Optimization of Screen-Hole-Clearing Devices for Mechanized Residual Film–Impurity Separation

Abstract

The airflow velocity in some nozzles is low, and the clearing of the nozzle is ineffective because of unreasonable airflow pipe arrangements and the distance from the nozzle to the screen surface of screen-hole-clearing devices for trommel-sieve-type residual film–impurity wind separators. In the present study, the main structure and working parameters affecting the screen hole clogging situation were determined through theoretical analysis and computational fluid dynamics simulations. In addition, a three-factor, three-level quadratic regression orthogonal center of rotation combination test was performed. The distance from the nozzle to the screen surface, fan wind speed, and the number of airflow pipes were selected as test factors, and the ratio of impurities in the residual film and the blockage ratio of the screen holes were selected as the evaluation indexes. The results indicated that the ratio of impurities in the residual film was reduced by 2.42% and the blockage ratio of the screen holes was reduced by 1.92% at a nozzle-to-screen distance of 102 mm, a fan wind speed of 24 m/s, and with four air pipes. The resulting impurity ratio in the film was 5.86%, and the blockage ratio of screen pores was 5.41%. The minimum airflow velocity of 15.8 m/s at each nozzle position of the optimized screen-hole-clearing device satisfied the requirements of screen hole clearing and blockage. Furthermore, the ratio of impurities in the residual film and the blockage ratio of the screen holes remained unchanged during the continuous operation of the device. This indicated that the optimized screen-hole-clearing device had a stable working performance. This study may provide a theoretical framework for the future development of screen-hole--clearing devices.

1. Introduction

Mulching techniques have been beneficial for preserving food supplies and increasing incomes but have caused severe farmland pollution. To address this problem, domestic institutions and related enterprises have developed various types of equipment to recover residual film [1]. A recovered residual film can be used only twice after the separation of impurities [2,3,4,5,6,7]. A trommel-sieve-type residual film–impurity wind separator (referred to as a residual film–impurity wind separator from hereon) is a key piece of equipment used for debris removal. However, the sieve holes are blocked to different degrees during the operation of the equipment; this severely affects the efficiency of wind selection. This problem can be solved by installing a screen hole blockage clearing device. Therefore, to ensure the effectiveness and reliability of the screen hole blockage clearing device, the mechanism of blockage should be analyzed, and the device structure and working parameters should be optimized.

The mechanism of airflow blockage clearing has been investigated by previous studies. Various studies have developed methods to evaluate the impact of airflow in solving the blockage problem; these methods have been useful in various fields. Li et al. analyzed the fluidization and transport characteristics of particles by varying the frequency, speed, and flow rate of airflow pulsation, and obtained a suitable sorting medium for fine-grained coal [8]. Li proposed a variable-diameter pulsating airflow sorting technique for sorting pulverized coal and demonstrated the effects of the air volume and handling capacity on the flow field and sorting effect through numerical simulations and experiments [9]. Wang used high-speed airflow, which had a strong impact and expansion force that destroyed the original static equilibrium of the ore in the bin, eliminated the phenomena of bonding and blockage, and caused a smooth flow of the material in the lower ore opening and the lower ore hopper [10]. Badretdinov simulated the grain cleaning process and analyzed the movement state and movement law of grains in the airflow using a mathematical model of the material and airflow; they also determined the optimal combination of parameters for the cleaning device [11]. Tong performed three-dimensional numerical simulations to analyze the influence of each factor of the vibrating screen surface on the grains in the airflow field, to optimize the influence of an uneven airflow field in the screening device on the grain during the screening process, and to improve cleaning quality [12]. The method of airflow impact dredging is extensively used to alter ores, silos, material tubes, and other static conditions to eliminate granular material blockage. However, the residual film–impurity wind separator of the trommel screen has a rotating state, airflow direction, and screen hole blockage position, and the changes in these characteristics are always relative. The motion of the residual film–impurity mixture is not only constant but also nonlinear. To assess the impact on the performance of blockage clearing, the motion of the mixture should be investigated theoretically and by evaluating the airflow size, distance between the nozzle and the screen surface, airflow pipe arrangement form, etc.

In the screen hole blockage clearing device for the residual film–impurity wind separator, the airflow pipe arrangement and nozzle end distance from the trommel sieve are unreasonable and cause low airflow speeds in part of the nozzle, ineffective clearing of blockages, and other problems. In the present study, through theoretical analysis, numerical simulations, three-factor three-level quadratic regression orthogonal combination tests, etc., to optimize the structural parameters of the screen hole cleaning device and to determine the optimum number of airflow pipes, distance between the nozzle and screen surface, and fan wind speed. Consequently, the blockage clearing effect of the screen hole blockage clearing device improved, thereby ensuring the reliability of the residual film–impurity wind separator. This study can serve as a theoretical framework for the optimization of screen hole cleaning devices.

