Residual Film–Cotton Stubble–Nail Tooth Interaction Study Based on SPH-FEM Coupling in Residual Film Recycling

Abstract

In the cotton fields in Xinjiang, residual film is present in the soil for a long period of time, leading to a decrease in the tensile strength of the residual film and increasing the difficulty of recycling. Existing technologies for residual film recovery focus on mechanical properties and ignore the dragging and tearing of residual film by cotton stubble. The effect of cotton straw–root stubble on residual film recovery can only be better determined by appropriate machine operating parameters, which are essential to improving residual film recovery. Through analyses of the pickup device, key parameters were identified, and a model was built by combining the FEM and SPH algorithms to simulate the interaction of nail teeth, residual film, soil and root stubble. The simulation revealed the force change law of residual film in root stubble-containing soil and the influence of root stubble. By simulating the changes in the characteristics of the residual film during the process, the optimum operating parameters for the nail teeth were determined: a forward speed of 1849.57 mm/s, a rotational speed of 5.5 r/s and a soil penetration angle of 30°. Under these optimized conditions, the maximum shear strain, pickup height (maximum deformation) and average peak stress of the residual film were 1293, 363.81 mm and 3.42 MPa, respectively. Subsequently, field trials were conducted to verify the change in the impact of the nail teeth at the optimized speed on the recovery of residual film in plots containing root stubble. The results demonstrated that when the root stubble height was 5–8 cm, the residual film averaged a recovery rate of 89.59%, with a dragging rate of only 4.10% at crossings. In contrast, 8–14 cm stubble plots showed an 82.86% average recovery and an 11.91% dragging rate. In plots with a root stubble height of 5–8 cm, compared with plots with a root stubble height of 8–14 cm, the recovery rate increased by 6.73%, and the dragging rate of residual film on root stubble decreased by 7.81%. The percentage of entangled residual film out of the total unrecovered film was 30.10% lower in the 5–8 cm stubble plots than in the 8–14 cm stubble plots. It was confirmed that the effect of cotton root stubble on residual film recovery could be reduced under appropriate machine operating parameters. This provides strong support and a theoretical and practical basis for future research on the correlation between root stubble and residual film and how to improve the residual film recovery rate.

1. Introduction

Residual film spreading can be very good at locking in soil moisture while promoting the nourishment of elements necessary for the growth of crops. The residual film material usually used is polyethylene, and the thickness of this film is usually 0.008~0.01 mm, while the residual film currently used in Xinjiang is 0.01 mm thick. This residual film material is highly corrosion-resistant, meets the time requirements of the cotton growth cycle and can be recycled [1,2]. However, when residual film is left on the land for long periods of time, exposed to the wind and sun, its mechanical performance declines significantly compared with factory standards, making the residual film very hard to recycle [3,4]. Since the use of chemical equipment can lead to an imbalance of nutrients in land, there is considerable interest in using mechanized equipment to address this type of white pollution. At present, common mechanical equipment for residual film recovery in China mainly includes the toothed chain type, the telescopic rod type and the guided chain harrow type [5,6]. In studies on residual film recycling, the main focus has been on the research direction of machines and performance, and there have also been a few studies combining the characteristics of residual film and soil. However, the impact of residual straw and roots on residual film recycling, which is quite important, has been neglected. The sharp decline in the tensile properties of residual film is related to its interaction with cotton stubble, which makes it extremely easy for the nail tooth hook to cause the residual film to tear again and hang in the stubble, increasing the difficulty of recycling residual film and resulting in its suboptimal recovery.

Therefore, this paper proposes the construction of a finite element model of cotton root stubble with soil, residual film and nail teeth. By using a combination of SPH-FEM, the soil was constructed in the form of SPH particles; the residual membrane, which was the main object of study, was constructed as a shell; and the cotton stalks and pegged teeth were divided into the FEM grid format. A simulation of the tearing scenario between the residual film and the stubble of cotton stalks during the nail tooth hooking process for surface residual film recycling was carried out. Various modeling approaches are currently available regarding the dynamic interactions between soil modeling and embedded columns. One of them is the LS-DYNA module in ANSYS 2020, which is a finite element method for nonlinear displays and is now the preferred choice for modeling soils dynamically in three dimensions [7]. Jin et al. [8] used the coupled FEM-SPH model to investigate the variation in soil cutting resistance, and the reliability of the model was verified by combining it with practical tests. Yang et al. [9] developed a simulation of stubble chopping in sugarcane stubble fields by using the coupled FEM-SPH method, which was combined with field trials to find out the reasons for the poor stubble-chopping effect. Wang et al. [10] used LS-DYNA dynamic simulation to develop a fluid–solid coupling (FSI) model of the weed–wheel–water–soil system, which was optimized by using simulation to improve the performance of mechanical weeding. Huo et al. [11] proposed two numerical models with different approaches, FEM-SPH and SPH-SPH, to simulate the problem of liquid droplet impacts on the elastic beams of ships in the study of liquid–solid interactions and proved the accuracy of the numerical simulations. Zhang et al. [12] modeled soil being crushed by using Abaqus, providing contact parameters and reliable data for soil crushing with a machine. The kinematic simulation of the peg–teeth–soil–straw–residual film combination studied in this paper is a typical kinetic model of multifactor nonlinear contact. The model has the functions of high residual membrane deformation and a high soil strain rate [13]. Following a literature review, the current method of parameter optimization using simulation became the focal point, as such methods are effective, with results that are accurate and applicable to this research problem.

In Figure 1, a mind map is presented to explain this study more clearly:

(1)

Research purpose: Existing residual film recycling technology focuses on mechanical performance, ignoring the dragging effect of cotton stubble on residual film. To determine whether the influence of stubble on residual film recycling exists, the mechanical parameters are optimized as much as possible to reduce the impact of cotton stubble on residual film recycling and improve the recycling rate.

