Design Optimization and Experiment of the Hammer Blade for Straw Crushers

Abstract

To address the low operational efficiency and suboptimal crushing quality of conventional straw crushers, a serrated hammer blade was designed and optimized. The working mechanism of straw crushing and the force interaction between the hammer blade and straw were theoretically analyzed, and a finite element model was established to simulate straw fragmentation under impact. The crushing performances of serrated, rectangular, and stepped hammer blades were comparatively evaluated, and cutting force and cutting time were selected as key response indicators to investigate the effects of structural parameters. Using Latin hypercube sampling and a Kriging surrogate model, the relative importance of hammer blade parameters was quantified, followed by multi-objective optimization using the NSGA-II algorithm. The results indicate that the significance of the influencing factors follows the order of blade thickness, blade width, tooth spacing, and blade length. The optimal hammer blade configuration was determined as 4 mm in thickness, 39 mm in width, and 4 mm in tooth spacing. Crushing experiments demonstrate that, compared with the conventional rectangular hammer blade, the optimized serrated design increases productivity by 17.49% and improves the pass rate by 5.02%. This study provides practical parameter support and technical guidance for the low-cost upgrading and performance improvement of straw crushing equipment.

1. Introduction

Straw from crops like corn can be chopped into segmental and thread-like feed using a straw crusher. This process effectively breaks down the epidermal structure of the straw, encourages fiber separation, and enhances the material’s softness and uniformity. Consequently, the straw feed’s palatability, digestion, and utilization rate are greatly improved [1], promoting nutrient absorption and increasing livestock productivity [2]. However, the large-scale utilization of straw resources is currently severely limited by issues associated with such equipment, including poor crushing effect and low working efficiency. In 2022, China produced approximately 864 million tons of crop straw, whereas only about 18% of it was utilized as feed [3]. Currently, there is a substantial inventory of straw crushers in the market. Investigating low-cost upgrade options for essential parts is crucial to raising the overall equipment level of the industry.

To improve the efficiency of straw crushers, early scholars both domestically and internationally adopted experimental methods, utilizing high-speed camera technology to explore the crushing mechanism and movement path of straw inside the crusher [4,5]. Orthogonal experiments and other methodologies can be employed to identify the optimal set of parameters for maintaining high-efficiency operation of the crusher. The data obtained through experimental methods is accurate; however, it poses challenges due to high economic costs and long equipment iteration cycles. The Discrete Element Method (DEM) and Finite Element Method (FEM), which enable the virtual simulation of the entire straw processing cycle—from feeding, crushing, to discharging—have gradually become commonplace research tools with the advancement of Computer-Aided Engineering (CAE) technology. Zhang, et al. [6] and Mu, et al. [7] investigated the extent to which the crusher’s structure influences the quality of straw crushing and determined the optimal structural parameters based on the precise establishment of the DEM model of straw. Huang, et al. [8] employed the FEM to create a finite element model of corn stalks, including their outer skin. By simulating the interaction process between the tool and the stalks, they resolved the problem and identified the ideal set of working parameters for the tool. Even though the aforementioned simulation studies have significantly reduced design costs, the majority of current research focuses on matching the machine’s overall structural parameters. In contrast, there is comparatively little research on optimizing the microstructural morphology of the hammer blade, the main executive component. Regarding the improvement of hammer blade structures, Ma, et al. [9] conducted research on high-efficiency straw crushers and established a design concept for optimizing hammer blade structures. Cao, et al. [10] and Zhang, et al. [11] optimized the design of a rectangular hammer blade to create L-shaped and V-shaped hammer blades, achieving good crushing effects. Chen [12], Yong, et al. [13] and Wang, et al. [14] optimized the rectangular hammer blade tooth structure using bionic methods, finding that it could significantly increase the stress at the material fracture and shorten fracture time. The aforementioned irregular hammer blade designs, based on bionics or complex topology optimization, are theoretically efficient. However, their intricate structures result in high processing costs, making it challenging to widely promote them during the renovation of existing equipment. In addition, existing studies on serrated or toothed hammer blades have mainly focused on qualitative comparisons or single-objective optimization. In conclusion, optimizing the hammer blade shape is an effective strategy for improving crushing efficiency, but the influence mechanism of the key structural parameters of serrated hammer blades on the dynamic straw-crushing process remains unclear. Given the widespread use of straw crushers, it is necessary to explore a practical and cost-effective approach to enhance their performance. To this end, this study takes a serrated hammer blade with a simple structure and low cost as the research object, and systematically optimizes its parameters using finite element analysis, the Kriging surrogate model, and the NSGA-II algorithm, followed by validation through full-scale machine experiments. Since extensive research on straw treatment and utilization has been carried out in China, the references cited in this paper are mainly from Chinese agricultural engineering research.

