Influence law on the effect of shredding characteristics of residual film in the mixture of mechanically recovered residual films and impurities in cotton fields

1.   Introduction

Mulching film is a petroleum-based long-chain polyethylene plastic product^[1,2]. When left too long in the field, some intermolecular covalent bonds of the polymer could break and the molecular chain could be invalid^[3], causing aged and fractured films which are hard to recover. Xinjiang is a major cotton production base in China. Due to the continuous cropping with mulching technology in this area, the residual mulch in the cotton field is 1.5-5.0 times higher than China’s residual mulch standard (75 kg/hm²)^[4], and soil and environmental pollution are particularly serious^[5,6]. Mechanical recovery technology has become a trend and an important means for recovery of residual films (RF)^[7], and has initially solved the problem of RF pollution. However, the recovered residue is usually mixed with a large amount of cotton straws, soil, and other impurities, which would eventually form a mixture of mechanically recovered RF and impurities in cotton fields (MRI)^[8]. Different from urban wastes or other agricultural wastes, MRI (Figure 1a) features an unstable structure, different mixture proportions, disordered distribution of film-soil-straw, strong adhesion of film and soil, and intertwined film and straw, which has increased the initial cleaning cost of RF and extended the production period. This has hindered the resource utilization process of RF to a certain extent and has reduced the quality of recycled products.

Figure  1.  RF and impurities (a) and cutting device (b)

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As energy recovery and utilization of waste plastics could cause waste of resources^[9], resource recovery and utilization has become a definite trend to treat waste plastics and has attracted global attention for its great development potential^[10,11]. The RF in MRI is such a recyclable waste plastic resource^[12]. Reasonable and suitable recovery, primary cleaning, and resource utilization not only can relieve environmental pollution, improve resource utilization, and reduce resource exploitation cost^[13-15], but also can solve the RF pollution effectively and environmentally. Therefore, it is urgent to carry out studies with regards to primary cleaning technology of MRI to form an organic circular economy involving the recovery, treatment, and resource utilization of MRI.

To realize the resource utilization of MRI in Xinjiang, the study on primary cleaning technology mainly focused on the separation technology of MRI^[16], and the shredding technology and equipment development require further enrichment. Shredding technology is a primary process in waste treatment^[9], which not only acts as the precondition for mixture separation but also significantly affects the follow-up process, quality of recycled products, and economic benefits after primary treatment^[17]. Restricted by technological condition, processing mode, and market orientation, current resource utilization of RF in Xinjiang cotton fields is still quite simple, and is mainly wash granulating^[18]. According to surveys, in order to satisfy the actual production need and ensure the cleaning effect and quality of recycled products, MRI is usually separated manually and then the separated residues are shredded by waste plastic shredder. Waste plastic shredder can shred residues with low levels of impurities, but it is not appropriate for direct shredding of MRI. Based on the characteristics of RF and cotton straws^[8], researchers developed a differential roller cutting device with a multi-blade tooth cutter as the core, solving the direct shredding problem of MRI (Figure 1b). Related works have shown that it is a challenge to obtain the influence rule of critical parameters of the cutting equipment on the material distribution properties^[17,19,20].

Consequently, by analyzing the stress characteristics of the RF in MRI, a mechanical model of the RF was developed and the main parameters affecting the distribution feature of the RF were obtained. Simultaneously, physical experiments were carried out with a multi-blade toothed shredding device of mixed materials collected during the mechanized harvesting of cotton fields. The model of the relationship between the distribution feature of the RF and the main parameters of the cutting device (e.g., number of teeth, rotational speed, and cutters gap) were obtained by analyzing the experimental results with the analysis of variance method. Then the significance of the main parameters influencing the RF distribution feature was investigated to reveal the rule of residue shredding characteristics of MRI. The objective of this study is to provide some theoretical foundation and technique support for the study of MRI shredding technology and the relevant shredding device development^[8].

2.   Dynamic properties of RF during cutting process of MRI

In Figure 2, the high-speed cutter (H-cutter) and low-speed cutter (L-cutter) are shown as the core parts of the shredding device^[8]. The cutter parts mainly consist of the rake face of tooth, back blade, side face of tooth, top blade, back blade, and V-shaped area. During the shredding process, H-cutter, L-cutter, and stationary cutter (S-cutter) interact with each other to realize the compression, cutting, and stretching of the RF. The purpose of this section is to analyze the force characteristics of the RF layer under the interaction condition between H-cutter, L-cutter, and S-cutter and investigate the influence rule of dynamic properties of the RF during the cutting process of MRI, as well as to determine the crucial factors of RF dynamic properties.

Figure  2.  Cutting parts of cutting device

Ⅰ. H-cutter Ⅱ. L-cutter Ⅲ. S-cutter 1. Side face of tooth 2. Rake face of tooth 3. Back blade 4. Top blade 5. V-shaped area 6. Back blade face

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2.1   Dynamic properties of RF during the compression and deformation process

A single layer of RF is usually very thin (nominal film thickness: 0.01 mm), but has high ductility and flexibility, and is usually fluffy and compressible in MRI. Starting from the rake face of H-cutter and L-cutter which coincides with the positive direction of the y-axis, when H-cutter and L-cutter turn ω₁t and ω₂t separately, the acting forces that cause the compression and deformation of the RF layer mainly include the compressing force (F_n1, F_n2), the frictional force (f₁, f₂), and the support force of the back blade face (F₁, F₂), etc. To analyze the force characteristics of the RF layer during the compressing process, the RF layer unit A was taken as the object of study in this part^[8]. It is assumed that the support force (F₁, F₂) is simplified to the plane stress ($F'_1$, $F'_2$) of a plane perpendicular to the y-axis, which projects on the line connecting point ac (point ec), and remains perpendicular to the line connecting points ac (ec).

The simplified diagram of the force characteristics of the constructed RF layer unit A is shown as Figure 3b. The equilibrium equation of the RF layer unit A on the x-axis and y-axis is:

Figure  3.  Force characteristics (a) and analysis (b) of RF layer unit

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where, $F'_1$ and $F'_2$ are the support forces of the side blade face of H-cutter and L-cutter on the RF layer unit, separately, N; γ₁ and γ₂ are the included angles of the support forces $F'_1$ and $F'_2$ with the positive direction of the y-axis, separately, (°); m is the mass of the RF layer unit, kg; g is the gravity acceleration, m/s²; F_n1 and F_n2 are the compressing forces produced by the elastic deformation of the RF layer unit when compressed by the rake face of H-cutter and L-cutter, separately, N; ω₁t and ω₂t are the turning angles of H-cutter and L-cutter, separately, (°); f₁ and f₂ are the frictional forces between the rake face of H-cutter and L-cutter with the RF layer unit, separately, N; F_e1 and F_e2 are the centrifugal forces of the rake face of H-cutter and L-cutter to the RF layer unit, separately, N.

