Study on Flat Die Wear Characteristics in Flat Die Pelletizing with Different Material Ratios Based on DEM-FEM

Abstract

Wear can occur in flat die pelletizers, often reducing service life. This study explores the issue of die hole wear in the pelletizing process of a standard Total Mixed Ration (TMR) feed. The selected TMR formulation comprises varying proportions of corn, alfalfa hay, and quinoa. A coupled DEM-FEM analysis was used to examine stress–strain conditions in various die hole regions at different material ratios, predict the fatigue life of flat die materials in the pelletizing process, and validate the accuracy of investigating flat die wear through friction wear tests. It was found that the entrance of the die hole experiences the most severe conditions in terms of equivalent stress and elastic strain. The fatigue life is shortest at the entrance, with a maximum equivalent stress of 42.8 MPa, a maximum equivalent elastic strain of 2.5 × 10⁻³, and a minimum fatigue life stress cycle of 5.0 × 10⁵. In contrast, the equivalent stress and equivalent elastic strain at the middle and upper parts of the die hole are minimal, with an equivalent stress of 4.8 MPa and a minimum equivalent elastic strain of 2.8 × 10⁻⁴. Material wear tests revealed that the most severe wear on the flat die specimen occurred when the ratio of corn, alfalfa hay, and quinoa straw was 7:2:1, consistent with the findings from the DEM-FEM coupling method. The pelleting process, arising from the contact between the material and metal, encompasses adhesive wear, abrasive wear, and fatigue wear.

1. Introduction

The flat die pelletizer is widely used in pellet feed processing and molding, capable of processing raw materials into pellets based on various formulas to meet the nutritional needs of different animals [1,2]. For instance, the Total Mixed Ration (TMR) pellet feed formulation [3] is employed to cater to the nutritional requirements of herbivores, while pelleting with formulas like fish meal [4] is ideal for meeting the dietary needs of aquaculture animals. Additionally, pelleting with maize and other feed formulations [5] effectively fulfills the nutritional needs of swine animals. Being a critical component of the flat die pelletizer, the flat die undergoes pressure and friction from the pressure roller. Prolonged exposure to the pressure and friction generated by the pellet feed during the pelletizing process results in significant wear of the flat die. This wear shortens the flat die’s lifespan and diminishes the quality of the molded pellet feed [6,7].

Numerous scholars have conducted extensive research on flat die pelletizers to enhance the quality of pellet feed. Studies have revealed that the structural parameters of the flat die play a crucial role in influencing the pelletizing effectiveness. Celik et al. [8] proposed that a higher compression ratio (C.R.), defined as the ratio of the effective length of the flat die hole to the internal diameter, leads to denser pelletized feed. They determined the optimal compression ratio (C.R.) parameters through finite element response surface analysis. Tian et al. [9] conducted force analysis on a flat die pelletizer, developed a mathematical model for single die hole forces, and utilized Workbench software (19.0) to perform finite element simulation and analysis of the material compression process in pelleting. Subsequently, they optimized the parameters of the die holes, such as the cone angle and length-to-diameter ratio, to investigate their impact on pellet feed density. Li et al. [10] investigated the fatigue damage to ring dies in the pelletizing process by analyzing the location and size of the damage through fluid–solid coupling. De et al. [11] examined the fractal characteristics of the surface morphology of the ring die concave die and its contact surface analysis function, utilizing Matlab’s W-M function method and Ansys for wear analysis. To evaluate the abrasion resistance of die hole, Ren et al. [12] employed licorice as the abrasion material and conducted abrasion tests on standard flat die materials 20Cr, 20CrMnTi, and 4Cr13 using the CFT-I type surface tester. Their findings indicated that 20CrMnTi exhibited superior abrasion resistance. Wu et al. [13] explored the wear mechanisms of alfalfa grass powder on 45# steel and HT200 gray cast iron utilizing the orthogonal test method. They determined that the primary wear mechanisms on 45# steel involved micro-cutting and multiple plastic deformations for hard and soft abrasives under similar conditions. Chen et al. [14] conducted a friction wear test using a straw briquette to examine the wear pattern on the inner wall of the ring die in the extrusion direction. They analyzed the impact of various molding factors on the coefficient of friction, revealing that the wear depth on the ring die module gradually decreases along the extrusion direction. The inlet portion exhibited deep indentations, while the wear in the tail portion was milder, primarily manifesting as spalling pits.

