Dynamic Mechanisms and Screening Experiments of a Drum-Type Mulch-Film Impurity-Removal System

Abstract

Efficient and clean separation of residual plastic mulch film is the primary bottleneck hindering its resource-oriented reutilization. Currently, the field faces critical technical challenges, most notably the elusive motion mechanisms of flexible materials and the inherent difficulty of film–impurity separation. To address these issues, this study investigates a drum-type mulch-film impurity-removal unit by modeling the throw-off motion mechanism of the material stream, followed by comprehensive multiphysics simulation and optimization. First, to overcome the simulation hurdles typical of flexible materials, “Meta-particles” and the “Bonding V2” contact model were implemented on the EDEM platform to establish a discrete element method (DEM) framework. The resulting analysis revealed a non-linear transport trajectory and morphological evolution within the drum flow field, characterized by a “wall-adhering–slipping–throwing” sequence. These findings were further quantified through MATLAB-based numerical calculations to determine collision frequency and axial residence behavior. Second, ANSYS modal analysis verified the dynamic stability of the frame structure, confirming that the operating frequency (2.37 Hz) remains well below the first natural frequency (6.77 Hz). Furthermore, Box–Behnken response surface methodology (RSM) was employed to elucidate the coupled effects of key process parameters. The results demonstrated that separation efficiency and impurity-removal mass are predominantly governed by the quadratic terms of the inclination angle and rotational speed, respectively. After multi-objective optimization and engineering refinement, the optimal operating parameters were established: a film length of 220 mm, an inclination angle of 3°, and a drum rotational speed of 25 r/min. Bench tests indicated that, under these optimal conditions, the impurity-removal rate stabilized between 71.5% and 72.4%, satisfying the design requirement (≥70%). By elucidating the drum’s throw-off screening mechanism, this study achieves a coordinated improvement in both impurity-removal mass and separation efficiency, resolving long-standing engineering uncertainties regarding film–impurity trajectories and providing a theoretical foundation for the clean treatment of waste mulch film.

1. Introduction

Plastic mulch-film technology has been widely adopted in modern agriculture, effectively enhancing crop yields, improving soil water retention, and increasing nutrient-use efficiency. However, after prolonged use, residual film and entrained contaminants—such as soil and cotton stalk residues—remain within the cultivated (plow) layer, forming a complex pollutant system. This, in turn, poses ecological risks including the deterioration of soil structure, constrained root development, and the accumulation of microplastics (Figure 1) [1,2,3,4,5]. Against the backdrop of growing demand for clean recovery and resource-oriented reutilization, the industry commonly employs a drum-based throw-off primary screening process. Dominated by gravitational and inertial effects, this method is widely used to achieve preliminary film–impurity separation due to its simple structure and continuous operation. Nevertheless, studies on the staged motion characteristics and separation behavior of the multiphase film–soil–stalk system inside the drum remain insufficient, thereby constraining the systematic optimization of equipment parameters [6].

Against the backdrop of escalating demands for clean recycling and resource valorization, drum-based tossing pre-screening processes—governed by gravity and inertia and characterized by structural simplicity and continuous operation—have been widely adopted for the preliminary separation of flexible films from mixed impurities. However, this separation efficiency is highly sensitive to the physical state of the recovered material, particularly its moisture content. Elevated moisture content markedly intensifies the adhesion between soil particles, cotton stalks, and flexible films while altering their frictional behavior; consequently, this not only increases the mass of agglomerated material but also substantially raises the risk of screen blinding, rendering film–impurity separation fundamentally more challenging. Furthermore, while recent studies on drum screening and pneumatic removal have progressed regarding critical rotational speeds and screen-aperture configurations, a comprehensive kinematic characterization of the full motion cycle of “bundled flexible agricultural mulch film” within the drum—encompassing adhesion, sliding, detachment, and re-contact—remains under-explored. Moreover, generic relationships between key structural parameters and separation performance have yet to be firmly established. Engineering practice indicates that current drum-based impurity removal still faces two major challenges: (1) insufficient analysis of the unfolding and re-mixing behavior of bundled flexible mulch film during tossing and tumbling, which hampers the accurate evaluation of collision cadence and separation effectiveness; and (2) strong coupling among multiple factors, including drum rotational speed, inclination angle, and screen-surface structure. This complexity makes it difficult to simultaneously achieve high throughput and superior impurity-removal quality, with parameter settings still relying heavily on empirical methods. Collectively, the limited understanding of these dynamic evolution mechanisms and the multi-parameter coupling problem constrain the systematic optimization and broader deployment of such separation equipment.

To address these challenges, this study focused on a drum-type agricultural mulch-film impurity-removal system, conducting a systematic investigation encompassing mechanistic modeling, simulation analysis, and parameter optimization. Initially, to bridge the gap in understanding flexible film kinematics, a novel simulation model for agricultural mulch film was developed on the EDEM2024 discrete element platform by integrating a meta-particle approach with the Bonding V2 contact model. The staged motion characteristics of the film within the drum—specifically “wall adhesion–sliding–tossing/cascading”—were further elucidated through analytical modeling based on governing dynamic equations. Subsequently, to resolve optimization difficulties arising from strong multi-parameter coupling, a Box–Behnken design (BBD) combined with multi-objective optimization was employed. This approach allowed for the examination of interaction mechanisms by which film length, drum inclination, and rotational speed jointly affect impurity-removal quality and separation efficiency, ultimately determining the optimal operating-parameter combination. Overall, these findings clarify the screening-driven transport behavior of flexible films, providing theoretical foundations and technical guidance for the structural refinement and process regulation of waste mulch film recycling equipment.

In summary, efficient impurity removal and clean treatment of waste residual mulch film directly determine the quality and economic value of regenerated plastic pellets, and constitute a pivotal step in transforming waste mulch film from an agricultural pollutant into a high-value resource. In this study, the structural configuration of a drum screening device featuring a perforated screen as the core component was first established. The vibration resistance of the frame was then verified via ANSYS modal analysis by examining the first six natural modes, thereby ensuring the rationality of the structural design. On this basis, the dynamic mechanisms of mulch film inside the drum were investigated in depth. At the theoretical level, a segmented mechanical model incorporating the “lifting–throwing” process and a hybrid dynamic equation describing axial conveying through “adhesion–slip” behavior were developed. At the simulation level, the “Meta-particles” and “Bonding V2” contact models were innovatively introduced to overcome the limitation of conventional DEM simulations that simplify mulch film as rigid particles, enabling reproduction of folding, entanglement, and nonlinear large-deformation behavior of flexible film. Subsequently, a Box–Behnken experimental design was used to analyze the coupled effects of film length, drum inclination angle, and rotational speed on impurity-removal mass and separation efficiency. The results revealed the dominant role of rotational speed in impurity removal and the regulating mechanism of inclination angle on separation. Multi-objective optimization further yielded the optimal process parameters, and bench tests confirmed that the optimized device maintained an impurity-removal rate stably above 70%, providing reliable theoretical support and an evaluation benchmark for mechanized recycling of waste residual mulch film.

2. Materials and Methods

2.1. Literature Review and Structural Design

In the pre-treatment stage of resource-oriented utilization of waste residual mulch film, the trommel screen (rotary drum screen) is the key functional component of the film–soil/impurity separation system, and the screen-surface type directly determines separation efficiency, anti-clogging performance, and operational stability. According to screen-surface configuration and manufacturing process, the commonly used engineering designs can be classified into three categories: bar screen, woven screen (wire-mesh screen), and perforated screen (Figure 2) [6,7,8,9]. (a) Bar screen: It relies on the slot spacing between bars to rapidly pre-screen large particles and agglomerates. Owing to its strong resistance to entanglement and wet clogging, it is suitable for coarse screening and high-throughput applications. However, the slot size is inherently limited, resulting in insufficient removal of fines and dust; thus, it is difficult to meet high-precision separation requirements. (b) Woven screen (wire-mesh screen): With uniform apertures, it provides relatively high screening accuracy and adapts well to fine impurities and low-density particles. Nevertheless, the stiffness and wear resistance of the wires are limited; under conditions involving hard foreign objects (e.g., stones and metal fragments) and high-moisture materials, it is prone to aperture blockage and deformation, leading to frequent maintenance. (c) Perforated screen: Featuring regular hole geometry, high screen strength, and good wear resistance, it can withstand impacts from hard particles while maintaining classification accuracy, and therefore shows strong overall adaptability under complex operating conditions involving soil clods and gravel. However, its self-weight and manufacturing cost are relatively high, and mismatched hole diameter and open-area ratio may cause a loss in screening efficiency.