2. Materials and Methods

2.1. Structure and Operating Principle of the Screen-Hole Blockage-Clearing Device

The structure of the screen hole blockage clearing device for the residual film–impurity wind separator is displayed in Figure 1. We installed a fan at the left and right ends at diagonal positions, ensuring that the airflow was uniform inside the pipe of the blockage clearing device. The airflow pipes in the screen hole blockage clearing device were located at 0°, 45°, 90°, 135°, and 180° around the trommel sieve. The nozzle was installed in the airflow pipe based on the nozzle jet airflow diffusion effect and the axial length of the trommel sieve; each airflow pipe had seven nozzles, and the distance between the nozzles was equal. Solenoid valves were installed on the left and right sides of each airflow pipe to determine whether a certain airflow pipe was circulating through the controller. The semicircular arc manifold at the left and right ends was connected to the airflow pipe through the solenoid valve. This minimized the loss along the airflow during circulation and was conducive to the installation of airflow pipes at each position in the radial direction of the trommel sieve.

After the residual film–impurity wind separator was in operation for a period of time, a flaky residual film, straw, and other materials formed and blocked the screen holes. In addition, the centrifugal blower induced airflow in each airflow pipe at a certain speed, and the airflow entered the pressure stabilization tube from the air inlet, forming a stable, high-speed airflow in each airflow pipe through the manifold. The opening and closing of the two ends of the airflow pipe at different positions was controlled by solenoid valves. Finally, the airflow was sprayed out through the nozzle and interfered with the movement of the residual film, straw, and other materials at the screen holes. Moreover, the airflow disrupted the equilibrium between the forces at the screen holes, thereby clearing screen hole blockages.

2.2. Computational Fluid Dynamics Simulation

Computational fluid dynamics (CFD) software is a special tool used for flow-field analyses, calculations, and predictions. CFD simulations are performed to analyze and visualize phenomena that occur during fluid flow. The flow properties of a fluid in the simulation area can be predicted in real time. Furthermore, numerical simulations performed using CFD can help to comprehensively analyze the mechanism of flows. The technique can be used to simulate experiments and can thus save manpower, materials, and time. It can also help organize experimental results and establish laws.

The CFD software is equipped with a geometric model-building and mesh-generation module, preprocessing module, core processing module, postprocessing module, etc. Most CFD software platforms can be interfaced with CAD to enhance the ability to handle complex geometry problems.

In this study, the numerical simulation method of fluid dynamics was applied to the designed clearing device. Using the CFD software shortened the design cycle, decreased the test difficulty, and thus satisfied the simulation requirements of the device.

2.3. Working Parameters of the Blocking Clearing Device

2.3.1. Nozzle Spraying Device

Nozzle Jet Airflow Coverage Area

As displayed in Figure 2, the airflow occurred from the circular section (with radius R) nozzle spray, with point M as the pole; ∠AMO was the diffusion angle ζ; and the exit velocity in the section with uniform distribution was v₀. The jet axis MO was regarded as the x-axis. The nozzle jet and the surrounding media had a constant mass and momentum exchange. This induced a flow in the surrounding media, and the mass flow rate of the jet and the cross-sectional area of the jet along the x direction increased, thereby forming a cone-like flow field involving diffusion in the surrounding media, as depicted by the cone CAMDF in Figure 2. The jet was continuously substituted in the surrounding media, enabling boundary expansion, and the velocity of the main body of the jet decreased gradually. The part of the jet with velocity v₀ was the core of the jet, represented by the cone AOD displayed in Figure 2. The section BOE was the transition section, and the section on the axis of the airflow velocity had a velocity v₀. The section between the exit section and the transition section was the jet start section, and the section beyond the transition section was the jet body section [13,14,15,16].

When the radius of any circular section is R and the nozzle radius is r₀, the radius of the jet along the shooting range according to the change law is as follows:

$$\{\begin{array}{l}\tan \zeta =\frac{\mathrm{BO}}{\mathrm{MO}}=\varphi \zeta \\ \frac{R}{r_0}=\frac{l_0+s}{l_0}=1+\frac{s}{r_0/\tan \zeta }\end{array},$$

(1)

where ϕ is the nozzle shape coefficient; circular nozzle, ϕ = 3.4; ζ is the turbulence coefficient; and the diffusion angle is 60°. According to the relational formula, the calculated value of the turbulence coefficient was 0.509.