Many of the research methods discussed above rely on the finite element method for analysis, necessitating the establishment of a robust mathematical model to ensure the accuracy of the results. Reviewing previous research approaches, it was noted that in the investigation of die hole wear, certain scholars [8,9] constructed a mathematical model based on the die hole wear process and applied a uniform load to the model. However, this approach overlooks the nonlinear characteristics of the material extrusion pressure in the pelleting process, leading to significant discrepancies between the simulation results and the actual scenario. Some scholars [10] have approached the study of granulation process die wear by considering the material as a fluid and employing the fluid–solid coupling method. However, the granulation material for the granular body exhibits irregular geometric morphology. The surrounding fluid medium structures, together with the material, form a complex particle system with multiscale and multimodal complex mechanical properties. Solely relying on the fluid–solid coupling method may overlook the pressure between particles during mutual squeezing, thus impacting the accuracy of the analysis results. Some researchers [12,13,14] have investigated the friction and wear mechanisms of various dies by creating samples of die hole materials, conducting friction and wear experiments, and utilizing scanning electron microscopes and digital image processing techniques. However, directly observing the internal wear of the die is challenging, thus providing only a partial depiction of the overall internal wear within the die hole.

The Discrete Element Method (DEM) is extensively employed in the realm of particulate material formation to facilitate the numerical simulation of granular materials’ mechanical properties [15]. Given that the pelletizing material is granular and forms a discontinuous medium, DEM is tailored to simulate issues related to such discontinuous media by offering load data at various locations within the die orifice at distinct stages of the forming process. The finite element method (FEM) involves dividing the object under study into finite small elements, connecting them through nodes, and solving equilibrium equations to determine stress and strain information. The FEM is commonly employed for simulating the mechanical response of continuous media to external loads, although it necessitates the development of intricate mathematical models or the application of uniformly distributed loads during loading [16]. Utilizing DEM-FEM coupled simulation enables the direct transfer of DEM analysis results to FEM software for material wear analysis. This approach integrates microscopic particle interactions with the macroscopic mechanical behavior of structural components, resulting in more precise research outcomes. There are two primary types of DEM-FEM coupling: unidirectional coupling, where DEM analysis outputs are utilized as input loads for FEM static structural analysis, and bidirectional coupling, where both DEM and FEM results are mutually exchanged for real-time bidirectional information exchange [17].

TMR pellet feed is produced by blending various types of granular materials based on animals’ nutritional needs. Variations in material ratios result in different contact modes among the granular materials during pelleting, leading to distinct force characteristics. This, in turn, causes varying degrees and types of wear in different sections of the internal die hole.

This study focuses on the friction and wear of flat die holes during the pelletizing process of a common TMR feed formulation in Gansu, China, involving corn, alfalfa hay, and quinoa straw. It employs coupled DEM-FEM analysis of granular materials to examine how the mixture particles affect the flat die molds and internal contact surfaces, as well as to assess the fatigue life of the flat die materials. The investigation explores the impact of varying material ratios on the flat die pelletizing process. Lastly, we conduct a wear test of the mixed material on the flat die material to validate the precision of the DEM-FEM approach in investigating the wear issue of the flat die during the granulation process of the mixed material. This will offer a novel method for examining the wear of mixed material particles on the metal die.

2. Structure and Theoretical Analysis of Flat Die Pelletizer

2.1. Structure of Flat Die Pelletizer

The flat die pelletizer comprises components such as a feeder, modulator, transmission mechanism, flat die, pressure roller, sweeping disk, motor, universal joints cutter, etc., as illustrated in Figure 1. As the material enters the flat die granulator, it relies on the centrifugal force produced by the flat die’s rotation to cause the material particles to adhere to the inner wall of the flat die. The rotating paddle knife then mixes the granular material on the die’s inner wall to ensure uniformity before feeding it into the pressing area formed by the flat die and the pressure roller. As the pressure roller and flat die extrude the material, the particles are compressed and deformed. This compression enhances the contact area between the particles, allowing those with a specific density and bonding force to be compacted into the die hole for shaping. Subsequently, the continuously extruded particles reach the outer end, where they are cut to a specific length by the cutter below. The shaped particles are ultimately discharged from the machine [18,19]. This process highlights the primary wear areas as the surface of the flat die and the interior of the die hole.