2.2. Structural Design and Modal Characterization

Structural Design

Based on the comparison of screen-surface configurations in Section 2.1, a perforated screen (Nanjing Institute of Agricultural Mechanization, Ministry of Agriculture and Rural Affairs, Nanjing, China) was selected as the core screening surface for the drum-type film–impurity separation unit. A three-dimensional model of the machine was developed in Solidworks 2024, as shown in Figure 3. The system primarily consists of the following components: Main frame: Provides rigid support and installation datum surfaces for the drum, drive train, and auxiliary components. Perforated drum (trommel): Serves as the core functional component, responsible for the tumbling action and through-screen separation of the film–impurity mixture. Drive system: Comprises an electric motor, speed reducer, and chain drive, enabling adjustable drum speeds and stable power transmission. Bearing assemblies: Support the drum while minimizing friction and vibration. Inclined chute: Conditions and stabilizes the incoming material stream to prevent accumulation and entanglement. Inclination mechanism: Enables continuous adjustment of the drum angle to accommodate varying operating conditions. Feed conveyor: Delivers material smoothly and continuously to mitigate transient load fluctuations. Discharge and impurity system: Collects and conveys undersize impurities passing through the screen, ensuring efficient segregation of the material streams.

Once delivered by the feed conveyor to the inclined chute, the material stream slides along the guide plate and enters the rotating drum. Driven by the synergy of centrifugal force, gravity, and friction, the mulch film exhibits a cyclic sequence of wall-adhesion climbing, detachment, cascading, and tumbling-induced disentanglement. Adhered soil and fine particles pass through the screen apertures to be collected and conveyed downstream, thereby achieving a continuous and integrated process of steady feeding, high-throw separation, and synchronized impurity removal [9]. The technical specifications of the device are detailed in

Table 1. Equipment technical parameters.

Technical Index	Technical Parameters
Dimensions (Length × Width × Height)/mm	$2240\times$ $1360 \times$ 2521
Total Weight/kg	450
Drum Dimensions (Diameter × Length)/mm	$1000 \times$ 2000
Adjustable Lifting Height/mm	0–100
Reduction Ratio	1:100
Rotational Speed Range/(r/min)	0–1420
Feeding Conveyor Speed (m/s)	0.13
Discharge Conveyor Speed (m/s)	0.12

.

2.3. Modal Analysis

As the primary load-bearing and integration component of the drum-type impurity-removal equipment, the frame’s dynamic characteristics directly determine operational stability and the effectiveness of film–impurity separation [10]. To verify the rationality of the structural design, a three-dimensional frame model was developed in SolidWorks 2024. To balance computational efficiency with solution accuracy, non-critical features with negligible influence on global stiffness—such as chamfers and weld beads—were simplified. The model was then imported into ANSYS Workbench 2022 R1. Using Q235 carbon structural steel, which offers good weldability and vibration resistance (mechanical properties listed in

Table 2. ANSYS simulation parameters.

Material Name	Young’s Modulus (N/m2)	Poisson’s Ratio	Density (kg/m3)	Shear Modulus (N/m2)	Yield Strength (N/m2)
Q235	$2.06 \times$ 1011	0.3	7850	$7.9 \times$ 1011	$2.35 \times$ 108

), a finite element modal analysis was performed. By characterizing the natural frequencies and mode shapes, this analysis provides a theoretical basis for subsequent structural refinement and resonance avoidance [11].

Following the assignment of predefined material properties, the model was discretized for finite element analysis. To ensure numerical accuracy and reliability, a tetrahedral mesh was employed for the frame’s geometry (Figure 4). Using ANSYS Workbench 2022 R1, the global element size was set to 10 mm, yielding a computational mesh consisting of 468,013 elements and 940,338 nodes.

Post-meshing, boundary conditions were established to reflect the frame’s in-service load-bearing characteristics. Fixed-end (fully constrained) supports were applied to the respective mounting interfaces. A modal analysis was then conducted using ANSYS Workbench 2022 R1 to extract the first six natural frequencies and their associated mode shapes, as illustrated in Figure 5.

According to $f=n/60$, the maximum operating frequency of the frame was calculated to be 2.37 Hz. Combined with the analysis of the first six mode shapes, it can be concluded that, during operation, the excitation frequency is lower than the first natural frequency (6.7715 Hz); therefore, resonance will not occur, and the frame design satisfies the requirements for normal operation of the device. The maximum deformation, mean deformation, and natural frequency of the frame for the first six modes are summarized in

Table 3. Results of the 1st- to 6th-order modal analysis.

Mode Order	Maximum Deformation (mm)	Average Deformation (mm)	Modal Frequency (Hz)
First Mode	10.83	1.16	6.77
Second Mode	10.68	1.35	7.30
Third Mode	6.50	2.01	13.17
Fourth Mode	5.66	2.01	13.49
Fifth Mode	7.45	1.85	15.65
Sixth Mode	8.22	1.92	17.02

.

2.4. Discrete Element Method (DEM) Analysis

To investigate the dynamic transport behavior and screening mechanism of mulch film and impurities within a trommel screen, a discrete element method (DEM) simulation model of the film-screening process was established in this study [12]. In existing DEM research, modeling flexible, irregular materials such as mulch film still faces substantial technical bottlenecks. Conventional rigid-body (planar) models offer low computational cost but cannot reproduce film folding and entanglement, leading to distorted predictions. In contrast, standard flexible agglomerate (clumped/connected-particle) modeling approaches often suffer from an excessive number of constituent particles, complicated geometric construction, and prohibitively high computational expense, which hinders their efficient adoption in engineering applications.

To overcome the trade-off between simulation accuracy and computational efficiency, this study—utilizing the Altair EDEM 2024 platform—proposes a cost-effective and efficient modeling scheme that integrates spherical meta-particles with the Bonding V2 contact model. In this framework, the morphology of agricultural mulch film is represented by meta-particles, effectively bypassing the computational overhead associated with complex meshing or filling strategies (Figure 6). Meanwhile, inter-particle bonds with prescribed mechanical properties are defined to constrain relative translation and rotation at the microscale. This mechanism endows the model with cloth-like macroscopic characteristics, such as low flexural stiffness and high deformability (Figure 6a–c). Beyond addressing the limitations of conventional modeling, the proposed approach markedly enhances structural fidelity during dynamic evolution, effectively capturing nonlinear large-deformation behaviors at the screening interface—including sliding, adhesion, dynamic wrapping, and screen-aperture penetration. Consequently, this method provides a high-fidelity simulation tool for elucidating film transport and migration within complex particle–airflow environments, offering a robust theoretical foundation for optimizing film detachment and screening efficiency in recycling equipment.

To accurately reproduce the mechanical behavior of mulch film as a flexible continuous medium, this study adopted the Hertz–Mindlin with Bonding V2 contact model, which is based on the parallel-bond theory proposed by Potyondy and Cundall and subsequently refined. This model establishes a virtual bonded disk with physical entity attributes between film particles (meta-particles), thereby enabling effective transmission of normal and tangential forces as well as moments, and allowing the tensile, shear, and bending responses of thin-film materials to be represented (Figure 7). The geometric size of the bonded disk is determined by the sizes of the contacting particles and preset parameters. Its radius $R_B$ is defined as $R_B=R_{\mathrm{m}\mathrm{i}\mathrm{n}}\times \lambda ,$ where $R_{\mathrm{m}\mathrm{i}\mathrm{n}}$ is the radius of the smaller particle in the contact pair, and $\lambda$ is the bonded-disk scale factor (Bonded Disk Scale). Based on this radius, the bond cross-sectional area $A$ and polar moment of inertia $J$ are calculated as $A=\pi R_B^2, J={\displaystyle \frac{1}{2}}\pi R_B^4.$

During simulation, the model updates the force state of the parallel bonds using an incremental scheme [12,13]. Within each time step $\delta t$, the increments of normal force $\delta F_n$, tangential force $\delta F_t$, normal moment (torsional moment) $\delta M_n$, and tangential moment (bending moment) $\delta M_t$ are computed according to the relative motion between particles, as given by the following equations [14]:

$$\left\{\begin{array}{c}\delta F_n=-v_n{S}_{n}A\delta t\\ \delta F_t=-v_t{S}_{t}A\delta t\\ \delta M_n=-{\omega }_n{S}_{t}J\delta t\\ \delta M_t=-{\omega }_t{S}_n{\displaystyle \frac{1}{2}}\delta t\end{array}\right.$$

(1)

where $v_n$ and $v_t$ denote the relative normal and tangential velocities between particles; ${\omega }_n$ and ${\omega }_t$ are the relative normal and tangential angular velocities; and $S_n$ and $S_t$ represent the normal and tangential stiffness per unit area, respectively.

To enhance the accuracy and reliability of the DEM simulations, the physical properties and contact parameters of the mulch film and cotton stalk residues were first calibrated against existing literature (

Table 4. Material parameters.

Parameter/Name	Plastic Film	Cotton Stalk	Q235
Poissons Ratio	0.41	0.34	0.29
Solids Density (kg/m3)	240	260	7850
$\mathrm{Shear} \mathrm{Modulus} (P_a$)	$8.9 \times$ 106	$1.1 \times$ 107	$8.0 \times$ 1010

and

Table 5. Interfacial contact parameters.