The hammer blade of a straw crusher was taken as the research object in this study. Based on the mechanical parameter tests of straw, a finite element model of the straw–hammer blade coupling was established. After comparing and evaluating the cutting performance of three types of hammer blades, the optimal hammer blade shape was selected. Subsequently, the sensitivity of key structural parameters to the crushing effect was investigated. Based on the Kriging model and Latin hypercube sampling, a surrogate model representing the interaction between the hammer blade and the straw was established. Ultimately, the hammer blade parameters were multi-objectively optimized using the NSGA-II algorithm, and the optimal hammer blade dimensions were determined. This study provides a theoretical basis and methodological reference for the design optimization and process improvement of straw-crushing equipment.

2. Analysis of the Working Mechanism of the Hammer Blade for Straw Crushing

2.1. The Structure and Working Principle of the Straw Crusher

As shown in Figure 1, the entire straw crusher is composed of a frame, drive motor, feeding hopper, discharge port, rotor system, screen, and tooth plate. The rotor system, which serves as the core component, comprises the chopper, hammer blade, hammer blade fixing frame plate, pin shaft, main shaft, and throwing vane.

During operation, straw stalks are conveyed into the chopper via the feeding hopper. Initially, the material is cut into coarse segments by high-speed rotary chopper knives. The segments are subsequently drawn into the crushing chamber, where they undergo further refinement into fibrous segments subjected to the impact of high-speed hammer blades and the frictional interaction between the hammers and the tooth plates. During this process, particles conforming to the specified size are discharged through the screen, facilitated by the internal airflow and throwing vane.

2.2. Analysis of the Force Between Hammer Blade and Straw

As the primary components in direct contact with the material, the hammer blades facilitate energy transfer; thus, their structural attributes and motion states significantly impact the overall crushing efficiency [15]. The interaction mechanism between the straw and hammer blades is depicted in Figure 2.

The principle of angular momentum is applied to the entire hammer system with respect to the rotation center O₁:

$${\displaystyle {\int }_0^{\Delta t}{M}_{O_1}dt=\Delta L_{O_1}}$$

(1)

where ΔL_O1 is the total change in angular momentum of the hammer piece around O₁. The magnitude of the torque generated by the impact force F acting at a distance R₁ from O₁ is given by:

$$M_{O_1}dt=F{R}_1$$

(2)

The angular momentum of the hammer system about O₁ is composed of two parts:

The motion of the center of hammer mass around O₁:

$$L_t=m\omega R_3^2$$

(3)

The rotation of the hammer piece around its own center of mass O₂:

$$L_r=J_{O_2}\cdot {\omega }_r$$

(4)

where ω_r represents the angular velocity of the hammer after the collision. The hammer is connected to the pin shaft via a hinge with clearance. Previous studies have indicated that this clearance influences the hammer’s displacement and velocity [16]. Accordingly, the parallel axis theorem is applied as follows:

$$J_{O_1}=J_{O_2}+m{R}_3^2$$

(5)

Accordingly, the total angular momentum of the hammer about O₁ is expressed as:

$$L_{O_1}=J_{O_1}\cdot \omega =\left(J_{O_2}+\mathrm{m}{R}_3^2\right)\omega$$

(6)

Defining k as the velocity loss coefficient to represent the change in angular velocity from ω to ω′ upon impact, the change in angular momentum is given by:

$$\Delta L=\left(J_{O_2}+\mathrm{m}{R}_3^2\right)\left(\omega -{\omega }^{\prime }\right)$$

(7)

By integrating this with Equation (1), the following relationship is obtained:

$$F\cdot R_1\cdot \Delta t=\left(J_{O_2}+\mathrm{m}{R}_3^2\right)k\omega$$

(8)

