Optimal Design and Tests of a Pulsating Roll-Cleaning Device for Tiger Nuts

Abstract

Aiming at the problems of low efficiency and poor cleaning quality in the cleaning process of harvested tiger nuts (Cyperus esculentus) with lots of soil and fibrous roots on the surface to meet the demand for mechanized harvesting of tiger nuts in the Yellow River, Huaihe River, and Haihe River regions in China, a pulsating roll-cleaning device was devised. The analytical software for meshing the transmission of pitch curves of elliptical gears with arbitrary orders was developed based on Visual Basic 6.0, thus obtaining a pair of elliptical gears that meet the steady transmission requirement. The meshing of this pair of elliptical gears enables pulsating variable-speed rotation of a brush roller, which reduces the breakage and accumulation of tiger nuts. Circular screen holes are distributed uniformly on the upper and lower cylindrical walls. Tiger nuts are cleaned under friction with the brush roller and the circular screen holes, while residues (including soil) fall in the settlement and accumulation tank through the screen holes, which realizes the rapid discharge and collection of residues, including soil, and reduction of dust. The separation process of soil from tiger nuts in the cleaning device was studied using RecurDyn 2023-EDEM 2022 simulation software. Taking the rate of rotation of the brush roller, order of elliptical gears, and eccentricity of the elliptical gears as the test factors while taking the cleaning efficiency, breakage rate, and impurity rate as the evaluation indices, a test bench for the cleaning performance of tiger nuts was established. Design-Expert V8.0.6 was applied to carry out a three-factor three-level Box–Behnken design (BBD) using response surface methodology (RSM), thus ascertaining the optimal parameter combination of the cleaning device. When the rate of rotation of the brush roller, order of elliptical gears, and eccentricity of the elliptical gears are, separately, 280 rpm, 2, and 0.122, the cleaning efficiency, breakage rate, and impurity rate of tiger nuts are 1.83 t·h⁻¹, 0.15%, and 0.16%, respectively. This satisfies the cleaning requirement of tiger nuts and provides a basis for the design of cleaning machines for tiger nuts.

1. Introduction

Agricultural production underpins the national economy and social development. Edible oil, as a necessity to daily living, is an important component of agricultural production [1]. In recent years, the demand for edible oil in China has increased year by year with the economy development. In the context of economic globalization, various countries have all enlarged their import and export trades of edible oil. The demand for edible oil in China, as a large importer of edible oil, has always exceeded supply due to the influence of factors including farmland, climate, and technology [2]. Therefore, China has no advantage over other countries in terms of the import and export trades of edible oil, giving rise to an urgent need to improve the import and export trades of edible oil in the country. Tiger nuts, as a new oil-bearing crop, do not compete with other oil-bearing crops such as soybeans, peanuts, and maize for cultivation land and are characterized by a high oil content and rich abundance of nutrients therein. Therefore, promoting the cultivation of tiger nuts is key to relieving the shortage of stock of vegetable oil in China [3,4,5,6,7].

Tiger nuts can be easily planted and managed and deliver high-volume oil production. Nevertheless, harvested tiger nuts are mixed with multiple impurities, including grass, gravel, and other soil. Although some cleaning and screening machines are available for removing grass and gravel, soil adhering to tiger nut surfaces must be manually removed (rather than by vibrating screen), owing to its strong bond with the tiger nut skin. This significantly decreases the production efficiency and economic benefit of the harvest.

There is little research into the impurity removal machinery of tiger nuts in foreign countries; the cleaning machinery used in the processing of tiger nuts commonly used in other countries is a type of soil removal device reliant on water washing [8,9]. After the removal of simple impurities, the harvested tiger nuts are delivered to a water washer, in which shells and bad tiger nuts floating in the water can be removed while tiger nuts coated with soil are cleaned by water flows [10]; because such a cleaning method consumes a huge amount of water and needs a perfect sewage disposal system, it is unsuitable for small- and medium-sized farmers [11]. Chinese scholars have also studied tiger nuts: Qi Jiangtao et al. [12] designed mechanical harvesting and conveying devices for tiger nuts and explored the vibration and soil removal rate in the conveying process through use of the extended distinct element method (EDEM). By doing so, they attained a group of optimal structural parameters, which screen out some soil while ensuring the conveying efficiency of tiger nuts. Zhao et al. [13] developed a harvesting and impurity removal system of tiger nuts that separates and removes different impurities mixed with tiger nuts through multi-stage screening. The tiger nut harvesting and screening mechanism devised by Zhang et al. [14] firstly threshed and then separated tiger nuts and was composed of a threshing system and a screening system. The angle of inclination of the screens and vibration amplitude on the screening efficiency were revealed by simulating the screen motion using ADAMS, which influences the rate of rotation of the crank. Finally, a group of optimal operation parameters of the screening mechanism were determined. The tiger nut harvester designed by Liu et al. [15] integrated functions including threshing, separation, and cleaning to good effect. In summary, the common washing cleaning method abroad has problems such as not being conducive to subsequent storage and easily causing tiger nuts to become moldy, while the dry cleaning method, which is less reported at present, has problems such as the uneven surface of tiger nuts and the bond between soil and nut surfaces, which makes it difficult to easily remove soil on its surface or the high breakage rate of nuts. Therefore, the optimization design of a tiger nuts dry cleaning machine needs to be carried out urgently.

The goal of the work is to design a pulsating roll-cleaning device aims to ensure efficient cleaning, reduce the breakage rate, improve the quality of harvested tiger nuts, and investigate the effect of the main parameters on the separation process of soil from tiger nuts in the cleaning device. Using RecurDyn 2023-EDEM 2022 coupling simulations and physical experiments, achieving the objectives to investigate the effect of the main parameters, such as the rate of rotation of the brush roller, order of the elliptical gears, and eccentricity of the elliptical gears, on the operational quality of the cleaning device; to evaluate the operational quality by introducing the cleaning efficiency, breakage rate, and impurity rate of tiger nuts; to determine a group of optimized parameters for the design of the cleaning device, the research findings in this work can provide a favorable material basis for the subsequent drying and other processes.

