Design of the Vibrating Sieving Mechanism for a Quinoa Combine Harvester and Coupled Analysis of DEM-MBD

Abstract

Quinoa is renowned for its high nutritional value, which not only meets the nutritional needs of the human body but also makes it a suitable option for individuals with diabetes and celiac disease due to its low sugar and gluten-free characteristics. In China, the primary cultivation regions of quinoa are the Tibetan Plateau, the Yunnan–Guizhou Plateau, and Northwest China, which are predominantly characterized by hilly and mountainous terrain, resulting in the gradual development of mechanized harvesting processes. The efficacy of the mechanized harvesting process in these regions is suboptimal, exhibiting poor clearance and efficiency. In this paper, the design and MBD-EDEM coupling analysis of the quinoa combine harvester’s cleaning and screening mechanism is carried out to simulate the cleaning process of quinoa threshing materials. The results show that the vibrating screen can complete the forward sliding and dispersed throwing up of the materials and effectively avoid the accumulation of the threshing materials. The coupling results of the permeability of each material in the cleaning and screening mechanism, as well as the vibrating screen movement condition, indicate that when the herringbone screen opening degree is set in the range of 15° to 30°, the cleaning and screening device can achieve a high cleaning efficiency while maintaining a low impurity rate. Field trial data further confirm that within this opening range, the cleaning effect and efficiency both exhibit significant advantages.

1. Introduction

In recent years, with the increasing attention to food security by various countries, the central No. 1 document in China in 2025 has set “continuously enhancing the supply guarantee capacity of grain and other important agricultural products” as the primary task [1,2]. Against this backdrop, quinoa, a grain crop with high nutritional value and strong adaptability, has gradually attracted attention. Quinoa is native to South America, and South American countries such as Bolivia, Peru, and Ecuador are the main global producers of quinoa. Due to its adaptability to high altitudes, infertile soils, and extreme climatic conditions, it has become an important food crop for local residents [3]. Quinoa has extensive potential applications in food, medicine, feed, and industry [4,5]. Owing to its high nutritional value and strong adaptability, quinoa has been identified as a complete nutrient food by the Food and Agriculture Organization of the United Nations and is acclaimed as the “super grain” that best meets human nutritional requirements. Moreover, its straw can also serve as feed for livestock [6,7,8]. Quinoa prefers strong light and is tolerant of cold, drought, and salinity. It is commonly cultivated in high-altitude cold regions and arid areas with low rainfall. In China, quinoa is mainly planted in high-altitude areas such as the Tibetan Plateau and the Yunnan–Guizhou Plateau. There is also some cultivation in the North China Plain, Northeast China Plain, Northwest China, and Central China regions [9,10,11].

Quinoa is cultivated in China over an area of approximately 2 × 10⁴ hm², with a yield maintained at 2.25 × 10³ kg/hm², showing an increasing trend year by year. In 2022, the planting area of quinoa in China further expanded to 3333 hectares [12]. Gansu Province, as one of the main quinoa-growing regions, accounts for about 40% of the national planting area [13,14,15,16,17]. Influenced by the geographical environment of the planting areas, quinoa is mainly harvested in two stages: it is first manually reaped and sun-dried, then transported to the threshing area for screening, or threshed using traditional threshing machines. This method is characterized by a long harvesting period, high labor consumption, low work efficiency, and high labor intensity. When using traditional rice–wheat combine harvesters for harvesting, there are high requirements for the scale of the fields, crop varieties, and uniform maturity. Large-scale machinery often struggles to enter the fields to complete the harvest. Small- and medium-sized tracked rice–wheat combine harvesters have high losses and high impurity content when harvesting quinoa. Moreover, quinoa has unique growth habits, such as inconsistent maturity and sensitivity to herbicides, which add to the difficulty of mechanized operations [18].

To address these issues, researchers have modified key components of rice–wheat combine harvesters to adapt them for quinoa harvesting. Wang et al. [19] constructed a simulation system for the feeding, conveying, and threshing of wheat using a coupled method of EDEM and RecurDyn. Shen et al. [20] optimized the structure of the cleaning system in a paddy combine harvester. Lu et al. [21] established a screen model using the multi-body dynamics software ADAMS 2018 to analyze the motion characteristics of grains on the screen surface.