(2)

Research tasks: In order to optimize the model more conveniently and intuitively, this study adopts the popular SPH (smooth particle hydrodynamics)-FEM (finite element method) coupling algorithm to establish a dynamic interaction model of nail teeth, residual film, soil and cotton stubble, and the effects of cotton stubble on the residual film were analyzed by accurately simulating the shear strain, stress and upward displacement of the residual film during residual film recycling. By optimizing the motion parameters of the nail teeth, the maximum shear strain, pickup height and average peak stress were 1293, 363.81 mm and 3.42 MPa, respectively, which reduced the influence of root stubble on residual film recovery.

(3)

Target results: Through multifactorial orthogonal testing, the optimal operational parameters were identified as a 6.7 km/h forward velocity, a 5.5 r/s rotational speed, and a 30° soil entry angle. Combined with field experiments, the effects of 5–8 cm and 8–14 cm root stubble on the residual film recovery rate were compared. It was confirmed that the effect of cotton root stubble on residual film recovery could be reduced under appropriate machine operating parameters. This provides strong support and a theoretical and practical basis for future research on the correlation between root stubble and residual film and how to improve the residual film recovery rate.

2. Overall Structure and Analysis of Key Components

2.1. Overall Structure of Residual Film Recycling Machine

As shown in Figure 2, the entire machine mainly consists of a beating rod device, a traction device, a frame, a soil discharge device, a film collection device (comprising a restrictor, nail teeth, a stripper plate and a toothed belt) and a baling device (comprising a leather belt and a corrugated pipe), among others.

The residual film is picked up by the nail teeth and transported to the film stripping device through the toothed belt, where it is dislodged and dropped onto the belt. The film is then conveyed to the baling unit, where steel rollers and the conveyor belt rotate relative to each other, gradually modeling the residual film into a roll. When the film roll reaches a certain size, the travel switch in the baler triggers an alarm, and the “Unload Film Roll” button in the control room lights up. The driver presses this button to open the baler's film bin via hydraulic transmission, releasing the film roll onto the ground and completing the process of residual film pickup and baling.

The structure of the residual film pickup mechanism is shown in Figure 3. It mainly consists of nail teeth, a toothed belt, a conveyor belt, a steel roller and other components. Long daylight hours can improve both the quality and quantity of cotton. However, prolonged exposure to sunlight causes the physical properties of the film to degrade more quickly due to wind and UV exposure, thereby reducing recycling efficiency. It is worth noting that the film lifting belt in the residual film recycler has been modified to be nearly perpendicular in order to increase the positive thrust during recovery. Due to the low film-breaking tendency of the nail teeth and the small spacing between the teeth, the film pickup process is simplified and shortened, which significantly reduces the risk of the secondary tearing of residual film.

2.2. Force Analysis of Membrane Pickup Nail Teeth

The residual film pickup device directly influences the recovery efficiency of the residual film recycler. During operation, the friction between the nail teeth and the soil and residual film cannot be ignored. The film is primarily lifted by the upward motion of the nail tooth unit within the residual film recycler. The residual film pickup mechanism moves at the same speed as the circumferential speed at the contact of the nail teeth with the soil. The speed of nail teeth that have not yet entered the work area do not affect the calculated time and speed results for the work area. When the nail teeth are within the working area, their movement can be approximated as a combination of translational motion from both the machine and the teeth themselves. During operation, the nail teeth penetrate and drive the residual membrane in clockwise translation and rotation. With the rotation of the nail teeth, the upward force F_r caused by the nail teeth on the residual film gradually increases; at this time, the soil pressure F and friction f_r on the residual film gradually decrease as residual film is picked up, until the residual film is picked up smoothly. Therefore, residual film was used as the object of study for force analysis to analyze the interaction force between it and the nail teeth [14]. As shown in Figure 4, the interaction forces of the residual film, soil and peg teeth are decomposed on the x- and y-axes.

$$\left\{\begin{array}{c}F+f=F_n+F_r\cdot \cos \eta ,\\ F_r\cdot \sin \eta =g\cdot \sin \gamma +f_r,\\ F_r=(G+g)v^2/R,\\ v=\cdot 2\pi \cdot R\cdot {\omega }_{\leftarrow }\end{array}\right.$$

(1)

where g is the gravity of the residual membrane itself, N; G is the soil gravity, N; F_n is the force of the nail tooth tip on the residual membrane, N; F is the pressure on the residual membrane caused by the soil attached around the residual membrane, N; F_r is the force exerted on the residual membrane by the rotation and movement of the nail teeth, N; f is the frictional resistance of the residual film to the nail teeth during film pickup, N; f_r is the friction formed by the soil on the residual film, N; η, γ represent the angle; v represents the forward direction and speed; and ω indicates the speed of rotation of the toothed-belt peg teeth.

According to the relevant literature references, the work performed by one week of rotation of the toothed-belt pegged teeth can be calculated as [14]

$$\left\{\begin{array}{c}P={\displaystyle \frac{2\pi G_0+0.1F_{1}ze}{zeHb}}\\ G_0=F_{n}R\end{array}\right.$$

(2)

where P is the work performed, J; F₁ is the traction force of the residual film recycler, N; z is the number of peg teeth; e is the spacing between nail teeth, mm; H represents the depth of the nail teeth into the soil, mm; G₀ stands for torque, Nm; b represents the cross-sectional diameter of the nail teeth, mm; F_n is the force of the nail tooth tip on the residual membrane, N; and R denotes the rotational radius measured between the nail tooth tip and the rotation center, mm.