2. Overall Design and Working Principle of the Pulsating Roll-Cleaning Device

2.1. Overall Structure

To avoid damage to tiger nut tubers while removing soil adhering to tiger nut surfaces and meet the design requirement for the dry state of tiger nuts, a pulsating roll-cleaning device of tiger nuts was composed of a cleaning chamber, a discharge tube, a rack, an adjustable counterweight, an impurity removal blower, a settlement and collection tank, and a variable-speed transmission system. The overall structure is shown in Figure 1, and key technical parameters are shown in

Table 1. Key technical parameters of the cleaning device.

Key Technical Parameter	Value	Unit
Length	3000	mm
Width	600	mm
Height	1970	mm
Diameter of brush roller	320	mm
Motor power	7.5	kW
Power of impurity removal blower	1.5	kW

. Therein, the cleaning chamber consisted of a spindle, an upper cylinder, a lower cylinder, circular screen holes, a brush roller, and a feeding hopper. The variable-speed transmission system was composed of a YE3-160M-6 motor (made in Lu’an Yisheng Motor Co., Ltd, Lu’an, China), a pulley drive unit, and elliptical gears. The spindle was fixed with the brush roller.

2.2. Working Principle

When the pulsating roll-cleaning device of tiger nuts works, the motor drives a pair of elliptical gears to realize the pulsating variable-speed rotation of the brush roller. Then, tiger nuts enter the cleaning chamber from the feed inlet after adjusting the feed quantity with a push–pull baffle. Soil on the tiger nut surface is removed by friction with the brush roller and the circular screen holes during migration of tiger nuts because of the rotation of the brush roller. Subsequently, removed impurities, including soil and rootstocks, fall into the settlement and collection tank under action of the impurity removal blower. Therein, heavy impurities are discharged from the lower impurity outlet under action of the adjustable counterweight, while their lighter counterparts are expelled by the blower and collected. Being pushed by the brush roller, tiger nuts migrate to, and are discharged from, the discharge hole. In this way, clean tiger nuts are obtained.

3. Design of Key Structures

3.1. Design of the Variable-Speed Transmission System

In existing cleaning devices, lots of tiger nuts are damaged during the high-speed and constant-speed rotation of brush rollers directly driven by a belt drive unit used in the drive system. To solve the problem, the active elliptical gear is driven by a belt drive, and the active elliptical gear is meshed with the driven elliptical gear. The driven elliptical gear rotates coaxially with the brush rollers, so as to realize the pulsating variable-speed rotation of the brush rollers.

To ensure the stability of high-speed transmission, the gear transmission was analyzed by taking the meshing of first-order and second-order elliptical gears as an example, so as to determine the basic parameters of the gears [16,17]. In the equations below, n = 2 and m = 1.

The schematic diagram for the transmission of the second-order and first-order elliptical gears is displayed in Figure 2. The center of gyration of the first-order elliptical gear is located at one focus, while that of the high-order elliptical gear is located at the center of gravity of the pitch curve. Based on the equations below, the polar equation of the parameters of the high-order elliptical gear was deduced according to the basic parameters of the first-order elliptical gear, namely, the semi-major axis a₁ and the eccentricity e₁:

$$R_2\left({\Phi }_2\right)={\displaystyle \frac{a_2(1-e_2^2)}{1+e_2\cos nm{\Phi }_2}}$$

(1)

$$R_1\left({\Phi }_1\right)=A-R_2\left({\Phi }_2\right)$$

(2)

$$A=a_1\left[1+\sqrt{1+\left(n^2-1\right)\left(1-e_1^2\right)}\right]$$

(3)

$$a_2=a_1\sqrt{1+(n^2-1)(1-e_1^2)}$$

(4)

$$e_2={\displaystyle \frac{e_1}{\sqrt{1+(n^2-1)(1-e_1^2)}}}$$

(5)

where e₁ and e₂ are, separately, eccentricities of the first-order and high-order elliptical gears; n is the average gear ratio; A is the center-to-center spacing; a₁ and a₂ are semi-major axes of the first-order and high-order elliptical gears (mm), respectively; m is the deformation coefficient.

When the first-order elliptical gear rotates by an angle Φ₁, the following high-order elliptical gear rotates by Φ₂. The arch lengths of the pitch curves of the two gears are identical, so the MN arc length is relative to the MP arc length, then

$$i_{21}\left({\Phi }_2\right)={\displaystyle \frac{R_1}{R_2}}={\displaystyle \frac{A-R_2}{R_2}}$$

(6)

$$1+i_{21}+i_{21}^{″}\ge 0$$

(7)

To ensure the steady transmission of the cleaning device, the pitch curve of the high-order elliptical gear should not be concave, so it needs to calculate the maximum eccentricity e₁ to provide reference for the parametric design of the high-order elliptical gear.

$$e_{1\mathrm{KP}}={\displaystyle \frac{1}{\sqrt{n^2{m}^4-2m^2+1}}}$$

(8)

$$e_1\le e_{1\mathrm{KP}}$$

(9)

where e_1KP is the maximum eccentricity that avoids the high-order elliptical gear having a concave pitch curve.

According to Equations (8) and (9), when the average gear ratio is 2 and the deformation coefficient is 1, the eccentricity of the first-order elliptical gear is shown as follows. Similarly, the eccentricities corresponding to different m and n can be deduced, which ensures the reasonability of the parametric design of key structures of the high-order elliptical gear.

