Design and Parameter Optimization of a Negative-Pressure Peanut Fruit-Soil Separating Device

Abstract

This study proposes a negative-pressure fruit-soil separating device for peanuts cultivated in hilly and mountainous areas after combined harvesting, and the mechanism of the movement of the material in the process of material screening, fruit-soil separating, and pneumatic conveying of the device was analyzed. In addition, a four-factor, three-level Box-Behnken regression design test was used to explore the optimum operating parameters of the peanut fruit-soil separation device. The results showed that the best fruit-soil separation effect was achieved when the wind speed of the blower was 13.58 m/s, the height of the suction nozzle from the screen surface was 27 mm, the length of the suction port was 64 mm, and the feeding rate was 600 kg/h. Validation tests demonstrated that the impurity rate of 0.16% and the peanut pod loss rate of 0.2% exceeded the industry standard, indicating superior performance.

1. Introduction

According to the latest data, China’s peanut production in 2021 reached 18.3078 million tones, making it the second-largest producer globally. Additionally, China also topped the list in terms of peanut cultivation, with a total of 480.53 million hectares planted [1]. Nearly one-third of them are planted in hilly and mountainous areas with mostly clay-heavy soil. Because of its small fields, sloping arable land, planting agronomic complexity and other multiple factors, the mechanization of peanut production and industrial development has been seriously constrained. The current peanut combine harvesting machinery is designed for planting in sandy loam soil. However, it is not suitable for hilly and mountainous areas with clay-heavy soil, as it lacks adaptability. As a result, the efficiency of peanut harvesting is low, and there are significant issues with impurity and loss rates. The development of combine harvesting machinery for peanuts grown in clay-heavy soils is an urgent matter [2,3]. The separation and cleaning process plays a crucial role in the peanut harvesting process as it directly impacts the impurity rate, loss rate, and other indicators used to evaluate the quality of peanut harvesting machinery. Therefore, the separation and cleaning of peanut combine harvesting in clay-heavy soil cultivation is of significant importance in bridging the technological gap in the industry.

In recent years, numerous scholars have conducted extensive research on the mechanism design and structural improvement of various components involved in the process of peanut combine harvesting. Michael J. Bader et al. [4] introduced the working principle of peanut diggers and combine harvesters in the United States and how to adjust their working parameters to achieve the highest efficiency so as to produce high-quality peanuts, which provides a reference for the development of peanut combine harvesting machinery in China. Zhichao Hu et al. [5] conducted motion analysis on the seedling raising device of the 4HLB-2 peanut combine harvester. They investigated how the main motion parameters and positional parameters of each component affected the effectiveness of seedling raising. Additionally, field tests were conducted to validate the positioning of the main parameters of each component from a side view perspective. The distance of the lowest point of the pawl finger from the digging surface is 170 mm. The distance of the lowest point of the pawl finger from the lead hammer surface where the clamping point is located is 325 mm. The distance of the clamping point from the digging surface is 290 mm, and the minimum distance of the digging production from the lead hammer surface where the clamping point is located is 25 mm. These findings serve as a foundation for refining the design structure and optimizing the operating parameters of this particular peanut seedling raising device. Shenying Wang et al. [6] designed a peanut picking device, conducted kinematic simulation analysis using ADAMS, and determined the optimal parameter combinations through multi-indicator field orthogonal tests. When the harvester’s forward speed was 1.0 m/s, with a rotary angular speed of 4 rad/s, and spring-fingertip bend angle at 150°, the comprehensive pickup performance was optimum (with a comprehensive test score of 0.106), which provided relevant technical references for peanut combine harvesters and picking devices for oilseed rape and forage. Hongguang Yang et al. [7] designed a tangential-axial flow picking device for a peanut combine harvester with reference to the tangential-axial flow threshing mechanism of grain combine harvester, determined the structural parameters and working parameters through theoretical analysis and design calculations of the key components of the peanut picking device. They obtained the optimal parameter combinations through the four-factor, four-level orthogonal test and the comprehensive fuzzy evaluation method. The feeding amount of the peanut plant was 2 kg/s, the picking clearance was 35 mm, the speed of the tangential cylinder was 360 r/min, and the speed of the axial cylinder was 425 r/min. At this time, the non-picking loss rate was 0.52%, the entrainment loss rate was 0.54%, and the damage rate was 0.75%. Lianxing Gao et al. [8] proposed a cleaning principle and scheme using double air-suction inlets combined with a vibration screen, taking into account the difference in floating velocity of each component of the peanut picker cleaning material. The researchers designed and developed the 5XT-2Z peanut picker, providing a valuable reference for the cleaning device used in peanut combine harvesting. Ashish S. Raghtate et al. [9] designed and manufactured a new medium capacity peanut shelling machine for the lack of peanut shelling machines in India and evaluated the machine performance in terms of productivity, shelling efficiency, material efficiency and mechanical damage. Mingyang Qin et al. [3] measured the suspension velocity of peanut pods and clay-heavy soil of different masses, shapes and moisture contents by means of one-way test and CFD-DEM coupling. The researchers obtained the values of the suspension velocity of each material and its separation characteristics, which verified the feasibility of the idea of separating the fruits and soil through the difference of suspension velocity and provided the basis of this study. Wei Hai et al. [10] conducted a study on the existing pneumatic conveying equipment used for peanut pod transportation. They observed that the equipment had issues such as high loss, cracked pods, and a high breakage rate. To address these issues, the researchers installed a silica gel buffer plate in the separating cylinder and made improvements to the air locker and other key components of the equipment. Additionally, they optimized the equipment parameters through orthogonal tests. As a result, the cracked pods rate and breakage rate were effectively reduced. This study serves as a valuable reference for optimizing the structure of peanut pneumatic conveying equipment.