2.2. Theoretical Analysis of the Pelletizing Process

The pelletizer is categorized into three distinct zones based on the material states during the pelletizing process: the feeding zone situated between the flat die and the pressure rollers, the deformation compression zone, and the extrusion molding zone. The extrusion molding of the material particles is primarily segmented into the loose stage, excessive stage, and pressure stage [20]. The molding process is illustrated in Figure 2. In the loose stage, the material particles are in a discrete state with large gaps between them, and the particles have not yet bonded to form larger particles. The particles mainly experience the squeezing force from the pressure roller between the particles and the flat die, as illustrated in region A of Figure 2. During the excessive stage, the space between the material particles becomes very narrow, leading to particle deformation while maintaining unchanged structure and physical properties. This stage is characterized by elastic deformation, as depicted in region B of Figure 2. The subsequent extrusion results in molecular structure changes between the particles, leading to sliding, shearing, and stretching phenomena. This stage marks the onset of primary plastic deformation between the particles, with increased radial pressure, modular friction wear, and evident power consumption. As the material particles undergo plastic deformation, their physical properties, density, and hardness increase. When the material particles are on the verge of being extruded from the die hole, signifying the completion of plastic deformation between the particles, the pressure beneath the lower part of the die hole is suddenly released. This release causes the expansion of the molded material particles, as depicted in region C.

The internal bonding mechanism of the particles is intricately linked to the types and modes of adhesive forces present within them, with material composition and microscopic structure playing pivotal roles in determining these differences. Hence, our study centered on the pelletizing process of a standard feed formulation for cattle and sheep in northwest China. This formulation includes corn, alfalfa hay, and quinoa stalks. To account for the discrete nature of the materials, we conducted simulation research utilizing the DEM grounded in Newtonian mechanics [21]. In the pelletizing process of mixed materials, the Hysteretic Spring model within the DEM method integrates plastic deformation into particle contacts, mirroring the contact, deformation, and force conditions of particle formation in mixed materials. When the contact deformation between particle bodies fails to reach a specified threshold, the particles undergo elastic deformation. Once this threshold is surpassed, irreversible plastic deformation takes place [22,23,24]. This model mainly utilizes the Walton–Braun theory to calculate normal forces [25]. The concept of force overlap quantity within the model is depicted in Figure 3, where the normal force F_n is determined by Equation (1) [25].

$${\mathrm{F}}_{\mathrm{n}}=\left\{\begin{array}{ccc}{\mathrm{K}}_1{\mathsf{\delta }}_{\mathrm{n}}\hfill & \mathrm{Loading}& \hfill {\mathsf{\delta }}_{\mathrm{n}}<{\mathrm{K}}_2\left({\mathsf{\delta }}_{\mathrm{n}}-{\mathsf{\delta }}_0\right)\\ {\mathrm{K}}_2\left({\mathsf{\delta }}_{\mathrm{n}} {-\mathsf{\delta }}_0\right)\hfill & \mathrm{Unload}/\mathrm{reload}& \hfill {\mathsf{\delta }}_{\mathrm{n}}>{\mathsf{\delta }}_0\\ 0\hfill & \mathrm{Unload}& \hfill {\mathsf{\delta }}_{\mathrm{n}}\le {\mathsf{\delta }}_0\end{array}\right.$$

(1)

where K₁ is the loading stiffness; K₂ is the unloading stiffness; ${\mathsf{\delta }}_{\mathrm{n}}$ is the average overlap, and ${\mathsf{\delta }}_0$ is the residual overlap. The relationship between K₁ in Equation (1) and the yield strengths of the materials R_eL1 and R_eL2 is as follows:

$${\mathrm{K}}_1=5\mathrm{R}*\times \min \left({\mathrm{R}}_{\mathrm{eL}1}{,\mathrm{R}}_{\mathrm{eL}2}\right)$$

(2)

where R* is the equivalent radius of the two powder contact models. The coefficient of restitution e is given by Equation (3) as:

$$\mathrm{e}=\sqrt{\frac{{\mathrm{K}}_1}{{\mathrm{K}}_2}}$$

(3)

Residual overlap ${\mathsf{\delta }}_0$ is updated at each time step according to the rule

$${\mathsf{\delta }}_0=\left\{\begin{array}{ccc}{\mathsf{\delta }}_{\mathrm{n}}\left(1-\frac{{\mathrm{K}}_1}{{\mathrm{K}}_2}\right)\hfill & \mathrm{Loading}& \hfill ({\mathrm{K}}_1{\mathsf{\delta }}_{\mathrm{n}}<{\mathrm{K}}_2({\mathsf{\delta }}_{\mathrm{n}}-{\mathsf{\delta }}_0\left)\right)\\ {\mathsf{\delta }}_0\hfill & \mathrm{Unload}/\mathrm{reload}& \hfill ({\mathsf{\delta }}_{\mathrm{n}}>{\mathsf{\delta }}_0)\\ {\mathsf{\delta }}_{\mathrm{n}}\hfill & \mathrm{Unload}& \hfill ({\mathsf{\delta }}_{\mathrm{n}}\le {\mathsf{\delta }}_0)\end{array}\right.$$

(4)