The impact force F exerted by the hammer on the straw is given by:

$$F={\displaystyle \frac{\left(J_{O_2}+\mathrm{m}{R}_3^2\right)k\omega }{R_1\cdot \Delta t}}$$

(9)

where J_O2 is the moment of inertia of the hammer about point O₂, which is expressed as:

$$J_{O_2}={\displaystyle \frac{1}{3}}m{L}^2$$

(10)

The mass m of the hammer is given by:

$$m=\rho TWL$$

(11)

where ρ is the material density of the hammer blade.

Consequently, Equation (9) simplifies to

$$F={\displaystyle \frac{\rho TWL\left(\frac{L^2}{3}+R_3^2\right)k\omega }{R_1\Delta t}}$$

(12)

Equation (12) demonstrates that the hammer length L significantly influences the impact force exerted on the straw. Additionally, the force depends on the hammer’s thickness T_h, width W, impact radius R₁, and the distance R₃ between the pin shaft and the main shaft center. Straw comminution typically involves multiple mechanical actions, including impact, collision, and friction, as a single impact is insufficient to fully fragment and separate the fibers. The interaction mechanism within the chamber is highly complex. Consequently, the impact force exerted by the hammer on the straw is determined using the FEM.

3. Development and Analysis of a Coupled Finite Element Model for Straw and Hammer Blade Interaction

3.1. Determination of Intrinsic Parameters of Corn Stalks

The experimental materials consisted of mature, disease-free corn stalks grown in Baicheng City, Jilin Province, China. To minimize variability among samples, five corn stalks with different diameters were selected and pre-treated to yield 20 specimens, each with a length of 100 mm and an average diameter of 25 mm.

The intrinsic properties of corn stalks include density (ρ_c), Poisson’s ratio, and elastic modulus. The water displacement method was employed to determine the density [17]. The tests were performed in multiple replicates to ensure reliability. Outliers, defined as values deviating from the median by more than 15%, were excluded, and the remaining data were averaged to obtain the final result. The densities of the pith and rind were 0.53 × 10³ kg/m³ and 1.17 × 10³ kg/m³, respectively.

Poisson’s ratio (μ) is a key mechanical parameter characterizing the transverse deformation of corn stalks. In this study, the resistance strain gauge method was employed to determine the Poisson’s ratio of the rind and pith, respectively [18]. The experimental setup is illustrated in Figure 3.

Based on multiple replicates, the average Poisson’s ratio for the corn stalk pith and rind were determined to be 0.13 and 0.32, respectively.

The elastic modulus (E) was determined through tensile tests. Specimen preparation was performed in accordance with GB/T 1927.2-2021 [19], and tensile testing followed ASTM D638-2010 [20]. Mechanical tests were performed using a TG-9000-M electronic universal testing machine (Dongguan Maisheng Electronic Equipment Co., Ltd., Dongguan, China). Prior to testing, the rind was isolated from the pith. The specimens were then fabricated into a dog-bone shape (with a reduced central cross-section) to ensure that the fracture occurred within the gauge length. The test results are presented in Figure 4.

Based on multiple replicates, the average elastic moduli of the corn stalk rind and pith were determined to be 3.960 GPa and 0.057 GPa, respectively.

3.2. Finite Element Modeling of Straw

A simplified finite element model of the corn stalk was developed using Abaqus. To reduce model complexity, the structural variations at the stalk nodes were neglected, and the stalk was represented by a cylindrical geometry with uniformly distributed internal fibers along the axial direction. In this model, the rind and pith were each treated as homogeneous isotropic materials with distinct properties, rather than assuming the entire stalk to be fully uniform. This piecewise homogeneous simplification was considered appropriate for radial-compression-based calibration and for capturing the dominant response under impact loading, although real corn stalks are inherently transversely anisotropic. Based on these assumptions, a cylindrical corn stalk model with a diameter of 25 mm and a height of 100 mm was constructed. The rind thickness was defined as 1 mm, and a cohesive layer with a thickness of 0.1 mm was inserted between the rind and pith to simulate the interface, thereby facilitating load and displacement transfer as well as interfacial damage evolution [21]. The corn stalk was discretized using C3D8R elements (eight-node linear brick elements with reduced integration), while COH3D8 cohesive elements (eight-node three-dimensional cohesive elements) were employed at the rind–pith interface to simulate the initiation and evolution of interfacial damage during the crushing process.