The objective of this study is to develop a fruit-soil separation device specifically designed for peanuts cultivated in hilly mountainous regions. The device aims to address the challenge of effectively separating peanuts from side-by-side clods during combine harvesting. The proposed device will adhere to the industry standard, ensuring a total loss rate of less than 3.5% and a pod splitting rate below 1.5% [11]. By achieving these targets, the integration of agricultural machinery and agronomy will be enhanced, leading to advancements in mechanized peanut production techniques.

2. Materials and Methods

2.1. Overall Structure of the Negative-Pressure Peanut Fruit-Soil Separating Device

The negative-pressure peanut fruit-soil separating device primarily comprises of two components: pneumatic conveying equipment and a linear vibrating screen, as depicted in Figure 1. Pneumatic conveying equipment consists of the frame, frequency regulator, motor, electric control box, high-pressure blower, gravity gate (Flip-flop air locker), separation cylinder, input pipe, connecting pipe and output pipe and other key components. The main technical parameters are shown in

Table 1. Main technical parameters of pneumatic conveying equipment.

Technical Parameters	Values
External dimensions (L × W × H)/(mm × mm × mm)	1780 × 1050 × 1550
Mass/kg	380
Diameter of input pipe/mm	150
Diameter of output pipe/mm	200
Max. conveying capacity/t·h−1	2.5~3
blower power/kW	5.5
Rotation speed of the blower/r·min−1	3100
air pressure/kPa	9.22
air flow/m3·h−1	780
air velocity/m·s−1	0~26
Max. conveying distance horizontally/m	20
Max. sucking distance/m	6.5
Max. lifting distance/m	5

.

The linear vibrating screen mainly consists of key components such as the frame, adjustable support foot, connecting spring, screen frame, woven screen, double vibrating motor, feeding port, feeding speed adjusting plate, and two discharging ports, as shown in Figure 2. The main technical parameters are shown in

Table 2. Main technical parameters of the linear vibrating screen.

Technical Parameters	Values
External dimensions (L × W × H)/(mm × mm × mm)	1900 × 820 × 770
Mass /kg	85
Motor power/kW	0.25 × 2
Angle of inclination of the screen surface/°	6.6
Specification of screen mesh (wire diameter × hole length × hole width)/(mm × mm × mm)	0.6 × 8.8 × 8.8
Size of screen surface (L × W)/(mm × mm)	1600 × 500

.

The combination of pneumatic conveying equipment and a linear vibrating screen is achieved through the variable diameter suction port from square to round. The round port has a diameter of 150 mm, while the square port measures 55 mm in length, 490 mm in width, and 900 mm in height. The three-dimensional schematic is shown in Figure 1 (10).

2.2. Working Principle

The negative-pressure fruit-soil separating device was developed to solve the problem of removing soil and debris from peanuts grown in hilly and mountainous areas on clay-heavy soils during combined harvesting, and the main object of this device is the peanut pods and the clay-heavy soils that are basically the same as their dimensions, which are referred to as “side-by-side clods” in this study.

After switching on the control switch of the pneumatic conveying equipment and linear vibrating screen, the motor drives the blower and vibrating screen to run. The motor speed is adjusted by the frequency converter to adjust the wind speed in the conveying pipe. The peanut pods and clods that are left on the screen surface after being screened by the linear vibrating screen are then sucked into the input pipe and transported to the cyclone separator (separator cylinder). This is achieved through the negative pressure airflow that passes through the variable diameter suction port from square to round. The filter screen then separates the air from the material, which is rotated down the wall of the separation cylinder to land at the gravity gate. When the set mass is reached, the gravity gate opens and allows the material to fall into the output pipe. The material is then conveyed by the positive pressure airflow to the unloader. The unloader separates the material from the air again and finally discharges it. The movement route of the material within the pneumatic conveying equipment is shown schematically in Figure 3.

2.3. Analysis of Material Movement Mechanism in the Process of Fruit-Soil Separation

2.3.1. Analysis of the Material Screening Process

An inertial double vibrating motor linear vibrating screen can be simplified as a vibrating system consisting of a parametric mass (physics) and springs moving in the amplitude direction under the action of an excitation force [12]. In this case, the parametric mass includes the overall mass of the screen box and the mass of the vibrating motor, and the excitation force is provided by the inertia force generated by the rotation of the eccentric block of the vibrating motor. The vibrating motor is symmetrically installed in the lower part of the vibrating screen body at a certain angle, and the internal eccentric block does synchronous reverse rotation, generating inertia force, so as to synthesize the excitation force along the vibration direction angle, and drive the vibrating screen to do straight line movement.