On the basis of analyzing the above elliptical gear transmission theory, the analysis software for the meshing transmission of the pitch curves of the elliptical gears with arbitrary orders was developed (Computer Software Copyright Registration Number: 2024SR0352583). The initial interface of the software is shown in Figure 3.

The work interface of the software includes seven parts, namely, ① menu bar, ② animation display area, ③ functional control area, ④ parameter adjustment area, ⑤ area to display changes in instantaneous gear ratio curves, ⑥ important data display area, and ⑦ area to display the progress toward the optimization goal, as shown in Figure 4.

• Buttons on the “menu bar” can be used to invoke and save data and to calculate the gear ratio of the two gears, which is displayed in the “area to display changes in the instantaneous gear ratio curves”.
• The “animation display area” intuitively shows pitch curves of the designed elliptical gears. The diagrams also change in real time when adjusting the parameters of the elliptical gears, thus fully exhibiting the human–computer interaction function.
• The “function control area” can control the start and pause of gear meshing and also achieve adjustment of the movement steps.
• The “parameter adjustment area” can adjust the parameters, including the length of the semi-major axis, length of the semi-minor axis, number of teeth, gear ratio, and deformation coefficient of the elliptical gears. Through adjusting these parameters, elliptical gears with different orders, gear ratios, and eccentricities can be obtained (Figure 5).
• The “area to display changes in the instantaneous gear ratio curves” can, in real time, show changes to the gear ratio, lending convenience to the computational process.
• The “important data display area” can accurately display key parameters, including the gear ratio, number of teeth, module, and center-to-center spacing directly as digits, which facilitates a comparative analysis.
• The “area to display the progress of the optimization goal” can intuitively exhibit whether the designed elliptical gears meet the design requirement or not. The parameters are regarded as satisfying the design requirement when all progress bars are red. As long as one progress bar is black, the parameters do not meet the design requirements and should be adjusted until they do.

SOLIDWORKS 2021 was adopted to establish 3D models of the elliptical gears, as shown in Figure 6.

3.2. Design of Circular Screen Holes

The cleaning chamber is composed of two semicircular cylinders to facilitate disassembly. Circular screen holes (6-mm diameters) are uniformly distributed on the cylindrical walls, which increase the number of collisions between tiger nuts and cylindrical walls and facilitate the discharge of soil. The structure is illustrated in Figure 7.

To ensure that the brush can push tiger nuts stuck onto the cylindrical wall, the clearance between the brush roller and drum screen was designed to be 5 mm, according to the typical dimensions of tiger nuts and the deflection variation of the brush roller shaft. Additionally, a sealed structure was formed by the perforated part of the drum screen and the settlement and collection tank to avoid environmental pollution due to excessive dust emission.

3.3. Design of the Settlement and Collection Tank

In order to improve the cleaning efficiency and reduce the impurity rate of tiger nuts, a settlement and collection tank was designed according to the falling characteristics of the particles, as displayed in Figure 8. The settlement and collection tank envelopes part of the circular screen holes to ensure that the whole device is in an intermittent, sealed state. Airflow can be formed under action of the impurity removal blower, so that particles including dust and fibrous roots fall rapidly and are then collected. Therein, heavy impurities are expelled via the impurity outlet under the action of the adjustable counterweight, while light detritus is discharged by the blower and collected. The dust pollution can be alleviated while efficiently discharging impurities in the settlement and collection process.

To guarantee the overall tightness and compact arrangement of the machinery, the length L_C is set to 2.24 m while the width can be calculated according to the principle of the constant air volume using the following formula [18]:

$$B_{\min }={\displaystyle \frac{Q_{\mathrm{F}}\eta }{L_1{\nu }_{\mathrm{F}}}}$$

(10)

where B_min is the minimum width of the settlement and collection tank (m); Q_F is the airflow (2.87 m³·s⁻¹); $\eta$ is the sealing efficiency factor of the dedusting system, which is set to 0.93; L_C denotes the length of the settlement and collection tank (m); v_F is the falling speed of particles with a diameter of 1 mm (m·s⁻¹), which is taken as 5.47.

In this way, the minimum width is calculated to be 0.218 m. To adapt to the size of the cleaning device, B is set to 0.3 m.

According to the critical formula for the falling of particles, the design is such that

$${\displaystyle \frac{B_{\min }}{{\nu }_{\mathrm{H}}}}={\displaystyle \frac{h_{\min }}{{\nu }_{\mathrm{S}}}}$$

(11)

where h_min is the minimum height of the settlement and collection tank (m); v_H is the horizontal component of the airflow velocity (m·s⁻¹); v_S is the vertical component of the airflow velocity (m·s⁻¹).

When designing the settlement and collection tank, it is necessary to ensure that the dust particles take the same time to arrive at either the side edge or the bottom. Generally, the height of the tank should be larger than or equal to the width, so H is 0.62 m.

4. Simulation of the Working Process of the Cleaning Device Based on RecurDyn 2023-EDEM 2022 Coupling

4.1. Establishment of the Distinct Element Model of Tiger Nut Aggregates

To truthfully reproduce the state of the tiger nuts, the 3D dimensions of five groups of 100 tiger nuts were measured by the 111N-101 digital vernier caliper (accuracy of 0.01 mm, made in Foshan Lenghui Quantity Cutting Tools Co., Ltd., Foshan, China) in basic tests; that is, the average length L, width W, and thickness T are 12.46 mm, 11.53 mm, and 10.15 mm, respectively, as shown in Figure 9.

SOLIDWORKS 2021 was used to establish a model representing a typical tiger nut. The distinct element model of tiger nuts was generated using the auto-filling function in EDEM 2022. The soil particles were appropriately enlarged (to have a diameter of 3 mm), while ensuring the binding force between soil and tiger nuts was unchanged. In this way, the distinct element model of the tiger nut–soil aggregate was developed, as displayed in Figure 10.