Zhao et al. [22] studied the mechanical properties of quinoa grains after soaking in water. Haimei et al. [23,24] tested and analyzed the aerodynamic characteristics of quinoa threshing materials to address the issue of poor cleaning efficiency and high impurity content when harvesting quinoa with general-purpose grain combine harvesters. At present, there is limited development in specialized combine harvesters for quinoa in the domestic market of China. When using grain combine harvesters to harvest quinoa, significant losses and high impurity content often occur. In most regions, quinoa is still planted and harvested manually, which is labor-intensive and inefficient. Quinoa at maturity will germinate if exposed to humid air for 24 h, and missing the harvesting time will severely affect its yield. Therefore, the development of quinoa combine harvesting technology is an urgent issue to be resolved [9,25,26].

This paper takes the vibration cleaning device of the 4LZ-4.0 quinoa combine harvester for hilly and mountainous areas as the research object and designs a double-layer reciprocating vibrating screening mechanism, which is mainly composed of the shaking plate, tail screen, eccentric wheel, herringbone screen opening adjustment device, herringbone screen, and lower screen, to achieve the cleaning and separation of quinoa harvesting materials. By simplifying the crank-link mechanism of the vibrating screen, a dynamic model of the mechanism and a discrete element model of the straw and grain are established to analyze the movement of the straw and grain under different screen types and screen surface openings as well as the cleaning effect, and the optimal range of herringbone screen opening is obtained, in the hope of improving the cleaning effect and providing a theoretical reference for the further optimization study of quinoa combined mechanized harvesting.

2. Structure and Working Principle of Quinoa Harvester

2.1. Machine Structure and Principle

The 4LZ-4.0 full-feed tracked quinoa combine harvester for hilly and mountainous areas consists of a header, overbridge, lower cutting knife, chain-tooth feeding device, threshing device, cleaning device, engine power system, and traveling system, as shown in Figure 1. The power system is a diesel engine. The single-side chain-tooth structure completes the crop-gathering process. The header is responsible for cutting and feeding the quinoa stalks, achieving the row-harvesting of quinoa with minimal deviation. The threshing drum adopts a longitudinal flow structure with rasp bars and rod teeth, which, together with the combined concave, realizes the efficient threshing and separation of quinoa materials. The cleaning system, composed of a fan and a specially designed double-layer reciprocating vibrating screen, accomplishes the cleaning operation of threshed materials. Suitable for operations on hilly and mountainous areas as well as slopes, the harvester has good passability and stability.

During the operation of the machine, the header divider separates the upper stems of quinoa. The straw and grain are then pushed by the chain fingers toward the double-layer cutting device. The upper cutting knife cuts the upper stems, which enter the threshing drum, while the lower cutting knife cuts the lower stems and lays them on the field. Under the beating and rubbing action of the rasp-bar threshing drum, the quinoa material is separated. Some of the threshed quinoa seeds fall through the grating concave, while the remaining straw and grain enter the rod-tooth section for further threshing and layering. Quinoa seeds, glumes, and short stems fall through the perforations of the combined woven sieve into the fan + vibrating screen combination cleaning device. The stems are discharged outside the machine through the straw guide plate, and lightweight impurities, glumes, and short stems are blown out of the machine by the fan. The cleaned quinoa seeds are conveyed into the grain bin by the primary conveying screw. Straw and grain with more panicle impurities are conveyed by the secondary screw to the threshing chamber for re-threshing and re-cleaning. The specific technical parameters of the machine are shown in

Table 1. Technical specifications of quinoa combine harvester for hilly and mountainous areas.

Parameter Name	Parameter Value	Unit
Structural Form	Full-Feed Tracked	-
Overall Machine Dimensions (Length × Width × Height)	4950 × 2150 × 2590	mm
Header Width	1900	mm
Feeding Capacity	4	kg/s
Operating Speed	0.75–1.50	m/s
Productivity	0–0.5	hm2/h
Rated Rotational Speed	2400	r/min
Threshing Drum Parameters (Diameter × Length)	550 × 1350	mm
Track Pitch × Number of Links × Width	90 × 44 × 400	mm
Track Gauge	1080	mm
Ground Clearance	320	mm
Rated Power	51.5	kW

.