In the screening process of the vibrating screen, the vibrating screen surface, and the material particles, as well as between the material particles themselves will be contacted, thus changing the state of motion of the material particles, which then makes the particles move to achieve the purpose of penetrating the screen. Elastic and plastic deformation occurs when particles collide, resulting in force.

Assuming that the force between particles is constant at a certain time step $∆t$, and according to Newton’s second law, the equation of motion for any particle unit $i$ can be expressed as

$$\left\{\begin{array}{c}{m}_i{\mathit{x}}_i=m_i\mathit{g}+\sum _{j=1}^n{\mathit{F}}_{ij}\\ {\mathit{J}}_i{\mathit{\omega }}_i=\sum _{j=1}^n\left({\mathit{x}}_{ij}-{\mathit{x}}_i\right)\times {\mathit{F}}_{ij}\end{array} \right.,$$

(1)

where, ${\mathit{x}}_i$, ${\mathit{\omega }}_i$ are the position vector and angular velocity vector of particle $i$’s motion, respectively; ${\mathit{x}}_{ij}$ is the position vector of the position point on particle $i$ in contact with particle $j$; $m_i$ is the mass of particle $i$, kg; ${\mathit{J}}_i$ is the rotational moment of inertia of particle $i$, kg·m²; ${\mathit{F}}_{ij}$ is the contact resultant force of the surrounding particle $j$ acting on particle $i$, N; and $n$ is the number of particles in contact with particle $i$ [13,14].

Figure 4 shows a schematic diagram of the displacements and forces on particle $i$ and particle $j$.

When particle $i$ collides with a certain velocity relative to particle $j$, the resulting force ${\mathit{F}}_{ij}$ can be divided into normal force ${\mathit{F}}_{nij}$ and tangential force ${\mathit{F}}_{tij}$, which can be expressed according to the Hertzian contact theory as

$${\mathit{F}}_{ij}={\mathit{F}}_{nij}+{\mathit{F}}_{tij},$$

(2)

$${\mathit{F}}_{nij}=\left(-k_n{\mathit{\alpha }}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}-c_n{\mathit{v}}_{ij}\mathit{n}\right)·\mathit{n},$$

(3)

$${\mathit{F}}_{tij}=-k_t\mathit{\tau }-c_t{\mathit{v}}_{ct},$$

(4)

where, $\mathit{\alpha }$ is the normal overlap vector; ${\mathit{v}}_{ij}$ is the velocity of particle $i$ with respect to particle $j$, ${\mathit{v}}_{ij}={\mathit{v}}_i-{\mathit{v}}_j$, m/s; $\mathit{n}$ is the unit vector from the center of mass of particle $i$ to the center of mass of particle $j$; $k_n$ and $k_t$ are the normal and tangential elasticity coefficients of particle $i$, respectively; $c_n$ and $c_t$ are the normal and tangential damping coefficients of particle $i$, respectively; $\mathit{\tau }$ is the tangential displacement of the contact point, m; and ${\mathit{v}}_{ct}$ is the slip velocity of the contact point, m/s. Among them, the elasticity coefficient and damping coefficient are related to the parameters of elastic modulus and Poisson’s ratio of the particle material.

When the time increases from moment $t$ to moment $t+∆t$, the velocity of motion of particle $i$ at that moment is as follows:

$$\left\{\begin{array}{c}{\mathit{v}}_i^{\left(t+\raisebox{1ex}{$∆t$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}={\mathit{v}}_i^{\left(t-\raisebox{1ex}{$∆t$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}+\frac{m_i\mathit{g}+\sum _{j=1}^n{\mathit{F}}_{ij}}{m_i}\times ∆t\\ {\mathit{\omega }}_i^{\left(t+\raisebox{1ex}{$∆t$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}={\mathit{\omega }}_i^{\left(t-\raisebox{1ex}{$∆t$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}+\frac{\sum _{j=1}^n\left({\mathit{x}}_{ij}-{\mathit{x}}_i\right)\times {\mathit{F}}_{ij}}{{\mathit{J}}_i}\times ∆t\end{array}\right.,$$

(5)

where $∆t$ is the minimum time step, s. Further, the new position of the particle’s form center can be obtained with the following:

$$\left\{\begin{array}{c}{\mathit{x}}_i^{\left(t+∆t\right)}={\mathit{x}}_i^{\left(t\right)}+{\mathit{v}}_i^{\left(t+\raisebox{1ex}{$∆t$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}\times ∆t\\ {\mathit{\phi }}_i^{\left(t+∆t\right)}={\mathit{\phi }}_i^{\left(t\right)}+{\mathit{\omega }}_i^{\left(t+\raisebox{1ex}{$∆t$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}\times ∆t\end{array}\right.,$$

(6)

where ${\mathit{\phi }}_i$ is the turning angle of particle $i$, °.

It can be seen that the force of the material on the vibrating screen surface is related to the speed of the material particles, which is determined by the vibration frequency, vibration amplitude, and the angle of inclination of the vibrating screen surface. In addition, it is also related to the vibrating screen surface material and particle material. Combined with the actual production requirements, the final device selected a stainless steel vibrating screen, inclination angle of 6.6°, and 250 W double vibration motor. And according to the size of the test material particles and the demand of feeding quantity, the screen specification was determined as 0.6 × 8.8 × 8.8 mm (wire diameter × hole length × hole width), and the screen surface size was 1600 × 500 mm (length × width).