Parameter/Name	Plastic Film–Plastic Film	Plastic Film–Cotton Stalk	Plastic Film–Q235	Cotton Stalk–Cotton Stalk	Cotton Stalk–Q235
Coefficient of Restitution	0.86	0.86	0.45	0.21	0.31
Coefficient of static Friction	0.71	0.66	0.42	0.6	0.45
Coefficient of Rolling Friction	0.65	0.55	0.35	0.24	0.32

) [12,13,14,15,16]. Additionally, adaptive adjustments were implemented to accommodate the mechanical characteristics of the Bonding V2 flexible model, ensuring that the simulated dynamic responses more closely aligned with practical conditions. In the construction of the multi-component model, a significant particle-size disparity exists between the soil and the mulch-film/stalk residues. Introducing soil particles at their actual scale into a full-scale drum flow field would lead to an exponential increase in DEM entities. This would not only impose a prohibitive computational burden but also potentially cause solver non-convergence due to excessively dense contact detection. This study primarily aims to characterize the macroscopic transport trajectory and morphological evolution (e.g., entanglement) of waste mulch film within the drum. Given that film motion is predominantly governed by the drum’s structural constraints and interactions with large cotton stalk residues, the perturbations from fine soil particles are considered negligible. Consequently, a three-body dynamic model comprising the mulch film, the cotton stalk residues, and the drum was established. This approach enables the effective simulation of key film motion characteristics at a manageable computational cost.

To achieve a precise calibration of the discrete element method (DEM) contact parameters for flexible agricultural mulch film, an image-based characterization workflow was established, integrating physical measurement, simulation reconstruction, and multidimensional feature extraction (Figure 8). For the physical measurement of the angle of repose (AoR), the hollow cylinder method was employed. A smooth, transparent PVC cylinder with a 100 mm inner diameter served as the receptacle to minimize boundary wall friction during material discharge. To ensure accuracy and repeatability, the cylinder was rigidly clamped to a UTM6000 universal testing machine and withdrawn vertically at a constant velocity of 5 mm/s. This quasi-static lifting protocol effectively eliminated human-induced errors—such as velocity fluctuations and lateral sway—ensuring that the flexible film collapsed naturally to form a stable heap under gravity. Simultaneously, DEM simulations were performed to replicate the film-particle piling behavior under identical conditions. Following the acquisition of macroscopic images from both physical tests and virtual simulations, a unified computer-vision pipeline—incorporating grayscale conversion, binary thresholding, and edge-detection operators—was applied to extract geometric boundary coordinates with high fidelity. Finally, using the least-squares principle, linear regression was performed on the sloping profiles of the heap. The quantified AoR served as the primary criterion for validating the calibrated DEM parameters. Statistical analysis from five replicates indicated that the image-derived AoR for physical heaps averaged 35.83° (with individual profile slopes of 40.29° and 31.37°), while the simulated AoR averaged 33.64° (35.29° and 31.99°). The mean relative error was approximately 6.1%, demonstrating that the developed simulation model and calibrated parameters meet the requirements for high-fidelity DEM modeling of flexible materials.

To replicate the flexible mechanical behavior of waste agricultural mulch film during drum screening, this study utilized the Hertz-Mindlin with Bonding V2 model within the EDEM framework. The film was represented as a discrete bonded-particle assembly, where constituent meta-particles were interconnected by cohesive bonds to form a flexible sheet. The bond stiffness parameters were iteratively calibrated through angle-of-repose (AOR) benchmark tests to ensure that the simulated heap morphology and AoR closely matched experimental observations, thereby validating the model’s ability to capture macroscopic piling behavior and frictional flow characteristics. Since the present study focuses on screening-separation mechanisms and kinematic evolution—rather than film tearing or fracture—the bond failure thresholds (normal and shear strengths) were assigned sufficiently high values to prevent unrealistic debonding or structural disintegration during simulation. In the Bonding V2 framework, bond failure is governed by a stress-based criterion, where the equivalent breakage force is a function of the effective bonded contact area. The specific Bonding V2 parameters adopted in this study, along with their calibration and assignment rationale, are summarized in

Table 6. Bonding V2 bonding parameters.

Parameter Name	Symbol	Unit	Value
Normal stiffness per unit area	$k_n$	$\mathrm{N}{/\mathrm{m}}^3$	$1\times {10}^8$
Shear stiffness per unit area	$k_S$	$\mathrm{N}{/\mathrm{m}}^3$	$5\times {10}^7$
Critical normal strength	${\sigma }_n$	${\mathrm{P}}_{\mathrm{a}}$	$1\times {10}^8$
Critical shear strength	${\sigma }_S$	${\mathrm{P}}_{\mathrm{a}}$	$1\times {10}^8$
Bonded disk scale	\	\	$1.15$

.

In this study, a three-dimensional solid model of the drum was developed in SolidWorks and imported into the EDEM discrete element simulation platform in STEP format. To investigate the influence of structural parameters on operating performance, the drum inclination angle was set to 2–6° to represent practical working conditions, while keeping the rotational angular velocity constant. Considering the physical characteristics of waste residual mulch film, the film was modeled using the Meta-particles approach in conjunction with the Bonding V2 bonding model. By representing flexibility via high-density sub-sphere filling, this method reduces computational time and overcomes the limitations of conventional rigid-particle models, enabling high-fidelity simulation of the film’s elasto-plastic deformation and complex transport trajectories. The kinematic characteristics of the mulch film under different inclination angles were extracted and analyzed, and validation against practical operating observations confirmed the effectiveness of the coupled model in reproducing the realistic dynamic behavior of flexible materials (Figure 9).

The drum inclination angle, as a key kinematic parameter governing the axial conveying characteristics of screening equipment, exerts a pronounced and decisive influence on the transport rate of flexible residual mulch film and its spatiotemporal distribution within the drum. DEM simulations indicated that, as the inclination angle increased from 2° to 6°, the dynamic evolution of the in-drum material bed shifted from localized accumulation near the feed end toward more dispersed axial flow along the full drum length (Figure 10). From a kinematic-mechanism perspective, increasing the inclination angle directly amplifies the axial component of gravitational force acting on the material, thereby increasing the pitch of the particles’ helical trajectories. Consequently, the axial conveying velocity increases markedly and the mean residence time is substantially reduced. However, although high-inclination operation enhances axial conveying and thus significantly improves system throughput, the concomitant thinning of the material layer may limit the effective contact frequency at the film–screen interface and reduce the time available for impurity detachment. This mechanistic interpretation clarifies the trade-off between conveying rate and screening quality, providing key theoretical criteria and numerical support for the coordinated matching of the “inclination angle–rotational speed” parameters in waste residual mulch-film recycling equipment.

2.5. Kinematic Modeling and Analysis of Baled Mulch Film

2.5.1. Analysis of Mulch-Film Detachment and Throwing Motion

Based on the DEM results and trajectory analysis under practical operating conditions, a segmented mechanical model was established for the transport of mulch film inside the drum of the rotary screening and recycling unit, following the typical motion chain of “pickup–lifting–throwing” [16,17,18]. In particular, the frictional interaction between the mulch film and the inner drum wall was incorporated into the dynamic description as a dominant, non-negligible factor. To facilitate subsequent force decomposition and derivation of the governing equations of motion, a global Cartesian coordinate system $XOY$ was defined, with the center $O$ of the drum cross-section as the origin $\left(O=(0,0)\right)$; the positive $X$-axis points horizontally to the right, and the positive $Y$-axis points vertically upward. In terms of model parameters, the drum is treated as a rigid cylinder with radius $R$ and a clockwise angular velocity $\omega$. The mulch-film agglomerate is represented as an equivalent point mass with mass $m$, and Coulomb sliding friction is assumed at the film–wall interface, with the kinetic friction coefficient denoted by $\mu$. Only gravity is considered as the external field, with gravitational acceleration $g$, while secondary effects such as aerodynamic drag are neglected. These assumptions and parameter definitions provide a unified geometric and mechanical basis for establishing, by motion stage, the contact-state criteria, friction-force expressions, and piecewise dynamic equations in the subsequent analysis.

(1) Stage One: $A$ → $A1$: Free Fall

As shown in Figure 11, the plastic film slides from the end of the conveyor system to the drum, reaching point $A$, where it naturally falls with an initial velocity, under the influence of gravity, until it reaches the drum’s inner wall at point $A1$. The coordinates of point $A$ are ($x_A$, $y_A$), and the initial velocity at point $A$ is ($v_{Ax}$, $v_{Ay}$).

The motion equation is derived with time $t$ starting from point $A$.

$$\left\{\begin{array}{c}x\left(t\right)=x_A+v_{Ax}·t\\ y\left(t\right)=y_A+v_{Ay}·t-{\displaystyle \frac{1}{2}}g{t}^2\end{array}\right.$$

(2)

When the plastic film reaches point $A1$, the plastic film makes contact with the inner wall of the drum, satisfying the following equation:

$${x\left(t\right)}^2+{y\left(t\right)}^2=R^2$$

(3)

(2) Stage $A1$ → $B$: Circumferential Constrained Motion on the Inner Wall

After the plastic film falls to the bottom of the drum, it adheres to the drum wall due to frictional and centrifugal forces, moving in a uniform clockwise circular motion with the drum until reaching point $B$.