2.2. Structure and Working Principle of Vibrating Screening Mechanism

The reciprocating vibrating screen, as an important component of the combine harvester, is located below the threshing device, as shown in Figure 2. The entire device consists of components such as the shaking plate, tail screen, eccentric wheel, herringbone screen opening adjustment device, herringbone screen, and lower screen [27,28,29]. The eccentric wheel provides power to the entire device, enabling the screen body to perform longitudinal reciprocating motion along the guide rail [30]. The shaking plate is fixed to the vibrating screen frame and is located on the top layer of the screen frame. It moves together with the screen frame, receives the grain mixture separated by the threshing device, and evenly distributes it onto the screen surface for cleaning. The herringbone screen opening mechanical adjustment device can achieve an opening adjustment range of 0–45°. Depending on the moisture content and type of threshed material, it changes the residence time of the straw and grain in the screen, thereby improving the threshing efficiency [31]. The lower screen uses a woven screen, which can adapt to the harvesting of grains of different sizes, ensuring that the threshed material does not accumulate and effectively removing fine impurities to reduce the impurity content [32]. The vibrating screen relies on the front guide rail and bearing to form a sliding support constraint, allowing for easy replacement of the lower screen.

The vibrating screening mechanism adopts a centrifugal fan + double-layer vibrating screen structure, as shown in Figure 3. The eccentric wheel provides power for the reciprocating motion of the vibrating screen. During the operation of the vibrating screen, quinoa seeds, finely crushed straw, and other residues produced by threshing begin to stratify. Under the action of the powerful fan, the finely crushed straw and glumes are discharged from the impurity outlet, while the broken long straw is ejected outside the machine. Short stems and remaining panicles are pushed to the rear conveyor at the tail and then sent back to the threshing device for re-threshing.

3. Key Component Design and Kinematic Analysis

3.1. Vibrating Screening Mechanism Design

The performance of the vibrating screening mechanism determines the impurity and loss rates of quinoa seeds. The screen plate area, screen mesh type and specifications, and the position of the fan outlet collectively affect the cleaning efficiency of the vibrating screening mechanism. Among these factors, the length of the vibrating screen significantly influences the feed rate. According to the Design Manual for Agricultural Machinery [33], the calculation method for the screen plate length L is as follows:

$$L={\displaystyle \frac{Q_s\left(1-\phi K\right)}{B_s{q}_s}}$$

(1)

In the equation

L 

—length of the sieve plate, mm;

Q_s 

—feeding rate, kg/s;

q_s 

—feeding rate per unit area of the sieve surface, kg/s;

φ 

—proportion of stalks and panicles in the total weight of quinoa threshing material;

K 

—working characteristic coefficient of the threshing and cleaning device;

B_s 

—width of the sieve plate, B_s = 650 mm.

Based on the design parameters in Table 1, Q_s = 4 kg/s is selected. Referring to the Design Manual for Agricultural Machinery, for the adjustable herringbone screen, q_s = 2.5 kg/s is chosen here [34,35]. According to the experimental data, the proportion of impurities in the total weight of threshed quinoa materials, φ = 0.6 [36], and the working characteristic coefficient, K = 0.75 [31,37]. By substituting the values of Q_s, q_s, φ, K, and B_s into Equation (1), the screen plate length L = 1350 mm can be calculated.

The double-layer reciprocating vibration herringbone screen structure is shown in Figure 4a, and the herringbone screen can achieve an opening adjustment ranging from 0 to 45 degrees. The woven screen structure is shown in Figure 4b. The designed spacing D is 6 mm × 6 mm, which ensures that all the quinoa grains can pass through and is also suitable for the cleaning of small grains with similar shapes. The diameter of the woven screen wire is j = 2 mm, and the overall size is 650 mm × 530 mm. A common centrifugal fan with a diameter D₀ = 350 mm is selected.