In Equation (1), the included angles γ₁ and γ₂ of the forces $F'_1$ and $F'_2$ with the positive direction of the y-axis are:

There is a certain function between the compressing forces F_n1 and F_n2 with the material properties and compression height. When the rake face of the cutters compresses the RF layer, the vertical distance h from the point c to the rake face is assumed as the compression height to be compressed. As the multi-blade toothed cutter is a rotational working part, the compressing forces F_n1 and F_n2 are the resultant forces of the x-axis and y-axis compressing forces, separately, which can be expressed by:

where, E_c is the elastic modulus of RF layer, MPa; A′ is the stressed area of the RF layer unit, m²; h_x, h_y are the original heights of the RF layer unit at the x-axis and y-axis, separately, which are ranged from 0~rsinα to 0~(r-rcosα), m; μ_c is the coefficient of friction between RF and cutters; μ_k is the friction angle between RF and cutters, (°); ω₁, ω₂ are the angular velocities of H-cutter and L-cutter, separately, rad/s.

Substituting the friction and centrifugal force equations of (3) into (2), the $F'_1$ and $F'_2$ are:

According to model (4), when the material properties, the top blade radius r, and the tooth hub radius r′ are constant, the support force has a certain function with the angular velocity ω₁ of H-cutter and the angular velocity ω₂ of L-cutter. When the RF layer is compressed completely to a certain degree, it is cut by the interactive force between H-cutter and L-cutter. Due to the speed discrepancy between H-cutter and L-cutter^[8], the rake faces of the two cutters interact with the top blade and back blade to cut the RF layer. Therefore, the mechanical properties and established mechanical model of the RF layer unit under the interactive conditions between the rake face with the top blade and the back blade of H-cutter and L-cutter, separately, will be studied in the next part^[8].

2.2   Dynamic properties of RF under the interaction between rake face and back blade of cutters

In Figure 4a, at the t₁ moment, the rake face of H-cutter interacts with the back blade of L-cutter to cut the compressed RF layer^[8]. The external forces exerted on the RF layer unit mainly include the centrifugal force F_e1 formed by the rotation of H-cutter, the support force F_n1 and the frictional force f_n1 of the rake face of the cutters, as well as the cutting force F_i2 and the frictional force f_i2 of the back blade of L-cutter. The simplified force characteristics of the RF unit are shown as Figure 4b.

Figure  4.  Force characteristics (a) and analysis (b) of RF layer unit

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The equilibrium equation of the RF layer unit on the x-axis and y-axis is:

where, F_i2 is the cutting force of the back blade of L-cutter on the RF unit, N; F_e1 is the centrifugal force of H-cutter on the RF unit, N; F_n1 is the support force of the rake face of H-cutter on the RF unit, N; f_i2 is the frictional force produced from the relative motion between the back blade of L-cutter and the RF layer unit, N; f_n1 is the frictional force between the rake face of H-cutter, N; ω₁t₁ and ω₂t₁ are the turning angles of H-cutter and L-cutter, separately, (°); β is the angle between the rake face and back blade of the cutters, (°).

By substituting the friction and centrifugal force equation of (3) into model (5), the results of F_n1 and F_i2 are acquired:

According to Equation (6), when the radius r of the cutters, the included angle β, and the frictional coefficient of the RF and cutters are all constant, the cutting force F_i2 and support force F_n1 on the RF layer produced by the interaction between the rake face of H-cutter and the back blade of L-cutter have a certain function with the rotational speed of H-cutter and L-cutter.

2.3   Dynamic properties of RF under the interactive condition between rake face and top blade of cutters

Figure 5a shows the force characteristics of the RF layer at the time t₂ under the interactive condition between the rake face and top blade of the cutters. At this time, the RF layer unit mainly receives the support forces F_n1 and F_i1 and the frictional forces f_n1 and f_i1 produced by the rake face and back blade of H-cutter. Meanwhile, the RF layer unit also receives the centrifugal force F_e1 produced by the rotation of H-cutter. In comparison with H-cutter, the main forces on the RF layer unit from L-cutter mainly include the cutting force F_r2 and frictional force f_r2 of the top blade. The simplified force analysis diagram of the residual unit is shown as Figure 5b.

Figure  5.  Force characteristics (a) and analysis (b) of RF layer unit

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The equilibrium equation of the RF layer unit on the x-axis and y-axis is:

where, f_i1 and f_n1 are the frictional forces of the rake face and back blade of H-cutter with the RF unit, separately, N; F_r2 is the cutting force of the top blade of L-cutter on the RF layer unit, N; F_n1 and F_i1 are the support forces of the rake face and back side blade of H-cutter on the RF unit, N; F_e1 is the centrifugal force of H-cutter on the RF unit, N; f_r2 is the frictional force between L-cutter and RF layer unit, N; ω₁t₂ and ω₂t₂ are the turning angles of H-cutter and L-cutter, (°); γ′ is the deviation angle of the connecting line between the force bearing point of the RF layer unit and the rotating center to the rake face of the cutters at ω₁t₂, (°).

Substituting the friction and centrifugal force equation of (3) into (7) yields F_i1 and F_r2 as follows:

According to Equation (8), when the radius r of the cutters, the included angle β, and the frictional coefficient between RF and the cutters is constant, there is a certain function between the cutting force F_r2 and the support force F_i1 with the rotational speed of H-cutter and L-cutter.

2.4   Dynamic properties of RF under interactive effect between rake face and back blade of cutters

According to the analysis of stretching and tearing characteristics of RF, the longer RF that was not cut thoroughly would intertwine with the cutters. To avoid such a problem, S-cutter was set under H-cutter and L-cutter, which can also cut the RF while preventing intertwining. Due to the same interactive features between S-cutter and H-cutter or L-cutter, the force characteristics of the RF layer under the interactive condition between the rake face of L-cutter and S-cutter were investigated, and the influence rule of the RF dynamic properties was explored^[8].

