five types of crushing cutters. The effects of cutter structure and rotational speed on the crushing effect of the forage crusher were examined using the discrete element method, a single-factor test. An orthogonal test was conducted, with the percentage of bond breakage as the evaluation index, and tool type and tool speed as influencing factors. The results of the orthogonal test were analyzed using range analysis. The findings revealed that the quality of alfalfa stalk crushing varied depending on the crushing structure and rotational speed. Within a certain rotational speed range, the crushing effect improved as the rotational speed increased. However, beyond a certain value, the improvement in the crushing effect became slower. Notably, the hob-type crushing structure exhibited the best crushing effect at 2400 r/min.

1. Introduction

Stalk crushing is a crucial aspect of the forage industry as it directly impacts the quality of the subsequent feed. In recent years, there has been extensive research on the utilization of straw powder and grass powder, leading to the specialized production of stem crushing. Meeting the market demand for efficient stem crushing machinery has become increasingly pressing, prompting researchers to conduct comprehensive studies in this field [1,2].

A growing body of evidence suggests that a reasonable crushing structure plays an important role in the crushing quality of materials. Li et al. [3] developed a bionic blade to enhance the efficiency and quality of banana straw crushing. Through determining the optimal combination of parameters, they achieved a straw crushing qualification rate of 93.89%. Zhang et al. [1] conducted a corn bale crushing test using a fatigue testing machine. The results of the test demonstrated that the crushing process consists of two stages: compression and shearing. It was observed that the crushing force of the corn bale increases with an increase in both water content and blade angle. Furthermore, there was an interaction between the water content and the blade inclination angle. El Ghobashy et al. [4] explored the crushing effect of corn ears under different rotational speeds of the cutter and different apertures of the sieve, and determined the optimal parameter combination when the efficiency is highest. To address the issue of the absence of precise discrete element models in the simulation analysis of corn straw crushing, Liu et al. [5] developed bonding models with various structures, and corn straw particle models with different properties. They utilized Hertz–Mindlin combined with bonding technology to establish these models and calibrated the relevant parameters. The accuracy of the discrete element model was validated through physical testing and simulation optimization design methods. In their research on the crushing problem, the scholars aimed to explore the relevant laws of the crushing process and determine more appropriate parameters. As the fields of crushing and types of materials continue to expand, extensive research will be conducted on crushing devices in the next few years. The aim is to enhance crushing quality and to minimize energy consumption through identifying the optimal structure and cutter for various material types and crushing needs.

Most studies in the field of material crushing have only focused on the study of the difference in performance of a certain structure before and after optimization. However, there are few relevant studies on the horizontal comparison of multiple common crushing structures.

To investigate the crushing effect of different structures of crushing devices on alfalfa, five different crushing tool structures were developed in this study, and the influence of different rotation speeds and different crushing results on the crushing effect was explored through the discrete element method. Through conducting range analysis, the study identified the primary and secondary influencing factors, as well as the optimal parameter combination. At the same time, a modal analysis was performed on the frame to ensure that resonances are avoided during operation. The findings of this study can serve as a valuable reference for the design of forage crushing devices.

2. Materials and Methods

2.1. Materials

This study primarily focused on the use of crushing devices for alfalfa stalks. The crushing device comprised a frame, crushing chamber, inlet, outlet, motor, and other components (Figure 1). In the experiment, forage stalks were placed into the crushing chamber through the feed inlet and were then crushed by the high-speed rotating crushing knife. The device has a power of about 4 kilowatts and a production efficiency of about 0.6 tons per hour.

This study designed five different crushing structures: hammer crushing structure with blades, hammer crushing structure without blades, hammer crushing structure, hob crushing structure, and round roller crushing structure. These crushing structures are represented by codes A1, A2, A3, A4, and A5, as shown in Figure 2.

2.2. Methods

This study utilized the finite element method to analyze the frame and the discrete element method to investigate the material crushing process. The former aimed to identify the first six modes and frequencies of the rack to assess the possibility of resonance and to determine if optimization was necessary. The latter focused on examining the crushing process of devices with various structures and selecting the one with a superior performance.