The average damping coefficient is determined by Equation (5) [26],

$${\mathrm{F}}_{\mathrm{n}}^{\mathrm{d}}{=-\mathrm{b}}_{\mathrm{n}}\sqrt{\frac{{4\mathrm{m}}^{*}\times \mathrm{K}}{1+{\left(\frac{\mathsf{\pi }}{\mathrm{lne}}\right)}^2}}{\mathrm{V}}_{\mathrm{n}}^{\mathrm{rel}}$$

(5)

where ${\mathrm{F}}_{\mathrm{n}}^{\mathrm{d}}$ is the average damping; bn is the average damping coefficient; m* is the equivalent mass; K is K₁ or K₂; and ${\mathrm{V}}_{\mathrm{n}}^{\mathrm{rel}}$ is the average relative velocity component during particle collision.

Taking into account the die hole surface deformation and the wear effects in flat die pelletizing, the contact model between the particles and the flat die is modeled using the Hertz–Mindlin with Archard Wear model [27].

3. Numerical Model of EDEM for Pelletizing Process

Three types of powders, corn, alfalfa hay, and quinoa straw, were used as raw materials for pelletizing. The Poisson’s ratio and shear modulus of corn powder were obtained from the literature [28]. The Poisson’s ratio of alfalfa hay and quinoa straw was determined using a Stable Micro Systems texture instrument for mechanical characterization. Pressure was applied along the longitudinal direction of the samples until they were no longer deformed. A testing machine measured the longitudinal deformation, while the transversal deformation was obtained using digital vernier calipers [29]. The mean value was calculated by repeating the process several times. The measured Poisson’s ratio is represented by Equation (6):

$$\mathsf{\epsilon }=\frac{\left|{\mathrm{e}}^{\prime }\right|}{\left|\mathrm{e}\right|}=\frac{{\mathrm{w}}_1-{\mathrm{w}}_2}{{\mathrm{L}}_1-{\mathrm{L}}_2}$$

(6)

where $\mathsf{\epsilon }$ is Poisson’s ratio, ${\mathrm{e}}^{\prime }$ is the longitudinal deformation (mm), $\mathrm{e}$ is the transverse deformation (mm), ${\mathrm{w}}_1$ is the initial longitudinal length (mm), ${\mathrm{w}}_2$ is the deformed longitudinal length (mm), L₁ is the initial transverse length (mm), and L₂ is the deformed transverse length (mm).

The shear modulus of alfalfa hay and quinoa straw was tested in tension using a CMT5305 microcomputer-controlled universal testing machine (Shenzhen, China, SANS Company), and the average value was obtained by repeated measurements. The modulus of elasticity was also measured. Additionally, the shear modulus is represented by Equation (7):

$$\mathrm{G}=\frac{\mathrm{E}}{2\left(1+\mathsf{\epsilon }\right)}$$

(7)

where G is the shear modulus (Pa) and E is the elastic modulus (Pa).

The samples of alfalfa hay and quinoa straw were weighed using an electronic balance with an accuracy of 0.001 g. The volume of the samples was measured using the specific gravity bottle test method and repeated three times to obtain the average value [30]. The process of determining the intrinsic parameters of alfalfa hay and quinoa straw is illustrated in Figure 4 and Figure 5, and the material parameters of the three particles are presented in

Table 1. Setting of material parameters.

Simulation Material	Poisson’s Ratio	Density (kg/m3)	Shear Modulus (Pa)
Corn Powder	0.4	1.197 × 103	1.37 × 108
Alfalfa Hay Powder	0.3	1.5 × 102	5.5 × 107
Quinoa Powder	0.4	5.3 × 102	2.89 × 107
Flat Die	0.25	7.8 × 103	6.73 × 1010

.

In this study, unidirectional coupling was conducted using the DEM-FEM method. The numerical simulation of the granulation process was initially carried out using EDEM software, and then the data from the numerical simulation were imported into Ansys Workbench. The specific workflow is illustrated in Figure 6.

The simulation model created in SolidWorks was imported into EDEM software (2018.2.0 version). Material parameters were defined for the model, and a virtual surface particle factory was established above the die hole. The particle generation location was set to random mode, with fixed particle sizes for three different types of particles dynamically generated. The simulation time step was set at 30%, and the total simulation time was set to 2 s, as depicted in Figure 7. The contact parameters are detailed in

Table 2. Contact parameter setting.

Contact Type	Coefficient of Restitution	Coefficient of Static Friction	Coefficient of Rolling Friction
Powder-Powder	0.2	0.45	0.05
Powder-Flat Die	0.34	0.54	0.03

[31].