Assume that at time t₃, the turning angle of the rake face of L-cutter against the positive direction of the y-axis is ω₂t₃, as shown in Figure 6a. Except for the gravity, the RF layer also received other external forces, e.g. the centrifugal force F_e2 produced from the rotation of L-cutter, the support force F_n2 and the frictional force f_n2 of the cutters rake face, and the support force F_d2 and frictional force f_d2 of the S-cutter. Meanwhile, the back blade of the cutters near the S-cutter is also ranged in the phase angle [π, 2π]. It is assumed that no support force or frictional force are produced from the back blade of the cutters on the RF layer unit. The simplified analysis diagram of the force characteristics of the RF layer unit is shown as Figure 6b.

Figure  6.  Force characteristics (a) and analysis (b) of RF layer unit

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The equilibrium equation of the RF layer unit on the x-axis and y-axis is shown as Equation (9):

where, F_d2 and F_n2 are the support forces of the S-cutter and the rake face of the cutters on the RF layer unit, separately, N; f_d2 and f_n2 are the frictional forces, N; F_e2 is the centrifugal force of the cutters on the RF layer unit, N; φ is the position angle clockwise of the S-cutter to the positive direction of the y-axis, (°); ω₂t₃ is the turning angle of L-cutter relative to the positive direction of the y-axis, (°).

Substituting the centrifugal force equation of (3) into (9), the acting forces of F_d2 and F_n2 are obtained as follows:

According to Equation (10), when the cutters, S-cutter, and RF material are at a certain level, there is a certain function between the acting forces F_n2 and F_d2 and the angular velocity ω₂ of L-cutter.

In conclusion, when cutting MRI with staggered H-cutter and L-cutter, the change rule of the dynamic properties of RF is related to the rotational speed n₁ of H-cutter and the speed discrepancy Δn between H-cutter and L-cutter^[8]. Meanwhile, relevant studies show that the tooth number and the gap also have an effect on the distribution feature of materials after shredding^[17,21-23]. Due to the complicated structural characteristics of MRI, the cotton straws also affect the distribution feature of RF after shredding. Therefore, the influence rule of the main parameters on the distribution feature of RF in MRI after shredding was obtained through physical tests on the basis of RF dynamic properties analysis.

3.   Test materials and methods

3.1   Materials and equipment

The experiments were conducted in the middle of October 2022 at the Key Laboratory of Northwest Agricultural Equipment, Ministry of Agriculture and Rural Affairs, Shihezi University. The test materials were obtained from Tuan Chang cotton field near Shihezi, Xinjiang. The materials were collected in late September 2022, shown in Figure 1a. The instruments and devices used in the test process in this paper are consistent with the reference [8].

3.2   Test methods

During the shredding of MRI, the particle size of soil-dominated bulk material is small and easily causes dust pollution, so it should be removed before the test. During the test, the MRI was first deposited uniformly on the infeed conveyor belt^[24]. The cutting device was started and the infeed conveyor belt was opened as the cutting device was stabilized. Due to the large volume and fluffy nature of MRI, overfeeding or excessive speed can cause the shredding device to become clogged, leading to overloads and momentary shutdowns. Therefore, the machining quantity for each group of materials and the feeding speed were set as 2.0±0.1 kg and 0.01 m/s based on the preliminary tests^[8]. After the test, the crossover method was used on samples with reference to GB/T26551-2011. The sample mass of each group was 400±10 g. After sampling, the RF was manually selected from the MRI, and the total mass of the RF was recorded as m. Meanwhile, to reveal the influence rule of the maximum outer scale distribution feature of the RF in the MRI, the ratio between the RF mass within each range of the maximum outer dimension and the total RF mass was counted.

Combined with the theoretical analysis results in Section 2, and considering the structural characteristics of the shredding device, the value range of these parameters of the tooth number of cutters z (a), gap between the teeth and from S-cutter δ (b), rotation speed of H-cutter n₁ (c), and speed discrepancy of H-cutter and L-cutter Δn (d) were determined. A four-factor, five-level central combination test scheme was designed using the Central Composite Design module of Design Expert data processing software^[8]. Each test group was repeated three times. The test protocol and results are listed in Table 1.

Table  1.  Test scheme and test results

No.	a	b	c	d	x1/%	x2 /%	x3/%	x4/%
1	–1 (6)	–1 (2 mm)	–1 (800 r·min–1)	–1 (–400 r·min–1)	5.68±1.52	16.29±3.06	59.56±3.09	18.47±3.87
2	1 (10)	–1	–1	–1	2.45±0.88	18.15±7.28	57.42±6.26	21.98±10.42
3	–1	1 (4 mm)	–1	–1	2.67±0.55	17.91±4.21	67.49±4.06	11.93±6.65
4	1	1	–1	–1	4.56±1.48	18.99±7.04	64.37±5.07	12.08±4.08
5	–1	–1	1 (1000 r·min–1)	–1	3.19±1.88	18.16±10.10	60.80±8.15	17.85±6.88
6	1	–1	1	–1	2.87±1.47	23.65±17.64	54.36±18.35	19.12±18.24
7	–1	1	1	–1	1.85±0.25	16.54±4.04	70.19±3.94	11.42±3.94
8	1	1	1	–1	2.43±0.53	14.61±5.37	66.78±7.06	16.18±10.24
9	–1	–1	–1	1 (–200 r·min–1)	5.44±2.20	11.84±6.10	59.12±6.29	23.60±2.80
10	1	–1	–1	1	2.13±0.67	14.61±8.60	62.93±9.99	20.33±14.99
11	–1	1	–1	1	2.02±0.58	20.82±3.78	44.65±5.76	32.51±8.47
12	1	1	–1	1	1.57±0.29	12.78±5.88	40.49±3.53	45.16±6.23
13	–1	–1	1	1	3.36±1.99	18.26±6.16	59.75±8.25	18.63±9.31
14	1	–1	1	1	1.45±0.43	18.31±5.36	64.69±6.69	15.55±3.23
15	–1	1	1	1	1.65±0.88	14.13±5.78	59.02±2.36	25.2±6.78
16	1	1	1	1	1.47±0.28	9.16±3.11	56.52±5.70	32.85±3.93
17	–2 (4)	0 (3 mm)	0 (900 r·min–1)	0 (–300 r·min–1)	4.39±2.16	18.78±7.67	62.57±6.50	14.26±8.91
18	2 (12)	0	0	0	2.11±1.15	17.25±7.65	63.51±11.98	17.13±8.29
19	0 (8)	–2 (1 mm)	0	0	2.97±1.14	24.15±7.79	60.82±3.12	12.06±10.20
20	0	2 (5 mm)	0	0	1.33±0.32	21.66±11.70	56.25±6.44	20.76±6.02
21	0	0	–2 (700 r·min–1)	0	4.58±2.29	12.83±8.18	56.55±8.09	26.04±12.03
22	0	0	2 (1100 r·min–1)	0	1.58±0.59	10.17±4.59	61.15±7.31	27.10±8.99
23	0	0	0	–2 (–500 r·min–1)	2.68±0.96	12.56±8.66	60.55±7.87	24.21±10.74
24	0	0	0	2 (–100 r·min–1)	1.62±0.63	5.14±2.54	45.58±13.75	47.66±15.84
25	0	0	0	0	1.57±0.89	18.78±4.25	56.83±4.80	22.82±8.07
26	0	0	0	0	2.60±0.42	18.90±6.79	55.55±4.91	22.95±7.20
27	0	0	0	0	1.75±0.36	20.02±4.34	59.38±5.64	18.85±8.18
28	0	0	0	0	2.19±0.64	17.39±3.47	62.10±8.04	18.32±6.75
29	0	0	0	0	2.34±0.40	19.58±13.17	55.76±5.54	22.32±13.61
30	0	0	0	0	2.22±0.64	15.04±7.17	61.91±8.89	20.83±15.38