2.3.2. Analysis of the Process of Fruit-Soil Separating

In the process of peanut pods leaving the vibrating screen surface and entering the suction nozzle, the negative pressure airflow overcomes gravity and friction to do work to suck up the peanut pods. In the process of peanut pods rising, the effect of its form on the acceleration is negligible. In order to simplify the analysis of the acceleration process, the peanut pods are considered as spheres in this study and the force analysis is shown in Figure 5.

The acceleration equation for the peanut pods from Newton’s second law is given by the following:

$${\mathit{F}}_p-\mathit{G}-f=\frac{\pi d_p^3{\rho }_p}{6\times {10}^9}\times \frac{{d\mathit{v}}_p}{d_t},$$

(7)

where ${\mathit{F}}_p$ is the force of the negative pressure airflow acting on the peanut pods, N; $\mathit{G}$ is the gravitational force of the peanut pods, N; $f$ is the friction force acting on the peanut pods, N; $d_p$ is the diameter of the peanut pods, mm; ${\rho }_p$ is the density of the peanut pods, kg/m³; and ${\mathit{v}}_p$ is the velocity of the peanut pods in the square-round reducer suction opening, m/s.

In this case, the suction force of the negative pressure airflow is calculated by the following formula:

$${\mathit{F}}_p=C\frac{\pi {\rho }_a{d}_p^2}{8}{\left({\mathit{v}}_a-{\mathit{v}}_p\right)}^2,$$

(8)

where ${\rho }_a$ is the air density, kg/m³; ${\mathit{v}}_a$ is the airflow velocity, m/s; and $C$ is the coefficient of fluid resistance of peanut pods [8,15,16].

During the acceleration process, the peanut pods are mainly affected by the suction of the negative pressure airflow and their own gravity. The equations obtained by solving the system of equations are as follows:

$$\frac{{d\mathit{v}}_p}{d_t}=\frac{3C{\rho }_a}{4{\rho }_p{d}_p}{\left({\mathit{v}}_a-{\mathit{v}}_a\right)}^2-\frac{\mathit{G}}{{\pi {d_p}^{3}p}_p},$$

(9)

Obtained by deforming the following:

$$\frac{{dl}_m}{{d\mathit{v}}_p}=\frac{4{\rho }_p{d}_p{\mathit{v}}_p}{3{C\rho }_a}{\left({\mathit{v}}_a-{\mathit{v}}_p\right)}^2-\frac{{\pi {d_p}^{3}p}_p{\mathit{v}}_p}{\mathit{G}},$$

(10)

where $l_m$ is the displacement produced by the acceleration of the negative pressure airflow.

Differential Equations (9) and (10) describe the acceleration of the peanut pods inside the variable diameter suction port from square to round. Based on these equations, it can be concluded that acceleration is positively correlated with the magnitude of the negative airflow, i.e., an increase in the negative airflow promotes the acceleration of the peanut pods. Therefore, increasing the blower air speed can achieve higher peanut pod collection speeds.

2.3.3. Analysis of Pneumatic Conveying Processes

Peanut pods are subjected to axial, tangential and radial airflow while being transported. However, there is a significant difference in the effect of airflow in each direction in different flow fields. In the conveying pipe, axial conveying is the primary method where the particles are lifted and conveyed by the axial air flow. The tangential and radial air flows have a lesser role in this process. The flow field becomes a cyclonic transport after entering the separation cylinder, and the effect of tangential airflow on particle motion is obviously strengthened, while the effect of radial airflow is relatively weak [17,18,19,20,21].

The axial conveying system only needs to consider the effect of axial airflow on peanut pods, so the axial flow field can be simplified to a two-dimensional flow field. The force on the peanut pods in the horizontal axial flow field is shown in Figure 6, where ${\mathit{v}}_a$ is the airflow velocity, ${\mathit{v}}_p$ is the velocity of the peanut pods, and ${\mathit{\omega }}_p$ is the angular velocity of the peanut pods.

Peanut pods are transported by a combination of forces, including their own gravity, the trailing force generated by the relative velocity difference between the gas and solid phases, the Saffman lift generated by the particle gradient, and the Magnus lift generated by the particle spin. According to Newton’s second law,

$$\left\{\begin{array}{c}{m}_p\frac{{\partial \mathit{v}}_p}{\partial t}={\mathit{F}}_D+{\mathit{F}}_S+{\mathit{F}}_M+m_{p}g\\ I_p\frac{{\partial \mathit{\omega }}_p}{\partial t}={\mathit{M}}_p^t+{\mathit{M}}_p^r\end{array}\right.,$$

(11)

where $m_p$ is the mass of the peanut pods, kg; $I_p$ is the rotational moment of inertia of the peanut pods, kg/m²; ${\mathit{M}}_p^t$ is the shear torque, N·m; ${\mathit{M}}_p^r$ is the rolling resisting torque, N·m; ${\mathit{F}}_D$ is the trailing force, N; ${\mathit{F}}_S$ is the Saffman lift force, N; and ${\mathit{F}}_M$ is the Magnus lift force, N.