Combining Equations (1) and (2) gives

$$P={\displaystyle \frac{2\pi \left[4{\pi }^2{R}^2{\omega }^2{G}_0\cdot (\sin \eta +\cos \eta )-(G\cdot \cos \gamma -f-f_r)\cdot R\right]+0.1ze{F}_1}{zeHb}}$$

(3)

From Equation (3), it can be seen that the rotational work performed by the nail teeth is related to the number of teeth, the tooth spacing, the depth of penetration, the radius and speed of the nail teeth and the diameter of the cross-section of the nail teeth. When the number of nail teeth, the spacing between the teeth and the depth of entry into the soil are constant, the larger the cross-section diameter of the nail teeth is, the smaller the work performed by the nail teeth is. And the greater the speed and radius of the nail teeth are, the more work they do.

2.3. The Parameters of the Motion of the Nail Teeth

The nail teeth are in direct contact with the residual film, so setting their motion parameter is extremely important for effectively picking up residual film. Therefore, it is necessary to analyze its motion. As shown in Figure 5, a portion of soil bulges along the rotation track of the nail teeth. Experimental verification and references from the literature indicate that when this soil bulge is larger, more soil is thrown up, which increases the likelihood of the secondary tearing of the residual film and increases the power consumption required for the rotation of the nail teeth. The effective depth of penetration h of the nail teeth is 80 mm, and the height of the soil puckered during operation shall be

$$h-h_0\le 80\mathrm{mm}$$

(4)

As shown in Figure 4, the trajectory equation of the nail teeth advancing in the x-axis direction is [15]

$$\left\{\begin{array}{c}x=vt+R\cos \alpha \\ y=R\sin \alpha \end{array}\right.$$

(5)

From the above equation, the velocity equation of the nail teeth is obtained as

$$\left\{\begin{array}{c}{v}_x={x^{\prime }}_t=v-{\omega }_{2}R\sin \alpha \\ v_y={y^{\prime }}_t={\omega }_{2}R\cos \alpha \end{array}\right.$$

(6)

where v is the forward speed of the nail teeth, km/h; ω₂ is the rotational speed of the nail teeth, r/s; R is the distance from the tip of the nail teeth to the center of the circle that it is circling, mm; and α is the angle of the nail teeth into the ground, °.

According to the current research status of residual film recycling machines, in order to consider both the quality and efficiency of residual film recycling, the parameters of the nail teeth are set as a forward speed v between 1150 and 2350 mm/s, a rotational speed between 3.5 and 8.5 r/s and a soil entry angle of the nail teeth between 15°and 40° to enhance the film–tooth friction and improve residual film recovery efficiency.

3. Simulation Model Parameter Establishment Method

Through theoretical analysis, it was found that the performance of residual film recycling is closely related to residual film, soil, and straw–root stubble. Setting the residual film parameter too large does not necessarily indicate that the recovery of the residual film in the simulation is more efficient; rather, it increases the simulation time. Therefore, considering both simulation efficiency and practicality, the residual film width was set to 38 cm and the length to 100 cm for the simulation optimization test. The simulation was conducted under conditions where the ground contains root stubble, in order to determine the effective rotational speed of the nail teeth, the forward speed, and the depth of penetration to improve the machine’s film collection performance and minimize secondary tearing between residual film and stubble.

Gingold and Monaghan presented smooth particle hydrodynamics (SPH) as a computational method for tracking discrete particle elements and simulating fluids and solids [16,17,18]. SPH is used to simulate the motion between particles and can represent the mass or velocity of each particle. The algorithm is derived from the kernel approximation function, which has a mathematical expression for the partial differential equation as follows [19]:

$$f(x_i)={\displaystyle \sum _{j=1}^N\frac{m_j}{{\rho }_j}}f(x_j)W(x_i-x_j,h)$$

(7)

where f(x_i) is the integral representation of the soil particle, W(x_i−x_j, h) is the smooth kernel function, m_j is the mass of soil particle j and p_j is the density of soil particle j.

This feature meets the needs of the soil model used in this paper, which is constructed as a smooth granular model by using a nodal meshless approach [20]. This study focuses solely on the use of this coupling algorithm and does not delve deeper into the underlying logic. The relevant contact conditions and solver usage are presented in the next subsection.

Setting of Model Boundary Conditions

The actual parameters of the staple teeth of the residual film recycler are consistent with this model. As shown in Figure 6, we establish the nail tooth model with the tooth spacing set to 7 cm and the length of the nail teeth set to 7 cm. The tooth tip is positioned 16.5 cm from the rotational center to ensure a minimum pickup depth exceeding 6 cm. The row spacing of cotton root stubble is set to 12.5 cm, and the column spacing is set to 9.5 cm, consistently with the cotton cropping pattern in Xinjiang. Since different cropping patterns have a negligible effect on residual film recycling, cotton plots with other cropping patterns are not considered for the time being. To avoid unnecessary computation time, 12 straw–root stubble elements with a height of 5 cm and a diameter of 1 cm are set up for this simulation experiment. The particle diameter settings are highly accurate for the simulated interactions [21,22]. Considering both calculation accuracy and efficiency, 5 mm SPH particles are used for the soil, generating 526,022 particle subgroups, with effective contact realized between the particles. The residual membrane is set as a shell cell, with a thickness of 0.01 mm. The surface is selected, and the generated mesh comprises 14,685 5 mm cells, set as a plastic deformable structure [23]. The nail teeth and root stubble are set to SOLID, and 5 mm grid cells are generated for each. Regarding the characteristics of soil, cotton root stubble and residual film, the group has a previous description of its research to compare and cite with existing research. The nail teeth are selected based on common steel properties. Each material parameter is shown in

Table 1. Simulated material parameters [24,25,26,27,28].

Structure	Density (kg/m3)	Elastic Modulus (MPa)	Poisson’s Ratio
Residual film	1030	0.66	0.34
Soil	1660	7.2	0.38
Root stubble	1250	0.0012	0.34
Nail teeth	7850	2.1 × 105	0.30

[24,25,26,27,28]. It is worth noting that since the main focus of the study was on the effect of root stubble on residual film recycling, only one material property of residual film in cotton fields was selected for analysis, and the material properties of different residual films were not explored.