The material forming states within the die hole were simulated at different stages, as illustrated in Figure 8. Initially, in the numerical simulation, mixed material particles accumulated above the die hole of the flat die, with some loose material entering the die hole, creating a zone ready for compaction. As the simulation progressed to the mid-stage, the rotation of the pressure roller and the increased influx of the mixed material particles into the compression zone gradually forced the material into the die hole. The pressure exerted by the die walls caused some particles to adhere to the pressure roller and the flat die, hindering the entry of external material into the die hole and leading to increased energy consumption. During the final stage of the numerical simulation, the material that has entered the die hole is compressed and extruded from the end of the die hole.

Based on the crushing of the mixture before pelletizing, particle sizes of 0.32 mm, 0.2 mm, and 0.26 mm were assigned to represent the crushed corn, alfalfa hay, and quinoa stover powder, respectively. The roller speed was set to 400 r/min according to actual pelletizing conditions. To investigate the wear of the die hole with different strip ratios, proportions were established based on the commonly used feeding ratios of the materials, as depicted in

Table 3. Setting the ratio of simulated material particles.

Proportional Serial Number	Corn Powder (g)	Alfalfa Hay Powder (g)	Quinoa Powder (g)
1	100	20	80
2	120	30	50
3	140	40	20

. The particle compressive force–time curves and flat die compressive force–time curves were calculated and obtained for the mixing ratios of the three materials, as illustrated in Figure 9a–c, respectively.

Figure 9 illustrates that the compressive force between particles of the three different ratios is higher than the compressive force between the particles and the die hole. With an increase in the proportion of corn and alfalfa hay, the compressive force between the particles and the die hole notably rises, signifying that corn and alfalfa hay have a more significant impact on the wear of the flat die. In contrast, quinoa stalks have a lesser effect on flat die wear. The maximum compressive force values and peak times for the particles and die hole obtained from the simulation are presented in

Table 4. Pellet pressure and flat mold pressure data at different ratios.

Particle Compressive Force				Flat Die Compressive Force
Considerations	Proportional Serial Number			Considerations	Proportional Serial Number
	1	2	3		1	2	3
Maximum Compressive Force (N)	569.8	658.2	765.1	Maximum Compressive Force (N)	305.3	399.6	434.1
Peak Time (s)	1.09	1.27	1.03	Peak Time (s)	1.09	1.27	1.03

. The peak times of maximum compressive force for the three ratios are 1.09 s, 1.27 s, and 1.03 s, respectively. When the ratio of corn, alfalfa hay, and quinoa stalks is 7:2:1 (Proportional serial number 3), the maximum compressive force between the particles is 765.1 N, and the maximum compressive force between the particles and the die holes is 434.1 N.

4. Coupled DEM-FEM Analysis of Die Hole Forces in the Pelletizing Process

4.1. Die Hole Force Analysis

The pelletizing process was simulated under three different ratios, and the compressive force applied to the flat die hole at 1.03 s for ratio number 3 was exported as Ansys Workbench Data. In Ansys, a Geometry project was set up, and the flat die model in igs format was imported. An EDEM project was then created, and the Ansys Workbench Data were imported into the Results section of the Ansys coupling plugin. Subsequently, a static structural project was established. The material 20CrMnTi was defined in the Engineering Data section with the following properties: density of 7800 kg/m³, Poisson’s ratio of 0.25, elastic modulus of 1680 MPa, tensile strength of 1080 MPa, and yield strength of 835 MPa. The setup was linked as shown in Figure 10 [32].

The contact between the roller and the flat die was configured as frictional contact with a rotational friction coefficient of 0.2. The roller speed was set at 400 rpm, and the bottom surface of the flat die was fixed. In the Model section, the mesh was generated for the model, and loads were applied to the region corresponding to the die hole. Equivalent stress, equivalent elastic strain, and lifespan parameters were included in the solution scheme. The calculations produced the equivalent stress map and equivalent elastic strain map of the die hole, displayed in Figure 11 and Figure 12.