The cyclonic conveying system needs to consider both axial airflow and tangential airflow on peanut pods, and the radial airflow effect can be neglected, so the cyclonic flow field should be investigated as a three-dimensional flow field. The force on peanut pods in the horizontal rotating flow field is shown in Figure 7. The peanut pods are only subjected to the trailing force in the axial direction, while they are subjected to their own gravity, trailing force and centrifugal force in the tangential direction, and the spinning force is negligible.

According to Newton’s second law, peanut pods in the axial direction are as follows:

$${\mathit{F}}_{Dp}=m_p\frac{{d\mathit{u}}_p}{dt},$$

(12)

where ${\mathit{u}}_p$ is the axial velocity of the peanut pods, and m/s; ${\mathit{F}}_{Dp}$ is the axial trailing force on the peanut pods, N.

Similarly, peanut pods in the tangential direction are as follows:

$$m_p\mathit{g}+{\mathit{F}}_{Dt}+{\mathit{F}}_p=m_p\frac{{d\mathit{w}}_p}{dt},$$

(13)

where ${\mathit{F}}_{Dt}$ is the tangential trailing force on the peanut pods, N; ${\mathit{F}}_p$ is the centrifugal force on the peanut pods, N; and ${\mathit{w}}_p$ is the tangential velocity of the peanut pods, m/s.

2.4. Parameter Optimization of the Negative-Pressure Peanut Fruit-Soil Separating Device

2.4.1. Test Material

The negative-pressure peanut fruit-soil separating device was successfully developed on the basis of previous parameter analyses. The device was tested using the peanut variety “Wanhua 17”, which is common in the hilly mountainous regions of China, and side-by-side clay-heavy clods of peanut combine harvester cleaned and fed into the fruit collection box. The moisture content of the peanut pods and the clay-heavy clods were measured to be 24.7% and 20.4%, respectively, using the drying method. The density of the clay-heavy clods was measured to be 1524 kg/m³ using the drainage method. The triaxial dimensions (length, width and height) of 50 peanut pods were measured using digital vernier calipers (TESA-CAL IP67, manufactured by TESA, Norderstedt, Germany, with an accuracy of 0.01 mm). The mass of 50 clayey soil blocks was measured using an electronic balance (Practum 612-1CN, manufactured by Sartorius Steinbeck, Hamburg, Germany, with a maximum range of 610 g). The mean and standard deviation of the triaxial dimensions of the peanut pods were calculated using IBM SPSS Statistics 26 software (SPSS, Chicago, IL, USA) as 33.23 ± 0.34 mm, 16.27 ± 0.19 mm, and 16.95 ± 0.26 mm, and for the mass of the clayey clods as 7.71 ± 0.50 g.

Measurement of air flow velocity at the variable diameter suction port was performed using an intelligent pressure anemometer (DP-2000, pressure range: 0~±2000 Pa, wind speed range < 500 m/s, air volume range < 99,999 m³/s, Manufactured by Kunshan Puritan Environmental Technology Co., Kunshan, China). The mass of peanut pods and soil clods after separation was measured using an electronic counting table scale (JSC-AHC-30plus, manufactured by Taiheng Precision Measurement (Kunshan) Control Co., Kunshan, China).

2.4.2. Parameter Optimization Test

The main factors affecting the separation effect of fruit and soil were obtained through theoretical analyses and pre-tests, including wind speed, height of the suction nozzle from the screen, size of the suction port, and feeding amount, and the level range of each factor was determined. In order to further analyze the working performance of the negative-pressure peanut fruit-soil separating device and explore the best working parameters, parameter optimization tests were conducted. The test factors include the wind speed of the blower, the height of the suction nozzle from the screen surface, the length of the suction port (shown in Figure 8a) and the feeding rate. A four-factor, three-level Box–Behnken regression design test was conducted using the impurity rate and loss rate of peanut pods as evaluation indicators. The coding of the test factors is shown in

Table 3. Coding table for test factors.

Factor	Code	Level
		−1	0	1
the wind speed of the blower/m·s−1	X1	13.54	17.72	19.42
the height of the suction nozzle from the screen surface/mm	X2	25	35	45
the length of the suction port/mm	X3	55	65	75
the feeding rate/kg·h−1	X4	537.12	671.40	789.88

.

During the parameter optimization test, the wind speed of the high-pressure blower was varied by adjusting the frequency converter and the distance between the suction port. The screen surface was varied by adjusting the retractable connecting piping, and the feeding speed was varied by adjusting the height of the feeding speed adjusting plate. The different lengths of the variable diameter suction ports are shown in Figure 8b,c.

The test data were processed and analyzed using the statistical analysis software Design-Expert 13 (Stat-Ease, Inc., Minneapolis, MN, USA). The regression model between the test factors and the evaluation indexes was optimized and validated to comprehensively assess the uniformity and stability of the operation of the negative-pressure peanut fruit-soil separation device. Based on the preliminary analysis of the material movement mechanism during each step of fruit-soil separation, the single-factor test, the pre-test, the requirements of actual production and operation, as well as the effective controllable range of the factors, each group of tests was repeated three times while keeping other parameters constant. The average value of the results was calculated.