Soil adheres to harvested tiger nuts [19,20,21,22], so the Hertz–Mindlin (with bonding) model was selected for soil particles and tiger nuts to simulate the adhesion between them. The Hertz–Mindlin (no-slip) model was selected for the relationship between soil particles and tiger nuts. It is the most commonly used model and can simulate the elastic contact between particles [23,24,25,26,27].

The contact radius needs to be set when setting the particle parameters in EDEM 2022. The contact radius is related to the water content of particles and is generally slightly larger than the particle diameter. It is calculated using the following formula:

$$\left\{\begin{array}{l}{Q}_2={\displaystyle \frac{m_4}{m_3+m_4}}={\displaystyle \frac{{\rho }_3{V}_2}{{\rho }_2{V}_1+{\rho }_3{V}_2}}\\ V_1={\displaystyle \frac{4}{3}}\pi {R_3}^3\\ V_2={\displaystyle \frac{4}{3}}\pi {R_4}^3-{\displaystyle \frac{4}{3}}\pi {R_3}^3\end{array}\right.$$

(12)

where Q₂ is the water content of particles (%); m₃ and m₄ are masses of particles and water (kg); V₁ and V₂ are volumes of particles and water (m³); ${\rho }_2$ and ${\rho }_3$ represent the densities of particles and water (kg·m⁻³); R₃ and R₄ are the particle radius and contact radius (mm), respectively.

The establishment of the EDEM 2022 simulation system mainly involves the setting of physical and contact parameters of tiger nut particles, soil particles, and machine parts [28,29,30,31,32,33,34]. Two materials, termed G and MS, are set in the Equipment Material stage to represent steel and brush, respectively. The physical and contact parameters are listed in

Table 2. Setting of the EDEM simulation parameters.

Simulation Parameter	Value
Tiger nut density	1102 kg·m−3
Soil density	1780 kg·m−3
Material density of the brush	1760 kg·m−3
Steel density	7801 kg·m−3
Poisson’s ratio of tiger nuts	0.360
Poisson’s ratio of the soil	0.260
Poisson’s ratio of the brush	0.400
Poisson’s ratio of steel	0.290
Shear modulus of tiger nuts	3.09 × 107 Pa
Shear modulus of the soil	2.77 × 106 Pa
Shear modulus of the brush	1.02 × 108 Pa
Shear modulus of steel	8.02 × 1010 Pa
Coefficient of restitution for collisions between tiger nuts	0.437
Coefficient of rolling friction between tiger nuts	0.268
Static friction coefficient between tiger nuts	0.780
Coefficient of restitution for collisions between soil particles	0.140
Coefficient of rolling friction between soil particles	0.270
Static friction coefficient between soil particles	0.560
Coefficient of restitution for collisions between tiger nuts and soil particles	0.260
Coefficient of rolling friction between tiger nuts and soil particles	0.320
Static friction coefficient between tiger nuts and soil particles	0.500
Coefficient of restitution for collisions between tiger nuts and steel plates	0.624
Coefficient of rolling friction between tiger nuts and steel plates	0.195
Static friction coefficient between tiger nuts and steel plates	0.420
Coefficient of restitution for collisions between tiger nuts and the brush	0.360
Coefficient of rolling friction between tiger nuts and the brush	0.180
Static friction coefficient between tiger nuts and the brush	0.410
Coefficient of restitution for collisions between soil and steel plates	0.150
Coefficient of rolling friction between soil and steel plates	0.360
Static friction coefficient between soil and steel plates	0.500
Coefficient of restitution for collisions between soil and the brush	0.010
Coefficient of rolling friction between soil and the brush	0.120
Static friction coefficient between soil and the brush	0.190

.

A particle factory is created to generate 1500 particles per second (and each particle is composed of six bonds). Particles are generated from the beginning (0 s) to the end of simulations, with no limit to the total number.

To accelerate the simulation speed, key parts, including the feeding hopper, drum screen, brush roller, and elliptical gears, were retained, and (.x_t) files were selected when exporting the model files using SOLIDWORKS 2021. The simplified model was exported to RecurDyn V9R4, in which the motion constraints and contacts were set, as shown in Figure 11.

4.2. Single-Factor Simulation Tests

4.2.1. Test Schemes and Results

According to the aforementioned trials, the rate of rotation of the brush roller, deformation coefficient of the elliptical gears, and eccentricity of the elliptical gears were selected as the test factors to conduct separate single-factor tests.

• Influence of the rate of rotation of the brush roller on the cleaning effect

EDEM 2022 was adopted to simulate the operation of the cleaning device when the brush roller was rotated at 240, 260, 280, 300, and 320 rpm, and the simulation process is shown in Figure 12.

The red part between the tiger nuts and soil particles in the figure is bonds, which may break and fail when forces thereon such as collision, friction, and extrusion exceed a certain limit, allowing simulation of the separation process of soil from tiger nuts. Figure 12 shows that there are many bonds between tiger nuts and soil particles at the feed inlet, and also, a large quantity of soil particles is removed. The front settlement and collection tank holds lots of soil particles; with the movement of tiger nuts towards the discharge hole, the number of bonds reduces, and soil particles are collected in the rear reduce. Basically, no red bonds are observed at the discharge hole, and tiger nuts are found not to be mixed with soil particles. This finding proves that soil particles are effectively removed in the cleaning process and soil particles fall into the settlement and collection tank via circular screen holes, thus accomplishing the separation of soil from tiger nuts.

