Design and Testing of Key Components for a Multi-Stage Crushing Device for High-Moisture Corn Ears Based on the Discrete Element Method

Abstract

To improve the crushing efficiency and crushing pass rate of high-moisture corn ears (HMCEs), a multi-stage crushing scheme is proposed in this paper. A two-stage crushing device for HMCEs is designed, and the ear crushing process is analyzed. Firstly, a simulation model for HMCEs was established in EDEM software (2018), and the accuracy of the model was verified by the shear test. Subsequently, single-factor simulation experiments were conducted, with the crushing rate serving as the evaluation index. The optimal working parameter ranges for the HMCE device were identified as a primary crushing roller speed of 1200–1600 revolutions per minute (r/min), a secondary crushing roller clearance of 1.5–2.5 mm, and a secondary crushing roller speed of 2750–3750 r/min. A Box–Behnken experiment was conducted to establish a multiple regression equation. With the objective of maximizing the qualified crushing pass rate, the optimal combination of parameters was revealed: a primary crushing roller speed of 1500 r/min, a secondary crushing roller clearance of 2.5 mm, and a secondary crushing roller speed of 3280 r/min. The pass rate of corn cob crushing in the simulation test was 98.2%. The physical tests, using the optimized parameter combination, yielded a qualified crushing rate of 97.5%, which deviates by 0.7% from the simulation results, satisfying the requirement of a qualified crushing rate exceeding 95%. The experimental outcomes validate the rationality of the proposed crushing scheme and the accuracy of the model, providing a theoretical foundation for subsequent research endeavors.

1. Introduction

HMCEs represent the main grain crop and feedstuff in China. HMCE wet storage refers to high-starch feedstuffs made from corn kernels or cobs with a moisture content of 28–33% that are crushed, placed in airtight storage or wrapped, and fermented under an anaerobic environment for more than 45 days [1,2]. The key factor in the wet storage of HCMEs is the crushing of corn ears, and the crushing size of corn ears seriously affects the quality of subsequent feed processing. A larger crushing size will lead to a smaller exposure area of internal starches and other nutrients, affecting the overall quality and time of fermentation [3]. A crushing size that is too fine will cause most of the starch in the feed to be degraded by microorganisms in the stomach of livestock, resulting in a serious waste of nutrients [4,5]. Therefore, developing an HCME crushing device with a stable crushing pass rate is of great significance.

At present, there are few machines dedicated to HMCE crushing [6], and most of them study whole-corn crushing. For example, Wu et al. conducted research on the impact of different shredding methods on the quality of whole-corn silage through a comparison of the differences in the content of crude protein and other nutrients. They obtained a better crushing method involving kneading and cutting to improve the quality of feed for subsequent crushing rollers and to provide a basis for the design of rollers [7]. Zhang et al. designed a silage corn crushing blade based on the geometry of the upper jaw of leaf-cutting ants and other herbivorous insects. Their design was able to address traditional silage corn harvester blades’ insufficient sharpness and poor sliding cutting performance [8]. John Deere’s 8000 series featured different forms of crushing rolls, including discs, spiral grooves, straight-toothed grooves, etc., to meet the crushing rate while also meeting different user needs [9,10]. CLAAS’s JAGUAR 800 series of green fodder harvesters, on the other hand, use a spiral groove crushing device to improve the efficiency of seed crushing by increasing axial rubbing, and combined with different types of crushing roll designs, they effectively expand the friction area with the crushed material and ensure a high crushing quality [11].

At present, discrete elements have been widely used in the field of agriculture. Some research scholars have used the discrete element method to establish a simulation model to analyze the material crushing process. Sun et al. carried out discrete element modeling of corn kernels and straw and compared three different types of crushing rollers (disc rollers, conventional serrated rollers, and helical notched serrated rollers) through simulation tests. They concluded that disc milling rollers perform better [12,13,14,15,16]. Li et al. used EDEM software to establish an HCME model and analyzed the effects of various parameters of a threshing device on BGR and UGR [17]. Liu et al. established a two-layer straw model of pulp epidermis based on the Hertz–Mindlin model and calibrated the bonding parameters of the epithelium and pulp through bending damage experiments to obtain a reliable discrete element model of straw [18]. Han et al. used a discrete element model of fertilizer and applied the fuzzy theory and a numerical simulation to analyze the optimal working performance of an orchard fertilizer applicator, which met the performance requirements of fertilizer applicator devices [19]. In the study by Ma et al., the three-dimensional discrete element method (DEM) was employed to investigate the rock breaking mechanism and cutting performance of five widely used carbide buttons. They found that the conical button had a high rock breaking efficiency when the penetration depth was low, and the saddle button had a high rock breaking efficiency when the penetration depth was great [20].

Aiming to solve the problems of the low crushing efficiency and poor crushing effect of high-humidity corn, this study takes HCMEs as its object, combines the material characteristics of HCMEs and the crushing process, and proposes a two-stage crushing method comprising first cutting and then crushing. Based on the above ideas, the main structural parameters of primary and secondary crushing rollers were determined through a theoretical analysis. After modeling the corn ears, the crushing process could be simulated, the influence of the main working parameters on the crushing qualification rate of HCMEs could be explored through a single-factor simulation test, and the optimal combination of parameters could be determined through the Box–Behnken test. Physical tests were conducted, which will provide a reference for future research on HCME crushing devices.