During the extrusion molding of mixed materials, as materials enter outside the die hole continuously and the contact distance between the material particles decreases, the particles among the fibers start to exhibit behaviors such as mutual bridging and interspersing. This leads to the generation of extrusion and friction forces between the materials, causing variations in the forces at different locations on the die hole [33]. In Figure 11 and Figure 12, it is observed that different parts within the flat die hole experience varying forces. The area near the entrance of the die hole (Figure 11 A area) exhibits the most significant force, with a maximum equivalent stress of 42.8 MPa and a maximum equivalent elastic strain of 2.4 × 10⁻³. This is primarily due to the energy required for the transition of the material from a loose state to a molded state. As the material forms particle prototypes, its surface roughness increases, leading to substantial friction within the flat die hole. Moreover, this area is exposed to friction from the pressure roller, further contributing to the high forces experienced in this region. As the material progresses downwards through the B area in Figure 11, the die hole experiences the minimum stress and strain within the entire die hole. The minimum equivalent stress in this region is 4.8 MPa, with a minimum equivalent elastic strain of 2.8 × 10⁻⁴. This is attributed to the fact that the material is being extruded into cylindrical particles in this region, resulting in lower stress and strain than in other areas of the die hole. The softening of material particles leads to heat generation within the die hole. As the material moves from area A to area B, the surface roughness of the particles decreases due to friction, resulting in smoother particle surfaces in area B. When the material is pushed into the C region, the equivalent stress strain on the die hole increases compared to the B region. In this region, the material undergoes continued extrusion, leading to a reduction in the contact distance between the material particles and an increase in the material hardness. This rise in hardness causes an increase in the force exerted by the particles on the surface of the die hole. As the material is extruded to the exit of the die hole (area D in Figure 10 and Figure 11), the equivalent strain on the die hole further increases but remains lower than that in area A. This is because area D is located at the exit of the die hole. When the particles reach this area, there is a noticeable decrease in the external force acting on the particles. The volume undergoes a slight expansion, leading to a stress concentration at the die hole’s edge.

4.2. Die Hole Fatigue Analysis

During the pellet molding process, the die hole is subjected to continuous extrusion by the material and pressure roller, making it vulnerable to cyclic fatigue, bending stress, and contact stress. The material is constantly extruded into the die hole, which can result in fatigue damage to the die hole after multiple cycles of superimposition, representing a form of high peripheral fatigue (stress fatigue) [34]. By utilizing predictive models for fatigue life and conducting thorough damage accumulation analysis of the die hole, engineers can establish the life expectancy and safety thresholds of the die hole in pelletizing operations. This approach enables engineers to design more resilient products and structures, enhance their reliability and safety, and provide guidance on implementing routine maintenance and inspections of molds. Ultimately, these practices contribute to prolonging the service life of materials and structures, reducing maintenance costs, and mitigating the risk of accidents. Stress fatigue analysis [35] can be conducted by developing the S-N curve of the material under consideration. In this study, the theoretical S-N curve is initially established in Ansys nCode DesignLife based on the flat die material (20CrMnTi), and then adjusted according to the material’s tensile limit to derive the accurate S-N curve, as illustrated in Figure 13 [36]. This corrected S-N curve represents the fatigue characteristics of the die hole material. Subsequently, the outcomes obtained from the static structural module are imported into the nCode SN Constant module to generate the fatigue life map and fatigue damage map of the die hole, depicted in Figure 14 and Figure 15.

Figure 14 and Figure 15 indicate that areas with significant fatigue damage include the entrance (region A) and exit (region D) of the die hole. This is attributed to the higher stress levels experienced in these regions, with a minimum fatigue life of 5.0 × 10⁵ cycles and cumulative fatigue damage of 1.9 × 10⁻⁶ at the entrance, and a minimum fatigue life of 5.4 × 10⁵ cycles and cumulative fatigue damage of 1.7 × 10⁻⁷ at the exit of the die hole. This is primarily due to the abrupt change in the cross-sectional shape of the die hole at the entrance and exit, leading to stress concentration. The middle region of the die hole (region B to C) has a minimum fatigue life of 6.6 × 10⁹ cycles and a cumulative fatigue damage of 1.0 × 10⁻¹⁰. To enhance the lifespan of the die hole, modifications can be made to the shape of the die hole inlet and outlet, or a higher abrasion-resistant material can be utilized at the two ends of the die hole to improve service life.

5. Wear Verification Test

5.1. Preparation of Wear Sample

To validate the accuracy of the coupled DEM-FEM method for analyzing the friction issue of the flat die, a wear specimen test is being conducted. The test uses the same material as the three powders (corn, alfalfa hay, and quinoa straw) in the EDEM simulation, in the same proportions. The flat die material is composed of carburized steel 20CrMnTi. The flat die specimen is subjected to varying degrees of quenching and tempering, resulting in three rectangular pieces measuring 50 × 25 × 5 mm each, as depicted in Figure 16. The chemical compositions of these specimens are outlined in

Table 5. Specimen chemical composition.

Specimen Material	C	Si	Mn	Cr	Ti
20CrMnTi	0.17–0.23	0.17–0.37	0.8–1.10	1.00–1.30	0.04–0.10

.