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3.3   Test indicators

During the separation process, the material size and distribution applicable to different separation technology instruments were significantly different^[25]. Preliminary field investigations showed that overlength RF or cotton straws could increase the probability of intertwined materials, which was regarded as the major cause of the low efficiency of separating MRI. Therefore, to reduce the maximum outside dimension of the RF to meet the working requirements, different separation technologies such as electrostatic method, air separation, and suspension method should be used^[23,26]. But because small RF may lead to microplastic pollution, excessive cutting of the films should also be avoided^[27]. Referring to the statistical range of shredded waste plastics in the literature^[9], the RF was classified according to the maximum outer dimensions of [0, 20) mm, [20, 100) mm, [100, 500) mm, [500, ~) mm based on the specific separation demands and the primary cleaning status of RF. The calculation of the ratio of RF mass to total RF mass of different maximum outside dimension distribution ranges is shown as Equation (11):

where, m, m₁, m₂, m₃, and m₄ are the mass of the total mass and maximum outside dimension of the RF samples at the ranges of [0, 20) mm, [20, 100) mm, [100, 500) mm and [500, ~) mm, separately, g. x₁, x₂, x₃, and x₄ are the ratio of m₁, m₂, m₃, and m₄ to m, %.

4.   Analysis and discussion of test results

4.1   Regression analysis of variance and model construction

The analytical results are shown as Table 2. According to the results of regression variance analysis of the test response index x₁, the p values of the odd factors a, b, c, d and the interaction term ab were all much smaller than 0.01, which were the extreme influence factors on x₁. The p values of the interaction terms of ad, a², and c² ranged from 0.01-0.05, which were found to be significant influence factors on x₁. The p values of the interaction terms of ac, bc, bd, cd, b², and d² were all higher than 0.05, and the effect on x₁ value was not significant. The order of the extremely significant factors and significant factors of the significance of p value to x₁ was: c>ab>b>a>d>a²>c²>ad.

Table  2.  Test results analysis table

Source	x1				x2				x3				x4
	F-Value	p-value			F-Value	p-value			F-Value	p-value			F-Value	p-value
Model	8.66	<0.0001**			11.21	<0.0001**			10.04	<0.0001**			14.19	<0.0001**
a	18.1	0.0007**			0.63	0.4392			0.67	0.4257			3.6	0.0771
b	18.54	0.0006**			5.17	0.0381*			1.8	0.1995			10.1	0.0062**
c	27.84	<0.0001**			0.21	0.6535			11.08	0.0046**			3.07	0.0999
d	10.45	0.0056**			21.33	0.0003**			37.89	<0.0001**			72.39	<0.0001**
ab	23.15	0.0002**			12.01	0.0035**			1.45	0.2477			4.49	0.0512
ac	2.2	0.1588			0.02	0.8906			0.026	0.8734			0.037	0.8495
ad	4.68	0.0471*			5.79	0.0294*			2.4	0.1424			0.11	0.7407
bc	0.41	0.5322			23.4	0.0002**			9.89	0.0067**			0.049	0.8277
bd	1.84	0.1952			0.089	0.7694			55.16	<0.0001**			43.57	<0.0001**
cd	0.66	0.4296			0.068	0.7976			7.05	0.018*			5.44	0.034*
a2	8.57	0.0104*			0.16	0.6962			5.65	0.0312*			7.95	0.013*
b2	0.1	0.7566			16.74	0.001**			0.064	0.8034			6.36	0.0234*
c2	6.37	0.0233*			20.45	0.0004**			0.16	0.6934			2.85	0.1122
d2	0.1	0.7566			42.55	< 0.0001**			5.41	0.0345*			31.01	<0.0001**
Lack of fit	2.61	0.1506			0.85	0.6121			0.81	0.6409			3.12	0.1106
	R2=0.8899；$R_{\rm adj}^2$=0.7871；C.V=21.01%				R2=0.9127；$R_{\rm adj}^2$=0.8313；C.V=10.48%				R2=0.9036；$R_{\rm adj}^2$=0.8135；C.V=4.72%				R2=0.9298；$R_{\rm adj}^2$=0.8643；C.V=14.4%
Notes: ** refers to extremely significant factor (p≤0.01), *refers to significant factor (0.01<p≤0.05)，p>0.05 refers to non-significant factor.

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For the test response index x₂, the p values of the odd factor d with the interaction terms ab, bc, b², c², and d² were all much smaller than 0.01, which were the extreme influence factors on x₂. The p values of the odd factor b with the interaction term ad were all between 0.01 and 0.05, which were significant influence factors on x₂. The p values of the odd factors a and c with the interaction terms of ac, bd, cd, and a² were all higher than 0.05, and the effect on x₂ value was not significant. According to the significance of p value to x₂ value, the extremely significant factors and significant factors were: d²>bc>d>c²>b²>ab>ad>b.

The results for the test response index x₃ show that the p values of the odd factors c and d with the interaction terms bc and bd were all much smaller than 0.01, which were the extreme influence factors on x₃. The p values of the interaction terms cd, a², and d² were all between 0.01 and 0.05, which were the significant influence factors on x₃. The p values of the odd factors a and b with the interaction terms of ab, ac, ad, b², and c² were all higher than 0.05, and the effect on x₃ value was not significant. According to the significance of p value to x₃ value, the extremely significant factors and significant factors were: d>bd>c>bc>cd>a²>d².