This study utilized ABAQUS 2022 software to analyze the first six modes and frequencies of the frame through finite element analysis. ABAQUS is a highly effective engineering simulation software extensively utilized in a range of industries including machinery, electronics, materials, and civil engineering. It offers a wide range of physical models and advanced numerical methods to accurately simulate the behavior and performance of complex systems and components. The results obtained using ABAQUS were compared with the external excitation frequency to assess the possibility of resonance. If the natural frequency of the rack falls within the range of excitation frequency, further optimization of the frame was carried out. This optimization involved modifying the structural size to enhance the stiffness of the frame, thereby increasing its natural frequency and avoiding the excitation frequency range.

This study employed the discrete element method to conduct a single-factor crushing simulation test on alfalfa stems. The objective was to investigate the impact of different rotation speeds and tool structures on the crushing of alfalfa stems. Subsequently, orthogonal experiments and range analysis were employed to identify the primary and secondary influencing factors, and to determine the optimal parameter combination. EDEM 2022 software is a simulation software that is suitable for analyzing discrete particles. It is based on particle collision theory and discrete element theory, and it is combined with powerful coupling functions to jointly simulate particles, fluids, and mechanical equipment [6,7]. This study used EDEM simulation software to conduct discrete element analysis to explore the effects of crushing structure and rotational speed on the stalk crushing effect. In addition, the type and rotation speed of the crushing tool were considered as influencing factors. The fracture of the bond in EDEM was used as the basis for evaluating the crushing effect [8,9].

In the EDEM software, the bonding model is utilized to bond particles together. When both the tangential force and normal force endured by the bonds exceed the limit value, the bonds will break and the particles will separate from each other, achieving the purpose of breaking [10,11,12]. Therefore, this study employed EDEM software to construct a bonding model of alfalfa stems. The alfalfa stems were simulated as fine particles that are held together by bonds. The fracture of these bonds was used to assess the effectiveness of the crushing device in breaking down alfalfa stems [13,14,15].

During the construction of the model, a particle diameter of 5 mm was chosen. A total of 1346 small particles were generated within the alfalfa stalk model as the target particles. The XYZ position parameters of these target particles were collected to compile an API. This API was then used to quickly replace and generate the alfalfa stalk model using the target small particles. Additionally, particle bonds were created to achieve the desired shape of the alfalfa stalk model. Contact parameters and bond parameters specific to alfalfa stalks were set accordingly. Previous studies have extensively investigated these parameters, taking into account factors such as the variety of alfalfa stalks and moisture content.

In the settings of simulation analysis, the material of the frame was Q235, and the material of the crushing device was steel 45. Based on a thorough search of the relevant literature, this study determined the simulation parameters outlined in

Table 1. Simulation parameters.

Parameter	Value
Alfalfa Poisson’s ratio	0.4
Alfalfa density/kg·m−3	256
Alfalfa shear modulus/MPa	5.00
Steel 45 Poisson’s ratio	0.3
Steel 45 density/kg·m−3	7800
Steel 45 shear modulus/MPa	70,000
Stalk–stalk collision recovery coefficient	0.11
Stalk–stalk static friction coefficient	0.45
Stalk–stalk rolling friction coefficient	0.08
Stalk–steel 45 collision recovery coefficient	0.16
Stalk–steel 45 static friction coefficient	0.54
Stalk–steel 45 rolling friction coefficient	0.24
Q235 elastic modulus/MPa	210 × 103
Q235 density/ton·mm−3	7850 × 10−12
Q235 Poisson’s ratio	0.3

[16].

EDEM is a simulation software designed for analyzing discrete particles. It is based on particle collision theory and discrete element theory and incorporates robust coupling functions to simulate particles, fluids, and mechanical equipment [14,15,16]. In this study, the EDEM simulation software is employed to conduct a discrete element analysis, which aims to uncover the microscopic interaction between alfalfa stem particles and the mechanism of crushing alfalfa stems.