For soil moisture, residual film aging, mechanical wear and tear, and other related issues, our group, in the early stages of the study, has already taken into account these issues. Therefore, this paper directly uses and cites the relevant findings and does not discuss these aspects further.

We define the rotational and translational speeds of the nail teeth as (0,0,1) and (1,0,0), respectively. Building upon prior group findings, the operational parameters were established as follows: a 1600 mm/s advancement velocity, a 3.6 r/s rotational frequency and an angle of soil entry of 25°. For computational streamlining, the mechanical simulation retained only the nail tooth and shaft assembly. The soil–other contact was set to automatic point–face contact, the nail tooth contact with residual film and cotton stalks was set to automatic face contact, and the residual film contact with straw and straw–root stubble was set to automatic face contact [29,30]. A penalty function was used as a control mechanism to allow for the accurate analysis of residual film tension [31]. The total computation time was 1 s, and the k-file after the setup was computed by using the post-processor Ls-Run 2023. The preset selection was MPP double–precision, with IntelIMPI.

4. Simulation Analysis

4.1. Simulation of Dynamic Properties

As shown in Figure 7a, the soil loosens as the nail teeth rotate. When the residual film is about to be picked up by the nail teeth, plastic deformation occurs, the residual film bends, and the entire film experiences varying stresses. As shown in Figure 7b, the pulling force on the film gradually increases. When the first row of nail teeth exits the soil, the soil is further disrupted, and the residual film, at this time, presents the state of being pulled by the straw. The pulling force makes the residual film undergo the phenomenon of the second tear. As shown in Figure 7c, with the second row of nail teeth hooking the residual film, there was more soil damage and noticeable pulling between the root stubble and the residual film. As shown in Figure 7d, with the continuous upward picking of the second row of peg teeth, the force on the soil and the whole film is maximized. At this point, and the whole film is rolled up with more tears at the intersection with the root stubble.

There is no research on the standard of the shear strain of residual film. However, after a lot of searching, the shear strain of aged residual film exceeds 2000, which indicates a serious deformation or wear state. From Figure 7, we can see that the distribution of the average shear strain across the whole residual film is not uniform. Most of the shear strain above 2000 is distributed near the root stubble, and the maximum shear strain reaches 2742. It is very necessary to pay attention to this kind of problem, as the residual membrane is damaged and remains entangled in root stubble in the actual situation.

As shown in Figure 8, to more intuitively observe the trend of residual film degradation, the residual film at the straw–root stubble is used as a reference. Six nodes are established in the first row, denoted by points.

As shown in Figure 9, during the periods 0~0.4 s and 0.7~1 s, the residual film at the straw–root stubble is subjected to a larger amount of shear stress and is the most severely damaged. In practice, the residual film is more significantly dragged by the root stubble, which affects the residual film recovery rate. Therefore it is necessary to investigate the situation to minimize the dragging situation.

4.2. Residual Film Peak Stress and Maximum Deformation

Figure 10a and Figure 10c represent the force distribution of the residual membrane at 0.3 s and 0.9 s, respectively, while Figure 10b and Figure 10d represent the residual membrane deformation at 0.3 s and 0.9 s, respectively. Figure 10a and Figure 10c show that the residual film stress is mainly concentrated at the intertooth contact and near the cotton root stubble; the peak residual film stress values at this time are 6.11 MPa and 7.21 MPa, respectively. The average peak stress during the residual film pickup process is 5.19 MPa, and there are multiple damages. The peak stress at the intersection of residual film and cotton root stubble is 6.93 MPa. In its actual state, it is very prone to tearing, which affects recycling efficiency. Therefore, straw–root stubble has a greater impact on residual film and should be used as the primary solution to the problem when performing operations that break up straw.

As shown in Figure 10b, at 0.3 s, the residual membrane is picked up by the further action of the nail teeth, and the deformation increases to 248.8 mm. At 0.9 s, the residual film is attached to the tips of the nail teeth, at which time the deformation reaches a maximum value of 316.4 mm, as shown in Figure 10d. The analysis shows that the residual film deformation reaches the maximum in the process of film collection by the nail teeth, which proves that there is no sliding or leakage connection between the nail teeth and the residual film and demonstrates the reliability and effectiveness of the structure. The simulation test provides a valuable reference for subsequent multifactor simulation optimization tests.

4.3. Maximum Shear Strain of Residual Film

As shown in Figure 11, the effect of straw–root stubble on residual film recovery was analyzed in terms of the maximum shear strain of the residual film. In Figure 11a, when the nail teeth lift the film at the first position, the maximum shear strain is 2426, and the residual film is torn at the intersection with the root stubble. In Figure 11b, when the nail teeth rotate to the intersection of the third row of residual film and root stubble, the maximum shear strain is 2211, and the residual film is torn at the root stubble. In Figure 11c, the maximum shear strain reaches 2512 when the nail teeth rotate to the point where the residual membrane at the fourth ground row intersects with the root stubble, and the residual membrane is torn. In Figure 11d, the nail teeth rotate to the point where the sixth column of residual film intersects with the root stubble, resulting in a maximum shear strain of 2093, at which point the residual film is torn. The remaining intersections are subjected to less shear strain, but the residual membrane still experiences varying degrees of tearing. This is due to the fact that the nail teeth lift the residual membrane to its highest point, forming an almost vertically upward angle. As a result, the root stubble exerts less effective tension on the residual membrane, which is not represented in the figure. From the above description, it can be seen that root stubble has a greater impact on residual film recovery, with more residual film tearing occurring at the root stubble, thereby reducing the recovery rate. This provides a valuable reference for the simulation optimization tests to be conducted subsequently.