Angle Definition: Let the angle between the position of the plastic film and the negative half-axis of the $Y$-axis (the lowest point) be $\theta$ (with the clockwise direction as positive). The angle at point $A1$ is denoted as ${\theta }_0$. The angular velocity at any moment $t^{\prime }$ ($t^{\prime }=t-t_1$) is given by: $\theta \left(t^{\prime }\right)={\theta }_0+\omega t^{\prime }$.

Force Analysis (Tangential and Normal): In this stage, the plastic film has not yet detached from the drum wall. A local coordinate system is established: $n$ points toward the center of the circle (normal direction), and $\tau$ points in the direction of motion along the tangential line.

Normal Force Balance (Providing Centripetal Force):

$$F_n-mgcos\theta +N=m{\omega }^{2}R$$

(4)

where $N$ is the support force exerted by the drum wall on the plastic film. The expression for the support force is derived as follows:

$$N=m\left(gcos\theta +{\omega }^{2}R\right)$$

(5)

Tangential Force Analysis (Determining Whether Sliding Occurs): The tangential component of gravity, $G_{\tau }=mgsin\theta$, attempts to pull the plastic film downward. The static friction force, $f$, prevents relative sliding between the plastic film and the drum. The maximum static friction force is given by $f_{\max }=\mu N$.

Critical Condition (Determining the Position of Point $B$):

There are typically two scenarios for the detachment or falling of the plastic film [19,20]:

Sliding Detachment: When the tangential component of gravity exceeds the maximum static friction force, the plastic film begins to slide relative to the drum (commonly regarded as the starting point of detachment).

$$mgsin\theta \ge \mu N$$

(6)

$$mgsin\theta \ge \mu m\left(g cos\theta +{\omega }^{2}R\right)$$

(7)

Normal Detachment: When the support force $N\le 0$, the plastic film separates from the drum wall (typically occurring at high speeds or at elevated points).

$$gcos\theta +{\omega }^{2}R\le 0$$

(8)

Under typical operating conditions, the detachment motion occurs at point $B$. For low-speed drum plastic film recovery, this primarily involves sliding detachment. By combining the above equations, point $B$ is reached when the plastic film attains the angle ${\theta }_B$ that satisfies the following equation:

$$gsin{\theta }_B-\mu gcos{\theta }_B=\mu {\omega }^{2}R$$

(9)

the coordinates of point $B$

$$\left\{\begin{array}{c}{x}_B=Rsin{\theta }_B\\ y_B=-Rcos{\theta }_B\end{array}\right.$$

(10)

(3) Segment $B\to B_1$: Projectile motion and re-contact

At point $B$, the plastic film detaches from the drum surface and subsequently moves under the action of gravity alone. Air resistance is neglected; therefore, the film undergoes oblique projectile motion. Initial position: ($x_B$, $y_B$); Initial speed: $v_B=\omega R$; Initial velocity direction: tangent to the circumferential trajectory at point $B$, oriented clockwise.

$$\begin{gathered} v{B}_x=v_{B}cos\left({{\theta }^{\prime }}_B\right) \\ v{B}_y=v_{B}sin\left({{\theta }^{\prime }}_B\right) \end{gathered}$$

(11)

Governing equations (with time $t$ reset to zero at the instant of detachment from point $B$):

$$\left\{\begin{array}{c}x\left(t\right)=x_B+v{B}_x·t\\ y\left(t\right)=y_B+v{B}_y·t-{\displaystyle \frac{1}{2}}g{t}^2\end{array}\right.$$

(12)

2.5.2. Analysis of Mulch-Film Sliding Behavior

During the mechanical separation of waste residual mulch film, the material stream enters the rotating drum via an inclined chute, and its in-drum motion characteristics directly affect separation efficiency and impurity-removal performance [21,22,23]. To elucidate the axial conveying mechanism of the material in an inclined drum, a simplified dynamic model was developed to analyze the effects of drum inclination angle and rotational parameters on the material sliding time (Figure 12).

In the kinematic description, to accurately characterize the slip state between the mulch-film point mass and the drum wall—and thereby determine the direction of the friction force—the absolute velocity of the point mass and the wall velocity were defined in the $\left(x,\theta \right)$ components of a cylindrical coordinate system in the ground-fixed inertial reference frame. The point-mass velocity consists of an axial component $v_x$ and a circumferential tangential component $v_{\theta }$. When the drum rotates about its axis with angular velocity $\omega$, the wall at the contact location possesses only a circumferential tangential velocity of magnitude $\omega R$, with zero axial component. Accordingly, the relative velocity, defined as the difference between the point-mass velocity and the wall velocity, is the key quantity governing the direction of the contact friction force and the slip criterion. Moreover, the magnitude of the relative velocity is used as a quantitative measure of slip intensity, providing a kinematic basis for subsequent piecewise modeling of static and kinetic friction [22].

Absolute velocity of the particle: $v=\left[v_x, v_{\theta }\right];$

Drum-wall velocity: ${\mathrm{V}}_{wall}=[0, \omega R]$;

Relative velocity: $v_{rel}=v-V_{wall}=\left[v_x,{ v}_{\theta }-\omega R\right]$;

Magnitude of the relative velocity: $v_{norm}=\parallel v_{rel}\parallel =\sqrt{v_x^2+(v_{\theta }-\omega R{)}^2}$.

In the mechanical analysis, the equivalent mulch-film point mass moving along the inner drum wall is primarily subjected to three external forces: gravitational force $G$, the wall-provided normal reaction $N$, and the contact friction force $f$. To formulate the dynamic equations in both the axial direction and within the cross-sectional plane, the weight $mg$ was first decomposed in the local cylindrical coordinate system $\left(x_m,{ \theta }_m, r\right)$ of the inclined drum. The axial component $G_x$ represents the driving effect along the drum axis; the circumferential tangential component $G_{\theta }$ depends on the circumferential angle $\theta$ and, for $\theta >0$, acts as a resistance to the upward motion of the point mass; and the radial component $G_r$ reflects the contribution of gravity to the contact pressure in the normal direction. In the radial direction, the centripetal acceleration required for the point mass to undergo curvilinear (circular) motion is jointly provided by the wall normal reaction and the radial component of gravity. Accordingly, an expression for the normal reaction can be derived from radial force balance (centripetal force condition). It should be noted that $v_{\theta }$ denotes the actual circumferential tangential velocity of the point mass with respect to the ground-fixed inertial frame: when there is no relative slip between the point mass and the drum wall, $v_{\theta }=\omega R$; when slip occurs, $v_{\theta }$ becomes an unknown to be solved, and it further affects the magnitudes of $N$ and the friction force.

Axial driving component:

$$G_x=mg sin\alpha$$

(13)

Angential component:

$$G_{\theta }=-mg cos\alpha sin\alpha$$

(14)

The radial component

$$G_r=-mg cos\alpha cos\theta$$

(15)

Normal reaction must provide the radial (centripetal) acceleration required for the particle’s curvilinear motion.

$$\begin{gathered} \sum F_r=m{a}_n\Rightarrow N+G_r=m{\displaystyle \frac{v_{\theta }^2}{R}} \\ N=mg cos\alpha cos\theta +m{\displaystyle \frac{v_{\theta }^2}{R}} \end{gathered}$$

(16)

To describe the transport of a film particle within an inclined drum with a variable inclination angle, the motion is modeled as a hybrid dynamical system comprising two discrete states—stick and slip/slide—with transitions governed by switching criteria. In the stick state, the particle exhibits no relative motion with respect to the drum wall and can be treated as rotating rigidly with the wall. The corresponding kinematic constraints imply zero axial relative velocity and a circumferential velocity identical to that of the wall, i.e., $\dot{x}=0$, $\dot{\theta }=\omega$. Whether sticking can be maintained is determined by whether static friction is sufficient to meet the resultant frictional demand associated with the axial and tangential components of gravity. The friction force required to maintain sticking is denoted as $f_{\mathrm{r}\mathrm{e}\mathrm{q}}$, and the maximum available static friction is $f_{max}={\mu }_s{N}_{stick}$. The system remains in the stick state when $f_{req}\le f_{max}$; otherwise, loss of stability occurs and the state switches to slip. Once in the slip state, a nonzero relative velocity ${\mathbf{v}}_{rel}$ develops between the particle and the wall. Kinetic friction is then adopted, acting opposite to ${\mathbf{v}}_{rel}$ with magnitude ${\mu }_{k}N$, from which the axial and tangential friction components are obtained. Together with the decomposed gravitational components and the expression for the normal reaction, Newton’s second law yields a coupled first-order ordinary differential equation system for $\left(v_x,v_{\theta }\right)$. The particle position is updated via $\dot{x}=v_x$ and $\dot{\theta }=v_{\theta }/R$. During slipping, when the relative speed approaches zero ($v_{norm}\approx 0$) and the static-friction condition is re-satisfied ($f_{req}\le f_{max}$), the system transitions back to the stick state. This stick–slip switching logic constitutes a hybrid-state dynamic framework capable of capturing the alternating stick–slip transport mechanism in the inclined rotating drum.

(1) State 1 (Stick):

In this state, the particle is stationary relative to the drum wall and undergoes rigid-body rotation with the drum.

Kinematic constraints: $v_x=0$, $v_{\theta }=\omega R$, $\dot{x}=0$, and $\dot{\theta }=\omega$.