To validate the accuracy of the established finite element model for corn stalks, a compression test was conducted. The corn stalk specimen was subjected to compression on a universal tension-compression testing machine at a rate of 0.1 mm/s, and its load–displacement curve was recorded. Similarly, a flat-plate compression fixture and a finite element model of the stalk with identical intrinsic parameters as previously tested were developed in Abaqus 2025 finite element analysis software. A comparative analysis between the simulation results and experimental data is illustrated in Figure 5.

As illustrated in Figure 5, the overall deformation pattern of the corn stalk in the finite element model shows high consistency with the experimental results. The variation trends within the elastic stage of both simulation and experiment are largely identical. Furthermore, the ultimate load and its corresponding displacement align closely with the experimental data, with a maximum relative error of 7.72%. These results demonstrate that the simulation is capable of accurately predicting the mechanical response characteristics of the corn stalk.

3.3. Establishment of the Hammer Element Finite Element Model

Currently, various types of hammer blades for straw choppers are available in the Chinese market. Prevalent designs include rectangular, sawtooth, stepped, Y-shaped, and acute-angled blades. Research indicates that rectangular, serrated, and stepped hammer blades offer low manufacturing costs, effective crushing performance, and superior overall characteristics [22]. The reference geometric models for these three types were developed using SolidWorks 2024, as shown in Figure 6.

The hammer blade models were discretized using C3D8R elements (eight-node linear brick elements with reduced integration). The hammer blade models were discretized using C3D8R elements (eight-node linear brick elements with reduced integration). The mesh configurations of the three hammer blade models are shown in Figure 7. The rectangular hammer model consisted of 30,428 elements and 34,695 nodes, the serrated hammer model consisted of 29,508 elements and 34,191 nodes, and the stepped hammer model contained 22,826 elements and 30,026 nodes. To ensure unit consistency in Abaqus, a uniform unit system of mm–tonne–MPa–s was adopted throughout the finite element analysis.

Boundary conditions were defined according to the actual operating characteristics of the crusher. A rotational constraint was applied to the hammer blade through the mounting hole, so that the blade was allowed to rotate about the specified axis while its axial and mirror-direction motions were restricted. The rotational speed of the hammer blade was set to 2600 r/min. In contrast, the corn stalk was left unconstrained in order to simulate its free state inside the crushing chamber. The material properties are listed in

Table 1. Material attribute parameters.

Part	Density (Tonne/mm3)	Poisson’s Ratio	Elastic Modulus (GPa)	Fracture Energy (MJ/mm2)	Direct Strain (mm)
Straw rind	1.17 × 10−9	0.32	3.960	0.350	0.02
Straw pith	0.53 × 10−9	0.13	0.057	0.275	0.04
Bonding unit	0.53 × 10−9	0.13	0.057	0.250	0.04
Hammer blade	7.82 × 10−9	0.28	197	-	-

.

3.4. Model Setup and Analysis of Results

Based on the above finite element model and boundary conditions, dynamic explicit analysis was carried out to simulate the crushing process. The total analysis time was set to 2 s, the field output interval was defined as 4000, and the history output was recorded at every time increment. Surface-to-surface contact was employed to describe the interaction between the hammer blade and the corn stalk. Tangential contact behavior was modeled using the penalty method with a friction coefficient of 0.3 [8], while the normal contact behavior was defined as hard contact. Using the above simulation settings, the crushing processes of corn stalks under the three hammer blade configurations were simulated and compared, as illustrated in Figure 8.