Combining the two equations in Equation (1) yields:

$$R=r_0+1.731s.$$

(2)

In the nozzle jet stream formed by the jet cone, the momentum at each cross-section was equal (in Figure 3), and the flow rate on the exit section and the relationship between the flow rate on any section was

$$\mathsf{\pi }\rho r_0^2{v}_0^2={\displaystyle {\int }_0^{R}2\mathsf{\pi }\rho v_{\mathrm{y}}{}^{2}ydy},$$

(3)

where ρ is the fluid density, kg/m³; v₀ is the speed of the nozzle exit section, m/s; and v_y is the speed at point y, m/s.

Dividing both sides by x obtained the following:

$$\{\begin{array}{l}{\left(\frac{r_0}{R}\right)}^2{\left(\frac{v_0}{v_{\mathrm{m}}}\right)}^2=2{{\displaystyle {\int }_0^1\left(\frac{v}{v_{\mathrm{m}}}\right)}}^2\frac{y}{R}d\left(\frac{y}{R}\right)\\ B\mathrm{n}={\displaystyle {\int }_0^1{\left(\frac{v}{v_{\mathrm{m}}}\right)}^n\eta d\eta }\end{array},$$

(4)

where v_m is the axial velocity of the section, m/s; and η is $\frac{y}{R}$.

According to the range of variation in $\frac{y}{R}$ and $\frac{v}{v_{\mathrm{m}}}$, B₂ was assumed to be 0.0464, and the velocity of the jet along the shooting range according to the law of change was

$$\frac{v_{\mathrm{m}}}{v_0}=\frac{1.897}{0.578+\frac{s}{r_0}},$$

(5)

where the velocity of airflow at other locations in the same circular section was expressed as the mass-averaged flow velocity, v₂; v₂ = 0.47 v_m.

Reasonable Range of Distance from the Nozzle to the Screen Surface

When the screen hole faced the nozzle, the trommel screen rotation process resulted in the formation of a screen hole between the two nozzles for the jet airflow. The nozzle structure determined the conditions, and adjusting the distance between the nozzle and the screen hole resulted in the coverage of the screen hole by the nozzle jet formed by the cone-like flow field boundary, as illustrated in Figure 4a. As displayed in Figure 4b, the outermost layer of the cone-shaped flow field was located within the orange and red dashed lines. Neglecting the air velocity, airflow occurred through the screen holes.

To satisfy the aforementioned requirements, according to Equation (2), the radius of the jet along the shooting range of the law was

$$s=\frac{R-r_0}{1.731},$$

(6)

where the nozzle radius r₀ = 12.5 mm, L₁ = 168 mm, and L₁ + L₂ = 198 mm. According to Figure 4 and Equation (6), the range of L₃ was

$$\frac{L_1}{1.731}\le L_3\le \frac{L_1+L_2}{1.731}.$$

(7)

Substituting each value into Equation (7), the range was 97.1 mm ≤ L₃ ≤ 114.4 mm.

2.3.2. Calculation of the Fan Wind Speed Range

The force state of the residual film–impurity mixture blocked at the sieve hole is illustrated in Figure 5.

The screen hole was located between the two nozzles, and the airflow resistance effect of the two nozzles on the residual film–impurity mixture was accounted for in the calculation of the fan wind speed range; the airflow resistance was twice the F_t2 component force. The residual film–impurity mixture underwent uniform rotation because of a blockage in the trommel sieve. Various force components in the vertical direction resulted in a centripetal force. F_N = 0 N when the film–hybrid mixture was separated from the trommel sieve moment. The relationships representing the residual film–mixture force equilibrium were as follows:

$$\{\begin{array}{l}2F_{\mathrm{t}2}\sin \delta +mg-F_{\mathrm{t}1}\sin \gamma =m{\omega }^{2}r\\ F_{\mathrm{t}1}=\frac{1}{2}CA{\rho }_{\mathrm{s}}{v}_1\\ F_{\mathrm{t}2}=\frac{1}{2}CA{\rho }_{\mathrm{s}}{v}_2\end{array},$$

(8)

where m is the mass of the membrane mixture, kg; g is the acceleration of gravity, regarded as 9.81 m/s²; ω is the rotational angular velocity of the trommel sieve, rad/s; r is the radius of the trommel sieve, m; C is the material resistance coefficient, regarded as 0.44; A is the material windward area, m²; ρ_s is the density of the material, kg/m³; v₁ is the velocity of the airflow inside the trommel sieve for clearing, according to the previous study, regarded as v₁ = 8.5 m/s, and the horizontal angle γ = 8°; v₂ is the nozzle jet blockage clearing the airflow at the screen hole speed; and the horizontal angle is δ, where α ≤ δ ≤ β, m/s [17].