5.2. Wear Quality Testing

The MLS-225 rubber wheel type three-body abrasive wear tester was utilized at room temperature for the wear specimen test, as illustrated in Figure 17. The test employed the rotational friction method. The gap between the specimen and the rubber wheel was set at 0.1 mm by adjusting the rolling distance. A load of 225 N was applied using a weight. As the mixed material entered the gap from the rubber wheel, the load started to have an effect. The adjustment of the rolling distance ensured that the gap between the specimen and the rubber wheel remained constant throughout the test. Consistent with the EDEM simulation conditions, the speed of the rubber wheel was set at 400 r/min, and the mixture proportions were varied. The test was conducted in three groups, with each test lasting for 4 h.

The mass before and after wear was analyzed using a balance with an accuracy of 0.1 mg. The data before and after wear are shown in

Table 6. Wear test data.

Specimen Number	Mass before Wear (mg)	Mass after Wear (mg)	Mass Loss (mg)
A	48,564.2	47,351.7	1212.5
B	48,574.1	47,242.3	1331.8
C	48,562.5	47,064.8	1497.7

. The mass of wear specimen 1 decreased from 48,564.2 mg to 47,351.7 mg, a reduction of 1212.5 mg. The mass of wear specimen 2 decreased from 48,574.1 mg to 47,242.3 mg, a reduction of 1331.8 mg. The mass of wear specimen 3 decreased from 48,562.5 mg to 47,064.8 mg, a reduction of 1497.7 mg. The wear test clearly indicates that wear specimen 3 experienced the most significant wear.

5.3. Characterization and Analysis of Wear Patterns

After the wear test, the worn specimen was cleaned with alcohol and dried on the surface, as depicted in Figure 18a. Subsequently, a KathMatic KC-X1000 laser spectroscopy confocal microscope (Nanjin, China, Mumuxili Company) was utilized for analysis, as shown in Figure 18b. The microscope had a range of ±5000 μm, a spot size of 24 μm, and a maximum tilt angle of ±14°. The specimen was scanned using fine scanning with a sweep range of 1000 μm × 1000 μm, a scanning spacing of 1 μm, and a sampling frequency of 4500 Hz. The cross-sectional profiles of the three samples within a region of 480 μm radius centered on the coordinate point were analyzed using the built-in ANAL software (1.0) of the KathMatic KC-X1000 laser confocal microscope. The cross-sectional profiles are illustrated in Figure 19. The 3D characterization of the wear on the surface of the flat die specimens was conducted, and the 3D contours of the surface of the three groups of wear specimens and the wear morphology planes are presented in Figure 20.

According to the

Table 7. Specimen surface test data.

Specimen Number	Average Height (um)	Maximum Height (um)	Minimum Height (um)	Height Difference (um)	Arithmetic Mean Height (um)
A	1828.311	1890.210	1753.352	136.858	6.170
B	1834.382	1891.579	1783.464	108.115	6.232
C	1855.552	1959.070	1748.680	210.391	8.104

analysis, in terms of average height, the surface height of specimen C is greater than that of specimen A and specimen B. Furthermore, considering the height difference and arithmetic mean height, specimen C exhibits the greatest surface fluctuation and roughness. Therefore, it can be inferred that the surface wear condition of specimen C is more severe compared to specimen A and specimen B.

The 3D morphology of the surface of the three groups of specimens after abrasion is depicted in Figure 20a–c, respectively. The 3D shape profiles reveal that the abrasion specimens with three different material mixture ratios exhibit distinctive patterns of spaced protruding ridges and grooves on the specimen’s surface. The height of the specimen and the spacing between these ridges and grooves directly indicate the influence of the three material mixture ratios on the abrasion of the flat mold material. In Figure 20a, the number of ridges and gullies is small, and the difference in height between the peaks and valleys is minimal, indicating that specimen A’s surface is relatively smooth at this stage, with a relatively small surface roughness. On the other hand, in Figure 20c, the number of ridges and gullies has increased, and the spacing of the grooves and abrasive marks is more noticeable, suggesting that the surface wear on specimen C is more severe. These test results align with the findings from the EDEM simulation analysis.