3. Key Steps in Modal Analysis and Results

Modal analysis is a useful technique for determining the natural frequency and mode shape of a structure. Through obtaining this information, it is possible to prevent the external excitation frequency from overlapping with the natural frequency of the structure, thus avoiding the risk of resonance. This not only extends the life of the machine but also ensures its performance. The theoretical model for modal analysis is represented by Equation (1).

$$\left[M\right]\left\{\stackrel{..}{{\displaystyle x}}\right\}+\left[C\right]\left\{\stackrel{.}{{\displaystyle x}}\right\}+\left[K\right]\left\{x\right\}=\left\{F\left(t\right)\right\}$$

(1)

In the formula, [M] is the mass matrix; [C] is the damping matrix; [K] is the stiffness matrix; and {F(t)} is the external load on the structure. The natural frequency is mainly related to its own material, mass, and dimensions and does not depend on the external load, so {F(t)} is zero, and the damping effect is considered to be approximately zero; therefore, Equation (1) can be expressed as Equation (2).

$$\left[M\right]\left\{\stackrel{..}{{\displaystyle x}}\right\}+\left[K\right]\left\{x\right\}=\left\{0\right\}$$

(2)

The frame, which is the main load-bearing component of the crusher, is primarily constructed using square hollow steel that is welded together. To reduce the calculation running time in the modal analysis, the frame structure was simplified appropriately. The frame, which was welded using multiple parts, was considered as a single part. The finite element model used is shown in Figure 3.

The vibration of the frame is determined by the superposition of various modes. Each mode represents a decoupling of the originally coupled modes. In theory, there are infinite orders of modes. However, the influence of lower-order vibration shapes on the structure is greater than that of higher-order vibration shapes. Therefore, the dynamic characteristics of the structure are primarily determined by the lower-order vibration shapes. In this study, ABAQUS finite element software was used for calculations, and the Lanczos solver was employed to extract the first six natural frequencies and vibration shapes. The specific vibration shapes and frequency information can be found in Figure 4 and

Table 2. Modal response values and vibration shape descriptions of each order.

Order	Natural Frequency/Hz	Maximum Deformation/mm	Vibration Shape Description
1	63.67	7.86	The upper beam deformed
2	76.11	6.74	The upper beam deformed
3	91.20	9.00	The upper short beam deformed
4	104.42	7.77	The support plate deformed
5	137.45	4.05	The upper long beam deformed
6	149.84	4.48	The upper beam deformed

.

The rotation speed range of the pulverizing device was set to 1800~5400 r/min, which corresponds to an excitation frequency range of 30~90 Hz. Based on the modal analysis, it was observed that the first two natural frequencies of the rack fell within this excitation frequency range, indicating a need for optimization. Consequently, the thickness of the square tube steel in the frame was increased from the original 6 mm to 8 mm, and beam and column structures were added, and another modal analysis was conducted. The results showed that the natural frequencies of the first two modes were 98.21 Hz and 100.24 Hz, respectively, and the maximum displacement when resonance occurs was significantly reduced, which were outside the excitation frequency range. This improvement measure effectively resolves the resonance problem. The information related to the first two mode shapes, the first six frequencies and the maximum displacement are shown in Figure 5 and Figure 6.

4. Key Steps in Discrete Element Simulation and Results

4.1. Construction of the Alfalfa Stalk Model

In this study, alfalfa stalks were used as the object of crushing. Considering the variations in physical and chemical indicators of alfalfa stems across different varieties and harvesting periods, this study aims to analyze the key parameters of the studied alfalfa stems through consolidating existing data. Specifically, the focus is on understanding the breakage patterns of alfalfa stems. Alfalfa is a perennial leguminous grass that typically grows to a height of 30 to 100 cm during the mowing period. To simplify the model, a length of 75 cm was used to construct the stem model. The specific simulation parameters are shown in Table 1.

To consider both simulation efficiency and the authenticity of the rules reflected in the simulation results, we set the parameters for the stalk as follows: a cylinder shape with a particle radius of 5 mm and filled with 1346 small particles. The simulation model of the alfalfa stalk is depicted in Figure 7.

4.2. Construction of the Crushing Device Model

A geometric model of the forage grinder was constructed based on the actual size of the grinder (Figure 8). To simplify the model, the motor, frequency converter, and other parts were removed during modeling, as the cutter shaft speed can be directly set in the EDEM software. Furthermore, a conveyor belt structure was added to the software to facilitate material feeding during simulation. The relevant parameters were set in the discrete element software EDEM, as shown in Table 1.