Existence condition (criterion): sticking can be sustained only if the available static friction is sufficient to counteract the tangential and axial components of gravity. The required static friction force is denoted as $f_{req}$:

$$f_{req}=\sqrt{(G_x{)}^2+(G_{\theta }{)}^2}=m\sqrt{(gsin\alpha {)}^2+(gcos\alpha sin\theta {)}^2}$$

(17)

The maximum static friction force is defined as $f_{max}$:

$$f_{max}=\mu N_{stick}={\mu }_s\left(mg cos\alpha cos\theta +m{\omega }^{2}R\right)$$

(18)

Criterion: if $f_{\mathrm{req}}\le f_{\mathrm{m}\mathrm{a}\mathrm{x}}$, the adhesive (sticking) state is maintained; otherwise, the system switches to State 2.

(2) State 2 (Sliding phase):

In this state, the particle slides relative to the drum wall, which constitutes the key phase for determining the downslope (sliding) velocity.

Friction model: $f=-{\mu }_{k}N{\displaystyle \frac{v_{rel}}{v_{norm}}}$

Axial component of the friction force: $f_x={-\mu }_{k}N{\displaystyle \frac{v_x}{\sqrt{v_{x }^2+(v_{\theta }-\omega R{)}^2}}}$

Tangential component of the friction force: $f_{\theta }={-\mu }_{k}N{\displaystyle \frac{v_{\theta }-\omega R}{\sqrt{v_x^2+(v_{\theta }-\omega R{)}^2}}}$

Coupled differential equations: based on Newton’s second law, the governing equations are formulated as [23]:

$$\left\{\begin{array}{c}{\displaystyle \frac{d{v}_x}{dt}}=g sin\alpha -{\mu }_k(g cos\alpha cos\theta +{\displaystyle \frac{v_x^2}{R}}){\displaystyle \frac{v_x}{\sqrt{v_x^2+(v_{\theta }-\omega R{)}^2}}}\\ {\displaystyle \frac{d{v}_{\theta }}{dt}}=-g cos\alpha sin\theta -{\mu }_k(g cos\alpha cos\theta +{\displaystyle \frac{v_x^2}{R}}){\displaystyle \frac{v_{\theta }-\omega R}{\sqrt{v_x^2+(v_{\theta }-\omega R{)}^2}}}\end{array}\right.$$

(19)

Position update: ${\displaystyle \frac{dx}{dt}}=v_x$, ${\displaystyle \frac{d\theta }{dt}}={\displaystyle \frac{v_{\theta }}{R}}$.

Condition for switching back to the stick state: if the relative speed approaches zero ($v_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}\approx 0$) and the static-friction criterion is satisfied ($f_{\mathrm{r}\mathrm{e}\mathrm{q}}\le f_{\mathrm{m}\mathrm{a}\mathrm{x}}$), the system transitions back to State 1.

2.6. MATLAB Validation

Based on the above mechanical model, an event-driven simulation of the “wall-adhering ascent–detachment and ballistic fall–bottom re-contact” process was implemented in MATLAB 2021. During the wall-adhering phase, the mulch film was represented as an equivalent rigid body co-rotating with the drum at a fixed radial position $r_c$, while the switching criteria were monitored in real time. Once either the normal reaction vanished ($N=0$) or a prescribed limiting elevation angle was reached, the motion transitioned to the detachment (ballistic) phase. The ballistic trajectory was then computed under gravity. When the radial distance returned to the inner-wall radius and the radial direction pointed toward the bottom region, the first re-contact time was determined using a bisection search, and the impact point was constrained to the bottom inner wall. For the bottom phase, a simplified axial-averaged model was adopted to generate the axial spacing between successive cycles, and a cycle-to-cycle attenuation factor $\rho$ was introduced to capture the progressive reduction in ascent height. The code automatically logged detachment and re-contact events, and the number of re-contacts was taken as the collision count. Figure 13 shows the three-dimensional trajectory, the cross-sectional projection (red: wall-adhering; blue: ballistic), and the corresponding axial displacement history [24].

In this study, numerical simulations were performed in MATLAB under identical initial conditions, with only the drum inclination angle varied. The corresponding collision counts were recorded, and the results are summarized in

Table 7. Simulation data from MATLAB.

Drum Inclination Angle	Simulated Number of Collisions	Predicted Time (s)
2°	46	118.70
4°	14	37.28
6°	8	21.99

. The outcomes clearly indicate that increasing the inclination angle shortens the residence time and reduces the number of collisions. By ensuring trajectory continuity as well as consistency in the detachment-angle criterion and re-contact geometry, the entire workflow constitutes a reusable computation and visualization tool, providing a reliable collision-statistics method and physical basis for subsequent experimental validation and operating-condition optimization.

2.7. Experimental Study

Experimental Design

During the pre-treatment of waste residual mulch film, the screening performance of a trommel is influenced by multiple factors, among which film length, drum inclination angle, and drum rotational speed are the key controllable parameters. Film length governs the tendencies of the material to entangle, knot, and pass through the screen, thereby directly affecting the stability and uniformity of separation. The drum inclination angle regulates the residence time and flow path of the material within the screening section, which in turn affects the adequacy of impurity separation and the processing capacity. Drum rotational speed primarily dictates the material agitation mode and dynamic behavior; variations in speed influence the degree of material dispersion and the risk of secondary re-mixing. To quantitatively evaluate the effects of these factors, two performance indices were adopted: impurity-removal mass and impurity-removal efficiency. The former reflects the thoroughness of impurity removal during screening and the purity of the recovered product, whereas the latter characterizes the throughput per unit time and overall engineering efficiency. Although correlated, these indices involve an inherent trade-off and jointly constitute a comprehensive evaluation framework for screening performance. Accordingly, this study aims to elucidate, through systematic experiments, the effects of the primary parameters on the trommel screening mechanism and performance, thereby providing a theoretical basis and technical support for equipment design and process optimization in the resource-oriented utilization of waste residual mulch film [25].

To ensure the scientific rigor and accuracy of the results, the experiments were divided into two parts—response surface methodology (RSM) optimization tests and bench tests—and cross-validated accordingly [8]. The drum throw-off screening tests were conducted in September 2025 at the Nanjing Research Institute for Agricultural Mechanization, Ministry of Agriculture and Rural Affairs (Nanjing, Jiangsu Province, China), with an average ambient temperature of 30 °C during the test period. The test material consisted of waste residual mulch film collected from cotton fields in Shihezi, Xinjiang Uygur Autonomous Region, which was recovered in a baled form. The main impurities included soil clods, cotton stalk residues, and gravel, as shown in Figure 14. Mass measurements were performed using an electronic balance (capacity: 0–100 kg; resolution: 0.05 kg). In accordance with the experimental protocol, the sampled mulch film was cut to specified sizes, numbered and labeled, and then weighed to obtain the initial mass $Q_1$. After drum throw-off screening, the oversize fraction retained on the screen was reweighed and recorded as the post-screening mass $Q_2$ [26,27].

When evaluating drum-screening performance, the recovered feedstock contains mulch film (a large, flexible sheet-like material) and impurities such as soil and cotton stalk fragments (fine granular or discrete materials), which differ markedly in physical form and size scale. Therefore, two macroscopic process responses were selected for response surface methodology (RSM) optimization: screening mass ($R_1$) and separation rate ($R_2$) [28,29,30].

In each run, the total feed mass was recorded as $Q_1$ (kg). After screening, the mass of the retained (oversized) fraction remaining inside the drum—i.e., the recovered mulch film—was weighed and denoted as $Q_2$ (kg).

Screening mass ($R_1$) quantifies the total mass of the passed (undersize) fraction discharged through the screen apertures, which predominantly consists of soil, gravel, and short cotton-stalk fragments.

Separation rate ($R_2$) is defined as the mass fraction of material passing through the apertures, reflecting the drum’s screening capability for fine and fragmented impurities.

The corresponding equations are given as follows:

$$R_1=Q_1-Q_2$$

(20)

$$R_2={\displaystyle \frac{Q_1-Q_2}{Q_1}}\times 100\%$$

(21)

A Box–Behnken design (BBD) was employed for the experimental scheme. Using Design-Expert 13.0, a response surface methodology (RSM) experiment was conducted with three factors: film length ($X_1$), drum inclination angle ($X_2$), and drum rotational speed ($X_3$). The coding and levels of the experimental factors are listed in

Table 8. Factor-level encoding table.

Level/Factor	Film Length (mm)	Inclination Angle (°)	Rotational Speed (r/min)
−1	100	2	20
0	200	4	30
1	300	6	40

.

3. Results

3.1. Test Results

A Box–Behnken design (BBD) was implemented using Design-Expert v13.0 software, comprising 17 experimental runs. Analysis of variance (ANOVA) and multiple regression were used to develop fitted regression models for the response variables—screening mass ($R_1$) and separation rate ($R_2$)—followed by a systematic evaluation of factor significance and interaction effects. To enhance the statistical reliability of the response surface analysis and minimize random disturbances, a standardized experimental protocol was applied in three aspects: feedstock pretreatment, feed control, and error management.