2. Materials and Methods

2.1. Structure and Working Principle

The HCME multi-stage crusher mainly comprises a feeding hopper, frame, primary crushing device, secondary crushing device, transmission system, and discharge hopper. As shown in Figure 1, the primary crushing device is a pair of differential rolls equipped with a beveled tooth blade, the secondary crushing device is a pair of serrated differential rolls, and the working gap of the two pairs of rolls can be adjusted according to the crushing requirements. A material receiving opening is set between the primary and secondary rollers to prevent the material from overflowing and being wasted. The primary crusher and secondary crusher are each powered by a YVF-250M-4 series three-phase asynchronous motor (Luhong Motor Factory, Qingdao, China) through the transmission system.

The multi-stage crushing machine for HCMEs divides the crushing process into two phases. The first stage uses two differential rotations of the oblique tooth crushing knife roll, as well as a differential rotation of the crushing rollers so that the corn cobs are trapped between the two teeth and HCMEs are chopped into particles of a relatively large size. The second phase utilizes serrated differential rollers to further crush the already chopped corn ears. The larger-particle products from the primary crushing unit fall into the secondary crushing unit, where they undergo a crushing process involving rubbing and pressing between the secondary crushing rollers. Upon the completion of the entire crushing process, the crushed corn is discharged through the outlet.

2.2. Key Component Parameter Design and Analysis

2.2.1. Primary Crushing Roll Design

To ensure a qualified rate of HCME crushing and improve the crushing efficiency, it is necessary to clarify the structural parameters of the first-stage differential crushing roller. The same blade spacer is set between the two blades to allow the chopped corn to have better fluidity. To improve the crushing effect and crushing rate, the two pairs of roller blades are arranged in a staggered manner.

The length of the ear fragmentation zone directly influences the final fragmentation effect, because maize ears generally fall with their axes aligned parallel to the axes of the crushing rollers. The corn ear crushing zone is defined as the area where the two primary crushing rolls overlap. The principle of the fragmentation process is illustrated in Figure 2. To ensure that the maize ears undergoing primary fragmentation are successfully transferred to the secondary roller crushing apparatus, the spacing (b) of the primary tooth-shaped rollers should be controlled at 60 mm.

The required productivity is 20 t/h, and the corn ear capacity is approximately equal to 500 g/L [21]; 20 t of high-moisture corn ear volume V ears must reach about 28 m³ to achieve this productivity; the calculation formula for the first level of the toothed crushing or roller crushing area S₀ is as follows:

S₀ = nbl,

(1)

where S₀ is the effective crushing area, m²; b is the number of blades; and l is the effective crushing length, m.

Bringing in the numerical value to derive the effective crushing area S₀ = 0.03 m² of the primary crushing roller leads to the maximum value of the primary crushing roller D_max, as follows:

$${\mathrm{D}}_{\max }={\displaystyle \frac{\mathrm{b}+\mathrm{dcos}{\mathsf{\alpha }}_1}{2(1-{\cos {\mathsf{\alpha }}_1}^2)}},$$

(2)

where D_max is the maximum diameter of the primary crushing roller, m; ${\mathsf{\alpha }}_1$ is the corn ear contact angle with the knife teeth; d is the corn ear diameter, m; and b is the effective crushing width, m.

To meet the strength requirements of the device, the blade material is selected as 65 Mn steel and the corn ear friction angle is 35.7°, so α ≤ 35.7°; to meet the productivity requirements, the above data will be analyzed to find D_max ≤ 420 mm. The primary crushing roller diameter D_min value of the formula for calculating the diameter of the primary crushing roller D_min is shown in Equations (3)–(5), to meet the crushing requirements of 20 t/h, based on the effective crushing area of the primary crushing mechanism obtained above, through the calculation of the falling speed of the crushed material (with the size of the crushing roller linear speed), and then we can obtain the minimum diameter of the primary crushing roller D_min.

Q = S₀ × v

(3)

$$\mathrm{v}=\mathsf{\omega }\times \mathrm{r}=\mathsf{\pi }\times \mathrm{D}\times {\displaystyle \frac{\mathrm{n}}{60}}$$

(4)

$${\mathrm{D}}_{\min }=60\mathrm{Q}/{\mathrm{S}}_0\mathrm{n}\mathsf{\pi },$$

(5)

where Q is the volumetric flow rate; v is the linear velocity, m/s; $\mathsf{\omega }$ is the angular velocity, rad/s; r is the corn ear radius, m; and D_min is the minimum diameter of the primary crushing roller, m.

We finally obtained a crushing blade diameter D ≥ 170 mm. Summing up the above, it can be concluded that the diameter of the first crushing blade D is 170 to 420 mm. According to the size of the three axes of the corn ear, according to the Agricultural Machinery Design Handbook [22], for the forage processing class, the standard blade diameter is 200–350 mm, so we can ultimately determine the diameter of the blade to be 350 mm.