The force of the nozzle jet airflow on the residual film–impurity mixture in the vertical direction is the sum of the resistance of the jet airflow and the weight of the residual film–impurity mixture. For the clearing of the plug, this force should be greater than the force of the internal flow field of the trommel screen on the residual film–impurity mixture in the vertical direction. The resistance of the clearing airflow and the centripetal force required for the residual film–impurity mixture should follow the circumferential motion of the trommel screen. The relationship between the equations was as follows:

$$2F_{\mathrm{t}}{}_2\sin \delta +mg\ge F_t{}_1\sin \gamma +m{\omega }^{2}r.$$

(9)

Substituting Equation (8) into Equation (9), the relationship for the airflow velocity v₂ was obtained as follows:

$$v_2\ge \raisebox{1ex}{$\left(v_1\sin \gamma +\frac{2m{\omega }^{2}r}{CA{\rho }_s}-\frac{2mg}{CA{\rho }_s}\right)$}\!\left/ \!\raisebox{-1ex}{$2\sin \delta $}\right..$$

(10)

The test revealed that the average mass of the residual film–impurity mixture was 1.03 × 10⁻³ kg, the average density was 162.5 kg/m³, the average windward area of the residual film–impurity mixture was 5.57 × 10⁻³ m², the angular velocity of the trommel sieve was 13π/15 rad/s, and the radius of the trommel sieve was 0.5 m [18]. According to the relationship between L₁, L₂, and L₃ in Figure 4, 0.44 ≤ sinδ ≤ 0.59, so v₂ ≥ 1.308 m/s. According to Equation (5) and the relationship between v₂ and v_m, v₀ ≥ 14.27 m/s. Repeated tests were performed to obtain the nozzle jet air velocity v₀; the fan wind speed v and v₀ were related as follows:

$$v_0=0.72v-2.31.$$

(11)

Substituting v₀ into Equation (11), v ≥ 23.03 m/s.

2.3.3. Arrangement of Airflow Pipes

To determine the optimal airflow pipe arrangement, each airflow pipe was numbered as displayed in Figure 6.

After the test, the airflow pipe was distributed symmetrically with respect to the blue dotted line, as displayed in Figure 6. The position of the trommel sieve was affected by the jet airflow of the nozzle for a longer period of time during a rotation cycle. When the airflow pipe was on the same side of the blue dotted line, one position of the trommel sieve was affected by the jet airflow of the nozzle for a shorter period of time and was more likely to cause blockage of the screen holes and increase the difficulty of blockage clearing. As illustrated in Figure 6, Fluent (Lancaster, PA, USA) software was used to simulate the airflow pipe. The divided mesh file was imported into Fluent software, the standard k-ε model was selected as the calculation model [19], and the SIMPLEC algorithm was used to calculate the equation solution [20]. The airflow pipes were arranged as follows: Ⅰ, Ⅱ, Ⅲ, Ⅳ, and V; Ⅰ, Ⅲ, and V; and Ⅱ and Ⅳ; the airflow pipe for the simulation calculations for the nozzle jet airflow velocity statistics were derived for the three arrangements.

The airflow velocity vectors of the device corresponding to different airflow pipe arrangement forms were derived as illustrated in Figure 7. With the same color scale, it can be observed that when the number of airflow pipes was large, because of the conservation of inlet and outlet air volumes, the airflow in some airflow pipes was sparse and the airflow velocity was low. The airflow velocity in the manifold was higher, resulting in a pressure difference in the manifold and gas backflow in some airflow pipes. Therefore, in this duct arrangement, increasing the fan speed did not improve the airflow uniformity and airflow velocity in the pipes. After the reduction in the airflow pipe length, the airflow uniformity and speed in each pipe improved considerably. Therefore, the number of airflow pipes should be reduced as much as possible while ensuring a certain airflow to improve the airflow velocity of each nozzle.

To further analyze the influence of the number of airflow pipes on the jet air velocity of each nozzle, the statistics on the nozzle jet air velocity for the three arrangements of airflow pipes are derived, as represented by the line graph displayed in Figure 8.

As discussed in the previous section, with a nozzle jet airflow velocity of at least 14.27 m/s, the nozzle jet airflow in a certain range of screen holes satisfied the requirements for plug clearing. As illustrated in Figure 8, when there were more airflow pipes, only 22.9% of the nozzles satisfied the requirements for plug clearing. Most of the nozzle jet airflow velocity did not satisfy the requirements for plug clearing. The minimum velocity of 3.13 m/s was considerably less than the airflow velocity required for plug clearing. When the number of airflow pipes was reduced to three, the nozzle jet air velocity change was small on both sides of the airflow pipe. The nozzle jet air velocity significantly increased in the middle section of the airflow pipe but was lower than the air velocity required to clear the plug; only 47.6% of the nozzles satisfied the requirements for nozzle plug clearing. When the number of airflow pipes was reduced to two, 85.7% of the nozzles satisfied the requirement for plug clearing, and the nozzle jet airflow velocity considerably increased compared with that corresponding to the arrangement with the five airflow pipes. In summary, to improve the nozzle jet air velocity, the number of airflow pipes should be reduced in the subsequent tests for improved performance.