In the pre-treatment phase, the basic physical parameters and contact parameters of the stalk and crusher were set. The dynamic parameters of the crushing device were determined based on the actual working requirements. A pellet factory was constructed above the feed inlet to generate stalks. Specifically, five stalks were generated at a rate of fifty per second. To ensure simulation efficiency and reliable results, the size of the generated particles was kept constant. The initial velocity of the particles was set to −1 m/s in the z-direction. The total duration of the simulation test was 2 s, with a fixed time step of 5.9669 × 10⁻⁶ s. Data were recorded every 0.01 s. The grid size was set to three times the minimum particle radius.

4.3. Discrete Element Analysis Results

4.3.1. The Influence of Crushing Structure and Rotation Speed on Stalk Crushing Effect

The simulation process (Figure 9) revealed that the stalk particles were randomly distributed at the bottom of the trommel screen. Additionally, some stalk adhesive blocks were broken upon impact with the knife, while others remained in the adhesive block state. Thus, the fracture of bonds could serve as an evaluation index for the effectiveness of stalk crushing.

In the EDEM post-processing module, a specific particle was randomly chosen, and the trajectories of other particles were concealed. The movement trajectory of the selected particle was then displayed (Figure 10). From the particle’s movement trajectory, it is evident that the device effectively accomplished the task of crushing and discharging stalks.

After the simulation was completed, the state of bond breaking was determined through post-processing. In this context, a value of one indicated that the bond remained intact, while a value of zero indicated that the bond was broken. The data regarding the number of bonds changing over time were exported and visualized through plotted curves.

Based on Figure 11, it is evident that the number of bonds decreased noticeably over time within the range of 0 s to 0.8 s. Upon observing the simulation process, it was observed that the stalk entered the feed inlet from the conveyor belt between 0 s and 0.4 s, subsequently entered the crushing chamber, and made contact with the crushing blade. This led to a rapid decrease in the bonds. After 1 s, the graph plateaued, although it did not reach zero.

When comparing the five crushing structures, it was observed that the bonds of the hob crushing structure, A4, and the roller crushing structure, A5, had decreased. However, the number of unbroken bonds was higher in these structures, leading to a poor crushing effect. Through simulation, it was discovered that the cutters in these two crushing structures were arranged horizontally, resulting in a large crushing blind area and limited contact between the stalks and the cutters. Overall, the hammer-type crushing structure, A1, with blades exhibited the most effective crushing.

Based on preliminary research, it was discovered that alfalfa stalks can be effectively crushed within 2 s. Therefore, during the simulation post-processing, data pertinent to the initial 2 s duration were extracted. Figure 12 illustrates the average speed of particles at a rotation speed of 3600 r/min for five different crushing structures. The average velocity of particles under the influence of A1, A2, and A3 gradually increased from 0 s to 1 s and then reached a stable state. This observation aligns with the gradual breaking of bonds over time, as seen in Figure 7. However, for the two crushing structures of A5 and A6, the average particle speed continued to increase between 0 s and 2 s. In conclusion, the changing pattern of average velocity for stalk particles was not necessarily consistent with the changing pattern of bond breakage, depending on the specific crushing structure.

4.3.2. Orthogonal Experimental Design and Range Analysis

The single-factor experimental method focuses on exploring the changing rules of evaluation indicators under a specific influencing factor. Determining the significance of a particular influencing factor and finding the optimal parameter combination can be challenging. In this study, tool speed and tool type were chosen as the influencing factors, and the percentage of broken bonds was used as the evaluation index. An orthogonal experiment with two factors and five levels was designed. The results of the orthogonal test were analyzed using range analysis to identify the main and secondary factors, as well as the optimal parameter combination. The factor level table of the orthogonal test is shown in

Table 3. The factor level table of the orthogonal test.

No.	Rotating Speed/r·min−1	Crushed Structure
1	2400	Hammer-crushing structure with a blade
2	3000	Hammer-crushing structure without blade
3	3600	Hammer rod-type crushing device
4	4200	Hob crushing structure
5	4800	Roller crushing structure

.

This study established an orthogonal table using the proportion of broken bonds to the total number of bonds (percentage of bonds) as the evaluation index. The smaller the number of bonds, the better the crushing effect. The two-factor five-level orthogonal table is shown in

Table 4. Orthogonal table.