The formulae for the rate of impurity content and the rate of peanut pods loss are as follows:

$$Y_1=\frac{M_1}{M_1+M_2}\times 100\%,$$

(14)

$$Y_2=\frac{M_3}{M_3+M_4}\times 100\%,$$

(15)

where $Y_1$ is the rate of impurity content, %; $M_1$ is the mass of clods in the fruit collection bag after completing the separation, kg; and $M_2$ is the mass of peanut pods. $Y_2$ is the rate of peanut pods loss, %; $M_3$ is the mass of peanut pods in the material collected at the discharge port of the vibrating screen after completing the separation, kg; and $M_4$ is the mass of clods, kg.

3. Results

Based on the test program and response values, Design-Expert 13 was applied to fit the regression to the data to establish a quadratic polynomial regression model of the impurity rate $Y_1$ and the peanut pod loss rate $Y_2$ on blower wind speed $X_1$, suction nozzle height from the screen surface $X_2$, suction nozzle length $X_3$, and feeding speed $X_4$ as shown in the following equation:

$$\left\{\begin{array}{c}\begin{array}{c}\begin{array}{c}{Y}_1=1.16+3.22X_1-3.63X_2-0.65X_3+0.74X_4-9.25X_1{X}_2-1.25X_1{X}_3-2.09X_1{X}_4\\ +2.89X_2{X}_3-0.05X_2{X}_4-0.36X_3{X}_4+4.14X_1^2+5.65X_2^2+0.96X_3^2+1.24X_4^2\end{array}\end{array}\\ \begin{array}{c}{Y}_2=0.73-1.62X_1+4.52X_2+0.61X_3-0.88X_4-2.51X_1{X}_2-0.78X_1{X}_3+0.84X_1{X}_4\\ +0.87X_2{X}_3-1.49X_2{X}_4-0.11X_3{X}_4+0.67X_1^2+4.07X_2^2+0.27X_3^2+0.1X_4^2\end{array}\end{array}\right.,$$

(16)

The results of the significance test of the regression equation are shown in

Table 4. Analysis of variance table.

Source		Sum of Squares	Degree of Freedom	Mean Square	F-Value	p-Value	Significance
$Y_1$	Model	967.86	14	69.13	22.93	<0.0001	**
	$X_1$	124.61	1	124.61	41.33	<0.0001	**
	$X_2$	158.41	1	158.41	52.54	<0.0001	**
	$X_3$	5.11	1	5.11	1.69	0.214	#
	$X_4$	6.54	1	6.54	2.17	0.1629	#
	$X_1{X}_2$	342.44	1	342.44	113.56	<0.0001	**
	$X_1{X}_3$	6.25	1	6.25	2.07	0.1719	#
	$X_1{X}_4$	17.47	1	17.47	5.79	0.0304	*
	$X_2{X}_3$	33.35	1	33.35	11.06	0.005	*
	$X_2{X}_4$	0.01	1	0.01	0.0033	0.9549	#
	$X_3{X}_4$	0.5041	1	0.5041	0.1672	0.6888	#
	$X_1^2$	110.94	1	110.94	36.79	<0.0001	**
	$X_2^2$	207.02	1	207.02	68.65	<0.0001	**
	$X_3^2$	5.92	1	5.92	1.96	0.1828	#
	$X_4^2$	10	1	10	3.32	0.09	#
	Lack of Fit	38.8	10	3.88	4.54	0.0788	#
	Model	443.98	14	31.71	63.21	<0.0001	**
$Y_2$	$X_1$	31.49	1	31.49	62.77	<0.0001	**
	$X_2$	244.89	1	244.89	488.12	<0.0001	**
	$X_3$	4.44	1	4.44	8.85	0.01	*
	$X_4$	9.31	1	9.31	18.56	0.0007	**
	$X_1{X}_2$	25.15	1	25.15	50.13	<0.0001	**
	$X_1{X}_3$	2.4	1	2.4	4.79	0.0461	*
	$X_1{X}_4$	2.81	1	2.81	5.59	0.033	*
	$X_2{X}_3$	3.05	1	3.05	6.07	0.0273	*
	$X_2{X}_4$	8.85	1	8.85	17.64	0.0009	**
	$X_3{X}_4$	0.0462	1	0.0462	0.0921	0.7659	#
	$X_1^2$	2.94	1	2.94	5.87	0.0296	*
	$X_2^2$	107.45	1	107.45	214.16	<0.0001	**
	$X_3^2$	0.4773	1	0.4773	0.9513	0.346	#
	$X_4^2$	0.0681	1	0.0681	0.1358	0.718	#
	Lack of Fit	6.48	10	0.6479	4.75	0.0733	#

Note: ** represents highly significant (p < 0.01); * represents significant (p < 0.05); # represents not significant (p > 0.05).

.