(1) Feedstock consistency. All test materials were collected from the same cotton-field plot in Shihezi, Xinjiang, using the same mechanized mulch-film recovery equipment (Model 4JMLQ210, Changzhou Hansen Machinery Co., Ltd., Changzhou, China). Prior to testing, the recovered film–impurity mixture (including soil clods, cotton stalk fragments, gravel, etc.) was thoroughly mixed and homogenized. This pretreatment minimized potential interference from feedstock compositional variability and ensured comparable initial impurity fractions across runs.

(2) Stratified control of feed mass ($Q_1$). A two-tier feed-mass control strategy was adopted: strict mass constancy at center points and response normalization at non-center design points. For the five center-point replicates (Runs 1, 5, 9, 12, and 13), the feed mass was maintained at 4.5 kg ($\pm 0.05 \mathrm{k}\mathrm{g})$ to eliminate input-load fluctuations, thereby allowing the observed variation to primarily reflect the system’s pure (random) error. In contrast, for non-center runs, variation in film length ($L$, 100–300 mm) markedly altered the bulk density and entanglement morphology of the feedstock, resulting in run-to-run fluctuations in the actual feed mass (2.5–5.0 kg) under a fixed feed volume. To account for this effect, separation rate ($R_2$) was used as a key performance metric; by normalizing the discharged undersize mass passing through the screen apertures by the actual feed mass, the influence of feed-load differences was effectively mitigated, improving the robustness of the evaluation.

(3) Model prediction accuracy and experimental repeatability. The five center-point replicates provided an estimate of pure error (4 degrees of freedom) for the ANOVA, which served as the basis for the lack-of-fit test and for assessing overall system stability (instrumentation and operation). Moreover, the run order of all 17 trials was fully randomized in Design-Expert to mitigate time-dependent systematic bias due to evolving environmental and machine-state effects (e.g., thermal drift and mechanical wear). The experimental results are presented in

Table 9. Box–Behnken design (BBD).

Run	Name
	Film Length (mm)	Inclination Angle (°)	Rotational Speed (r/min)	Screening Mass (kg)	Separation Rate (%)
1	200	4	30	3.6	79
2	300	2	30	2.95	67
3	100	6	30	2.65	53
4	200	6	20	2.5	56
5	200	4	30	3.65	80
6	200	6	40	2.35	60
7	200	2	20	2.85	73
8	100	4	20	2.15	76
9	200	4	30	3.75	82
10	100	4	40	2.3	70
11	300	6	30	3.15	63
12	200	4	30	3.7	81
13	200	4	30	3.65	80
14	100	2	30	3.15	71
15	300	4	20	2.9	77
16	200	2	40	2.25	65
17	300	4	40	2.05	80

.

The experimental data in Table 9 were analyzed using Design-Expert v13.0, and the following second-order (quadratic) regression models were obtained for the drum-screening responses: screening mass $R_1$ and separation rate $R_2$:

$$\begin{gathered} R_1=3.67+0.1X_1-0.0688X_2-0.1813X_3+0.175X_1{X}_2-0.25X_1{X}_3\hspace{1em} \\ +0.1125X_2{X}_3-0.4163X_1^2-0.2787X_2^2-0.9038X_3^2 \\ {R}_2=80.4+2.13X_1-5.5X_2-0.875X_3+3.5X_1{X}_2+2.25X_1{X}_3\hspace{1em} \\ +3X_2{X}_3-2.33X_1^2-14.58X_2^2-2.32X_3^2 \end{gathered}$$

3.2. Experimental Results and Analysis

Based on the Box–Behnken design (BBD), this study systematically examined the effects of film length ($X_1$), drum inclination angle ($X_2$), and drum rotational speed ($X_3$) on the screening mass ($R_1$) and separation rate ($R_2$) [23]. ANOVA indicated that the quadratic response-surface models for both responses were highly significant ($p<0.0001$), demonstrating excellent model fit and strong predictive capability. For $R_1$, the coefficients of determination were $R^2=0.997$, adjusted $R^2=0.993$, and predicted $R^2=0.981$; for $R_2$, they were $R^2=0.994$, adjusted $R^2=0.986$, and predicted $R^2=0.956$. Moreover, the lack-of-fit for both models was not significant, indicating that the models adequately captured the experimental data and supporting the reliability of subsequent parameter optimization. With respect to factor effects, the quadratic term of rotational speed ($X_3^2$) was the most influential contributor to $R_1$, exhibiting the highest statistical significance and the largest coefficient magnitude. This suggests a pronounced nonlinear effect of rotational speed on the discharge capacity of undersize impurities. In addition, the quadratic terms $X_1^2$ and $X_2^2$, as well as the interaction terms $X_1{X}_3$ and $X_2{X}_3$, were all significant, indicating that impurity removal is governed by strong coupling between “film length–rotational speed” and “inclination angle–rotational speed,” rather than by any single factor. In contrast, the dominant contributor to $R_2$ was the quadratic term of inclination angle ($X_2^2$), which showed the greatest effect size and significance, while the linear term $X_2$ also exhibited a strong negative main effect. Although the main effects of $X_1$ and $X_3$ were less pronounced than that of $X_2$, their interactions with other factors ($X_1{X}_2$, $X_1{X}_3$, and $X_2{X}_3$) were all statistically significant, demonstrating that separation performance is jointly and synergistically influenced by multiple coupled factors (the results are summarized in

Table 10. Analysis of variance (ANOVA).

Source	Screening Mass R1				Separation Rate R2
	Sum of Squares	Degree of Freedom	F-Value	p-Value	Sum of Squares	Degree of Freedom	F-Value	p-Value
Model	5.68	9	237.03	<0.0001	1369.4	9	126.05	<0.0001
X1	0.08	1	30.07	0.0009	36.13	1	29.93	0.0009
X2	0.0378	1	14.21	0.0070	242.00	1	200.47	<0.0001
X3	0.2628	1	98.78	<0.0001	6.13	1	5.07	0.059
X1X2	0.1225	1	46.04	0.0003	49.00	1	40.59	0.0004
X1X3	0.25	1	93.96	<0.0001	20.25	1	16.78	0.0046
X2X3	0.0506	1	19.03	0.0033	36.00	1	29.82	0.0009
X12	0.7295	1	274.19	<0.0001	22.76	1	18.85	0.0034
X22	0.3272	1	122.96	<0.0001	894.44	1	740.96	<0.0001
X32	3.4400	1	1292.51	<0.0001	22.76	1	18.85	0.0034
Residual	0.0186	7			8.45	7
LackofFit	0.0056	3	0.5769	0.6603	3.25	3	0.8333	0.5413
PureError	0.0130	4			5.20	4
CorTotal	5.69	16			1377.88	16

).

A comprehensive assessment of the effects of film length ($X_1$), drum inclination angle ($X_2$), and drum rotational speed ($X_3$) on screening mass ($R_1$) and separation rate ($R_2$) indicates that both responses are governed by significant multi-factor interactions and nonlinear (quadratic) effects. However, the dominant contributors differ between the two responses. For screening mass ($R_1$), the response is primarily dominated by the quadratic term of drum rotational speed ($X_3^2$), indicating a pronounced nonlinear dependence on rotational speed. In addition, the quadratic terms of film length and inclination angle, as well as their interaction terms with rotational speed, contribute appreciably, suggesting that rotational speed not only has a strong main effect but also regulates the undersize discharge through interactions with the other factors. In contrast, separation rate ($R_2$) is mainly governed by drum inclination angle, with both the quadratic ($X_2^2$) and linear ($X_2$) terms jointly shaping the response profile. Although the main effects of film length and rotational speed are comparatively weaker, their interaction effects with inclination angle and with each other remain influential, demonstrating that separation performance arises from coupled factor effects rather than a single-parameter control. Accordingly, improving $R_1$ should emphasize precise regulation of drum rotational speed, whereas enhancing $R_2$ should prioritize optimization of drum inclination angle. Ultimately, operating-parameter selection should account for the interaction effects among all three factors to achieve stable and overall improvements in screening (undersize discharge) and separation performance.

Figure 15 illustrates the interaction effects of film length ($X_1$), drum inclination angle ($X_2$), and drum rotational speed ($X_3$) on screening mass ($R_1$) and separation rate ($R_2$). The upper row shows the three-dimensional response surfaces for $R_1$, whereas the lower row presents those for $R_2$. Each plot depicts the combined effects of two factors (including their interaction) on the response while holding the third factor at its coded zero (center) level. As indicated by the upper response surfaces, $R_1$ exhibits pronounced nonlinear dependence on the operating factors. When drum rotational speed is fixed at 30 rpm, $R_1$ increases with film length and then approaches a plateau, with the highest values occurring at intermediate film lengths (approximately 200–250 mm). In contrast, increasing the inclination angle produces an overall decrease in $R_1$, suggesting that excessive inclination accelerates axial transport of the material bed and reduces the effective residence time available for collision-assisted liberation and discharge of undersize impurities. When inclination angle ($X_2$) is held constant, the $R_1$ response with respect to rotational speed is the steepest and follows a concave-down quadratic (unimodal) trend. A distinct maximum occurs at approximately 25–35 rpm, indicating that rotational speed is the primary factor governing $R_1$ (i.e., the discharge of undersize impurities). Moreover, at the center level of film length ($X_1$), the interaction between inclination angle and rotational speed yields a pronounced parabolic response surface, with $R_1$ peaking at a moderate rotational speed (~30 rpm) and a relatively small inclination angle (3–4°). Overall, $R_1$ is most strongly affected by the quadratic term of drum rotational speed, followed by film length, whereas the influence of inclination angle is comparatively weaker and more gradual.