2.4. Whole-Machine Performance Test

2.4.1. Test Material

In April 2022, the sieve hole-clearing and -plugging device was tested in a real machine at the pilot plant of the Shandong Agricultural Machinery Research Institute through the test process illustrated in Figure 9. The test material was a mixture of residual film, cotton stalk, and soil that were collected from Binzhou City, Shandong Province, using a CMJD-1500 machine that can be used for residual film picking and baling operations. The average mass ratios of the main components of the mixture were 42.65% for soil and broken soil pieces, 21.39% for cotton stalks, and 35.96% for the residual film.

2.4.2. Test Method

The residual film–impurity mixture was continuously fed from the feeding port of the residual film–impurity wind separator, and the airflow speed at the air inlet and each nozzle was determined using a handheld thermal anemometer (measuring range: 0–30 m/s, error: ±1%). The material movement inside the device was recorded using a high-speed camera. The residual film–impurity wind separator and the screen-hole-clearing device worked separately for 30 min under each test scheme, and each group of tests was repeated five times.

At the end of the test, the working performance of the screen-hole-clearing device was evaluated according to the impurity ratio in the residual film and the blockage ratio of the screen holes using images captured with the high-speed camera. The quality of the residual film and impurities in the residual film collection box were calculated as follows:

$$Y_1=\frac{m_2}{m_1}\times 100\%,$$

(12)

where Y₁ denotes the ratio of impurities in the residual film, %; m₁ denotes the mass of the residual film in the collection box, kg; and m₂ denotes the mass of impurities in the collection box, kg.

$$Y_2=\frac{n_2}{n_1}\times 100\%.$$

(13)

where Y₂ denotes the blockage ratio of the screen holes, %; n₁ denotes the total number of holes in the trommel sieve; and n₂ denotes the number of blocked holes in the sieve.

2.4.3. Test Design

The operating requirements of the screen-hole-clearing device, the theoretical analysis results, and the limitations of the fan parameters were accounted for in the test design. The distance from the nozzle to the screen surface X₁ (95–115 mm), the fan speed X₂ (23–25 m/s), and the number of airflow pipes X₃ (1–5) were selected as test factors. The impurity ratio in the residual film Y₁ and the blockage ratio of the screen holes Y₂ of the screen hole were used as the evaluation indexes of the operating performance of the screen-hole-clearing device. The distance from the nozzle to the screen surface was changed by adjusting the nozzle length, the fan speed was changed using the inverter, and the number of connected airflow pipes was controlled using the solenoid valve. The Box–Behnken test design principle was used. The test factors and range of values are displayed in

Table 1. Test factor levels and coding.

Levels	Test Factors
	Distance from the Nozzle to Screen Surface X1/mm	Fan Wind Speed X2 (m·s−1)	Number of Airflow Pipes X3
–1	95	23	1
0	105	24	3
1	115	25	5

. The response surface analysis test groups are summarized in

Table 2. Results of response surface analysis.

Test Serial Number	Test Factors			Evaluation Indexes
	X1	X2	X3	Impurity Rate in the Residual Film Y1	Blockage Rate of the Screen Holes Y2
1	0	0	0	8.32	7.21
2	–1	0	1	8.41	9.27
3	–1	1	0	8.78	8.97
4	–1	0	–1	16.72	11.78
5	0	0	0	6.81	7.58
6	–1	–1	0	8.91	9.05
7	1	1	0	8.32	8.24
8	0	1	–1	12.29	13.21
9	0	1	1	8.89	10.27
10	0	0	0	8.37	6.07
11	0	–1	–1	14.85	16.27
12	1	–1	0	13.27	9.82
13	0	0	0	7.85	6.95
14	1	0	–1	12.32	12.21
15	0	0	0	8.54	6.47
16	1	0	1	12.22	11.27
17	0	–1	1	10.77	15.32

. The average value of the five tests was considered the result for each group of tests. Data processing and analysis were performed using Design-Expert (Shanghai, China) software [21,22].