When the positive-pressure fan is in operation, the airflow is blown along the direction of the duct under the action of the high-speed rotating blades. The spatial position of the outlet determines the area and intensity of the airflow, which in turn affects the degree of dispersion of the separated materials [38]. The two factors need to meet the following conditions:

$$H=K_1{W}_1\sin {\theta }_0$$

(2)

In the equation

H 

—outlet height, mm;

K₁ 

—working coefficient, K₁ = 0.4;

θ₀ 

—angle between airflow and sieve surface, θ₀ = 30°.

Substituting the respective values into Equation (2), the calculated value of H is 240 mm.

3.2. Kinematic Analysis of Vibrating Screen

The vibrating screen is the core component of the cleaning device, and its motion directly affects the cleaning and loss rates of quinoa harvesting [39]. Driven by the eccentric wheel, the screen surface has certain horizontal and vertical swing amplitudes, which enable the material to be cleaned to slide, jump, and stratify on the screen surface, thereby achieving the screening and cleaning of the straw and grain. To analyze the mechanism motion, the reciprocating vibrating screen motion is simplified into a crank-slider mechanism with three revolute joints and one prismatic joint. The schematic diagram of the motion is shown in Figure 5.

The motion states of the straw and grain on the screen, such as jumping and sliding, are influenced by multiple parameters. The inclination angle of the vibrating screen can change the component of the material’s velocity perpendicular to the screen surface, resulting in significant changes in the motion trajectory [40]. The eccentricity of the eccentric wheel directly affects the amplitude of the vibrating screen. An appropriate eccentricity can ensure a uniform distribution of the straw and grain on the screen surface, thereby improving the screening efficiency [41]. Assuming that the motion trajectory on the screen is a straight line and considering the screen body motion as simple harmonic motion [42], the displacement x of any point on the screen body can be expressed as follows:

$$x=-r\cos \left(\omega t\right)$$

(3)

In the equation

r 

—eccentric radius, mm;

ω 

—angular velocity of the eccentric wheel, rad/s;

t 

—rotation time of the eccentric wheel, s.

The first-order derivative of the displacement with respect to time yields the velocity v_x of the sieve body, and the second-order derivative with respect to time yields the acceleration a_x of the sieve body.

$$v_x={\displaystyle \frac{dx}{dt}}=\omega r\sin \left(\omega t\right)$$

(4)

$$a_x={\displaystyle \frac{d^{2}x}{d{t}^2}}={\omega }^{2}r\cos \left(\omega t\right)$$

(5)

To ensure that the motion state of the material on the screen is maintained between upward sliding and a certain degree of jumping, the acceleration a_x must satisfy Equation (6), that is, the rotational speed n of the eccentric wheel must meet Equation (7):

$$g{\displaystyle \frac{\sin \left(\phi -\alpha \right)}{\cos \left(\alpha +\beta +\phi \right)}}<a_x<g{\displaystyle \frac{\cos \alpha }{\sin \left(\alpha +\beta \right)}}$$

(6)

$${\displaystyle \frac{30}{\pi }}\sqrt{{\displaystyle \frac{g\sin \left(\phi -\alpha \right)}{r\cos \left(\alpha +\beta +\phi \right)}}}<n<{\displaystyle \frac{30}{\pi }}\sqrt{{\displaystyle \frac{g\cos \alpha }{r\sin \left(\alpha +\beta \right)}}}$$

(7)

In the equation

α 

—inclination angle of the sieve surface (°);

n 

—rotational speed of the eccentric wheel, r/min;

β 

—oscillation direction angle of the sieve surface (°);

φ 

—Friction angle between threshing material and sieve surface (°).

The inclination angle of the reciprocating vibrating screen surface α was designed to be 2°, the swing direction angle β of the screen surface was 12°, and the friction angle φ between the material and the screen surface was 22° [43]. The eccentric radius r was set at 15 mm. Substituting the above data into Equation (6), the rotational speed range of the eccentric wheel was solved to be 223 r/min < n < 569 r/min. The rotational speed of the eccentric wheel was set at 386 r/min.

3.3. Analysis of Quinoa Grain Movement Patterns

A theoretical analysis of the relative motion of the material grains was conducted. Based on the force conditions of quinoa grains on the screen surface, the motion trajectories of the grain clusters within the cleaning screen were determined [44]. The forces acting on the material during the two states of throwing and upward sliding were mainly analyzed to investigate the separation effect of the herringbone screen on the material.