The lower row presents the response surfaces for the separation rate ($R_2$). The overall response trends are similar to those observed for screening mass ($R_1$); however, $R_2$ exhibits distinct sensitivity to the operating factors. When rotational speed is held at 30 rpm, $R_2$ increases gradually with increasing film length, indicating a positive dependence. In contrast, $R_2$ decreases sharply as the inclination angle increases, suggesting that an excessively steep inclination accelerates axial transport and likely weakens material-bed stratification within the drum, thereby reducing the probability of fines passing through the apertures. When inclination angle is fixed at 4°, $R_2$ increases with rotational speed and film length and then shows a slight decline, consistent with a unimodal (quadratic) response. Notably, when rotational speed exceeds 35 rpm, the separation rate is markedly suppressed. This behavior can be attributed to centrifugal adhesion (pinning) at high speeds, where elevated centrifugal forces promote sticking of the material bed to the drum inner wall and hinder cascading and percolation of fine particles through the screen. At a fixed film length of 200 mm, a pronounced local maximum appears near the center of the response surface, indicating that peak separation performance is achieved within an optimal operating window—an inclination angle of 3.5–4.5° and a rotational speed of 28–33 rpm. Overall, $R_2$ is highly sensitive to inclination angle, whereas the interaction between rotational speed and film length plays a key role in maintaining stable separation performance.

A comprehensive interpretation of the response surface results indicates that both screening mass ($R_1$) and separation rate ($R_2$) exhibit pronounced nonlinear dependence on the experimental factors, with broadly similar response trends. Drum rotational speed ($X_3$) is the primary factor governing screening performance, showing a strong quadratic effect with a distinct optimum within 25–35 rpm. In contrast, separation performance is highly sensitive to the drum inclination angle ($X_2$); excessive inclination accelerates axial transport of the material bed and reduces the effective residence time for cascading collisions, thereby causing a substantial decline in separation rate. When film length ($X_1$) is fixed at approximately 200 mm, the optimal operating windows for both responses largely overlap. Specifically, at a rotational speed of 28–33 rpm and an inclination angle of 3.5–4.5°, the drum screen simultaneously achieves high undersize discharge (impurity removal via screening) and stable material-bed stratification. Collectively, these results highlight an operating principle in which product quality is predominantly regulated by rotational speed, whereas separation efficiency is strongly influenced by inclination angle, thereby providing a sound basis for equipment design and operating-parameter selection for mulch-film recycling systems.

3.3. Bench-Scale Experimental Optimization Results

To further improve the overall performance of the drum separation system, multi-objective optimization was performed in Design-Expert based on the preceding RSM results [24,25]. Film length ($X_1$), drum inclination angle ($X_2$), and drum rotational speed ($X_3$) were selected as the independent factors, whereas screening mass ($R_1$) and separation rate ($R_2$) were defined as the response variables. The three factors were constrained within their respective experimental ranges ($X_1$: 100–300 mm; $X_2$: 2–6°; $X_3$: 20–40 rpm). Both responses were set to be maximized, and equal importance (weight = 3) was assigned to $R_1$ and $R_2$.

Using the desirability function for multi-response optimization, the optimal operating conditions were identified as a film length ($X_1$) of 216.00 mm, a drum inclination angle ($X_2$) of 2.33°, and a drum rotational speed ($X_3$) of 25.00 rpm. Under these conditions, the model predicted a screening mass ($R_1$) of 3.467 kg and a separation rate ($R_2$) of 75.636%, with an overall desirability of 1.000. These results indicate that the identified parameter set provides the best trade-off between the two objectives within the design space. Specifically, it promotes effective impurity detachment and discharge through the screen apertures while maintaining efficient recovery of the mulch film as the oversize fraction, thereby representing an optimal operating parameter combination for the drum separation process.

To validate the predictive accuracy of the optimization model, a bench-scale confirmation test of the drum separation apparatus was performed under the model-derived optimal conditions (Figure 16). Because the predicted optima (216.00 mm, 2.33°, and 25.00 rpm) included non-integer setpoints that were impractical to implement via manual adjustment on the test bench, the settings were rounded to practical engineering setpoints: a film length of 220 mm, an inclination angle of 3°, and a rotational speed of 25 rpm. The measured screening mass ($R_1$) and separation rate ($R_2$) were 3.65 kg and 80.5%, respectively. Compared with the corresponding model predictions ($R_1=3.467$ kg and $R_2=75.636\%$), the relative errors were 5.28% for $R_1$ and 6.43% for $R_2$. Both errors were below 10%, indicating good agreement between experimental measurements and model predictions. These results confirm that the established quadratic regression model provides reliable predictions of drum-screening performance and adequately captures the coupled screening/separation dynamics within the drum. Moreover, satisfactory performance was maintained after minor engineering adjustment of the operating parameters, demonstrating the robustness and practical applicability of the proposed optimization scheme.

In summary, the optimized parameter combination—mulch-film length of approximately 220 mm, drum inclination angle of approximately 3°, and drum rotational speed of approximately 25 r/min—can substantially enhance the impurity-removal and separation performance of the drum-type separation unit for waste residual mulch film. This parameter set provides a sound theoretical basis and experimental reference for drum structural refinement and the selection of operating parameters, and is of significant importance for improving the cleaning efficiency of equipment used for the recycling and subsequent reutilization of waste residual mulch film.

3.4. Experimental Data

In this experiment, six waste residual mulch-film samples were collected and divided into three paired control groups. After washing and oven-drying, the soil/impurity mass before treatment was measured as 20.38 g, 18.471 g, and 17.179 g, respectively. The mulch film was then processed in the drum, followed by washing and oven-drying again, and the soil/impurity mass after treatment was measured as 14.605 g, 13.204 g, and 12.437 g, respectively. The impurity-removal rates for each group were subsequently calculated based on the mass ratios, as shown in Figure 17. The device is designed for pre-treatment impurity removal, with a target impurity-removal rate of ≥70%. The experimental results showed impurity-removal rates of 71.7%, 71.5%, and 72.4% for the three groups, respectively, all of which meet the design requirements for the drum throw-off unit.

4. Discussion

To address the severe deformation and poorly characterized motion trajectories of waste agricultural mulch film during preliminary screening in mechanized recycling, the simulation strategy proposed in this study—integrating the meta-particles framework with the Bonding V2 bonded-particle contact model—demonstrates clear advantages. Unlike conventional DEM implementations that approximate materials as rigid particles, the proposed model reproduces key flexible-film behaviors, including folding and entanglement, and captures the nonlinear in-drum kinematics associated with the staged sequence of wall adhesion, sliding, and tossing/cascading. Comparisons with high-speed imaging under representative operating conditions further confirm that film motion follows complex trajectories arising from the combined effects of friction, gravity, and centrifugal forces. Collectively, these results validate the proposed approach as an effective tool for mechanistic analysis of flexible-material kinematics. To elucidate the drum-screening mechanism more comprehensively, this study synthesizes evidence from theoretical modeling, DEM simulations, and RSM-based statistical experiments, revealing strong consistency between microscale kinematic mechanisms and macroscale screening performance. First, rotational speed is identified as the key dynamic parameter governing the transition between cascading and centrifugal pinning regimes. Theoretical analysis and DEM simulations indicate that excessively high rotational speed promotes centrifugal pinning, which severely impairs separation by suppressing cascading and percolation through the screen apertures. This mechanistic insight provides a coherent explanation for the highly significant quadratic dependence ($X_3^2$) of screening mass ($R_1$) on rotational speed observed in the RSM analysis. Moreover, the RSM-derived optimal rotational-speed window (25–30 rpm) aligns well with the “optimal cascading zone” predicted by the theoretical model. Second, drum inclination angle primarily regulates material residence time. MATLAB-based numerical calculations and DEM trajectory analysis show that increasing the inclination angle (from 2° to 6°) increases the axial transport component of particle/film motion, thereby reducing the number of effective collisions (collision frequency) during screening. This kinematic characteristic is consistent with the high sensitivity of separation rate ($R_2$) to inclination angle ($X_2$) revealed by the RSM results. Although a larger inclination angle can increase throughput, it shortens the effective screening duration and may lead to incomplete impurity separation.