2.2.2. Mechanical Analysis of the Primary Crushing Plant

The teeth of the knife are directly involved in the corn ear level one crushing workpiece. The first level of corn ear cutting and crushing effect has a decisive impact on the quality of the machine, and the operational efficiency has an important impact, and to ensure that the crushing teeth can smoothly grasp the corn ear, the tooth width and height should be larger than the diameter of the corn ear, as shown in Equations (6)–(9).

$$\mathrm{h}\ge {\displaystyle \frac{\mathrm{r}\cos \mathsf{\alpha }-\mathsf{\beta }-\mathsf{\gamma }}{\sin \mathsf{\alpha }}}$$

(6)

$$\mathsf{\beta }={\sin }^{-1}{\displaystyle \frac{\mathrm{h}\tan \mathsf{\alpha }}{\mathrm{R}}}$$

(7)

$$\mathrm{R}={\displaystyle \frac{\mathrm{D}}{2}}=175$$

(8)

$$\mathsf{\tau }={\sin }^{-1}{\displaystyle \frac{\mathrm{R}-\mathrm{r}}{\mathrm{R}-\frac{\mathrm{b}}{2}}}$$

(9)

where h is the height of the blade teeth, m; α is the angle between the blade line and blade mating line; β is the primary crushing plant central angle; γ is the cutting edge inclination; R is the crushing blade radius, m; and $\mathsf{\tau }$ is the blade angle of the primary crushing roller.

The force analysis of the contact process between the knife teeth and the corn and the establishment of the contact force model between the knife teeth and the corn are shown in Figure 3. The shear force on the corn is taken as the objective function, and the genetic algorithm is used to solve the corn contact force model.

Corn ears make contact with the primary crushing roller by the fast roller squeezing pressure F_N1 and the slow roller squeezing pressure F_N2 and F_N3 subject to friction F_f2 and F_f3. To avoid the excessive friction crushing of kernels on the primary crushing rollers, the level of corn cob friction should be as low as possible; the friction of the cob will be counted as the maximum static friction when the cob friction is calculated. The force on the corn cob is decomposed in the X and Y directions, and the positive pressure and friction on the corn are analyzed by force analysis and the relationship between the geometries of the knife teeth, as shown in the following formula:

$$\mathrm{A}=\mathsf{\beta }+\mathsf{\gamma }+\mathsf{\tau }$$

(10)

$$\mathrm{B}=\mathsf{\beta }+\mathsf{\gamma }$$

(11)

$$\mathrm{C}=2\mathsf{\alpha }-\mathsf{\beta }-\mathsf{\gamma }$$

(12)

$${\mathrm{F}}_{\mathrm{N}1}\left|\begin{array}{cc}\sin \mathrm{A}& 0\\ 0& \cos \mathrm{A}\end{array}\right|=\left|\begin{array}{cc}{\mathrm{F}}_{\mathrm{a}1}& {\mathrm{F}}_{\mathrm{b}1}\\ {\mathrm{F}}_{\mathrm{a}2}& {\mathrm{F}}_{\mathrm{b}2}\end{array}\begin{array}{cc}{\mathsf{\mu }\mathrm{F}}_{\mathrm{a}1}& {\mathsf{\mu }\mathrm{F}}_{\mathrm{b}1}\\ {\mathsf{\mu }\mathrm{F}}_{\mathrm{a}2}& {\mathsf{\mu }\mathrm{F}}_{\mathrm{b}2}\end{array}\right|\left|\begin{array}{c}\begin{array}{cc}\sin \mathrm{B}& \sin \mathrm{C}\\ \cos \mathrm{B}& \cos \mathrm{C}\end{array}\\ \begin{array}{cc}\cos \mathrm{B}& \cos \mathrm{C}\\ \sin \mathrm{B}& \sin \mathrm{C}\end{array}\end{array}\right|$$

(13)

$$\mathrm{K}=\sqrt{{\left({\mathrm{F}}_{\mathrm{N}2}\sin 2\mathsf{\alpha }\right)}^2+{\left({\mathrm{F}}_{\mathrm{N}3}-{\mathrm{F}}_{\mathrm{N}2}\cos 2\mathsf{\alpha }\right)}^2}$$

(14)

The roulette method is selected as the selection operator, and the value of the operator is selected as 0.2. For the crossover method, we select the two-point crossover method, and the total crossover rate is 0.6. The variation rate of the mutation operation is 0.2, the population size in each generation is 40, and the number of iterations is 500. The specific optimization process is carried out by Matlab software (Version 2023A). After the above objective function, constraints, and parameters are set up in Matlab software, the Genetic Algorithm Toolbox in Matlab software is used to solve the problem. The optimum geometrical parameters of the cutter tooth are found: $\mathsf{\alpha }$ = 30, $\mathsf{\gamma }=10$.