• Force analysis of quinoa sliding upward on the screen.

As shown in Figure 6a, the grain on the screen surface is subjected to the normal force N, frictional force f, gravitational force G, and the thrust P from the fan airflow. When the inertial force U acts in the upper right direction, the material tends to slide upward. The equilibrium equation of the grain on the screen at this time is as follows:

Equation (8):

$$\left\{\begin{array}{l}P\cos \beta +U\cos \alpha =f+G\sin \theta \\ N+P\sin \beta +U\sin \alpha =G\cos \theta \end{array}\right.$$

(8)

Equation (9):

$$\left\{\begin{array}{l}P=k\rho A_1{u}_1^2\\ U=m{\omega }^{2}r\cos \left(\omega t\right)\\ f=N\tan \phi \\ G=mg\end{array}\right.$$

(9)

In the equation

α 

—vibration direction angle (°);

β 

—angle between grain inertial force and sieve surface (°);

θ 

—inclination angle of the sieve surface (°);

φ 

—friction angle (°).

Substituting Equation (9) into Equation (8) and rearranging, the following equation is obtained:

$${\omega }^{2}r\cos \left(\omega t\right)={\displaystyle \frac{g\sin \left(\phi +\theta \right)-\frac{k\rho A_1{u}_1^2}{m}\cos \left(\beta -\phi \right)}{\cos \left(\alpha +\phi \right)}}$$

(10)

Since cos(ωt) ≥ 1, the condition for quinoa grains to slide upward is as follows:

$${\omega }^{2}r>{\displaystyle \frac{g\sin \left(\phi +\theta \right)-\frac{k\rho A_1{u}_1^2}{m}\cos \left(\beta -\phi \right)}{\cos \left(\alpha +\phi \right)}}$$

(11)

2.

Force analysis of quinoa during its throwing motion on the screen.

When the grain is thrown from the screen surface, the frictional force f and the normal force N disappear. At this time, the forces acting on the grain include its own gravitational force G and the thrust P from the airflow, which should satisfy Equation (12):

$$N=0=P\sin \beta +U\sin \alpha -G\cos \theta$$

(12)

Again, Equation (9) was substituted into Equation (12) and collapsed to obtain the conditions when the quinoa kernels were thrown up:

$${\omega }^{2}r>{\displaystyle \frac{g\cos \theta -\frac{k\rho A_1{u}_1^2}{m}\sin \beta }{\sin \alpha }}$$

(13)

From the force analysis of the material in Figure 6 and Equations (11) and (13), it can be seen that factors such as fan speed, herringbone screen opening, and vibration frequency affect the motion state of quinoa grains on the screen. Equation (11) shows the critical condition K_a = rω²/g = 0.41, and Equation (13) shows the critical condition K_b = rω²/g = 4.13. When K_a ≤ K₀ < K_b, the threshed material meets the conditions for sliding and stratification, which will promote material stratification, improve grain cleaning efficiency, and reduce grain loss rate. K₀ is taken as 2.5.

4. Modeling and Coupling Analysis

4.1. Numerical Models

The multi-body dynamics software RecurDyn 2018 was used to add kinematic pair constraints and contacts to the vibrating screen, and the discrete element method software EDEM 2020 was employed to establish models of various materials. A coupled simulation between the two was conducted to verify the cleaning efficiency of the vibrating screening system under different screen types and screen opening conditions. The motion conditions of the material and screen surface, the screening process of quinoa threshing, and the particle permeation process through the screen were analyzed [45,46].

The simplified three-dimensional model was imported into the multi-body dynamics analysis software RecurDyn. The system parameters, contact forms, motion parameters, and calculation methods were set accordingly. The coupling interface Connect was activated to enable coupling with EDEM. Figure 7 shows the completed virtual prototype of the reciprocating vibrating screen.

Under the Geometries model tree in the discrete element software, “Import Geometry from RecurDyn” was selected to import the file into EDEM. Based on the straw and grain size data obtained from experiments, discrete element models for quinoa grains and short and long stalks were established, respectively. The specific measured data are shown in

Table 2. Material size data.