Changes in the number of bonds with time were plotted using Origin 2022, as illustrated in Figure 13. A total of 9000 bonds are generated per second during simulations, and the cleaning requirement is regarded as being met when the real-time number of bonds less than 6000. The cleaning device is shown to reach the steady state more than 3.5 s, and the number of bonds fluctuates within a certain range. By exporting the data and calculating the means, the average number of bonds after the cleaning device reaches steady-state operation as the optimal rate of rotation is obtained, which can be used to reflect the influence of the rate of rotation on the quality of cleaning.

2.

Influence of the order of elliptical gears on the cleansing effect

The speed of elliptical gears with different orders varies with time in each period, which enables the brush roller to have accelerated and decelerated motions at different frequencies. The tiger nuts in the chamber move to the discharge hole in a tidal manner, which can avoid their excessive wear at a sustained high speed. The four levels selected for the order of elliptical gears include the first, second, third, and fourth orders. The four orders were used to conduct virtual simulation tests driven by different gears, and at the same time, comparative tests driven by circular gears were conducted, as shown in Figure 14.

Figure 14 demonstrates that, as the tiger nuts move to the discharge hole, tiger nuts have more contact between each other, and the force between them also increases. This is because, with the separation of soil from tiger nut surfaces, the number of tiger nuts with direct surface contact increases. Origin 2022 was adopted to plot the change in the number of collisions of tiger nuts with time, as shown in Figure 15.

Through multiple tests, the optimal number of collisions was determined to be between 7000 and 16,000. The larger the number of collisions, the slower the motion of the tiger nuts, where it becomes difficult for soil to fall from the nuts; the lower the number of collisions, the faster the motion of the tiger nuts, at which the excessive contact force resulting from collisions with the drum screen may damage the tiger nut surface and increase the rate of breakage of tiger nuts. Appropriate structural and operation parameters were obtained via statistical analysis of the number of collisions.

3.

Influence of the eccentricity of elliptical gears on the cleansing effect

The eccentricity of elliptical gears affects the gear ratio of elliptical gears during operation, which enables pulsating variable-speed rotation of the brush roller and changes the motion state of, and stress on, the tiger nuts. This delivers a large force to the brush roller in the acceleration process, which makes it easier for soil to fall from the nuts. The five levels selected for the eccentricity of the elliptical gears were 0.075, 0.1, 0.125, 0.15, and 0.175. EDEM 2022 was used to simulate the operation of the brush roller driven by elliptical gears with different eccentricities, as illustrated in Figure 16.

Origin 2022 was used to plot the change in the stress on the tiger nuts with time in the cleansing process (Figure 17). A good cleaning effect was achieved when the force on the tiger nuts is between 80 and 140 N in the cleansing process.

4.2.2. Analysis of the Simulation Test Results

Simulation analysis reveals that the cleaning effect is good—that is, there are a small number of bonds—when the rate of rotation of the brush roller accelerates or changes significantly. With the elevation of the order of the elliptical gears, the stress on the tiger nuts decreases and the number of collisions between tiger nuts increases. The cleansing effect of all brush rollers with added elliptical gears is superior to that without elliptical gears. The numbers of bonds are, separately, 4100 and 3770 when using circular gears and fourth-order elliptical gears, under which, the forces on tiger nuts are 90.2 N and 93.7 N, respectively. Comparison shows that the two do not differ obviously; that is, the fourth-order gears do not improve the quality of cleaning to any significant extent. Figure 18 shows the influences of the order of elliptical gears on the number of collisions, number of bonds, and stress on tiger nuts.

With the acceleration of the rate of rotation of the brush roller, the stress on tiger nuts increases while the number of collisions of tiger nuts decreases. The cleaning quality is improved significantly after the rate of rotation of the brush roller reaches 260 rpm. Figure 19 displays the influences of the rate of rotation of the brush roller on the number of collisions, number of bonds, and stress on tiger nuts.

With the increasing eccentricity of the elliptical gears, the stress on the tiger nuts increases while the number of collisions between tiger nuts is reduced. All output parameters increase abruptly when the eccentricity is 0.175, whereupon the number of collisions, number of bonds, and force on the tiger nuts are, separately, 7560, 2580, and 139.3 N. Despite the small number of bonds and a good cleaning effect in the simulation tests, tiger nuts are subjected to significant stress, which may result in a high rate of breakage of the tiger nuts. In the simulation process, tiger nuts are found to bounce out of the feed inlet in the cleaning process using the brush roller driven by elliptical gears with an eccentricity of 0.175. This is a result of the overly rapid motion of tiger nuts, which causes a loss of some tiger nuts in the cleansing process. Figure 20 shows the influences of the eccentricity of the elliptical gears on the number of collisions, number of bonds, and force on tiger nuts.

In summary, the rate of rotation of the brush roller, order of the elliptical gears, and eccentricity of the elliptical gears all significantly influence the cleaning effect of tiger nuts. Firstly, with the acceleration or enlarged variation of the rate of rotation of the brush roller, the stress on tiger nuts enlarges while the number of bonds and collisions decreases. Secondly, the stress on tiger nuts is large when the rate of rotation of the brush roller is high or the eccentricity of the elliptical gears is large, which increases the rate of breakage of tiger nuts. Thirdly, as the order of the elliptical gears is increased, the stress on the tiger nuts declines, while the number of bonds and collisions both grow. The cleaning effect of the fourth-order elliptical gears is similar to that of circular gears, without large improvement. Through an overall consideration, 260~300 rpm, 1~3, and 0.1~0.15 are selected as the reference ranges of the rate of rotation of the brush roller, order of the elliptical gears, and eccentricity of the elliptical gears in prototype testing.

5. Bench Tests for Performance Optimization

5.1. Test Conditions

Prototype testing was performed in the Agricultural Engineering Training Centre, College of Mechanical & Electrical Engineering, Henan Agricultural University, Zhengzhou City, China.