2.2.3. Optimization Design and Analysis of Secondary Crushing Rolls

The configuration of the secondary crushing roller is based on the technical specifications of the optional seed crushing roller utilized in John Deere’s 7000 series self-propelled green fodder harvester. This roller demonstrates optimal operational performance, resilience to high pressure, minimal noise generation, and straightforward disassembly and reassembly [23,24,25]. In this study, the parameters were selected according to the specifications outlined in the Agricultural Machinery Design Handbook, as shown in

Table 1. Parameter values for the secondary crushing rolls.

Structural Parameters	Design Values
Number of teeth on the crushing rolls	500
Crushing roll face length (mm)	740
Diameter (mm)	230
Length of the crushing roll shaft (mm)	1120
Adjustable gap (mm)	1–5

.

The crushing process of a secondary crushing device is divided into three stages: the contact stage, extrusion stage, and crushing stage. To analyze the crushing process more clearly, the force analysis of each stage is shown in Figure 4. In the contact stage, the material is clamped by two sticks and sent into the crushing gap for extrusion and crushing. The large particles are sent into the gradually narrowed gap at the extrusion stage. The force at this stage is shown in Formula 15 at the extrusion stage for the large particles in the two rollers at the differential speed of extrusion, in order to complete further crushing, achieve the crushing requirements, and be thrown down. The force at this stage is shown in Formula (16).

G + F₁cosτ₂ = F₂cosτ₂

(15)

G + F₃cos(τ₂ + β₂) = F₄cos(τ₄ + β₂)

(16)

where G means gravitational, N; F₁ is the contact force of the fast rollers on the material in the contact stage, N; F₂ is the contact force of the slow rollers on the material in the contact stage, N; F₃ is the contact force of the slow rollers on the material during the extrusion stage, N; F₄ is the contact force of the slow rollers on the material during the extrusion stage, N; τ₂ is the blade angle of the secondary crushing roller; and β₂ is the secondary crushing plant central angle.

In the crushing stage, the materials are crushed into fine materials and thrown downward by inertia and then thrown out of the machine along the wall of the throwing brief. The whole crushing process includes squeezing, rubbing, and shearing; that is, the material larger than the crushing gap is squeezed and crushed into the material that can fit in the gap and then rubbed under the action of the two differential discs to complete the second stage of crushing, and, finally, the discs meet in the rubbing process for the toothed edges of the cutting edge to complete the third stage of crushing, meaning that the whole process of the material crushing effect is better.

2.3. Experiment: EDEM Discrete Element Simulation

The discrete element method is commonly used to study the relationship between crops and other multiarticulate media and implements. It can observe and analyze the displacements and stresses of the kernels after the action of the working parts, thus providing a basis for the optimization of the structure and parameters of the working parts [26]. In this paper, the interaction between corn ears and the crushing device is modeled by discrete element software EDEM2020. It simulates and analyzes the crushing process of a corn ear in the crushing device, selects the crushing qualification rate as the evaluation index, explores the effects of the primary crushing roller speed, secondary crushing shaft clearance, and secondary crushing roller speed on the crushing effect, and determines the best parameter interval in the crushing device for high-humidity corn ears. The Box–Behnken response surface test was carried out to determine the optimal parameter combinations of the high-humidity corn crushing device in crushing corn ears.

A corn ear model must be established to simulate the crushing process of the HCME crushing device. The results of the previous test indicate that the destructive force of the tip of the corn ear shear is relatively small, which reduces the impact on the crushing. Therefore, in the modeling process, the tip of the geometrical model was not taken into account in facilitating the modeling of the corn ear approximation for the cylindrical shape. The HCME model was divided into two distinct components: the corn cob and the corn kernel. The modeling of the corn kernel shaft was based on the methodology of the three-layer discrete element model, as described in references [27,28,29,30]. The glumes, wooden annulus, and kernel pith were geometrically modeled using SolidWorks 2022 software. The particle alignment method was employed to determine the coordinates of each grain. The modeling of the corn kernels was conducted using nine balls, with the coordinates of the lowest particle determined and the remaining particles then stacked in sequence. The coordinates and radii were imported into EDEM software. The corn ear model was created using the meta-particle function, resulting in a rapid modeling process. The final model was 160 mm long and 53 mm in diameter, comprising 3586 particles.

Given that the primary objective of the test is to ascertain the corn crushing rate, it was deemed pertinent to observe the impact of corn crushing. Accordingly, the Hertz–Mindlin (with bonding) model was selected in EDEM software to construct the corn ear model, as illustrated in Figure 5. As the intrinsic properties of the corn ear, the contact parameters, and the bonding parameters between the corn kernel and corn cob have a minimal impact on the simulation process of corn ear crushing, all the aforementioned parameters have been derived from references [31,32], as shown in

Table 2. Intrinsic parameters of materials and contact materials.

Material	Density/(kg·m−3)	Poisson Ratio	Shear Modulus/MPa
Corn kernel	1394	0.4	131
Corn cob	627	0.4	109
Steel	7850	0.3	8 × 104

. The bonding parameters between corn kernels and corn cob particles were adjusted in the EDEM software according to the relevant literature data [33,34,35,36], and the final simulation parameter settings are presented in

Table 3. Interaction parameters of materials.