5. Multifactor Simulation Optimization Test

In order to confirm that suitable operating parameters of nail teeth are able to reduce the resistance effect of cotton root stubble on residual film, a multifactorial orthogonal test was used to optimize the nail tooth parameters. The maximum shear strain of residual film Y₁, the residual film pickup height Y₂ and the average peak stress of the residual film Y₃ are the test factors, and the advancement speed of the nail teeth X₁, the rotation speed X₂, and the soil entry angle X₃ are the test indexes for the simulation test. The table of the test factors is shown in

Table 2. Experimental factors.

Code	Forward Speed of Nail Teeth X1/(mm/s)	Rotation Speed of Nail Teeth X2/(r/s)	Entry Angle of Nail Teeth X3/(°)
−1.682	740.92	1.80	17.57
−1	1150.00	3.50	22.00
0	1750.00	6.00	28.50
1	2350.00	8.50	35.00
1.682	2759.08	10.20	39.43

.

5.1. Analysis of Test Results

The above test factors were compiled into Ls-Run 2023 for simulation tests with 20 groups, and each group of tests was repeated five times. The average values of maximum shear strain, pickup height, and mean peak stress of the residual film were extracted and recorded. The results are shown in

Table 3. Multiple regression.

No.	Forward Speed of Nail Teeth, X1 (mm/s)	Rotation Speed of Nail Teeth, X2 (r/s)	Entry Angle of Nail Teeth, X3 (°)	Maximum Shear Strain of Residual Film, Y1	Pickup Height of Residual Film, Y2 (mm)	Mean Peak Stress of Residual Film, Y3 (MPa)
1	−1.000	−1.000	−1.000	2146	256.3	3.95
2	1.000	−1.000	−1.000	2345	315	3.28
3	−1.000	1.000	−1.000	2075	323.2	3
4	1.000	1.000	−1.000	1592	320.3	3.35
5	−1.000	−1.000	1.000	1773	282.2	3.68
6	1.000	−1.000	1.000	1895	275.2	2.66
7	−1.000	1.000	1.000	2004	359.8	3.19
8	1.000	1.000	1.000	1698	349.7	2.96
9	−1.682	0.000	0.000	2237	290.1	3.45
10	1.682	0.000	0.000	1935	307.8	3.04
11	0.000	−1.682	0.000	2154	280.6	3.59
12	0.000	1.682	0.000	1932	366.2	3.21
13	0.000	0.000	−1.682	1945	305.4	3.14
14	0.000	0.000	1.682	1836	328.1	3.05
15	0.000	0.000	0.000	935	350.9	2.13
16	0.000	0.000	0.000	1002	343.5	2.15
17	0.000	0.000	0.000	1164	352.4	2.26
18	0.000	0.000	0.000	1125	358.9	2.38
19	0.000	0.000	0.000	1006	346.3	2.19
20	0.000	0.000	0.000	977	340.5	2.2

.

Based on the analysis of the above results, multiple regression models were developed for the advancement speed X₁, rotational speed X₂ and angle of entry X₃ of the nail teeth, as well as the maximum shear strain Y₁, pickup height Y₂ and average peak stress Y₃ of the residual film. The maximum shear strain Y₁ and pickup height Y₂ of the residual film are analyzed in

Table 4. Significant characteristics of maximum shear strain and pickup height of residual film.

Source	DOF	Maximum Shear Strain of Residual Film, Y1			Pickup Height of Residual Film, Y2 (mm)
		Sum of Squares	F	Significant Level, p	Sum of Squares	F	Significant Level, p
Model	9	4.16	38.88	<0.0001 **	19,373.40	31.90	<0.0001 **
X1	1	69,736.68	5.87	0.0359 *	343.26	5.09	0.0477 *
X2	1	99,100.56	8.34	0.0162 *	9930.29	147.17	<0.0001 **
X3	1	69,082.79	5.81	0.0366 *	596.76	8.84	0.0140 *
X1X2	1	1.54	12.96	0.0048 *	523.26	7.76	0.0193 *
X1X3	1	1250.00	0.11	0.7524	664.30	9.85	0.0106 *
X2X3	1	92,020.50	7.74	0.0194 *	798.00	11.83	0.0063 *
X12	1	1.72	144.67	<0.0001 **	4537.91	67.26	<0.0001 **
X22	1	1.57	132.22	<0.0001 **	1193.57	17.69	0.0018 *
X32	1	1.10	92.56	<0.0001 **	1889.94	28.01	0.0004 *
Residual	10	1.19			674.73
Lack of fit	5	78,794.59	1.97	0.2376	452.13	2.03	0.2276
Pure error	5	40,034.83			222.59
Cor total	19	4.28			20,048.13

Notes: p < 0.01 (** highly significant); 0.01 ≤ p < 0.05 (* significant).

, while the average peak stress Y₃ of the residual film is presented in

Table 5. Significant properties of average peak stress of residual film.

Average Peak Stress of Residual Film, Y3 (MPa)
Source	DOF	Sum of Squares	F	Significant Level, p
Model	9	5.86	56.34	<0.0001 **
X1	1	0.37	32.32	0.0002 *
X2	1	0.21	18.49	0.0016 *
X3	1	0.11	9.76	0.0108 *
X1X2	1	0.41	35.41	0.0001 *
X1X3	1	0.11	9.35	0.0121 *
X2X3	1	0.06	5.15	0.0467 *
X12	1	1.79	154.72	<0.0001 **
X22	1	2.39	206.58	<0.0001 **
X32	1	1.29	111.65	<0.0001 **
Residual	10	0.12
Lack of fit	5	0.07	1.79	0.2696
Pure error	5	0.04
Cor total	19	5.98

Notes: p < 0.01 (** highly significant); 0.01 ≤ p < 0.05 (* significant).