The force analysis of the residual film–impurities clogged at the screen holes was performed. The theoretical range of values of the distance from the nozzle to the screen surface and the fan wind speed were obtained. Numerical simulation tests were performed, and the range of values for the number of airflow pipes was obtained. Based on the range of the aforementioned test factors, a three-factor, three-level quadratic regression orthogonal center-of-rotation combination test was designed to verify the significance of the test results. The results of this study are discussed in the following section.

3. Results and Discussion

3.1. Regression Model Building and Testing

The experimental results were analyzed using Design-Expert software [23]. In the results, p < 0.01 indicated that the parameter had notable effects on the model, and p < 0.05 indicated that the parameter had notable effects on the model. The results of the analysis of variance and the significance test of the regression coefficients of the secondary regression model are summarized in

Table 3. Box–Behnken test protocol and results.

Source of Variation	Impurity Rate in the Residual Film			Blockage Rate of the Screen Holes
	Sum of Squares	F-Value	p-Value	Sum of Squares	F-Value	p-Value
Model	120.67	20.2	0.0003 **	136.77	14.45	0.001 **
X1	1.37	2.06	0.194	0.76	0.72	0.4227
X2	11.33	17.07	0.0044 **	11.93	11.34	0.012 *
X3	31.56	47.55	0.0002 **	6.73	6.4	0.0392 *
X1X2	5.81	8.75	0.0212 *	0.56	0.53	0.4884
X1X3	16.85	25.39	0.0015 **	0.62	0.59	0.4691
X2X3	0.12	0.17	0.6889	0.99	0.94	0.3643
X12	6.90	10.39	0.0146 *	0.23	0.22	0.6519
X22	1.33	2.01	0.1997	24.24	23.05	0.002 **
X32	42.04	63.33	<0.0001 **	85.72	81.49	<0.0001 **
Residual	4.65			7.36
Lack of Fit	2.68	1.82	0.2840	5.94	5.56	0.0655
Pure Error	1.97			1.43
Cor Total	125.32			144.13

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

.

As displayed in Table 3, P₁ and P₂ were less than 0.01 in the quadratic regression models based on the influencing factors and the ratios of impurities in the residual film and of blockages of the screen holes were highly significant. The outlying values of P₁ and P₂ were greater than 0.05, which were not significant. The R² values of the coefficients of determination were 0.9591 and 0.9489, indicating that the regression models could fit more than 94% of the sample data [24]. The quadratic regression equation fitted by the model was consistent with the actual situation and correctly represented the relationships between the ratio of impurities in the residual film Y₁, the ratio of the blockage of the screen holes Y₂, and X₁, X₂, and X₃, indicating that the model can better predict the results of various tests with real machines.

For the ratio of impurities in the residual film, X₂, X₃, X₁X₃, and X₃² had significantly strong effects on the model (p < 0.01), and X₁X₂, X₁² had significant effects on the model (p < 0.05). For the ratio of blockages of the screen holes, X₂², X₃² had a highly significant effect on the model (p < 0.01), and X₂, X₃ had significant effects on the model (p < 0.05). The quadratic regression models of the ratio of impurities Y₁ in the residual film and the ratio of blockage Y₂ of the screen holes were expressed using coded values obtained by eliminating the nonsignificant terms, as depicted in Equations (14) and (15).

$$Y_1=7.98-1.19X_2-1.99X_3-1.21X_1{X}_2+2.05X_1{X}_3+1.28X_1^2+3.16X_3^2,$$

(14)

$$Y_2=6.86-1.22X_2-0.92X_3+2.4X_2^2+4.51X_3^2.$$

(15)

The data in Table 3 and the p value of each factor indicated that the factors influencing the ratio of impurities in the residual film, in the descending order of influence, were as follows: the number of airflow pipes, fan air speed, and distance from the nozzle to the screen’s surface. The factors affecting the ratio of blockage of the screen holes, in the descending order of influence, were as follows: the fan air speed, number of airflow pipes, and distance from the nozzle to the screen’s surface [25].

3.2. Analysis of Model Interaction Factors

To analyze the effect of interaction factors on the response values, response surface plots of the relationship of the ratio of impurities in the residual film and the ratio of the blockage of the screen holes with each factor were constructed using the quadratic regression model [26].

As illustrated in Figure 10a, the airflow pipes were located at zero level. When the fan wind speed was high, the effects of the distance from the nozzle to the screen surface on the ratio of impurities in the residual film were not significant. When the fan wind speed was small, the ratio of impurities in the residual film increased with the increase in the distance from the nozzle to the screen surface. When the distance from the nozzle to the screen surface was small, the effects of the fan wind speed on the ratio of impurities in the residual film were not significant. When the distance from the nozzle to the screen surface was large, the ratio of impurities in the residual film decreased with an increase in the fan wind speed. This was mainly because the device was more sensitive to a change in the nozzle-to-screen distance or fan wind speed when the fan wind speed was small or the distance from the nozzle to the screen surface was large.