The results for the test response index x₄ show that the p values of the odd factors b and d with the interaction terms bd and d² were all much smaller than 0.01, which were the extreme influence factors on x₄. The p values of the interaction terms cd, a², and b² were all between 0.01 and 0.05, which were significant influence factors on x₄. The p values of the odd factors a and c with the interaction terms of ab, ac, ad, bc, and c² were all higher than 0.05, and the effect on x₄ value was not significant. According to the significance of p value to x₄ value, the extremely significant factors and significant factors were: d>bd>d²>b>a²>b²>cd.

As shown in Table 2, the model coefficients’ p values of X₁, X₂, X₃,and X₄ were much smaller than 0.01, which indicate the extreme significance of the second-order response models. The determination coefficients R² of models X₁, X₂, X₃, and X₄ were 0.8899, 0.9127, 0.9036, and 0.9298, separately. The adjusted determination coefficients $R_{\rm adj}^2$ were 0.7871, 0.8313, 0.8135, and 0.8643, separately. These results indicate a good explanation of the four models, which can make precise and robust predictions of the test response indices of x₁, x₂, x₃, and x₄.

The quadratic response surface regression models X₁, X₂, X₃,and X₄ were established as Equation (12):

4.2   Analysis of influence rule of main parameters on the distribution feature of RF

4.2.1   Influence rule of tooth number of cutters z on the distribution feature of RF

In Figure 7, when tooth number z rose from 4 to 8, the curves x_a1, x_a2 and x_a3 all showed a decreasing trend, while x_a4 showed an increasing trend, and the decreasing trend of x_a3 and the increasing trend of x_a4 were obvious. As tooth number z increased, the rake face, back blade, and V-shaped area increased, while the top blade arc length became shorter^[8]. The increase of the area of rake face and back blade strengthened the interaction of the rake face and back blade between H-cutter and L-cutter. But the reduction of top blade arc length significantly reduced the interaction formed by the rake face and top blade between H-cutter and L-cutter, which may be one of the causes of the progressive decrease of x_a1, x_a2, x_a3 and the progressive increase of x_a4. Similar conclusions were drawn by references [21] and [28] when they studied the shredding characteristics of municipal wastes. But this phenomenon was different from the working mode of reducing the particle size of materials by adding the number of hammers, or changing the cutting length of the straws by increasing the number of cutting blades^[22,29].

Figure  7.  Influence rule of number of teeth z on the distribution feature of RF

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When tooth number z rose from 8 to 12, the interaction of the rake face and back blade between H-cutter and L-cutter was further strengthened. The interaction between the rake face and top blade of cutters was further weakened, but the times of interaction increased, which may be one of the causes of the progressive decrease of x_a1, x_a2, and x_a3 and the progressive increase of x_a4. This was the same as the working mode of reducing the particle size of materials by increasing the number of hammers^[22], or changing the cutting length of the straws by increasing the number of cutting blades^[30,31]. The cotton straws in MRI can change the cutting effect of RF to a certain extent, but they were still very fluffy with good compressibility. The increase of the V-shaped area on the cutters may increase the mass of the mixture and result in invalid cutting of the RF, which may be a cause of the slow decrease of x_a2 and obvious changing trend of other curves.

4.2.2   Influence rule of cutters gap δ on the distribution feature of RF

In Figure 8, the gradual increase of the gap δ raises the pass rate of materials and weakens the interaction between the cutters, which reduces the probability of producing fractured RF under external force. This might be one of the causes of the increase of the mass of RF with large outer dimension. Guillaume et al. argued that the gap between the teeth was also one of the major factors influencing the size and distribution feature of shredded thermoplastic composite material^[23]. Due to the effect of various factors (thickness, pliability, and compressibility of RF), the RF shredded by cutters may be deformed and the shredding stress may be hindered^[28]. The shredded films may be embedded into the gap between the cutters and S-cutter and cannot be chopped sufficiently, thus increasing the mass of the RF with large outer dimension. This change rule of gap impact is different from that of rigid plastics^[23]. Khodier et al. applied different shapes of cutting tools to cut solid waste materials^[17]. Their findings showed that a small gap between the cutting tool and S-cutter could reduce the passing rate of materials, while a large gap may lead to a sudden increase of materials and affect the cutting effect. Besides, with the increase of the gap δ, the interactive characteristics between the two parts would be weakened and the film stripping effect would be reduced. This may also be a cause of the increase of the mass of larger RF. Shi et al. pointed out that a smaller gap between the rake teeth and the stripping plate was better for film stripping^[32]. This finding is similar to the above conclusion.

Figure  8.  Influence rule of size of gap δ on the distribution feature of RF

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4.2.3   Influence rule of the rotational speed n₁ of H-cutter on the distribution feature of RF

According to Figure 9, lower rotational speed of H-cutter is good for the stretching and tearing of flexible materials and can improve the cutting mass of RF. Large-torque and low-speed plastic shredding machines all adopted such a method to shred flexible materials such as plastics and woven bags^[25]. If the speed discrepancy Δn between H-cutter and L-cutter is a constant value, the rotational speed n₁ will increase and the rotational speed L-cutter will also increase^[8]. The interaction between the two cutters would improve the stretching and tearing characteristics on RF, and the mass of excessively long RF would be reduced.

Figure  9.  Influence rule of rotational speed n₁ on the distribution feature of RF

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The instantaneous impact force of H-cutter increases with the increase of rotational speed n₁. As RF feature good flexibility and malleability, the impact stress can be easily absorbed and hindered for effective transmission^[28,33]. Rácz et al. also found that rotational speed has a large impact on the shredding probability of PET, HDPE, and textile fabrics^[34]. The higher the rotational speed, the lower the stress value under a certain shredding probability. The cotton straws in MRI may shorten the time of RF layer compressing and film shredding, which is also one of the reasons why the curves of x_c2 and x_c3 presented an increasing trend and the x_c4 curve presented a decreasing trend. Luo et al. used a saw tooth type shredding mechanism to shred urban wastes and drew the same conclusion^[19,28]. When the rotational speed n₁ of H-cutter increased to a certain level, RF with outside dimension larger than 500 mm were easily taken by H-cutter to S-cutter. At this time, under the interactive effect of the cutters and S-cutter, the cutting and stripping of the RF would happen simultaneously, which may be a reason why the curves of x_c3 and x_c4 presented an increasing trend and the x_c2 curve presented a decreasing trend.