From the data in Table 4, it can be seen that the regression model is highly significant while the lack-of-fit term is not significant, which indicates that the model established is accurate and effective. Based on the F-value obtained from the variance analysis, the primary and secondary factors that affect the impurity rate are $X_1{X}_2$ > ${ X}_2^2$ > $X_2$ > $X_1$ > $X_1^2$ > $X_2{X}_3$ > $X_1{X}_4$ > $X_4^2$ > $X_4$ > $X_1{X}_3$ > $X_3^2$ > $X_3$ > $X_3{X}_4$ > $X_2{X}_4$. Similarly, for the impact on the rate of peanut pod loss, the primary and secondary factors are $X_2$ > $X_2^2$ > $X_1$ > $X_1{X}_2$ > $X_4$ > $X_2{X}_4$ > $X_3$ > $X_2{X}_3$ > $X_1^2$ > $X_1{X}_4$ > $X_1{X}_3$ > $X_3^2$ > $X_4^2$ > $X_3{X}_4$. In order to demonstrate more intuitively the effects of the test factors and their interactions on the evaluation indicators, response surface plots were drawn, as shown in Figure 9.

From the variance analysis data, it can be seen that the p-value of the interaction of blower wind speed and suction nozzle height from the screen surface affecting the impurity rate is less than 0.01, which reaches to be highly significant. When the blower wind speed and the suction nozzle height from the screen surface interact with each other, the impurity rate increases gradually with the increase in the blower wind speed, decreases first and then increases with the increase in the suction nozzle height from the screen surface, and the latter increases faster than the former, as shown in Figure 9a. The effect of the interaction of blower wind speed and feeding speed on the impurity rate is significant. When the blower wind speed and feeding speed interact with each other, the impurity rate decreases firstly and then increases with the increase in wind speed, and increases gradually with the increase in feeding speed, and the growth rate of the two is close to each other, as shown in Figure 9b. The effect of the interaction of the suction nozzle height from the screen surface and suction port length on the impurity rate is also significant. When the suction nozzle height from the screen surface and the suction port length interacts, the impurity rate with the increase in the suction nozzle height shows a trend of decreasing and then increasing, and the increase in the suction port length increases gradually as shown in Figure 9c.

The impact of the interaction between the blower wind speed and suction nozzle height, the interaction between the blower wind speed and suction port length, the interaction between the blower wind speed and feed rate, the interaction between the suction nozzle height and suction nozzle length, and the interaction between the suction nozzle height and feed rate on the rate of loss of peanut pods are all significant. With the interaction of blower wind speed and suction nozzle height, the peanut pod loss rate increases with the increase in the blower wind speed, and with the increase in suction nozzle height. It first stabilizes and then climbs rapidly, as shown in Figure 9d. When the blower wind speed and suction port length interacted, the peanut pod loss rate showed a trend of decreasing and then increasing with the increase in the blower wind speed, and a trend of increasing with the increase in suction port length, as shown in Figure 9e. When blower wind speed and feed rate interact, peanut pod loss rate decreases gradually with increasing blower wind speed and increases gradually with increasing feed rate, as shown in Figure 9f. When the suction nozzle height and the suction port length interact with each other, the peanut pod loss rate decreases and then increases with the increase in suction nozzle height and decreases with the increase in suction port length, and the decrease is slow, as shown in Figure 9g. When the suction nozzle height and the feeding speed interact, the peanut pod loss rate decreases slowly with the increase in the suction nozzle height at first, and then rises rapidly, and increases slowly with the increase in the feeding speed, as shown in Figure 9h.

In order to find the optimal combination of parameters for each test factor and ensure that the optimized design conditions fall within a reasonable range of design parameters, this study employed an optimization scheme that aims to minimize the impurity rate and peanut pod loss rate. Equation (17) shows the objective function as well as the constraint ranges of the operating parameters.

$$\left\{\begin{array}{c}min{Y}_1\left(X_1,X_2{,X}_3,X_4\right)\\ min{Y}_2\left(X_1,X_2{,X}_3,X_4\right)\\ s.t.\left\{\begin{array}{c}13.51 {\mathrm{m}·\mathrm{s}}^{-1}<X_1<19.15{ \mathrm{m}·\mathrm{s}}^{-1}\\ 25 \mathrm{mm}<X_2<45 \mathrm{mm}\\ 55 \mathrm{mm}<X_3<75 \mathrm{mm}\\ 537 {\mathrm{k}\mathrm{g}·\mathrm{h}}^{-1}<X_4<790{ \mathrm{k}\mathrm{g}·\mathrm{h}}^{-1}\end{array}\right.\end{array}\right.$$

(17)

The results after parameter optimization were as follows: the blower wind speed was 13.582 m/s (rounded to 13.58 m/s), the height of the suction nozzle from the screen surface was 27.432 mm (rounded to 27 mm), the length of the suction port was 63.662 mm (rounded to 64 mm), and the feeding speed was 601.706 kg/h (rounded to 600 kg/h). Under these conditions, it was obtained that the impurity rate was 0.24%, and the loss rate of peanut pods was 0.22% after applying the device for fruit-soil separation.

In order to verify the actual debris removal effect of the negative-pressure peanut fruit-soil separating device under the optimal parameter combination, a bench test was conducted under the same operating parameters and the data were statistically analyzed according to the theoretical values after parameter optimization. The results of the bench-top validation test show that when the wind speed of the blower is 13.58 m/s, the height of the suction nozzle from the screen surface is 27 mm, the length of the suction port is 64 mm, and the feeding speed is 600 kg/h. The impurity rate is 0.16% and the loss rate of the peanut pod is 0.2%, with a relatively small error and the actual effect of the fruit-soil separation is even better than the theoretical value.