.

From Table 4, it can be seen that for the maximum shear strain Y₁ of the residual film, significant influence is exerted by, in descending order, X₁², X₂², X₃², X₁X₂, X₂, X₂X₃, X₁ and X₃. Non-significant influence is exerted by X₁X₃. For the pickup height Y₂ of the residual film, all of them exert significant influence, according to the descending order of influence of X₂, X₁², X₃², X₂², X₂X₃, X₁X₃, X₃, X₁X₂ and X₁, of which the rotational speed X₂ and the square term of the forward speed X₁² are extremely significant. From Table 5 (peak average residual film stress Y₃), important influence is exerted by, in descending order, X₂², X₁², X₃², X₁X₂, X₁, X₂, X₃, X₁X₃ and X₂X₃, with X₁², X₂² and X₃² being extremely important.

The mathematical models of the multiple regression equations relating the advancement speed X₁, rotational speed X₂ and angle of entry X₃ of the nail teeth with the maximum shear strain Y₁, pickup height Y₂ and average peak stress Y₃ of the residual film are established based on the experimental results as

$$\begin{array}{l}{Y}_1=1038.85-71.46X_1-85.18X_2-71.12X_3-138.75X_1{X}_2+12.5X_1{X}_3+107.25X_2{X}_3+345.38{X_1}^2+330.18{X_2}^2\\ +276.26{X_3}^2\end{array}$$

$$Y_2=348.77+5.01X_1+26.97X_2+6.61X_3-8.06X_1{X}_2-9.11X_1{X}_3+9.99X_2{X}_3-17.75{X_1}^2-9.10{X_2}^2-11.45{X_3}^2$$

(8)

$$\begin{array}{l}{Y}_3=2.22-0.1655X_1-0.1251X_2-0.0909X_3+0.2262X_1{X}_2-0.1163X_1{X}_3+0.0862X_2{X}_3+0.3524{X_1}^2+0.4072{X_2}^2\\ +0.2993{X_3}^2\end{array}$$

The results are analyzed to obtain that the above models all present p < 0.0001, and the misfit P-values are 0.23, 0.22 and 0.26, respectively. The coefficients of determination R² are 0.97, 0.96 and 0.98, respectively, all close to 1, indicating that the regression equation fit very well. The difference between the adjusted coefficient of determination, Adjusted R², and the predicted coefficient of determination, Predicted R², is less than 0.2, which indicates that the model has a small error and is well fitted. The coefficients of variation are 6.45%, 2.55% and 3.65%, respectively. A larger coefficient of variation indicates lower model effectiveness, and the results of the model in the present study show a high level of reliability. From the above, the model can be used to analyze and optimize the maximum shear strain Y₁, the pickup height Y₂ and the average peak stress Y₃.

5.2. Response Surface Analysis

As shown in Figure 12a, when the advancement speed of the nail teeth is in the range of 1400~2000 mm/s and the rotational speed is in the range of 5~8 r/s, the effect on the maximum shear strain of the residual film is not significant, indicating that the strain is small. On the contrary, the maximum shear strain on the residual film gradually increases as the advancement and rotation speeds of the nail teeth increase or decrease outside of these ranges. As shown in Figure 12b, when the advancement speed of the nail teeth is 1500~2100 mm/s and the angle of entry is 25~32°, the effect on the maximum shear strain of the residual membrane is not significant, indicating that the strain is small. Conversely, as the speed of the nail teeth and the entry angle into the soil increase or decrease, the maximum shear strain of the residual film becomes larger, making it more prone to tearing during the recovery process. As can be seen in Figure 12c, when both the rotational speed of the nail teeth and the angle of entry into the soil are smaller, their influence on the average peak stress in residual film is greater. However, as both factors gradually increase simultaneously, their influence on the maximum shear strain of the residual film is reduced. When the rotational speed of the nail teeth exceeds 8 r/s and the angle of entry exceeds 32°, the effect on the maximum shear strain of the residual film shows a gradually increasing trend.

From Figure 13a, when the forward speed of the nail teeth is 1400~2000 mm/s, the pickup height of the residual film increases with the rotational speed, and the pickup speed also increases. As shown in Figure 13b, when the advancement speed of the nail teeth is 1400~2200 mm/s and the entry angle into the soil is 24~34°, the pickup height of the residual film increases, indicating faster pickup speed. As seen in Figure 13c, when both the rotational speed of the nail teeth and the entry angle into the soil are larger, the influence on the pickup height is greater, indicating faster pickup speed. Conversely, as the rotational speed of the nail teeth and the angle of entry decrease, the influence on the pickup height gradually diminishes, and the residual film pickup speed decreases.

From Figure 14a, it can be seen that when the rotational speed of the nail teeth is 4.5~8.0 r/s and the forward speed is 1450~2300 mm/s, the effect on the peak average stress of the residual film is small. This indicates a negligible amount of damage to the residual film membrane. On the contrary, outside of this range, the effect of the average peak stress on the residual film becomes progressively larger, the pickup conditions become unstable, and the residual film becomes susceptible to tearing. As shown in Figure 14b, when the advancement speed of the nail teeth is 1400~2200 mm/s and the angle of entry is 25~34°, the average peak stress of the residual film has less influence, indicating that the residual film pickup condition is more stable. When the advancement speed and the angle of entry are either smaller or larger, the influence on the average peak stress of the residual film is larger, the pickup state becomes unstable, and the residual film easily tears. As seen in Figure 14c, when the rotational speed and the angle of entry of the nail teeth are smaller, the effect on the peak average stress of the residual film is greater. When the two factors gradually increase at the same time, the effect on the average peak stress value of the residual membrane is reduced. However, when the rotational speed of the nail teeth exceeds 6 r/s and the entry angle exceeds 32°, there is a gradual increase in the effect on the peak average stress of the residual film.