Material	Coefficient of Restitution	Coefficient of Static Friction	Coefficient of Rolling Friction
Corn kernel–corn kernel	0.182	0.086	0.3
Corn cob–corn cob	0.21	0.78	0.01
Corn cob–corn kernel	0.28	0.48	0.01
Corn kernel–steel	0.702	0.344	0.059
Corn cob–steel	0.38	0.47	0.053

and

Table 4. Corn kernel bonding parameters.

Parameters	Corn Kernel	Corn Cob	Corn Kernel–Corn Cob
Normal stiffness per unit area/(N·m−3)	8.7 × 108	1.12 × 109	5.5 × 1010
Shear stiffness per unit area/(N·m−3)	4.79 × 108	1.29 × 109	6.0 × 1010
Critical normal strength/Pa	1.57 × 105	5.0 × 106	3.0 × 106
Critical shear strength/Pa	8.59 × 105	5.2 × 106	1.675 × 106
Bond disc scale	1.2	1.2	1.2

. The load–displacement diagrams, obtained by verifying the shear test with the bonding parameters given in Table 4, are shown in Figure 6a. The relative error of the maximum destructive force as a function of displacement is shown in Figure 6b. The relative error is less than 5%, indicating that the corn ear bonding parameters are reliable and can be used for subsequent research.

To enhance the efficiency of the computer simulation, the HCME crushing apparatus was streamlined, with only the essential components, namely, the primary and secondary crushing devices, retained. The models of the primary and secondary crushing devices were created using SolidWorks 2022 and saved as STEP files for importation into EDEM software. The rotary motion with the center axis as the centerline was added to each crushing roll to simulate the operational dynamics of the crushing roll. The material of the crushing roll was steel 45, and the simulated physical parameters of the steel model were presented in Table 2. A particle plant was positioned above the initial crushing device to facilitate the unimpeded descent of the corn ear into the crushing apparatus. The simulation time was set to 1 s to reduce the computational burden, and the number of corn ear granule factories generated was set to three ears. This was carried out to ensure the stability of the bonding, and the fixed time step for the simulation was determined through the preliminary experimentation as 7.5 × 10⁻⁸ s. The post-processing module of statistical EDEM software was employed to calculate the qualification rate of corn ear crushing. The simulation test was repeated five times, and the resulting experimental data are averaged to determine the final test results. A box is set in the effective crushing area of the device to prevent the splashing of corn particles after crushing from affecting the crushing results.

2.4. Evaluation Standards

The evaluation index for the HCME crushing qualification rate is comparable to that of silage corn feed. The latter is typically assessed using a corn silage seed crushing scoring screen, which enables the measurement of the ear crushing effect. This is achieved by the “whole plant corn silage making machinery kneading quality evaluation technical specifications” and the HCME feed industry crushing standard requirements. According to the literature review, material with a particle size of 2 mm or less is classified as an impurity. The literature review also indicates that corn feeds with a particle size of 2–10 mm are consistent with the range of feeds typically fed on commercial dairy farms. Therefore, this test finally classified materials retained on the 2 mm sieve and removed from the 10 mm sieve as being qualified. Following the conclusion of the simulation test, the 3D model of the silage corn kernel crushing scoring sieve was imported into EDEM software. The crushed corn ear particles were then screened using 2 mm and 10 mm sieves, and the resulting data were calculated according to Formula (17) to obtain the corn ear crushing qualification rate for the simulation test:

$$\mathrm{S}=1-{\displaystyle \frac{{\mathrm{G}}_1+{\mathrm{G}}_2}{{\mathrm{G}}_3}}\times 100\%$$

(17)

where S is the crush rate, %; G₁ is the mass of material not passing the 10 mm filter sieve, g; G₂ is the mass of material passing through a 2 mm filter sieve, g; and G₃ is the material quality, g.

2.5. One-Factor Experimental Program

The main parameters affecting the crushing qualification rate of HCME crushing devices include the primary crushing roller speed, secondary crushing roller gap, and secondary crushing roller speed. We took the HCME crushing qualification rate as the test index, and the primary crushing roller speed, secondary crushing roller clearance, and secondary crushing roller speed as the test factors. According to the existing research data, combined with the related literature [36], the selected single-factor test is as follows: a primary crushing roller speed of 800–1600 r/min, a secondary crushing gap of 1–3 mm, and a secondary crushing roller speed of 1750–3750 r/min. The selected primary crushing roller speed is 1200 r/min, the secondary crushing gap is 2 mm, and the secondary crushing roller speed is 2250 r/min; see

Table 5. Table of single-factor experimental factor levels.

Levels	Primary Crusher Roll Speed/(r/min)	Secondary Crushing Roller Gap/(mm)	Secondary Crusher Roller Speed/(r/min)
1	800	1	1750
2	1000	1.5	2250
3	1200	2	2750
4	1400	2.5	3250
5	1600	3	3750

. Each group test set 5 test factor levels, exploring the above test factor in the investigation of the index influence in each group of tests after the end of the statistics for the HCME crushing pass rate, to ensure the accuracy of the results of the test; each group of tests was repeated 3 times, and we took the average value as the result.