4. Discussion

In this study, when the blower wind speed is in the range of 13~15 m/s, the impurity rate is stable below 5%, and when the blower wind speed reaches 19 m/s, the impurity rate climbs rapidly to about 15%. This is because when the wind speed of the blower is between 13~15 m/s, it is exactly at the suspension velocity of peanut pod and side-by-side clod. It is also the ideal wind speed for separating fruits from the soil. However, the current motor power is only operating at approximately 60% of its rated power. Further research will concentrate on reducing power loss and external dimensions of the fruit-soil separating device. This will maximize cost savings while ensuring the effectiveness of peanut fruit-soil separation. The aim is to better adapt to the complex landscapes of hilly and mountainous areas. Additionally, exploring the feasibility of integrating the device into a combine harvester is also an area of interest. Furthermore, the effect of different sizes of fruit-soil separation devices on the impurity rate and peanut pod loss rate can be investigated and analyzed by means of a coupled CFD-DEM approach, and the optimal structural parameters can be explored. The results were then processed and quantitatively analyzed to understand the trajectory and forces applied to the peanut pods throughout the separation process.

The external dimensions of peanut pods vary considerably from one variety to another. This study exclusively utilized “Wanhua 17” peanuts for testing. The majority of peanuts of this variety are either single- kernel or double- kernel, displaying a relatively regular shape and size. As a result, the difference in suspension velocity with the side-by-side clods is more pronounced, leading to a more satisfactory fruit-soil separation effect. However, there are many other peanut varieties in the hilly and mountainous regions of China, and they vary significantly in shape and size, which will limit the generalizability of the test conclusions of this study. Therefore, future research could investigate the impact of various peanut varieties on the efficacy of fruit-soil separation. The specific method is to model peanut pods of different form dimensions by means of the discrete element software EDEM 2021.2, and to optimize the structure and operating parameters of the negative-pressure fruit-soil separating device by means of the CFD-DEM coupling method, in order to improve the fruit-soil separating effect as well as the general applicability of the device. In addition, it is necessary to consider the effect of the fruits of different sub-soil crops on the suitability and stability of fruit-soil separation devices. For example, crops such as sweet potatoes, potatoes and carrots have very different fruit sizes, shapes and densities compared to peanut pods. Further evaluation is necessary to determine the suitability of current fruit-soil separating devices for fruit-soil separation conditions in these crops [22,23,24]. The evaluation includes whether there is a need to adjust the structure and operating parameters of the fruit-soil separating device and, if so, how to adjust them to suit the characteristics of different sub-soil crop fruits.

The current device for separating peanut fruit from soil consists of two parts: a linear vibrating screen and pneumatic conveying equipment. These two parts are connected by a variable diameter suction port from square to round. The conclusion of the parameter optimization concluded that the best fruit-soil separation was achieved when the height of the suction nozzle from the screen surface was 27 mm, but in the validation tests the author found that this height had limitations. Due to the potential height of a peanut pod reaching up to 20 mm, the height difference between the suction nozzle and the screen surface, minus the height of the peanut pod and the amplitude of the vibrating screen, is significantly constrained. However, this limited height may be advantageous for the fruit-soil separation process. During field operations, the vibrating screen produces vibrations that can potentially cause congestion of the material at the inlet due to the combined effect of additional vibrations and the negative pressure wind field. This congestion ultimately results in a decrease in the efficiency of fruit and soil separation. Therefore, it is necessary to study the force and movement of peanut pods and side-by-side clods at the inlet when the vibrating screen is additionally vibrating, so as to provide a reference for improving the structure of the peanut fruit-soil separating device and reducing the vibration of the machine.

5. Conclusions

• Based on the difference in suspension speeds of peanuts and clay-heavy clods and the principle of negative pressure, a fruit-soil separating device for peanuts grown on clay-heavy soils in hilly and mountainous areas after combined harvesting has been developed. The device solves the problem of difficult separation of peanut pods and side-by-side soil during combined harvesting, and provides a technical reference for mechanization of peanut production in hilly mountainous areas;
• The Box–Behnken regression design test was conducted to investigate the effects of factors and interactions on the test indexes and the optimal operating parameters of the negative-pressure peanut fruit-soil separating device. The results showed that the best fruit-soil separation effect was achieved when the wind speed of the blower was 13.58 m/s, the height of the suction nozzle from the screen surface was 27 mm, the length of the suction port was 64 mm, and the feeding rate was 600 kg/h. Validation tests demonstrated that the impurity rate of 0.16% and the peanut pod loss rate of 0.2% exceeded the industry standard;
• Due to the device consisting of two components, namely the linear vibrating screen and the pneumatic conveying equipment, considerable efforts were made to ensure that the device operates under optimal conditions during field validation tests and parameter adjustments. This task proved to be both time-consuming and labor-intensive. Consequently, the movement and adjustment of the entire machine emerged as a crucial matter that required thorough exploration and resolution. Future research could focus on enhancing the completeness and convenience of the peanut fruit-soil separating device by making structural and functional improvements. Additionally, efforts could be made to enhance the device’s adaptability in hilly and mountainous areas while ensuring the effectiveness of fruit-soil separation.