Adhesive wear occurs when the surface of a specimen experiences plastic deformation or shearing at high temperatures and stresses during sliding friction. This leads to localized softening of the surface metal, eventually resulting in the phenomenon of adhesion at the contact points of the convex bodies [37]. Figure 20d,e depict the presence of shallow furrows on the specimen’s surface, without significant pits, resulting in a relatively smooth wear surface. The analysis indicates that in the case of specimen A’s ratio, the mixture causes shallow furrows due to micro-cutting and plastic deformation of the metal surface, leading to an increase in surface roughness. Figure 20f,g reveal the occurrence of adhesive wear on the specimen’s surface, characterized by some surface dents, and more severe abrasion compared to specimen A. It is analyzed that in the case of specimen B, the microscopic cutting and plastic deformation of the mixture material on the specimen increase, leading to an increase in the roughness of the specimen’s surface. This, in turn, increases the actual contact area with the specimen and contributes to the occurrence of the adherence effect that causes adherent wear. Abrasive wear is a phenomenon in which material particles adhere to the metal surface and cut each other, ultimately resulting in the corresponding destruction of the metal material [38,39]. Figure 20h,i reveal that specimen C exhibits deeper grooves with abrasive wear on its surface. In contrast, noticeable dents are present on the surface, and the level of abrasion is more severe compared to specimens A and B. Analysis indicated that the proportion of corn and alfalfa hay was higher in specimen C. Consequently, its crude fiber content exceeded that of specimens A and B, leading to the formation of deeper cutting marks and scratches upon contact with the specimen’s surface. The surface roughness of specimen C was also higher than that of specimens A and B, intensifying the material’s cutting action on the specimen’s surface and exacerbating wear by generating debris and abrasive abrasion. Fatigue wear occurs when spalling craters form in metallic materials under reciprocating stresses, ultimately resulting in fatigue damage [40]. From the SEM image on the right side of Figure 20, it is apparent that the wear direction on the specimen caused by the mixtures at the three different ratios is parallel to the direction of the three-body wear tester. As the ratio of maize to alfalfa hay increases, the extent of wear on the specimen also increases, with the depth and number of furrows on the specimen’s surface increasing. This suggests that fatigue wear is likely to occur on the surface.

6. Conclusions

In this study, a coupled DEM-FEM method has been developed to simulate and predict the frictional wear phenomenon in the TMR flat die granulation process under varying material ratios. This approach is deemed to be more representative of real-world conditions compared to traditional finite element analysis methods. The accuracy of this method in assessing the wear issue of the flat die has been validated through wear testing. The study has yielded the following conclusions.

(1)

The pressure exerted on the pellets and die hole during extrusion was examined through EDEM simulation for three distinct material ratios. The simulation outcomes indicated that, under unchanged conditions, an escalation in the ratio of corn to alfalfa hay led to an increase in the pressure between the pellets and the pressure on the die hole. This escalation was attributed to the heightened presence of coarse fibers in the material.

(2)

The maximum compressive force of the particles and die hole, as determined through EDEM simulation, was integrated into Ansys for a combined simulation. The equivalent stress and equivalent elastic strain of the die hole under the maximum compressive force were then analyzed. The analysis revealed that the entrance segment of the die hole experienced the most intense force and deformation, indicating the shortest fatigue life. The maximum equivalent stress recorded was 42.8 MPa, the maximum equivalent elastic strain measured 2.5 × 10⁻³, and the minimum fatigue life cycles were found to be 5.0 × 10⁵. On the other hand, the equivalent stress and equivalent elastic strain in the middle and upper sections of the die hole were minimal. Specifically, the equivalent stress was 4.8 MPa, and the minimum equivalent elastic strain was 2.8 × 10⁻⁴. In summary, it can be concluded that in the pelletizing and molding process of the flat die granulator, the critical areas of wear in the die hole are concentrated at the entrance and exit points. This wear phenomenon is primarily associated with stress concentration, leading to a predicted shorter fatigue life at these specific locations. To enhance the service life of the die hole, potential solutions include modifying the shape of the entrance and exit of the die hole or utilizing materials with superior abrasion resistance at these critical points.

(3)

A wear test was performed using an MLS-225 rubber wheel wear testing machine. The findings revealed that, with a corn, alfalfa hay, and quinoa straw ratio of 7:2:1, and all other conditions held constant, sample C of the flat die displayed the most pronounced wear. This outcome corroborates the conclusion derived from the DEM-FEM coupling method, affirming the effectiveness of employing this methodology to investigate wear problems in flat dies. Through the examination of the three-dimensional morphology and microscopic surface of the worn samples, it was established that the primary forms of wear encountered by the flat die pelletizer in the granulation process include adhesive wear, abrasive wear, and fatigue wear. The analysis indicates that adhesive wear occurs as a result of plastic deformation in the flat die sample under elevated temperatures and stress levels, causing localized softening of the surface and subsequent adhesive wear. Abrasive wear is generated by the cutting action of material particles on the flat die sample surface, leading to the creation of grooves and abrasive wear. Fatigue wear occurs due to the repeated cyclic loading experienced by the flat die sample, causing the development of visible grooves. With the continued formation of grooves, it is anticipated that fatigue-induced pits will emerge, ultimately culminating in fatigue wear.