5.3. Optimization

As a result of these analyses, the advancement speed, rotational speed, and angle of entry of the nail teeth have different and significant effects on the maximum shear strain Y₁, pickup height Y₂, and average peak stress Y₃ of the residual film in soil containing root stubble. Optimization tests are performed by using multiple quadratic regression equations through the Response Optimization feature in Design Expert 13.

$$\left\{\begin{array}{l}\begin{array}{c}\min Y_1\\ \max Y_2\\ \min Y_3\end{array}\\ st.\left\{\begin{array}{c}1150\mathrm{mm}/\mathrm{s}\le X_1\le 2350\mathrm{mm}/\mathrm{s}\\ 3.5\mathrm{rad}/\mathrm{s}\le X_2\le 8.5\mathrm{rad}/\mathrm{s}\\ 22°\le X_3\le 35°\end{array}\right.\end{array}\right.$$

(9)

The optimal parameter combinations were obtained through calculations: the propulsion speed of the nail teeth is 1849.57 mm/s, the rotation speed of the nail teeth is 5.5 r/s, and the entry angle is 29.38°. Under these optimized conditions, the maximum shear strain, pickup height (maximum deformation) and average peak stress of the residual film are 1293, 363.81 mm and 3.42 MPa, respectively. Compared with the pre-optimization results, residual film damage at the root stubble intersection is greatly reduced when tests are conducted by using the optimized parameter combination. This further verifies that this parameter configuration can be used for simulation parameter setting in the mathematical model of the toothed-belt residual film recycler.

As shown in Figure 15a, when the residual film is in the second row of cotton root stubble during the simulation, the maximum shear strain of the residual film is 1831. The intersection of residual film and stubble is not subjected to significant shear strain, indicating that there is no dragging phenomenon and that the residual film is picked up smoothly. As shown in Figure 15b, when the peg teeth rotate to the third row where the residual film meets the root stubble, the maximum shear strain is 1872, and there is no tearing of the residual film due to the root stubble. As shown in Figure 15c, the maximum shear strain is 1845 when the nail teeth rotate to the point where the fourth column of residual film meets the root stubble, and there is no tearing of the residual film. As shown in Figure 15d,e, the maximum shear strains are 1783 and 1805, respectively, when the nail teeth rotate to the point where the residual film in the fifth and sixth columns intersects with the root stubble. No residual film tearing occurs at any of the intersections. As the nail teeth pick up the residual film to the highest point, the residual film nearly forms a vertical upward angle. Consequently, the effective tension exerted by the root stubble on the residual film is small, and the shear strain at the stubble intersection gradually decreases. From the above description, it can be seen that at the nail teeth advancement speed of 1849.57 mm/s, the rotational speed of 5.5 r/s and the angle of entry of 29.38°, the tearing caused during residual film recycling is minimal. This improves the rate of residual film recycling and enhances work efficiency.

6. Field Trials

6.1. Test Condition

In order to better verify the accuracy of the optimized parameters obtained from the simulation test, a field test was carried out in combination with the optimization results of the simulation. The field trial was carried out from 16 to 23 March 2025, in a cotton plantation located 500 meters northwest of the Tuhe Expressway in Keping County, Akesu Region, Xinjiang Uygur Autonomous Region. Most of the soils at the southern border have a fine sandy surface layer, which does not affect contact with the soil and shows relatively small differences in properties. Therefore, a relatively flat test site of about three hundred acres was chosen, and no other sites were considered throughout the test. Cotton species in Xinjiang are similar, so the trials no longer considered different species of cotton on a comparable basis. The test site was a post-harvest cotton field, with a residual film thickness of 0.01 mm. The width of the field was 2050 mm. Soil density was tested by using a soil densitometer and was 2611.46 kg/m³ for the deep soil layer and about 1659.7 kg/m³ for the top soil layer of the working layer. Soil moisture content was measured by using a soil moisture meter at 0–100 mm depth and recorded as 16.56%. As shown in Figure 16, the Zoomlion RC1204-F tractor was chosen as the power source for this test. The working width of the residual film recycler was 2050 mm, the working depth was 0–80 mm, and the hitching method was traction type. The optimal combination of parameters for the nail teeth simulation was applied to the residual film recycler as follows: a forward speed of 6.7 km/h, a turning speed of 5.5 r/s, and an entry angle of 30°.

The residual film recovery rate is the most direct type of data to test the recovery effect of a residual film recycling machine, as shown in the following formula:

$$W=(1-{\displaystyle \frac{S}{S_0}})\times 100\%$$

(10)

where W represents the recovery rate of residual film, %; S represents the quality of the residual film picked up, g; and S₀ represents the quality of the residual film before it is picked up, g.

The simulation revealed that the majority of residual film breakdown occurred at the junction between the residual film and the root stubble. In order to facilitate verification and to more intuitively and effectively obtain the intersection rate between residual film and root stubble after operation, the following formula was used:

$$W_1={\displaystyle \frac{S_1}{S_0}}\times 100\%$$

(11)

where W₁ denotes the residual rate at the intersection of residual film and root stubble, %; S₁ denotes the mass of residual film not picked up at the root stubble, g; and S₀ denotes the mass of residual film before it is picked up, g. The residual film at the intersection of residual film and root stubble was not picked up at the root stubble.

6.2. Experimental Design and Analysis of Results

The experimental design was carried out in accordance with the program developed for the GB/T25412-2010 and GB/T14290-2021 residual film recycling machine [32,33]. To better validate the effectiveness of this study, root stubble of varying heights was selected and used for comparative analysis.