4.2.4   Influence rule of speed discrepancy Δn on the distribution feature of RF

According to Figure 10, when rotational speed n₁ of H-cutter is a constant value, the speed discrepancy Δn will be smaller. As the rotational speed of the L-cutter decreases, the action of the individual blades of the H-cutter becomes stronger. While this enhances the stretching, tearing, and cutting of the residual film, it also results in a weaker action of the individual blades of the H-cutter, which may contribute to the higher mass of longer RF. As Δn increased, the rotational speeds of H-cutter and L-cutter became closer and the single-roll effect of both teeth were strengthened, which may be the main reason why the x_d2 curve presented an increasing trend, the x_d4 curve presented a decreasing trend, and the x_d3 curve gradually changed. With the rotational speeds of the H-cutter and L-cutter being close, the effectiveness of the individual rollers diminishes, resulting in less favorable conditions for stretching and tearing the RF. Consequently, this could be the primary reason for the increase in the curve of x_d4 and the decrease in the curves of x_d2 and x_d3.

Figure  10.  Influence rule of speed discrepancy Δn on the distribution feature of RF

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4.3   Influence rule of interactive effect of main parameters on the distribution feature of RF

The interactive terms ab and ad are extremely significant or significant factors on test response indicator x₁; bc, bd, and cd are extremely significant or significant factors on x₃; bd and cd are extremely significant or significant factors on x₄. Only the influence rules of extremely significant and significant factors on the test responding indicators were analyzed.

4.3.1   Influence rule of significant interaction terms on test response indicator x₁

(1) Influence rule of significant interaction term ab on test response indicator x₁

In Figure 11, when the level value of the test factor b is –2 and a increases from low level (–2) to high level (2), x₁ presents a clear downward trend. This indicates that lower x₁ can be achieved by increasing tooth number when δ is small. When the level value of the test factor b is 2 and a increases from low level (–2) to high level (2), x₁ shows a tendency to decrease and then increase, and x₁ reaches the minimum when the level value of b is around –1. This indicates that x₁ is small under the effect of δ when tooth number is close to 6.

Figure  11.  Influence rule of interaction term ab on x₁

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When the level value of the test factor a is –2 and b increases from low level (–2) to high level (2), x₁ exhibits a significant downward trend. This means that for a small number of cutters, x₁ can be reduced by increasing δ. When the value a is 2 and b increases from –2 to 2, x₁ presents an increasing trend. This means that when tooth number is large, x₁ can be effectively reduced by reducing δ. Moreover, under the dual influence of increasing both test factors a and b from –2 to 2, x₁ exhibits a trend of first reduction and then increase. This trend is the same as the odd factor a influencing x₁, showing that the impact of a on x₁ is more obvious.

(2) Influence rule of significant interaction term ad on test response indicator x₁

In Figure 12, when the level value of the test factor d is –2 and a increases from low level (–2) to high level (2), the value of x₁ shows a trend of first falling and then rising, and there is a smaller x₁ when tooth number is close to 8. Under the above conditions, the trend of x₁ is the same as that influenced by an odd factor a. The test factor also exerts some impact on x₁, but the impact is smaller than that of the odd factor a. When the level value of the test factor d is 2 and a increases from low level (–2) to high level (2), x₁ shows a clear reduction trend. This trend is identical to the one influenced by an odd factor b, indicating that the value of x₁ can be effectively reduced by increasing the number of teeth when Δn is –100 r/min.

Figure  12.  Influence rule of interaction term ad on x₁

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When the level value of the test factor a is –2 and d increases from low level (–2) to high level (2), the value of x₁ exhibits a clear increasing trend, which is contrary to the change trend of x₁ influenced by the odd factor d. With a small number of cutters, the value of x₁ may be effectively reduced by reducing Δn. When the level value of the test factor a is 2 and b increases from low level (–2) to high level (2), x₁ shows a declining trend, which is the same effect as that of the odd factor d, which indicates that when Δn is –100 r/min, the value of x₁ can be effectively reduced by increasing tooth number. With a large number of cutters, the impact of the factor d on the change trend of x₁ is significant, and x₁ can be reduced by increasing Δn. In addition, with the double effect of a and d both increasing from –2 to 2, the value of x₁ presents a decreasing trend. This trend is the same as that of x₁ influenced by odd factor d, which indicates that the impact of odd factor d on x₁ is more obvious.

4.3.2   Influence rule of significant interaction terms on the test response indicator x₂

(1) Influence rule of significant interaction term ab on the test response indicator x₂

In Figure 13, when factor b is –2 and a increases from low level (–2) to high level (2), the value of x₂ presents a distinct increasing trend. For smaller δ, the increase of tooth number can effectively raise the value of x₂. When the factor b is 2 and a increases from low level (–2) to high level (2), the value of x₂ exhibits a clear reduction trend. For larger δ, the decrease of tooth number can effectively raise the value of x₂.

Figure  13.  Influence rule of interaction term ab on x₂

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When the level value of the test factor a is –2 and b increases from low level (–2) to high level (2), the value of x₂ shows a tendency to descend first and then to rise. This tendency to vary is consistent with the tendency for the odd factors a and b to affect x₂ separately. Higher x₂ can be obtained when tooth number is small, whether the gap δ is large or small. The increase of x₂ is more significant when tooth number is small and δ is large.

When the factor a is 2 and b increases from low level (–2) to high level (2), the value of x₂ also presents a tendency to first decrease and then increase. This trend is the same as that of the odd factors a and b influencing x₂, separately. Higher x₂ can be obtained when tooth number is large and δ is small. Furthermore, with the double effect of test factors a and b both increasing from low level (–2) to high level (2), the value of x₂ presents a decreasing trend. To prevent a decrease of x₂, it is recommended to avoid simultaneously increasing the levels of both factors.

(2) Influence rule of significant interaction term ad on the test response indicator x₂

In Figure 14, when the level value of the test factor d is –2 and a increases from low level (–2) to high level (2), the value of x₂ presents an increasing trend. When the factor d is 2 and a increases from low level (–2) to high level (2), the value of x₂ presents a decreasing trend. Therefore, the value of x₂ can be effectively increased by increasing tooth number when the speed discrepancy Δn is small. For large speed discrepancy Δn, x₂ can be increased by reducing tooth number.