As illustrated in Figure 8, the serrated hammer exhibits superior performance compared to the stepped and rectangular hammers during straw cutting. At the initial cutting stage (adequate depth of 2.9 mm), the serrated hammer achieved the shortest cutting time of 0.143 s and the minimum stress of 237.20 MPa. The stepped hammer followed with a cutting time of 0.148 s and a minimum stress of 148.44 MPa. In contrast, the rectangular hammer recorded the longest cutting time (0.163 s) and the lowest stress (82.78 MPa). According to the principle of stress concentration, the impact effect is governed by the relationship σ = F/A, where σ is the stress, F is the impact force, and A is the contact area. Since the rotational speed of the hammers is constant, the initial impact momentum applied to the straw is theoretically identical across designs. However, the serrated hammer possesses the smallest contact area with the straw. Consequently, it generates the highest local stress at the contact point. This high-stress concentration facilitates rapid fracture initiation, resulting in the highest cutting efficiency and the shortest cutting time. At a cutting depth of 12.5 mm, the serrated hammer retains a significant performance advantage due to its unique structural design. Specifically, the cutting time for the serrated hammer was recorded at 0.584 s, compared to 0.609 s for the stepped hammer and 0.644 s for the rectangular hammer. When the cutting depth reached 25 mm, the serrated hammer achieved a total cutting time of 1.555 s with a minimum cutting stress of 242.52 MPa. In comparison, the stepped hammer required 1.667 s (minimum stress: 176.38 MPa), while the rectangular hammer took the longest time at 1.764 s with the lowest stress of 160.33 MPa. Simulation results reveal that frictional resistance from the straw delays the cutting process [22], with the magnitude of resistance increasing with cutting depth. The serrated and stepped hammers, characterized by optimized geometries and smaller contact areas, are less affected by this friction compared to the rectangular hammer. While the stepped hammer’s sharp tip offers better performance than the rectangular design, its overall efficiency remains inferior to that of the serrated hammer. This suggests that the serrated tooth profile plays a critical role in enhancing cutting efficacy. Therefore, a more detailed exploration of the tooth shape parameters is necessary.

4. Multi-Objective Optimization of Hammer Blade Structural Parameters

4.1. Structural Parametric Design

Previous analyses have demonstrated that sawtooth hammer blades exhibit superior performance in the corn stalk crushing process. To further investigate the influence of structural parameters on crushing performance, the complex geometry of the sawtooth blade was parameterized, with parameters of distinct physical significance defined as design variables. By establishing mathematical constraints among these parameters, a controllable design and analysis framework for the blade structure was established. Based on the structural characteristics of the hammer blade, seven geometric parameters were selected as design variables: length (L), width (W), thickness (T_h), tooth pitch (S), tooth top angle (α), tooth height (H), and the distance from the pin hole to the bottom edge (A). Figure 9 illustrates the parametric model of sawtooth blade.

To accurately characterize the geometric features of the serrated hammer blade and ensure structural consistency, geometric constraints among the parameters must be established. Assuming the serrations are uniform isosceles triangles, the apex angle (α) is not an independent variable; its value is determined by the tooth height (H) and pitch (S). The constraint relationship is defined as follows:

$$\tan \left({\displaystyle \frac{\alpha }{2}}\right)={\displaystyle \frac{S/2}{H}}={\displaystyle \frac{S}{2H}}$$

(13)

Specifically, the expression for the apex angle (α) is given by:

$$\alpha =2\cdot \arctan \left({\displaystyle \frac{S}{2H}}\right)$$

(14)

To ensure manufacturability, the number of teeth (N) must be an integer and should align with the effective working length of the hammer blade. Consequently, the constraint relationship for N is expressed as:

$$N=floor\left({\displaystyle \frac{L}{S}}\right)$$

(15)

In this context, the effective cutting edge length of the hammer blade is approximated by:

$$L\approx N\cdot S$$

(16)

A Cartesian coordinate system (xOy) is established to describe the serrated blade’s contour, with the origin (0, 0) positioned at the bottom-left corner. For the domain x ∈ [0, L], a triangular wave function (period S, amplitude H) is employed. Accordingly, the profile function is given by:

$$\phi \left(x,S,H\right)={\displaystyle \frac{2H}{S}}\left|\left(x\left(\mathrm{mod}S\right)\right)-{\displaystyle \frac{S}{2}}\right|$$

(17)

Consequently, the profile functions of the upper and lower surfaces are given by:

$$y_{upper}\left(x\right)=W-\left(H-{\displaystyle \frac{2H}{S}}\left|\left(x\left(\mathrm{mod}S\right)\right)-{\displaystyle \frac{S}{2}}\right|\right)$$