As displayed in Figure 10b, the fan wind speed was zero. When the number of airflow pipes was small, the distance from the nozzle to the screen surface had no significant influence on the ratio of impurities in the residual film. When the number of airflow pipes was large, the ratio of impurities in the residual film increased with the increase in the distance from the nozzle to the screen surface. At the same nozzle-to-screen-surface distance, the ratio of impurities in the residual film first decreased and then increased with an increase in the number of airflow pipes. The main reason was that when the number of airflow pipes was small, the screen-hole-clearing and -plugging devices were ineffective. Simply increasing the distance from the nozzle to the screen surface did not effectively reduce the ratio of impurities in the residual film. According to the results of ANOVA, the number of airflow pipes had the greatest influence on the ratio of impurities in the residual film. Therefore, the ratio of impurities in the residual film considerably fluctuated when the number of airflow pipes changed at the same distance from the nozzle to the screen surface.

Figure 10c depicted that the distance from the nozzle to the screen surface was zero. With the same number of airflow pipes, the ratio of impurities in the residual film exhibited a trend of decreasing and then increasing with an increase in the fan wind speed. At the same fan wind speed, the rate of impurities in the residual film first decreased and then increased with an increase in the number of airflow pipes. The influence of the number of air pipes on the rate of impurities in the residual film was more significant than that of the fan wind speed; this was consistent with the results of ANOVA.

As illustrated in Figure 10d, the number of airflow pipes was zero. When the wind speed of the fan was certain, varying the distance from the nozzle to the screen surface had no significant effect on the ratio of the blockage of the screen holes. At the same nozzle-to-screen-surface distance, the screen hole clogging ratio first decreased and then increased with an increase in the fan wind speed. This phenomenon occurred mainly because the selected distance from the nozzle to the screen surface satisfied the requirements for blockage clearing, and the influence of this factor on the blockage rate of the screen holes was small. The influence of the fan speed was more significant. Therefore, the effects of the variation in the fan speed on the ratio of the blockage of screen holes were more obvious.

Figure 10e depicted that the fan wind speed was zero. When the number of airflow pipes was certain, varying the distance from the nozzle to the screen surface did not significantly influence the ratio of the blockage of the screen holes. With the same distance from the nozzle to the screen surface, the ratio of the blockage of the screen holes first decreased and then increased with the increase in the number of airflow pipes. Further considering the analysis results illustrated in Figure 10d, the distance from the nozzle to the screen surface had a small effect on the ratio of the blockage of the screen holes.

As illustrated in Figure 10f, the distance from the nozzle to the screen surface was zero. With the same number of airflow pipes, the screen hole clog ratio first decreased and then increased with an increase in the fan air speed. At the same fan speed, the screen hole blockage ratio first decreased and then increased with an increase in the number of airflow pipes, mainly because of the poor clearing effect when the number of airflow pipes was small. Thus, the long-term clearance of the blockage of the screen surface is challenging. When the number of airflow pipes was large, some of the airflow pipes exhibited a smaller flow, and the high-speed airflow in the manifold tends to generate negative pressure in some airflow pipes, thereby causing an increase in the ratio of the blockage of screen holes. When the wind speed of the fan was small, clearing the blockage of the screen hole was ineffective. When the fan wind speed was larger, generating a negative pressure in the airflow pipe was convenient. Therefore, the number of airflow pipes and the fan speed should be taken as the middle level so that the ratio of the blockage of the screen holes is small.

3.3. Parameter Optimization and Experimental Validation

To maximize the clearing effect of a screen-hole-clearing device, the regression equation model of the influencing factors and performance indexes were optimally solved by applying the optimization-seeking function of Design-Expert software [27]. The screen hole cleaning device was used to clear screen hole clogging to improve the clearing effect of the residual film–impurity wind separator. Therefore, the ratio of impurities in the residual film should be appropriately increased during the optimization process. The optimal parameter values for each influencing factor were calculated: the distance of the nozzle from the screen surface was 102 mm, the wind speed of the fan was 24 m/s, and the number of airflow pipes was 4. The optimal value of the performance index corresponding to these parameters was 7.3% for the ratio of impurities in the residual film and 6.6% for the ratio of the blockage of the screen holes.