Ten test areas of 2 m in length and 2 m in width were randomly selected within the test area; five groups had root stubble in the range of 5–8 cm, and five groups had root stubble in the range of 8–14 cm. Due to the small amount of root stubble in the range of 0–5 cm, it was not considered in this experiment. As shown in Figure 17A–C show 5–8 cm root stubble, it can be seen that the residual film recovery rate was high at this speed, and residual film dragging by root stubble was very low. Figure 17D–F show 8–14 cm root stubble and clearly show that residual film recovery was not satisfactory, and there was more residual film dragging by root stubble.

The residual film in the ground was separated, air-dried, weighed, and averaged. The results are shown in

Table 6. Test data.

No.	1	2	3	4	5	Average Value
Original residual film content in the ground (g)	176	182.5	188.3	177.4	181.7	181.18
Residual film content in 5–8 cm root stubble area (g)	18.9	19.1	21.3	16.7	18.3	18.86
Content of remaining residual film entangled in 5–8 cm stubble (g)	6.4	7.3	8.1	6.3	9.0	7.42
Residual film content in 8–14 cm root stubble area (g)	29.4	33.8	30.1	34.5	27.5	31.06
Content of remaining entangled residual film in 8–14 cm stubble (g)	19.5	23.4	20.4	24.7	19.9	21.58

.

Substituting the above data into Equation (7) yielded average residual film recovery rates of 89.59% for the 5–8 cm stubble test field and 82.86% for the 8–14 cm stubble test field.

By substituting the residual film entangled in root stubble into Equation (8), the residual film dragging rate at root stubble crossings was calculated to be 4.10%, which accounted for 39.39% of the total residual film content in the 5–8 cm root stubble plots. The residual film dragging rate at root stubble crossings was calculated to be 11.91%, which accounted for 69.49% of the total residual film content in the 8–14 cm root stubble plots.

When the field test parameters of the nail teeth residual film recycler were set as a forward speed 6.7 km/h, a rotational speed 5.5 r/s and an angle of entry 30°, the results indicated a 6.73% improvement in film recovery rate and a 7.81% reduction in root stubble dragging rate. The total percentage of residual film entangled in root stubble was 30.10% lower in the 5–8 cm root stubble experimental plot compared with the 8–14 cm root stubble experimental plot, and the residual film recovery rate was greatly improved. With this parameter configuration, the residual film is recovered cleanly, causing little damage to the soil and reducing unnecessary losses. Above this speed, the toothed belt is prone to chipping, and the efficiency of residual film recovery is affected.

6.3. Comparison of Past Studies

This study examines the recovery process of residual film from cotton root stubble land through theoretical modeling, simulations and field experiments. The maximum shear strain, pickup height and average peak stress were effectively predicted during the simulation. During the test, the maximum peak stress reached 7.2 MPa, which is close to the maximum stress of residual film pickup studied by Xie et al. [34]. This further illustrates the accuracy and reliability of the discrete element model used in this study. Compared with previous studies, this paper proposes to determine the optimal parameter combinations for nail teeth through simulation and field trials in the context of residual film recovery from root stubble, providing both theoretical and practical support with reference value. From the test results, it can be seen that the residual film recovery rate was 89.59% in the field experiment conducted with this parameter combination, which reduced the residual film dragging rate at the root stubble and thus increased the residual film recovery rate.

Staple-toothed residual film recyclers are more suitable for wetter land than bullet-toothed residual film recyclers. Previous tests on our jitter chain membrane soil separation unit showed a significant reduction in residual film recovery to 68% due to chain vibration [4]. The present study achieved a recovery rate 2.39% higher than the 87.2% rate obtained with a toothed chain film recycler by Xie et al. [15]. The recovery rate of the nail tooth residual film recycler in this study was 1.29% higher than the 88.3% rate obtained by Cao et al. [35]. Compared with the chain-tooth residual film recycler previously studied in this research field, the methodology of this study is more innovative and can present the working process more intuitively, revealing the strain, stress and deformation of the residual film when recycling residual film in the presence of root stubble [26]. The speed pairing in this study effectively reduced belt and nail tooth damage rates, as well as fuel consumption, compared with previous studies, resulting in lower labor maintenance costs, longer working hours, and improved efficiency by reducing the impact of cotton root stubble on residual film. In conclusion, the analysis elucidated the variations in the maximum shear strain, pickup height and peak stress of residual film, revealing the effect of root stubble on residual film when it is recovered. This study offers a solid theoretical foundation, as well as an optimal basis, for residual film recycling tests and simulations.

7. Summary

In this study, a novel coupling algorithm, a combination of SPH and FEM, was used to simulate and analyze residual film recovery in the presence of root stubble. The optimized results showed that the maximum shear strain, pickup height and average peak stress are 1293, 363.81 mm and 3.42 MPa, respectively.

The optimal combination of parameters for the nail tooth simulation was applied to a residual film recycler as follows: a forward speed of 6.7 km/h, a turning speed of 5.5 r/s, and an entry angle of 30°. The effect of the residual film dragging rate at root stubble crossings on residual film recovery was revealed, and the experimental results showed that the average residual film recovery rate in the 5–8 cm straw–root stubble experimental field was 89.59%, with a residual film dragging rate at the intersection of root stubble of 4.10%; the average residual film recovery rate in the 8–14 cm straw–root stubble experimental field was 82.86%, with a residual film dragging rate at the intersection of root stubble of 11.91%. The recycling effect of the 5–8 cm straw–root stubble experimental field was more ideal than that of the 8–14 cm straw–root stubble experimental field, with the residual film recycling rate being increased by 6.73%, and the residual film dragging rate at the intersection of residual film and straw–root stubble being reduced by 7.81%. The dragging rate between residual film and root stubble was greatly reduced, and the residual film recovery rate was improved. This confirms that the reduction in cotton stubble under suitable machine operating parameters is extremely important for improving residual film recovery and more conducive to the direct response optimization of residual film recovery, which will provide strong support for future research on the correlation between root stubble and residual film.