(18)

$$y_{lower}\left(x\right)=H-{\displaystyle \frac{2H}{S}}\left|\left(x\left(\mathrm{mod}S\right)\right)-{\displaystyle \frac{S}{2}}\right|$$

(19)

4.2. Design of Experiments and Sample Generation

4.2.1. Evaluation Indices and Parameter Ranges

To ensure optimal crushing performance, a multi-objective optimization was conducted with the objectives of minimizing both the surface stress of the hammer blade and the straw breakage time. Consequently, the structural parameters of the sawtooth hammer blade were comprehensively optimized.

To analyze the influence of each structural parameter on crushing performance, a design variable vector was constructed. As indicated by Equation (12), the length (L), thickness (T_h), and width (W) of the hammer blade, along with the effective impact radius (R₁), significantly influence the impact performance. Previous simulation results demonstrated that serrated hammers outperform rectangular and stepped designs; therefore, the tooth pitch (S), apex angle (α), tooth height (H), and the rotation radius (R₃) around the pin shaft. Thus, the established design variables are:

$$X={\left[L,T_h,W,S,\alpha ,H,R_3\right]}^T$$

(20)

The optimization objective is expressed as:

$$\begin{array}{l}MinimizeT=MinT\left[L,T_h,W,S,\alpha ,H,R_3\right]\\ Minimize\sigma =Min\sigma \left[L,T_h,W,S,\alpha ,H,R_3\right]\end{array}$$

(21)

For a constant rotational speed, the hammer length (L) determines the balance between collision probability and mechanical load. While a larger L expands the sweeping area, it elevates rotational inertia and bending moments, increasing the risk of fatigue failure at the pinhole. Conversely, a reduced L compromises the crushing stroke and throughput. Accounting for chamber dimensions and assembly constraints, the optimization range for L is set to 165–185 mm.

Inadequate width of the hammer (W) weakens the structural integrity of the pinhole region. However, an overly large width leads to higher energy consumption and lower specific impact force [23]. To balance structural strength and energy economy, the optimization range of W is defined as 35–45 mm.

Increasing the blade thickness (T_h) improves structural stiffness but diminishes the impact pressure per unit area while increasing energy demands. However, a nominal T_h that is too small elevates the risk of plastic deformation and fatigue failure [1]. Considering these trade-offs, the optimization range of T is defined as 3–6 mm.

Regarding the tooth profile parameters, an insufficient tooth pitch (S) results in a sharp increase in the number of teeth per unit length (N), narrowing the root spacing. This leads to the entanglement and accumulation of straw fibers, thereby reducing the effective cutting probability. Furthermore, under geometric constraints, a reduction in S decreases the apex angle (α), which elevates local contact stress at the tooth tip and increases wear risk. In contrast, an excessively large S reduces the number of effective cutting edges, compromising crushing efficiency. Considering integer constraints and anti-clogging requirements [12], the optimization range for S is set to 4–8 mm.

Tooth height (H) governs both cutting depth and tip sharpness: a smaller H leads to a larger α, which weakens penetration and causes material slippage; a larger H results in a smaller α, intensifying stress concentration at the tooth root and the risk of fatigue fracture [24]. Consequently, the optimization range of H is defined as 2–4 mm.

The selection of the hammer’s rotation radius (R₃) about the pin shaft involves a trade-off between structural strength and mass distribution. For a given total length (L), an insufficient R results in increased non-working mass and energy consumption. Conversely, an excessive R leads to an inadequate bearing cross-section at the pinhole edge, which is prone to crack initiation. Considering structural integrity and assembly constraints, the optimization range for R₃ is set to 25–30 mm.

Accordingly, the constraints for the design variables are formulated as follows:

$$s.t.\left\{\begin{array}{c}165\le L\le 185\\ 35\le W\le 45\\ 3\le T_h\le 6\\ 4\le S\le 8\\ 2\le H\le 4\\ 25\le R_3\le 30\end{array}\right.$$

(22)

4.2.2. Sample Generation Procedure

Utilizing the optimal Latin Hypercube Sampling (LHS) method, 50 sample points were generated in the design space to assess parameter significance under a limited sample size. This approach provides uniform coverage of the variable domains and mitigates issues related to parameter aggregation, thereby maximizing information gain.