2.6. Box–Benhnken Experimental Program

From the one-factor test, it can be seen that the primary crushing roller speed in the interval of 1200–1600 r/min, the secondary crushing roller gap in the interval of 1.5–2.5 mm, and the secondary crushing in the interval of 2750–3750 r/min for roller speed represent the optimal parameter range for a high-humidity maize ear crushing device. This interval not only ensures a higher crushing qualification rate but also achieves the objective of enhancing the crushing efficiency. Using the design of the test program in the Design-Expert software (Version 13.1.0), the test was conducted a total of 17 times. The test parameters are presented in Table 4, and the test factor levels are shown in

Table 6. Table of Box–Behnken experimental factor levels.

Levels	Primary Crusher Roll Speed/(r/min)	Secondary Crushing Roller Gap/(mm)	Secondary Crusher Roller Speed/(r/min)
−1	1200	1.5	2750
0	1400	2	3250
1	1600	2.5	3750

.

3. Analysis and Verification of Crushing Test Results

3.1. Single-Factor Test Results and Analysis

With the crushing rate as the experimental indicator, after the simulation test through the grading screen for grading treatment, the curve of crushing rate is shown in Figure 7, and the crushing effect of the simulation process is shown in Figure 8. It can be seen from Figure 7a that with the increase in the speed of the first crushing roller, the qualified rate of crushing increases first and then decreases. This is because when the speed of the first crushing roller is low, the impact force of the crushing roller on the corn ear is small, and the contact frequency with the crushing roller is small. At this time, the ear is not easy to break, resulting in a low crushing rate in the corn ear. With the increase in the speed of the crushing roller in the range of 800 r/min–1400 r/min, the impact force of the corn ear receiving the crushing roller increases, and the contact frequency between the ear and the crushing roller increases, the degree of ear crushing increases, and the crushing rate increases. When the speed of the first crushing roller exceeds 1400 r/min, the collision between the ear and the crushing roller is more intense, the contact frequency between the ear and the crushing roller is higher, and the extrusion and kneading effect of the crushing roller increases, resulting in a large degree of ear crushing (less than 2 mm), which does not meet the crushing requirements, so the crushing qualification rate is reduced.

The crushing rate in corn ears changes with the gap between the two rollers, as shown in Figure 7b. When the gap between the two rollers is 1 mm, the clamping and squeezing effect of the crushing roller on the corn ear is too strong. At this time, the ear will be subjected to greater pressure and friction when passing through the crushing roller, resulting in a greater degree of crushing. The particle size after crushing is less than 2 mm, which does not meet the crushing requirements, so the crushing pass rate is low. With the increase in the two single stage rolling gap to 2 mm, the clamping effect and extrusion effect of the ear are reduced compared with those at 1 mm, and the breaking degree of the ear is reduced. At this time, the size of the broken material is mostly within the crushing standard range, and the crushing qualification rate increases. After the gap of the secondary crushing roller exceeds 2 mm, the clamping and squeezing effect of the crushing roller on the corn ear is weakened, resulting in insufficient impact force on the ear when passing through the crushing roller, and the degree of ear crushing is reduced. After the crushing, the ear size is larger and the crushing pass rate is reduced.

The curve of the qualified rate of crushing with the rotation speed of the secondary crushing roller is shown in Figure 7c. When the rotation speed of the secondary crushing roller is 2000 r/min, the contact frequency with the ear is low, and the extrusion effect on the ear is small, resulting in a low qualified rate of crushing. With the increase in the speed of the secondary roller, the frequency of contact with the ear increases, the extrusion and friction force of the ear increases, the degree of ear crushing increases, and the qualified rate of crushing increases. When the rotation speed is too large, the corn ear is subjected to severe extrusion and friction, and the degree of fragmentation is too large to meet the crushing standard, resulting in a decrease in the qualified rate of crushing.

A comprehensive analysis of the aforementioned data indicates that the optimal range for the primary crushing fast roller speed is within the 1200–1600 r/min interval, while the secondary crushing roller gap should be within the 1.5–2.5 mm interval. Additionally, the secondary crushing fast roller speed should be within the aforementioned range. The optimal parameter interval for the high-humidity maize ear crushing device is determined to be within the range of 2750 to 3750 r/min for the roller speed. This interval not only ensures a higher crushing qualification rate, but achieves the purpose of improving the crushing efficiency, as well.

3.2. Results of Multifactorial Experiments

The superior parameter intervals were obtained from the results of the one-factor experiments. Orthogonal tests were conducted using the factor level table provided in the aforementioned Table 6. The response surface test scheme, as outlined in Design-Expert software, was employed to perform the orthogonal tests. Subsequently, data collection and data processing were undertaken, and the results of the experimental trials are presented in

Table 7. Response surface test protocol table.