To verify the feasibility of the optimization results, a real machine test was conducted based on the predicted values. According to the optimal working parameters of the original residual film–impurity wind separator, the distance between the nozzle of the screen-hole-clearing device and the screen surface was 102 mm, the fan wind speed was 24 m/s, and the number of airflow pipes was 4. The minimum air velocity value was 15.8 m/s, greater than the theoretical air velocity required to clear the screen hole plugging. The test was conducted three times to obtain the average value, as illustrated in

Table 4. Comparison of optimization results with actual values.

Projects	Distance from Nozzle to Screen Surface/mm	Fan Wind Speed/(m·s−1)	Number of Air Pipes	Impurity Rate in the Residual Film %	Blockage Rate of the Screen Holes %
Predicted value	102	24	4	7.3	6.6
Actual value 1				6.27	5.97
Actual value 2				5.38	4.75
Actual value 3				5.94	5.51
Pre-optimization values				8.28	7.33

. The results indicated that the average ratio of impurities in the residual film in the validation test was 5.86%, which was 2.42% lower than the ratio before optimization. The ratio of the blockage of the screen holes was 5.41%, which was 1.92% lower than the preoptimization rate. The relative error with the predicted value was less than 19.7%. The test results were close to the predicted value and thus verified the accuracy of the model.

The device continued to operate, and the ratio of the blockage of the screen holes and the ratio of impurities in the residual film were recorded after 1 h, 3 h, and 5 h of operation. The results were basically consistent with the test results. This indicated that the optimized screen-hole-clearing device had stable working performance and effectively reduced the ratio of the blockage of the screen aperture of the residual film–impurity wind separator, thereby improving the screening performance and reliability of the device.

3.4. Discussion

This paper proposed a screen-hole-clearing device, which can be used to reduce sieve hole blockages during mechanized residual film–impurity separation. The device can be used to clear blockages in a high-speed rotating trommel sieve. As discussed in the experimental results in Section 3.3, the impurity ratio in the residual film and the blockage ratio of the screen holes can be significantly reduced using this device, thereby exhibiting a clearing effect. However, the clearing and plugging device proposed in this study requires multiple fans to maintain a high-speed airflow. The matching residual film–impurity separation device is noisy during operation. Further research is warranted to optimize the structure of the gas transmission pipeline to ensure that the number of fans is reduced at the same air flow rate. Moreover, suitable measures should be adopted to reduce noise during operation.

4. Conclusions

(1) This study engaged in a theoretical analysis and a numerical simulation of a trommel-sieve–type residual film–impurity wind separator and screen-hole-clearing device. The simulation results indicated that the distance from the nozzle to the screen surface should be between 97.1 and 114.4 mm, the fan wind speed should be greater than 23.03 m/s, and the number of airflow pipes should be as small as possible. The limitation of the fan was accounted for. Accordingly, the distance from the nozzle to the screen surface was set as 95–115 mm, the fan wind speed was set as 23–25 m/s, and the number of airflow pipes was set as 1–5. The results of the force analysis of the blockage at the screen hole can provide theoretical support for solving the problems of small airflow speeds and the poor cleaning effect of some nozzles of various cleaning devices.

(2) A Box–Behnken test was designed. Furthermore, a three-factor, three-level response surface analysis method was performed. The screen-hole-clearing device was tested for the clog-clearing performance. The analysis of the response surface revealed that the factors influencing the rate of impurities in the residual film in the descending order were the number of airflow pipes, air speed of the fan, and distance from the nozzle to the screen surface. The factors influencing the blockage rate of screen holes in the descending order were the air speed of the fan, number of airflow pipes, and distance from the nozzle to the screen surface.

(3) After the optimization of the screen-hole-clearing device, the distance from the nozzle to the screen surface was 102 mm, the optimal number of airflow pipes was four, and the optimal fan air speed was 24 m/s. The actual machine verification test revealed that the minimum airflow velocity at each nozzle position in such a structure and for such working parameters was 15.8 m/s, which was greater than the theoretically calculated airflow velocity required for screen-hole clearing. The ratio of impurities in the residual film was 5.86%. Furthermore, blockage was observed in 5.41% of the screen holes. The ratios of impurities in the residual film and that of the blockage of the screen holes were 2.42% and 1.92% lower, respectively, than those before optimization. The clearing performance was significantly improved after optimization compared with that before optimization. The relative error between the experimental results and the predicted values was less than 19.7%, which indicated the accuracy of the model.

(4) The key factors affecting the blockage-clearing effect of the screen-hole-clearing device were determined. The results indicate that the device should be enabled to process more details. For example, a more energy-efficient, high-efficiency, and low-noise fan should be selected; the manufacturing materials should be replaced with low-cost materials that also satisfy the strength requirements. Furthermore, more efficient and stable feeding methods should be developed to ensure the good working performance of the original device. This can help achieve low power consumption and low costs and can promote further research.