No.	Rotating Speed/r·min−1	Crushed Structure	Percentage of Bonding Bonds
1	2400	Hammer-crushing structure with a blade	Y1
2	2400	Hammer-crushing structure without blade	Y2
3	2400	Hammer rod-type crushing device	Y3
4	2400	Hob crushing structure	Y4
5	2400	Roller crushing structure	Y5
6	3000	Hammer-crushing structure with a blade	Y6
7	3000	Hammer-crushing structure without blade	Y7
8	3000	Hammer rod-type crushing device	Y8
9	3000	Hob crushing structure	Y9
10	3000	Roller crushing structure	Y10
11	3600	Hammer-crushing structure with a blade	Y11
12	3600	Hammer-crushing structure without blade	Y12
13	3600	Hammer rod-type crushing device	Y13
14	3600	Hob crushing structure	Y14
15	3600	Roller crushing structure	Y15
16	4200	Hammer-crushing structure with a blade	Y16
17	4200	Hammer-crushing structure without blade	Y17
18	4200	Hammer rod-type crushing device	Y18
19	4200	Hob crushing structure	Y19
20	4200	Roller crushing structure	Y20
21	4800	Hammer-crushing structure with a blade	Y21
22	4800	Hammer-crushing structure without blade	Y22
23	4800	Hammer rod-type crushing device	Y23
24	4800	Hob crushing structure	Y24
25	4800	Roller crushing structure	Y25

.

After EDEM software performed simulation analysis according to the above test arrangement, the test results were obtained, which were: Y1 = 0.2044, Y2 = 0.1477, Y3 = 0.1418, Y4 = 0.4418, Y5 = 0.6203, Y6 = 0.0502, Y7 = 0.1277, Y8 = 0.3017, Y9 = 0.6210, Y10 = 0.7617, Y11 = 0.0539, Y12 = 0.2046, Y13 = 0.2959, Y14 = 0.6129, Y15 = 0.6685, Y16 = 0.0133, Y17 = 0.1698, Y18 = 0.2885, Y19 = 0.7943, Y20 = 0.6863, Y21 = 0.1289, Y22 = 0.2256, Y23 = 0.4551, Y24 = 0.6962, Y25 = 0.6513.

The orthogonal test results were analyzed using range analysis. First, analyze the influence of each speed on the crushing effect. Using v1, v2, v3, v4, and v5 to represent the rotational speeds of 2400 r/min, 3000 r/min, 3600 r/min, 4200 r/min, and 4800 r/min, respectively, we could obtain the sum M of the evaluation indicators for the five crushing structures at each speed, see Formulas (3)–(7) for details.

M_v1 =Y1 + Y2 + Y3 + Y4 + Y5 = 1.556

(3)

M_v2 = Y6 + Y7 + Y8 + Y9 + Y10 = 1.8623

(4)

M_v3 = Y11 + Y12 + Y13 + Y14 + Y15 = 1.8358

(5)

M_v4 = Y16 + Y17 + Y18 + Y19 + Y20 = 1.9492

(6)

M_v5 = Y21 + Y22 + Y23 + Y24 + Y25 = 2.1571

(7)

According to the sum of the five levels of this factor, the average value m could be obtained. For details, see Equations (8)–(12).

m_v1 = (Y1 + Y2 + Y3 + Y4 + Y5)/5 = 0.3112

(8)

m_v2 = (Y6 + Y7 + Y8 + Y9 + Y10)/5 = 0.37246

(9)

m_v3 = (Y11 + Y12 + Y13 + Y14 + Y15)/5 = 0.36716

(10)

m_v4 = (Y16 + Y17 + Y18 + Y19 + Y20)/5 = 0.38084

(11)

m_v5 = (Y21 + Y22 + Y23 + Y24 + Y25)/5 = 0.43142

(12)

Based on the data analysis, it could be observed that the crushing effect was ranked in the following order: m_v5 > m_v4 > m_v2 > m_v3 > m_v1. This indicated that level 1 provided the best results while level 5 yielded the poorest results. Specifically, the rotation speed of 2400 r/min resulted in a more effective crushing effect.