Level	A/(r/min)	B/(mm)	A/(r/min)	S/(%)
1	1400	2.5	2750	95.5
2	1400	2	3250	97.2
3	1600	2.5	3250	96.4
4	1200	1.5	3250	95.2
6	1200	2.5	3250	90.5
7	1200	2	2750	91.5
8	1400	2	3250	96.7
9	1600	2	3750	90.5
10	1200	2	3750	89.4
11	1400	2	3250	98.2
12	1400	2	3250	97.6
13	1400	1.5	2750	98.1
14	1400	1.5	3750	89.5
15	1400	2.5	3750	95.9
16	1600	2	2750	95.3
17	1400	2	3250	97.0

. In Table 7 A, B, and C, the factor-coded values represent the first-stage crushing roller rotational speed, the second-stage crushing shaft clearance, and the second-stage crushing roller rotational speed, respectively. S is an experimental index, representing the qualified rate of corn ear crushing. Each group of experiments was repeated three times to obtain the average value. The simulation experiment effect is shown in Figure 9.

3.2.1. Significance Test and Regression Model Analysis

Using Design-Expert software to fit a multiple regression to the results of the response surface test of the HCME crushing qualification rate, a quadratic regression equation for the corn ear crushing qualification rate was obtained:

$$\mathrm{S}=97.38+0.68\mathrm{A}+0.7\mathrm{B}-1.88\mathrm{C}+2.79\mathrm{AB}-0.66\mathrm{AC}+2.26\mathrm{BC}-3.72{\mathrm{A}}^2-0.63{\mathrm{B}}^2-1.92{\mathrm{C}}^2.$$

(18)

We used Design-Expert software to perform a Box–Behnken simulation test analysis of variance, as shown in

Table 8. Analysis of variance criteria.

Error Source	Sum of Squares	Degree of Freedom	Mean Square	F-Value	p-Value	Significance
Model	139.50	9	15.50	31.41	<0.0001	**
A	3.00	1	3.00	6.08	0.0431	*
B	3.25	1	3.25	6.59	0.0372	*
C	23.12	1	23.12	46.85	0.0002	*
AB	25.50	1	25.50	51.68	0.0002	*
AC	1.44	1	1.44	2.92	0.1314
BC	16.81	1	16.81	34.06	0.0006	*
A2	47.75	1	47.75	96.75	<0.0001	**
B2	1.36	1	1.36	2.75	0.1414
C2	12.78	1	12.78	25.91	0.0014	*
Residual	3.45	7	0.49
Lack of fit	2.44	3	0.81	3.22	0.1442
Pure error	1.01	4	0.25
Sum	142.96	16

* Represents the level of significance of the effect on the outcome. ** represents the level of significance of the grade of the effect on the results.

. In the p-value analysis, it can be seen that A² on the crushing rate of conformity is extremely significant, A, B, C, AB, BC, and C² on the crushing rate of conformity of the impact are significant, and AC and B² on the crushing rate of conformity of the impact are not significant. According to the size of the F-value in statistics, the level of influence of the factor on the results can be determined: the larger the F-value, the greater the influence of the F-value. The F-value of the model represents the impact of the test factors on the crushing pass rate from large to small for the secondary crushing roll speed > secondary crushing roll gap > primary crushing roll speed. The p value of the regression model is less than 0.0001, which indicates that the regression model is highly significant. The coefficient of determination of the regression equation is R² = 0.9758, the corrected coefficient of determination is adjusted R² = 0.9448, which is very close to 1, and the coefficient of variation is C.V = 0.82. This summary shows that the regression model is extremely significant.

The results of the ANOVA demonstrate that the three selected parameters represent the primary factors influencing the crushing effect in corn ears. Among the aforementioned parameters, the secondary crushing roller speed exerts a considerable influence on the quality of corn ear crushing. When the secondary crushing roller speed is excessive, the crushing roller exerts a disproportionate extrusion and shear effect on the material, resulting in an elevated proportion of impurities in the crushed material. The impact of the primary crushing roll speed and the secondary crushing roll gap on the quality of corn ear crushing is moderately lower than that for the secondary crushing roll gap.

3.2.2. Effects of Interactions on Indicators

The effects of interaction factors on the corn ear crushing pass rate are shown in Figure 10. Response surfaces were generated using Design-Expert software to analyze the effects of AB, AC, and BC on S. According to the response surface ANOVA, the interaction of ab and bc had a significant effect on the corn ear crushing pass rate. Among the three factors, the level of one of the factors was set at 0 level to explore the interaction effect of the other two factors on corn ear crushing.

Figure 10a shows that the changes in crushing pass rate caused by the changes in A and B are smaller, while the contour lines present a larger curvature of the ellipse, indicating that the interaction of A and B is significant. Figure 10b shows that the changes in crushing pass rate caused by the changes in A and C are larger, while the contour lines present a smaller curvature of the ellipse indicating that the interaction of A and B is insignificant. Figure 10c shows that the changes in crushing pass rate caused by changes in B and C are smaller, while the contour lines show a larger curvature of the ellipse, indicating that the interaction of B and C is significant. The optimal parameter combination is determined by imitating the Box–Behnken test: the primary crushing speed is 1506.97 r/min, the secondary crushing roll gap is 2.5 mm, and when the secondary crushing roll speed is 3279.96 r/min, the qualified rate of HCME crushing is 98.2%, which meets the technical requirements for corn crushing device operation.