Table 2. Sample parameters based on optimal Latin hypercube sampling.

Sample Number	Design Variables						Output Response
	L/mm	W/mm	Th/mm	S/mm	H/mm	R3/mm	σ/MPa	T/s
1	170	42	4	6	4	25	468.3	0.186
2	166	44	4	7	3	27	452.1	0.191
3	166	39	6	6	3	26	439.5	0.178
4	172	40	3	7	3	30	483.7	0.182
5	169	36	5	5	3	28	462.4	0.171
6	171	41	4	5	4	29	470.6	0.184
7	173	36	3	5	2	27	498.9	0.172
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
48	165	37	3	5	3	27	501.6	0.174
49	184	41	4	5	4	29	470.9	0.183
50	178	38	3	7	4	28	492.4	0.176

presents the distribution of these sample parameters.

Table 2 demonstrates the comprehensive distribution of the sample points, which establishes a reliable basis for the subsequent finite element analysis (FEA) and sensitivity study.

4.3. Parameter Sensitivity Analysis

4.3.1. Construction and Validation of Surrogate Models

To ensure the surrogate model satisfies the required precision for analysis, its fitting accuracy must be rigorously evaluated. Accordingly, this study utilizes the coefficient of determination (R²) and the root mean square error (RMSE) as evaluation criteria [25], calculated as:

$$R^2=1-{\displaystyle \frac{{\displaystyle \sum _{i=1}^m{\left(y_i-{\widehat{y}}_i\right)}^2}}{{\displaystyle \sum _{i=1}^m{\left(y_i-{\overline{y}}_i\right)}^2}}}$$

(23)

$$RMSE=\sqrt{{\displaystyle \frac{1}{m}}{\displaystyle \sum _{i=1}^m{\left(y_i-{\widehat{y}}_i\right)}^2}}$$

(24)

where $y_i$ denotes the actual response value; ${\widehat{y}}_i$ is the predicted value from the surrogate model; ${\overline{y}}_i$ represents the mean of the actual response values; and m is the number of samples.

As illustrated in Figure 10, the R² values for crushing time and minimum stress reach 0.8738 and 0.8848, while the RMSE values are 0.1023 and 0.0989. These results demonstrate sufficient model precision for subsequent sensitivity analysis and optimization.

4.3.2. Sensitivity Analysis

Based on the Kriging model, a sensitivity analysis was performed to evaluate the impact of various structural parameters on the hammer’s crushing performance.

The relative importance of each design variable regarding crushing time (T) and minimum stress (σ) was determined, as shown in Figure 11. Positive correlations are represented in red, whereas negative correlations are indicated in blue.

As illustrated in Figure 11, hammer thickness (T_h) and tooth spacing (S) are the predominant factors affecting the minimum stress. In contrast, for crushing time, hammer width (W) exerts the most significant influence, followed by tooth spacing (S). These results demonstrate that the crushing performance of the sawtooth hammer exhibits distinctly varied sensitivities to changes in geometric parameters, establishing a solid foundation for the ensuing optimization of key variables.

4.4. Optimization Procedure and Results Analysis

In this study, the optimization is conducted using the NSGA-II algorithm within the Isight platform. The algorithm configuration includes a population size of 40 and a maximum generation count of 80, resulting in a total of 3200 function evaluations. Figure 12 presents the convergence histories of the best objective values in each generation over the 80 generations. Both the minimum contact stress and crushing time gradually diminish and reach a steady state as the generations progress, demonstrating the satisfactory convergence of the NSGA-II algorithm.

A total of 33 Pareto optimal solutions were identified using the NSGA-II algorithm (Figure 13). The Pareto front indicates a clear negative correlation between minimum contact stress and crushing time. The well-distributed and continuous nature of the solution set demonstrates the robustness of the optimization process in searching for optimal structural configurations.

A representative optimal solution was selected from the Pareto set. These values were subsequently refined to align with practical manufacturing constraints. The resulting optimal parameters for the serrated hammer are summarized in

Table 3. Optimal design parameters of the hammer blade.