In addition, the average values of the five levels of effects of the crushing structure were calculated. Specifically, the average values for mD1, mD2, mD3, mD4, and mD5 were found to be 0.09014, 0.17508, 0.2966, 0.63324, and 0.67762, respectively. These results indicate that the hammer-type crushing structure with blades exhibited a superior crushing effect.

Further, the average range of the rotational speed factor and the crushing structure factor were found, which were:

R_v = m_v5 − m_v1 = 0.43142 − 0.3112 = 0.12022

(13)

R_D = m_D5 − m_D1 = 0.67762 − 0.09014 = 0.58748

(14)

The range of the two demonstrated that changes in the crushing structure had a more pronounced impact on the crushing effect of alfalfa stalks. Based on the aforementioned test results, it can be concluded that the hammer-type crushing structure, A1, with blades exhibited the most effective crushing effect at 2400 r/min.

5. Discussion

At present, scholars have conducted research and achieved many results on the material crushing device. Niu et al. [17] designed a corn straw crushing and scattering device, and through simulation tests and physical tests, they determined that when the crushing knife shaft speed is 700 r/min, the device has better working performance and the corn straw crushing qualification rate is 93.65%. Wang et al. [18] studied the cutting and crushing mechanism of cotton straw based on ANSYS/LS-DYNA 13.0. The results showed that when the rotation speed was 1800 r/min, the crushing pass rate was 84.6% and the removal rate was 95.1%. Zhang et al. [19] studied the crushing performance of the square bale straw crusher and analyzed the effect of feeding speed and spindle speed on the crushing effect. Among these existing studies, longitudinal studies were mainly conducted on a specific device, while direct horizontal comparative studies of different structures were rare.

The crushing device used as a test platform often has a high-speed range and requires certain requirements for the frame. In order to avoid resonance problems, the natural frequency of the frame is often required to be higher than the excitation frequency. Previous research has highlighted the significance of crushing work for the subsequent production of high-quality feed. However, there is a lack of comparative experiments and analysis on the crushing effects of typical crushing structures. In comparison to other research methods, the use of discrete element analysis as a related technology is well-established. Through utilizing EDEM software, this study was able to observe the dynamics of stalk particles during the crushing process. The findings revealed that for certain crushing structures, the average speed of the stalk particles no longer significantly increases when the rotational speed exceeds a certain value. This could be attributed to the fact that when the crushing tool rotates too fast, the stalks maintain a relatively constant speed due to inertia. Consequently, some cutters are unable to effectively contact the stems that have not experienced significant positional changes, resulting in a plateau in the average speed. However, to consider simulation efficiency, this study utilized a smaller number of stalks and focused more on exploring the changes in the crushing effect over time. Therefore, the specific values obtained may differ from those observed during actual crushing operations. In the future, as computer technology and software performance continue to advance, it will be possible to construct a model that closely resembles the actual scenario in terms of quantity and stem appearance, leading to more accurate results. At the same time, for materials similar to alfalfa stalks, more detailed parameters can be further explored based on the results of this study, such as the angle of the blade, the diameter of the cutter head, etc., to promote further optimization of the stalk crushing device.

6. Conclusions

This study mainly optimized the rack based on modal analysis and investigated the impact of five different crushing structures on alfalfa stalks at various rotation speeds using the discrete element method. The test platform used for the crushing device often operates at a high-speed range and has specific requirements for the frame. To prevent resonance issues, it is necessary for the natural frequency of the frame to be higher than the excitation frequency. This problem can be effectively addressed by increasing the thickness of the frame and adding support rods. The discrete element analysis results revealed that each crushing structure had varying effects on alfalfa stalks depending on the rotational speed. The crushing effects of all five types of cutters improved with increasing rotational speed, with the hob-type crushing structure performing the best among them. The optimal crushing effect was observed at a rotational speed of 4200 r/min, but there was no significant improvement in the crushing effect when the speed reached 5400 r/min. Furthermore, an increase in rotational speed for the hammer cutter head resulted in a slight decrease in crushing effect, possibly due to the small amount of stalks fed. The trends observed for the hob-type grinding structure and round roller grinding structure were similar, with the best grinding effect observed at 2400 r/min. However, beyond a certain speed, the grinding effect declined.