3.3. Verification

The test material was selected from the experimental field of Jilin Agricultural University, and the simulation parameters were optimized by a quadratic regression orthogonal test. This was to facilitate the adjustment of each parameter. The optimization was conducted as an integer test, and the final parameter combinations were determined as follows: the primary crushing roller speed was 1500 r/min. Following the adjustment of the working parameters, namely, the primary crushing roller speed (1500 r/min), the primary crushing roller gap (2.5 mm), the secondary crushing roller speed (3280 r/min), and the secondary crushing roller gap (2.5 mm), the actual crushing rate test was conducted. The aforementioned parameters were selected for testing purposes.

The test was conducted on 50 corn ears, divided into five groups, to verify the results and adjust the working parameters for the actual crushing rate test. This process was repeated on the same ears, with the resulting material being screened using both a scoring sieve and a silage corn kernel crushing scoring sieve. The results were subjected to statistical analysis, with the crushing rate calculated and the data averaged. The final measurement of the actual crushing rate was found to be 97.5% on average. This value represents the average qualified rate, which meets the working and design requirements. The HCME crushing test bench and HCME after crushing, as illustrated in Figure 11, demonstrate a simulation test and bench test relative error of 0.7%, which aligns with the standards for enterprise use.

4. Discussion

The simulation test results show that the crushing rate of the machine designed in this research is 98.2%. Compared to the traditional corn crusher with only one crushing roller, it was found that the crusher designed in this research not only has a high crushing rate but also a uniform crushing size. The effects of the primary crushing roll speed, the secondary crushing roll gap, the secondary crushing roll speed on the crushing qualification rate were investigated through a one-factor test, and the better parameter intervals obtained were similar to the results of Herrera et al. [36]. Afterward, the variance and response surface analyses of the test factors through a multifactor test allowed us to obtain the p value of the regression model < 0.0001, indicating that the regression model is highly significant. The coefficient of determination of the regression equation, R² = 0.9758, and the corrected coefficient of determination, adjusted R² = 0.9448, are very close to 1, and the coefficient of variation, C.V = 0.82. This indicates that there is a significant correlation. In response surface analysis, the interaction of significant parameters also has a significant effect on the angle of repose; the test factors on the crushing pass rate in descending order are the secondary crushing roll speed > secondary crushing roll clearance > primary crushing roll speed. The results of this study are similar to the results of Mou et al. [16]. At the same time, the optimal working parameters were obtained through a multifactor test, which is similar to the results of Geng et al. [12]. Finally, we carried out simulations and physical tests, respectively, and the crushing qualification rate was more than 95%, which meets the crushing requirements.

In this study, to determine the optimal combination of key parameters affecting the crushing rate of HCME crushing devices, single-factor tests and multifactor tests were carried out sequentially, based on the discrete element method. The impact of key test factors on the crushing rate is analyzed, the optimal parameter combination of high-moisture corn crushing is obtained, and finally, the bench test is carried out to validate the reliability of the simulation model. The test results show that the high-moisture corn crushing device designed through this research has a crushing rate of more than 95%, which meets the crushing requirements and can provide a theoretical basis for related research.

It should be noted that there are some limitations to this study, and only one of the maize varieties widely grown at present was selected as the research object. However, there are some differences in the physico-mechanical properties of maize varieties grown in different regions. In the future, we will carry out a multi-species analysis of the physical and mechanical properties and crushing mechanisms of corn ears with different moisture contents, using the results of this study in the field of feed milling research and crushing equipment design to provide a theoretical basis.

5. Conclusions

In this paper, for the problems of low crushing efficiency and low qualification rate in HCMEs, a crushing program comprising first slicing and then crushing was determined, and a two-stage crushing device for HCMEs was designed to achieve effective crushing in high-humidity corn ears.

The preliminary establishment of the corn ear model was carried out by using EDEM software, and a one-factor simulation crushing test was carried out by using the discrete element model to analyze the effects of the primary crushing roller speed, secondary crushing roller gap, and secondary crushing roller speed on the crushing qualification rate. The test results show that the performance of the primary crushing roll speed is best in the interval of 1200–1600 r/min, the performance of the secondary crushing roll gap is best in the interval of 1.5–2.5 mm, and the performance of the secondary crushing roll speed is best in the interval of 2750–3750 r/min.

Using the EDEM software for multifactor simulation fracture tests, a response surface methodology was employed to establish a model for the impact of three factors on the breaking rate of high-moisture corn. The Box–Behnken design was used for optimization analysis, revealing that the optimal combination of operating parameters for the HCME breaking device was as follows: a primary breaking roller fast roller speed of 1500 r/min, a primary breaking roller slow roller speed of 1150 r/min, a secondary breaking roller gap of 2.5 mm, a secondary breaking roller fast roller speed of 3280 r/min, and a secondary breaking roller slow roller speed of 2523 r/min. With these parameters, the breaking rate of HCMEs was 98.2%. Verification under the optimized parameters showed a breaking rate of 97.5%.