Spanish round tiger nuts planted in the Jingjiazhuang test site in Guojia Town, Xinzheng City, Henan Province, China, were used, as shown in Figure 21. The tiger nuts were brown and had a length of 12.46 mm, width of 11.53 mm, and thickness of 10.15 mm. The shape index and water content of the tiger nuts were 91% and 34.58% (the harvested tiger nuts need to be dried until the water content reaches 30–40% before the cleaning process can be carried out), respectively.

Based on the optimal ranges of the various parameters determined above, a cleaning test platform was built for tiger nuts, as shown in Figure 22. In the tests, the hoisting and feeding devices were used to transport tiger nuts to the inlet of the feeding hopper to ensure continuous feeding. A frequency converter (22KWG3/30KWP3 made in Shenzhen INDVS Technology Co., Ltd., Shenzhen, China) was used to adjust the motor speed to allow the brush roller to rotate at different speeds. The average rate of rotation of the brush roller was measured using a VC6236P non-contact photoelectric tachometer (made in Dongguan Wenxiang Technology Co., Ltd., Dongguan, China). Various test indices were measured after each test.

5.2. Test Indices

By referring to the Enterprise Standard [35], the cleaning efficiency, breakage rate, and impurity rate of tiger nuts were taken as the evaluation standards evincing the operational quality of the cleaning device. The calculation methods of various evaluation indices are described below.

The cleaning efficiency reflects the operational capability of the cleaning device. Tiger nuts, after being cleaned for 5 min, are collected and weighed. Then, the mass of the tiger nuts cleaned by the cleaning device per hour is computed using Equation (13).

$$Q={\displaystyle \frac{12M_1}{1000\times 1}}$$

(13)

where Q is the cleaning efficiency (t·h⁻¹); M₁ is the mass of tiger nuts cleaned in 5 min (kg).

The impurity rate refers to the mass fraction of impurities in the cleaned tiger nuts. The impurities include soil, fibrous roots, and shell fragments from the tiger nuts.

The impurity rate of cleaned tiger nuts can be calculated using Equation (14).

$${\eta }_{\mathrm{z}}={\displaystyle \frac{M_2}{M_1}}\times 100\%$$

(14)

where η_z is the impurity rate of tiger nuts (%); M₂ denotes the mass of impurities (kg).

The breakage rate denotes the proportion of broken tiger nuts in the cleaned tiger nuts and is calculated using Equation (15).

$${\eta }_p={\displaystyle \frac{M_3}{M_1}}\times 100\%$$

(15)

where η_p is the breakage rate of tiger nuts (%); M₃ is the mass of broken tiger nuts (kg).

5.3. Box–Behnken Design Using Response Surface Methodology

Design-Expert V8.0.6 was utilized to conduct a Box–Behnken design (BBD) based on the response surface methodology (RSM). A total of 17 groups of three-factor three-level combined tests were designed. To eliminate the errors and ensure the accuracy of the test data, each test was repeated three times. Codes representing the test factors are listed in

Table 3. Codes of the factors.

Group	Rate of Rotation of Brush Roller A/rpm	Order of Elliptical Gears B/-	Eccentricity of Elliptical Gears C/-
−1	260	1	0.100
0	280	2	0.125
1	300	3	0.150

, and the specific test schemes and results are summarized in

Table 4. Test schemes and results.

Serial Number	Test Factors			Test Indices
	A	B	C	Cleaning Efficiency Q (t·h−1)	Breakage Rate ηp %	Impurity Rate ηz %
1	280.00	3.00	0.150	1.82	0.24	0.40
2	260.00	1.00	0.125	1.61	0.21	0.29
3	280.00	2.00	0.125	1.83	0.17	0.17
4	300.00	3.00	0.125	1.58	0.30	0.39
5	280.00	2.00	0.125	1.84	0.17	0.16
6	280.00	1.00	0.150	1.77	0.19	0.34
7	260.00	3.00	0.125	1.62	0.22	0.33
8	300.00	2.00	0.100	1.57	0.30	0.31
9	280.00	2.00	0.125	1.84	0.16	0.17
10	280.00	2.00	0.125	1.85	0.16	0.19
11	300.00	2.00	0.150	1.53	0.28	0.42
12	300.00	1.00	0.125	1.55	0.28	0.35
13	260.00	2.00	0.100	1.59	0.22	0.27
14	280.00	3.00	0.100	1.82	0.21	0.30
15	280.00	1.00	0.100	1.79	0.21	0.31
16	260.00	2.00	0.150	1.63	0.23	0.30
17	280.00	2.00	0.125	1.80	0.15	0.19

. A, B, and C separately represent the levels of the rate of rotation of the brush roller, order of the elliptical gears, and eccentricity of the elliptical gears.

5.4. Establishment of Regression Models and Significance Analysis

Design-Expert V8.0.6 was used for analysis of variance of the cleaning efficiency, breakage rate, and impurity rate. Regression models were established for the cleaning efficiency Q, breakage rate η_p, and impurity rate η_z. The test results are listed in

Table 5. Analysis of variance of the cleaning efficiency, breakage rate, and impurity rate.

Source of Variation	Cleaning Efficiency Q		Breakage Rate ηp		Impurity Rate ηz
	F	p	F	p	F	p
Model	105.60	<0.0001	69.23	<0.0001	83.85	<0.0001
A	23.79	0.0018	159.53	<0.0001	65.65	<0.0001
B	7.08	0.0324	13.02	0.0086	14.15	0.0071
C	0.20	0.6708	0.000	1.0000	61.04	0.0001
AB	0.39	0.5505	0.41	0.5438	0.000	1.0000
AC	6.29	0.0405	3.66	0.0972	10.72	0.0136
BC	0.39	0.5505	10.17	0.0153	8.21	0.0242
A2	883.56	<0.0001	314.62	<0.0001	161.84	<0.0001
B2	2.00	0.1998	35.48	0.0006	219.66	<0.0001
C2	7.30	0.0305	52.78	0.0002	151.33	<0.0001
Lack-of-fit term	0.27	0.8445	0.71	0.5927	0.60	0.6473

.