To clarify the contributions of this study relative to prior work, we conducted a focused comparison of the proposed methodological advances and their engineering applicability against representative studies in the literature. In conventional DEM-based investigations of drum screening (e.g., Xie Chenshuo et al. [31]), flexible agricultural mulch film is typically represented as an assembly of rigid particles. Such simplifications can provide a coarse assessment of screen blinding (aperture clogging); however, they cannot faithfully capture key large-deformation behaviors of the film—such as folding, wrinkling, and entanglement—under realistic in-drum flow conditions. More recently, several studies have introduced multi-physics coupling to extend the modeling scope. For example, Shen Shilong [32] et al. investigated the dynamic response of film–soil mixtures in vibratory conveying using a coupled DEM–MBD (multibody dynamics) model, whereas Fang Weiquan [33] et al. employed a CFD–DEM framework to analyze aerodynamic suspension and pneumatic discharge of flexible films in airflow-assisted separation. These approaches primarily emphasize the influence of external fields (vibration or airflow) on bulk transport and migration behavior, yet they do not directly resolve the intrinsic challenge of representing the film’s large-deformation mechanics within DEM. In contrast, the present study introduces a DEM modeling framework that integrates the meta-particles strategy with the Bonding V2 bonded-particle contact model to represent the film as a deformable, sheet-like assembly. This approach moves beyond rigid-particle approximations and alleviates key modeling bottlenecks associated with high-fidelity simulation of flexible agricultural residues, enabling more realistic reproduction of the film’s dynamic evolution during drum screening. As a result, the proposed framework provides a robust mechanistic tool for analyzing flexible-material kinematics and for guiding the design and parameterization of mulch-film recycling equipment.

More importantly, the theoretical breakthroughs in the aforementioned methodological dimension not only deepened the understanding of complex material kinematic mechanisms but also directly drove the scientific optimization of core process parameters, thereby achieving separation performance in practical engineering applications that is significantly superior to existing literature benchmarks. Taking classic drum-type separation equipment as an example, the residual film–impurity separation device developed by Zhou Pengfei [19] was constrained by empirical parameter tuning. To circumvent severe material centrifugal pinning effects, its operating rotational speed was forced to be limited to a low-speed range of 14 r/min, ultimately yielding an impurity removal rate of merely ~66.7%. In contrast, benefiting from the flexible-body model’s precise capture of the non-linear “pinning–sliding–cascading” periodic motion, our team elucidated the unfolding behaviors and collision cadences of materials at high rotational speeds from a micro-dynamic perspective. Consequently, this study successfully broke through traditional low-speed operational limitations, substantially elevating the optimal operating rotational speed to 25 r/min. Bench-scale validation experiments demonstrated that the impurity removal rate of the apparatus in this study stabilized at 71.5–72.4%, exhibiting significantly superior processing efficacy compared to the existing literature baseline. Furthermore, compared with other current cutting-edge separation processes, this study demonstrates distinct advantages in engineering practicality. For instance, although the vibratory conveying separation device for film–soil mixtures designed by Shen et al. controlled the soil content at 18.11% (with a film loss rate of 7.61%), and the pneumatic unloading device developed by Fang et al. achieved a film–impurity separation rate as high as 96.6%, such composite separation processes inevitably rely on complex mechanical excitation mechanisms or high-energy-consumption aerodynamic systems. In stark contrast, this study relies solely on the pure mechanical cascading and screening mechanism of a single drum. Under the premise of ensuring structural simplicity and low energy consumption, it successfully achieves highly efficient preliminary impurity removal. The aforementioned qualitative and quantitative analyses fully demonstrate that this study not only bridges existing cognitive gaps in characterizing the fundamental kinematic mechanisms of flexible materials but also achieves critical breakthroughs in the scientific optimization of core process parameters and their engineering translation.

Although this study has achieved substantial progress in flexible-body dynamic modeling and operating-parameter optimization, it remains important to clearly delineate the validity of the simplifying assumptions and the applicability domain (operating envelope) for broader deployment. First, to reduce computational cost, fine dust-sized particles (fines) were not explicitly represented in the DEM simulations. Under the scale and operating conditions considered here, omitting fines is expected to have a second-order influence on the prediction of the primary separation mechanisms. From a kinematic standpoint, individual fines have negligible inertia and are typically transported in a film-attached manner during screening; therefore, they are unlikely to dominate the macroscopic trajectories or the primary collision statistics of film agglomerates. Nevertheless, fines may indirectly affect the process by altering the effective friction and energy dissipation at the film–wall and film–impurity interfaces—effects that were not quantified in this work. In terms of separation physics, the dominant pathway involves the unfolding and cascading of film agglomerates, which releases entrapped impurities. While the passage of fines through screen apertures is generally not rate-limiting, the process may become controlled by aperture accumulation and screen blinding under high-moisture or strongly adhesive feedstocks. Second, from an engineering perspective, the optimal settings identified herein (25 rpm rotational speed and 3° inclination angle) are primarily applicable to typical operating conditions with low moisture content (naturally air-dried, <15%) and impurities dominated by loose soil particles/aggregates and rigid cotton-stalk fragments. Comparisons across studies are also most meaningful when impurity-removal definitions and statistical procedures are consistent. Under these conditions, film–soil interfacial adhesion is weak, and mechanical impacts combined with centrifugal cascading are sufficient to achieve efficient separation. However, caution is warranted when extrapolating these findings to high-moisture (e.g., post-precipitation) or strongly adhesive soils. Elevated moisture promotes capillary liquid bridges at the film–soil interface, which increases adhesion strength nonlinearly and elevates the risk of screen blinding, thereby markedly deteriorating separation efficiency. Future work will investigate the critical adhesion–detachment conditions across a range of moisture contents. In addition, airflow fields will be incorporated via CFD–DEM coupling to examine the synergistic mechanisms of pneumatic-assisted separation, thereby improving the environmental adaptability of the equipment.

5. Conclusions

To address the prevalent industry bottlenecks encountered in the mechanized recycling of waste agricultural mulch film—namely, suboptimal film–impurity separation efficacy, highly non-linear kinematic behaviors of flexible media, and severe constraints imposed by strong multi-parameter coupling—this study utilized a drum-type impurity removal apparatus as the investigative platform. Centered on two core objectives: the elucidation of micro-dynamic transport mechanisms and the multi-objective synergistic optimization of process parameters, a systematic investigation encompassing theoretical modeling, numerical simulation, and physical machine validation was conducted. The research findings comprehensively substantiate the underlying theoretical hypotheses. The principal conclusions are drawn as follows:

(1) Development of the separation apparatus and verification of whole-machine dynamics. A drum-type separation unit incorporating a perforated cylindrical screen was developed. The vibration characteristics of the frame (chassis) were evaluated and verified via finite element (FE) modal analysis, confirming adequate vibration resistance. This structural verification ensured the dynamic stability and structural integrity of the shredding–separation process under severe dynamic loading, thereby providing a reliable experimental testbed for subsequent investigation of nonlinear material-transport and separation dynamics.

(2) High-fidelity modeling of flexible materials and elucidation of microscale kinematic mechanisms. To address the limitations of conventional rigid-particle DEM representations in capturing the mechanics of flexible media (e.g., geometric distortion and kinematic artifacts), this study integrated the meta-particles strategy with the Bonding V2 bonded-particle model to develop a high-fidelity DEM framework for flexible agricultural mulch film. The simulations resolved the nonlinear, stage-wise in-drum kinematics of the film, characterized by a sequence of wall adhesion and climbing, sliding and detachment, and subsequent cascading and spreading. These results clarify the coupled mechanisms by which drum inclination angle primarily controls axial transport, whereas rotational speed strongly influences radial motion through the cascading–centrifugal-pinning regime transition. In addition, the analysis demonstrates the critical role of chopped film length in reducing material entanglement and improving the passage (percolation) of entrained impurities through the screen apertures.

(3) Regarding the elucidation of multi-factor coupling effects and targeted optimization of process parameters: Based on the Box–Behnken response surface methodology (RSM), the non-linear synergistic influence patterns of multi-factor interactions on screening performance were thoroughly analyzed. This clarified the dominant non-linear quadratic effect of rotational speed on impurity removal quality, as well as the high sensitivity of separation efficiency to the inclination angle. Through multi-objective optimization, the optimal parameter matrix for the comprehensive efficacy of the whole machine was established (a chopped film length of 220 mm, an inclination angle of 3°, and a rotational speed of 25 r/min). Bench-scale validation experiments demonstrated that under these optimal operating conditions, a dynamic balance between the centrifugal unfolding and gravitational settling of the material is achieved. The actual impurity removal rate stabilized within the range of 71.5–72.4%, with the relative error between the measured and predicted values strictly controlled to within 10%. This successfully breaks through the multi-objective optimization bottleneck characterized by the inherent trade-off between “processing efficiency” and “impurity removal quality”.

In summary, by integrating microscale DEM-based simulations with macroscale engineering experiments, this study systematically elucidated the nonlinear in-drum kinematics of flexible waste agricultural mulch film during drum screening and developed a multi-parameter optimized operating strategy. The findings not only advance the mechanistic understanding of separation behavior and dynamic evolution in complex multiphase material systems, but also mitigate the conventional reliance on empirical parameter setting. Moreover, the results provide a sound mechanistic basis and experimentally validated guidance for targeted structural and operating-parameter optimization of pretreatment equipment used in the mechanized recycling and resource valorization of waste agricultural mulch film.