Parameter	Hammer Length (mm)	Hammer Width (mm)	Hammer Thickness (mm)	Tooth Pitch (mm)	Tooth Angle (°)	Tooth Height (mm)	Pin-Bottom Distance (mm)	Fracture Stress (MPa)	Fracture Time (s)
Value	172	39	4	4	67.38	3	30	423.6	0.174

.

5. Experimental Verification

5.1. Test Conditions

To verify the effectiveness of the optimized structural parameters, a field test was conducted to compare the performance of the optimized serrated hammer with that of a standard rectangular hammer under identical operating conditions.

The experimental setup consisted of a Model 9ZF-600 corn stalk chopper (rated power: 4 kW), standard rectangular hammers, and optimized serrated hammers, as shown in Figure 14. The measuring instruments included an electronic timer (resolution: 0.01 s), an electronic scale (resolution: 0.1 g), and multi-level sieves. Testing was conducted in compliance with GB/T 6971-2007 [26]. A comparative analysis was employed to evaluate the operational performance of both the standard and optimized hammer configurations.

5.2. Analysis of Experimental Results

In accordance with relevant technical specifications, the mass proportion of filamentous material (with a length of 10–180 mm and a width ≤ 5 mm) was adopted as the evaluation metric to ensure compliance with livestock feeding requirements [26]. A higher proportion signifies enhanced fiber separation and superior shredding quality. To ensure reproducibility, experiments were performed in multiple trials. The average of three consistent replicates was taken as the final result, following the removal of any data points with excessive dispersion.

Table 4. Performance comparison of the stalk chopper pre- and post-optimization.

	Before Optimization	Optimized	Unit
Productivity	1.83	2.15	kg·min−1
Pass rate	87.02	91.39	%

presents result of the experiment.

According to the results in Table 4, the optimized crusher exhibited a significant performance boost: throughput improved from 1.83 kg·min⁻¹ to 2.15 kg·min⁻¹, while the proportion of qualified material increased from 87.02% to 91.39%. Testing demonstrates that the serrated design enhances the mechanical interaction between the blades and the straw, optimizing the loading conditions for fiber separation. This leads to a significant boost in operational efficiency without compromising the quality of the chopped straw. Figure 15 presents the morphology of the processed material.

6. Conclusions

• The influence of structural parameters on the impact force exerted on the straw during the crushing process was theoretically deduced. The analysis indicates that the hammer length and rotation radius significantly affect crushing performance, while hammer mass, width, thickness, and angular velocity also contribute to variations in impact force. These relationships provide a theoretical basis for hammer structural design.
• A finite element model describing the hammer–straw interaction was established based on experimentally obtained mechanical properties. Comparative analysis of serrated, rectangular, and stepped hammers indicates that the serrated design offers superior performance, specifically in terms of shorter cutting duration and optimized impact force.
• A parametric model of the serrated hammer was further developed. Subsequently, the sensitivity of the crushing performance to structural parameters was evaluated utilizing Latin hypercube sampling and a Kriging model. The analysis identified the hierarchy of factor significance as follows: hammer thickness > hammer width > tooth spacing > hammer length. These findings corroborate the theoretical deductions.
• On the basis of the surrogate model, multi-objective optimization was carried out using the NSGA-II algorithm with the objectives of minimizing cutting force and cutting time. The optimized hammer configuration was determined to have a thickness of 4 mm, a width of 39 mm, and a tooth spacing of 4 mm, achieving a balanced improvement in crushing efficiency and load characteristics.
• Experimental results indicate that the optimized serrated design outperforms the standard rectangular hammers, achieving a 17.49% increase in throughput and a 5.02% improvement in processing quality. These results demonstrate the practical feasibility of the proposed design for improving the productivity and shredding quality of straw crushing equipment.
• The present study mainly focused on the crushing performance of the machine, with cutting time and minimum cutting force adopted as the primary evaluation indices. However, a comprehensive assessment of machine performance should not be limited to these two indicators alone, but should also consider additional factors such as noise, power consumption, moisture content, and feeding rate. Moreover, this work only investigated hammer geometry and did not address the effects of straw moisture content or other relevant performance parameters. Therefore, future research should establish a more comprehensive evaluation system and methodology for straw crusher performance.