Analysis showed that test factors A and B significantly influence the cleaning efficiency; test factors A and B also significantly affect the breakage rate; test factors A, B, and C exert significant influences on the impurity rate.

$$\begin{array}{l}Q=1.83-0.028A+0.015B-0.02AC-0.23A^2-0.021C^2\\ {\eta }_p=0.16+0.035A+0.01B+0.012BC+0.068A^2+0.023B^2+0.028C^2\\ {\eta }_z=0.18+0.035A+0.016B+0.034C+0.02AC+0.018BC+0.076A^2+0.088B^2+0.073C^2\end{array}$$

(16)

Meanwhile, regression equations for the influence of each factor on the cleaning efficiency Q, breakage rate η_p, and impurity rate η_z were obtained, as expressed by Equation (16).

The influence of the interactions of different factors on the cleaning efficiency, breakage rate, and impurity rate was revealed through response surface analysis of the test results. The results are displayed in Figure 23, Figure 24 and Figure 25.

As shown in Figure 23a, when the rate of rotation of the brush roller remains unchanged, the cleaning efficiency of the tiger nuts is improved with the increment of the order of elliptical gears; under a fixed order of elliptical gears, the cleaning efficiency increases, then decreases with the acceleration of the rate of rotation of the brush roller. Variation of the surfaces indicates that the rate of rotation of the brush roller exerts a more significant influence on the cleaning efficiency.

Figure 23b shows that, at a fixed rate of rotation of the brush roller, the cleaning efficiency of tiger nuts increases, then decreases with the increasing eccentricity of the elliptical gears; when keeping the eccentricity of the elliptical gears constant, the cleaning efficiency first increases, then decreases with the acceleration of the rate of rotation of the brush roller. According to the variation of the surfaces, the rate of rotation of the brush roller more significantly influences the cleaning efficiency of the device as applied to the processing of tiger nuts.

It can be seen in Figure 23c, when keeping the order of the elliptical gears unchanged, the cleaning efficiency of tiger nuts increases, then decreases with the increasing eccentricity; under a fixed eccentricity of the elliptical gears, the cleaning efficiency is improved with the increasing order of the elliptical gears. Variation of the surfaces suggests that the order of elliptical gears more significantly influences the cleaning efficiency.

As shown in Figure 24a, the breakage rate of tiger nuts is shown to decrease, then increase with the increasing order of elliptical gears when keeping the rate of rotation of the brush roller constant; under a fixed order of elliptical gearing, the breakage rate of tiger nuts also decreases, then increases with the acceleration of the rate of rotation of the brush roller. Variation of the surfaces indicates that the rate of rotation of the brush roller more significantly influences the breakage rate of tiger nuts.

It can be seen from Figure 24b that, when keeping the rate of rotation of the brush roller unchanged, the breakage rate of tiger nuts decreases, then increases with the increase in eccentricity; the breakage rate of tiger nuts also shows a similar tendency to decrease, then increase with the accelerated rate of rotation of the brush roller under a fixed eccentricity of the elliptical gears. According to the variation of the surfaces, the rate of rotation of the brush roller exerts a more significant influence on the cleaning efficiency of tiger nuts.

As shown in Figure 24c, when keeping the order of the elliptical gearing constant, the breakage rate of tiger nuts tends to decrease, then increase with the increasing eccentricity; when keeping the eccentricity constant, the breakage rate of tiger nuts also decreases, then increases as the order of the elliptical gears is increased. In accordance with the variation of the surfaces, the order of the elliptical gears more significantly influences the breakage rate of tiger nuts.

Figure 25a shows that, under a constant rate of rotation of the brush roller, the impurity rate of tiger nuts decreases, then increases as the order of the elliptical gears is increased; when keeping the order of the elliptical gears constant, the impurity rate also tends to decrease, then increase with the acceleration of the rate of rotation of the brush roller. The variation of the surfaces shows that the rate of rotation of the brush roller more significantly affects the impurity rate of tiger nuts.

As shown in Figure 25b, when keeping the rate of rotation of the brush roller unchanged, the impurity rate of tiger nuts decreases, then increases as the eccentricity of the elliptical gears is increased; when keeping the eccentricity of the elliptical gears constant, the impurity rate also tends to decrease, then increase with the acceleration of the rate of rotation of the brush roller. The variation of the surfaces shows that the rate of rotation of the brush roller more significantly affects the impurity rate of tiger nuts.

According to Figure 25c, for a given order of the elliptical gears, the impurity rate of tiger nuts decreases, then increases as the eccentricity of the elliptical gears is increased; when keeping the eccentricity of the elliptical gears constant, the impurity rate of tiger nuts also decreases, then increases with the increment in the order of the elliptical gears. Variation of the surfaces indicates that the eccentricity of the elliptical gears exerts a more significant influence on the impurity rate of tiger nuts.

By way of summary, various factors are listed, in descending order of their influence on the cleaning efficiency, as the rate of rotation of the brush roller, order of the elliptical gears, and eccentricity of the elliptical gears; various factors are also listed, in descending order of their influence on the breakage rate, as the rate of rotation of the brush roller, order of the elliptical gears, and eccentricity of the elliptical gears; they are listed, in descending order of their influences on the impurity rate, as the rate of rotation of the brush roller, eccentricity of the elliptical gears, and order of the elliptical gears.