Figure  14.  Influence rule of interaction term ad on x₂

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When the factor a is –2 and d increases from low level (–2) to high level (2), the value of x₂ exhibits a first increasing and then decreasing trend. When d is around 0, i.e., the speed discrepancy Δn is –300 r/min, the value of x₂ is quite high. The change trend of x₂ under the aforementioned conditions is consistent with that observed under the influence of the single-factor term d, and the level value of factor d corresponding to the highest x₂ value is also similar. The change trend of x₂ under the above-mentioned condition is identical to that influenced by the single-factor term d, and the maximum value of x₂ is also close to the level value of d. This shows that the speed discrepancy Δn has significant impact on the value of x₂, even with a small number of cutters.

When the factor a is 2 and d increases from low level (–2) to high level (2), the value of x₂ also shows a trend of first increasing and then decreasing. When d is close to –1, i.e., the speed discrepancy Δn is close to –400 r/min, the value of x₂ is quite high. The change trend of x₂ under the aforementioned condition is the same as that influenced by the factor d. This shows that the speed discrepancy Δn has significant impact on the value of x₂, even when tooth number is large. For a large number of cutters, the level value of the test factor corresponding to the maximum x₂ drops to some extent. Meanwhile, with the double effect of test factors a and d both increasing from –2 to 2, the value of x₂ exhibits a first increasing and then decreasing trend. This indicates that when both experimental factors are adjusted to near the 0 level, higher x₂ values can be achieved.

(3) Influence rule of significant interaction term bc on the test response indicator x₂

In Figure 15, when the level value of the test factor c is –2 and b increases from low level (–2) to high level (2), the value of x₂ presents a first decreasing and then increasing trend, and the increasing trend is more obvious. x₂ is small when the gap δ is close to 2 mm. The change trend of x₂ under the above condition is the same way as it is affected by the factor b. This indicates that when the rotational speed n₁ is low, the gap δ has significant impact on the value of x₂. Therefore, in order to obtain a higher x₂ when the rotational speed n₁ is low, the gap δ should be increased.

Figure  15.  Influence rule of interaction term bc on x₂

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When the factor c is 2 and b increases from low level (–2) to high level (2), the value of x₂ also presents a first decreasing and then increasing trend. The change trend of x₂ under the above condition is the same as that influenced by the single-factor term b. This indicates that when the rotational speed n₁ is high, the gap δ still has significant impact on the value of x₂. Therefore, in order to obtain a higher x₂ with the rotational speed n₁, the gap δ should be reduced.

When the factor b is –2 and c increases from low level (–2) to high level (2), the value of x₂ shows an increasing trend followed by a decreasing trend. The change trend of x₂ under the above condition is the same as that influenced by the odd factor c. This means that when the gap δ is small, the rotational speed n₁ still has significant impact on the value of x₂. Therefore, in order to obtain a higher x₂ when the gap δ is minor, higher rotational speed n₁ should be used.

When the level value of the test factor b is 2 and c increases from low level (–2) to high level (2), the value of x₂ presents a first increasing and then decreasing trend, and x₂ is quite high when the level value of the test factor c ranges from –2 to –1. The change trend of x₂ under the above condition is the same as that influenced by the odd factor c, which indicates that the rotational speed n₁ has significant impact on the value of x₂ when the gap δ is large. Therefore, in order to obtain a higher x₂ when the gap δ is large, lower rotational speed n₁ should be used. Meanwhile, with the double effect of b and c both increasing from –2 to 2, the value of x₂ presents a first increasing and then decreasing trend. This trend is the same as that influenced by the odd factor c, indicating that a higher x₂ can be obtained when the level values of the two test factors are adjusted close to 0.

4.3.3   Influence rule of significant interaction terms on the test response indicator x₃

(1) Influence rule of significant interaction term bc on the test response indicator x₃

In Figure 16, when the level value of the test factor c is –2 and b increases from low level (–2) to high level (2), the value of x₃ presents a decreasing trend. When the factor c is 2 and b increases from low level (–2) to high level (2), the value of x₃ presents an increasing trend. Therefore, the reduction of δ can help to achieve a higher x₃ when n₁ is low; the increase of δ can also increase x₃ when n₁ is high.

Figure  16.  Influence rule of interaction term bc on x₃

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When the factor b is –2 and c increases from low level (–2) to high level (2), the value of x₃ presents a decreasing trend. When b is 2 and c increases from low level (–2) to high level (2), the value of x₃ presents an increasing trend. Therefore, the reduction of n₁ can help to achieve a higher x₃ when δ is small, and the increase of n₁ can also raise the value of x₃ when δ is large. Meanwhile, when the dual effect of test factors b and c are both increased from –2 to 2, the value of x₃ exhibits a first decreasing and then increasing trend. This trend is the same as that of x₃ influenced by the single-factor term b, indicating that the impact of b on the value of x₃ is more obvious when the level values of the two test factors are adjusted simultaneously.

(2) Influence rule of significant interaction term bd on the test response indicator x₃

In Figure 17, when the factor d is –2 and b increases from low level (–2) to high level (2), x₃ presents an increasing trend. When the factor d is 2 and b increases from low level (–2) to high level (2), x₃ presents a decreasing trend. Therefore, the increase of δ can help to achieve a higher x₃ when Δn is small; the reduction of δ can also increase x₃ when Δn is large.

Figure  17.  Influence rule of interaction term bd on x₃

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When the factor b is –2 and d increases from low level (–2) to high level (2), x₃ shows an increasing trend. When the level value of the test factor b is 2 and d increases from low level (–2) to high level (2), x₃ presents a decreasing trend. Therefore, when δ is small, the increase of rotational speed n₁ can help to achieve a higher x₃. But when the gap δ is large, the reduction of n₁ can also help to achieve a higher x₃. In addition, with the double effect of test factors b and d both increasing from –2 to 2, the value of x₃ exhibits a first increasing and then decreasing trend. This trend is the same as that of x₃ influenced by the single-factor term d, and when both b and d are adjusted to near the 0 level simultaneously, higher x₃ can be achieved.

(3) Influence rule of significant interaction term cd on the test response index x₃

According to Figure 18, when the factor d is –2 and c increases from low level (–2) to high level (2), x₃ presents a decreasing trend. When d is 2 and c increases from low level (–2) to high level (2), x₃ presents an increasing trend. Therefore, when Δn is small, the reduction of n₁ can help to achieve a higher x₃. But when Δn is large, increasing n₁ can help to achieve a higher x₃.

Figure  18.  Influence rule of interaction term cd on x₃

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When the factor c is –2 and d increases from low level (–2) to high level (2), x₃ presents a decreasing trend. So, when n₁ is low, the reduction of Δn can help to achieve a higher x₃. When the factor c is 2 and d increases from low level (–2) to high level (2), x₃ presents a first increasing and then decreasing trend. When n₁ is high and Δn is –300 r/min, a higher x₃ can be achieved. Meanwhile, with the double effect of test factors c and d both increasing from –2 to 2, the value of x₃ presents a decreasing trend. When n₁ is 700 r/min and Δn is –500 r/min, a higher x₃ can be achieved.

4.3.4   Influence rule of significant interaction terms on the test response indicator x₄

(1) Influence rule of significant interaction term bd on the test response indicator x₄

In Figure 19, when the factor d is –2 and b increases from low level (–2) to high level (2), x₄ performed a reducing trend. When the level value of the test factor d is 2, i.e. the speed discrepancy Δn is –100 r/min and the gap δ is gradually increased, x₄ presented an increasing trend. RF with large maximum outer dimension may intertwine with cotton straws, causing trouble for the separation of MRI. Based on the above information, when Δn is small, the increase of δ can effectively reduce the mass of RF with maximum outside dimension ranged in [500, ~) mm. When Δn is high, use of smaller δ can also effectively reduce the value of x₄.

Figure  19.  Influence rule of interaction term bd on x₄

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When the factor b is –2 and d increases from low level (–2) to high level (2), x₄ exhibits a first decreasing and then increasing trend. This trend is the same as that of x₄ influenced by the single-factor term d, which indicates that Δn also has significant impact on x₄ when δ is 1 mm. Based on the above information, when δ is small and Δn ranges from –300 to –200 r/min, the value of x₄ is quite small.

When the level value of the test factor b is 2, i.e., the gap δ is 5 mm, x₄ presents an increasing trend, and the speed discrepancy Δn also increases. When δ is large, the reduction of Δn can help to reduce the value of x₄. Meanwhile, with the double effect of test factors b and d both increasing from –2 to 2, the value of x₄ presents a first decreasing and then increasing trend, and there is a small level value in the range of –1 to 0. When δ is adjusted to 2-3 mm and Δn ranges from –400 to –300 r/min, a smaller x₄ can be achieved.

(2) Influence rule of significant interaction term cd on the test response indicator x₄

In Figure 20, when the factor d is –2 and c increases from low level (–2) to high level (2), the value of x₄ shows a down then up trend. The comparative analysis of the change rule of the single-factor term c affecting the value of x₄ shows that the change rule of the x₄ value under this condition is the same as the change rule of the single-factor term c influencing the x₄ value. When the test factor d is 2, i.e., the speed discrepancy Δn is –100 r/min, x₄ presents a decreasing trend. Therefore, a smaller x₄ can be obtained when the speed Δn is small and the rotational speed n₁ ranges from 800 to 900 r/min. When the speed Δn is large, the increase of the rotational speed n₁ can help to reduce the value of x₄.

Figure  20.  Influence rule of interaction term cd on x₄

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When the level value of the test factor c is –2 and d increases from low level (–2) to high level (2), the value of x₄ shows a trend of dropping and then rising. When the level value of the test factor c is 2, i.e., the rotational speed n₁ is 1100 r/min, the value of x₄ also presents a first decreasing and then increasing trend as the speed discrepancy Δn increases. According to the change rule of the single-factor term d influencing the value of x₄, the change rule of x₄ obtained under the above condition is the same as the change rule of the single-factor term d influencing the value of x₄. Therefore, a smaller x₄ can be obtained when the rotational speed n₁ is small and the speed discrepancy Δn ranges from –500 to –400 r/min. The value of x₄ is also small when the rotational speed n₁ is small and the speed discrepancy Δn ranges from –400 to –300 r/min.

In addition, the value of x₄ shows a tendency to decrease and then increase under the combined effect of increasing the test factors c and d from –2 to 2, which is the same as the change rule of the single-factor term d influencing the value of x₄. According to the changes in the projection contour in the figure, a smaller x₄ can be obtained when the rotational speed n₁ is around 900 r/min and the speed discrepancy Δn is around –400 r/min.

5.   Target enhancement and test validation

Considering that the broken small RF easily caused microplastic pollution, when the outer size of the RF and the length of the cotton straw were large, it still tended to membrane straw winding. Therefore, the objective function of the maximum outer size of the RF and the size distribution of the cotton straw length was set, and the boundary conditions of the main parameters such as tooth number z (a), gap δ (b), rotational speed n₁ (c), and speed discrepancy Δn (d) were constrained. The best optimized combination of main parameters of the cutting device under the given target value was obtained. The objective function value and constraint conditions were set as follows:

In the objective function optimization process, the weight level of each experimental factor and objective function is 3+. According to the optimized results, the ideal parametric combination was: tooth number z, gap δ, rotational speed n₁, and speed discrepancy Δn of 10, 2 mm, 1000 r/min, and –297.37 r/min, respectively, and the comprehensive desirability of the optimal combination parameters was 88.3% (the highest comprehensive desirability of the optimization results). Under this condition, the prediction results of each test indicator ranged from [0, 20) mm, [20, 100) mm, [100, 500) mm and [500, ~) mm and were 1.58%, 22.22%, 61.04%, 15.17%. For repeated test and test results statistics, refer to Sections 3.1 and 3.2. The prediction results of each test indicator ranged from [0, 20) mm, [20, 100) mm, [100, 500) mm and [500, ~) mm and were (1.68±0.51)%, (21.29±4.09)%, (60.41±4.52)% and (16.62±4.73)%, separately. The errors between the physical test value and model predictions were 6.33%, 4.19%, 1.03%, and 9.56%, separately, and the mean value was 5.28%. This indicates that the experimental validation results are generally consistent with the model predictions.

6.   Conclusions

1) The stress characteristics of RF material layer under the conditions of H-cutter and L-cutter and their interaction with fixed cutters were evaluated, and the influence rule of RF dynamic properties in the cutting process of MRI was revealed.

2) Physical test results were analyzed using regression analysis of variance method to obtain the significance of the main parameters of cutting device influencing the distribution feature of RF. The influence of main parameters on the distribution feature of RF and their significant interaction were analyzed.

3) The best parameter combination obtained was: tooth number z, gap δ, rotational speed n₁, and speed discrepancy Δn of 10, 2 mm, 1000 r/min, and –297.37 r/min, respectively. The error between the verified value and predicted value ranged from 1.03%-9.56%, and the mean value was 5.28%.