5.5. Parameter Optimization

The Optimization module in Design-Expert V8.0.6 was used to optimize the test factors. The regression equations were solved to maximize the cleaning efficiency while minimizing the breakage and impurity rates.

$$\begin{array}{l}\mathit{max}{Y}_1\left(A,B,C\right)\\ \mathit{min}{Y}_2,Y_3\left(A,B,C\right)\\ \left\{\begin{array}{l}260\le A\le 300\\ 1\le B\le 3\\ 0.1\le C\le 0.15\end{array}\right.\end{array}$$

(17)

Through optimization, the optimal parameter combination is predicted as follows: the rate of rotation of the brush roller is 276.97 rpm, the order of the elliptical gears is 1.94, and the eccentricity of the elliptical gears is 0.122. Under these conditions, the cleaning device designed for use on tiger nuts works best, of which the cleaning efficiency, breakage rate, and impurity rate of tiger nuts are predicted to be 1.83 t·h⁻¹, 0.16%, and 0.17%, respectively.

5.6. Test Verification

The parameters are rounded based on the predicted values and actual working conditions, so the rate of rotation of the brush roller, order of the elliptical gears, and eccentricity of the elliptical gears are set to 280 rpm, 2, and 0.122, respectively, under which conditions, verification tests were conducted. Tiger nuts before and after cleaning are compared in Figure 26. The tests were repeated three times, and the mean average values were recorded. The test results are summarized in

Table 6. Bench test results.

Times of Tests	Cleaning Efficiency Q t·h−1	Breakage Rate ηp %	Impurity Rate ηz %
1	1.85	0.16	0.18
2	1.83	0.15	0.16
3	1.82	0.13	0.14
Average	1.83	0.15	0.16

.

The test results indicate that the cleaning efficiency, breakage rate, and impurity rate basically agree with the optimization and prediction results and meet the design requirements. Finally, the following are selected as the optimal operation parameters of the cleaning device of tiger nuts: the rate of rotation of the brush roller is 280 rpm, the order of the elliptical gears is 2, and the eccentricity of the elliptical gears is 0.122. Under these conditions, the cleaning efficiency, breakage rate, and impurity rate are 1.83 t·h⁻¹, 0.15%, and 0.16%, respectively.

6. Discussion

A pulsating roll-cleaning device of tiger nuts was designed through theoretical analysis and coupling simulations; combined with the analysis results above, it is confirmed that the rate of rotation of the brush roller mainly determines the cleaning performance, which proves Zhao et al.’s [13] point. On another hand, the work analyzes the effects of the structural and motion parameters of the cleaning device on the cleaning performance of tiger nuts; the deficiencies in the cleaning performance of tiger nuts were investigated:

• Environmental influence:

The pulsating roll-cleaning method is realized mainly by a variable-speed transmission system consisting of a pair of elliptical gears and appropriately improves the cleaning efficiency and reduces the breakage rate compared to the traditional cleaning method using circular gears. However, the rack is installed on rough ground, and the frequency of vibrations of the cleaning device increases due to the unevenness of the ground. Tiger nuts in the cleaning chamber cannot move axially under the rotation of the brush roller, which reduces the cleaning efficiency and increases the breakage rate of tiger nuts, impairing the efficiency of the process, as evidenced by decreases in the cleaning indices.

2.

Random distribution of attitudes of tiger nuts mixed with impurities:

The specific attitudes of large amounts of soil and fibrous roots adhering to the surface of harvested tiger nuts are inconsistent; this differs from the distinct element model of tiger nut–soil aggregate established in virtual simulations. Hence, the time taken to separate impurities including soil and fibrous roots from tiger nuts differs in actual operation, which may influence the cleaning quality of tiger nuts. In the follow-up study, the maximum quality of tiger nuts that the brush roller can withstand can be obtained by flexible treatment of the brush, so as to further improve the cleaning efficiency and obtain better quality tiger nuts.

3.

Entanglement of soil and fibrous roots:

When non-uniform quantities of tiger nuts are fed to the hoisting and feeding devices, or much soil is stuck to the tiger nuts and fibrous roots are entangled therewith, the tiger nuts may be accumulated at the bottom of the hoisting hopper and cannot timeously enter the feed-hopper by way of the hoisting device. This prevents tiger nuts in the feed-hopper from continuously and uniformly entering the cleaning chamber, which prolongs the time taken to clean the tiger nuts while also reducing the quality of the cleaning process.

7. Conclusions

• By adjusting the number of teeth, gear ratio, and deformation coefficient of the elliptical gears and other parameters through the analysis software for the meshing transmission of pitch curves of the elliptical gears with arbitrary orders, the elliptical gear satisfying the transmission stability is obtained, and the pulse variable speed transmission of the brush roller is realized, which ensures the increase in the cleaning efficiency and reduces the breakage rate of tiger nuts.
• The RecurDyn 2023-EDEM 2022 coupling simulations were used to clarify the influence of key factors on the number of collisions, the number of bonds, and the total stress of tiger nuts during the cleaning process. The optimal ranges of the various parameters of the cleaning device are ascertained as follows: the rate of rotation of the brush roller is 260~300 rpm, the order of the elliptical gears is 1~3, and the eccentricity of the elliptical gears is 0.1~0.15.
• The results of the bench performance test show that the rate of rotation of the brush roller has the greatest influence on the cleaning efficiency, breakage rate, and impurity rate. Meanwhile, the optimal operation parameters of the cleaning device are as follows: when the rate of rotation of the brush roller is 280 rpm, the order of the elliptical gears is 2, and the eccentricity of the elliptical gears is 0.122; the cleaning efficiency, breakage rate, and impurity rate are, separately, 1.83 t·h⁻¹, 0.15%, and 0.16%. The cleaning effect is favorable under these conditions, meeting the design requirements of the cleaning device.