Material	Diameter (mm)	Length/Thickness (mm)
Quinoa grains	2.2	1.2
Short stalks	0.7	11.85
Long stalks	3.5	35.5

.

The discrete element models of quinoa grains, short stalks, and long stalks are shown in Figure 8, and the contact parameters are set according to

Table 3. Material properties and contact parameters.

(a)
Item	Poisson’s Ratio	Shear Modulus (MPa)	Density (kg/m3)
Quinoa grains.	0.25	156	870
Long stalks	0.3	160	590
Short stalks	0.3	150	360
Screen mesh	0.3	79,000	7800
(b)
Item	Coefficient of Restitution	Static Friction Coefficient	Kinetic (Dynamic) Friction Coefficient
Quinoa grain–Quinoa grain	0.22	0.26	0.08
Quinoa grain–Screen mesh	0.46	0.38	0.12
Long stalk–Long stalk	0.21	0.25	0.18
Long stalk–Short stalk	0.21	0.25	0.18
Short stalk–Short stalk	0.21	0.25	0.18
Long stalk–Quinoa grain	0.21	0.25	0.18
Long stalk–Screen mesh	0.42	0.34	0.12
Short stalk–Screen mesh	0.42	0.34	0.12

. Three particle factories were added above the screen, and the total mass of the material was set to 0.5 kg. The proportions of grains, short stalks, and long stalks in the material were 78.4%, 4.03%, and 2.8%, respectively, with the remaining part being unthreshed panicles and glumes. After all the parameters were set, the coupled calculation was initiated.

4.2. Coupling Analysis

4.2.1. Displacement and Acceleration Analysis at the Center of Mass of the Vibrating Screen

Taking the center of mass of the screen surface as the object of study, the motion state of the vibrating screen was analyzed. The displacement of the center of mass in the horizontal direction changes regularly in a periodic manner, with a range of 0–35.57 mm, as shown in Figure 9a. This indicates that the reciprocating vibrating screen can cause the threshed material to have a tendency to slide in a plane. The displacement of the center of mass in the vertical direction also changes regularly in a periodic manner, with a range of 0–21.58 mm, as shown in Figure 9b, indicating that the reciprocating vibrating screen can cause the threshed material to have a tendency to jump up and stratify. Meanwhile, the amplitude of the horizontal displacement of the vibrating screen is larger than that of the vertical displacement. The stronger reciprocating motion in the vertical direction reduces material accumulation and is beneficial for the screening and cleaning of threshed material.

Similarly, taking the center of mass of the vibrating screen as the object of study, the changes in acceleration of the vibrating screen in the horizontal and vertical directions were examined. The acceleration of the center of mass in the horizontal direction changes regularly in a periodic manner, with a range of −21,604.94 to 21,896.93 mm/s², as shown in Figure 10a. The acceleration of the center of mass in the vertical direction also changes regularly in a periodic manner, with a range of −12,686.76 to 13,700.76 mm/s², as shown in Figure 10b. The forces acting on the material in the horizontal direction are greater than those in the vertical direction, which enables the quinoa material to be thrown up, stratified, and transported horizontally.

The results above show that the screen structure designed based on the selected K₀ value can achieve the forward sliding and dispersing of quinoa screenings while effectively preventing screening material accumulation.

4.2.2. Analysis of Horizontal and Vertical Average Velocities of Threshed Material

A comparative study was conducted on the velocities of quinoa grains and long and short stalks in the horizontal and vertical directions. The screening and transportation mechanisms of quinoa threshing material under different herringbone screen openings were analyzed. The average velocity in the horizontal direction changes regularly in a periodic manner, as shown in Figure 11a. The average velocity in the vertical direction also changes regularly in a periodic manner, as shown in Figure 11b.

From the curves in Figure 11a,b, it can be seen that the amplitude of the average velocity in the horizontal direction and the amplitude of the average velocity in the vertical direction for straw and grain vary with different opening degrees. The amplitude variation data in the horizontal direction are organized in

Table 4. Amplitude of average velocity changes for materials in horizontal and vertical directions.

(a)
Opening Angle (°)	Amplitude of Average Velocity Changes in the Horizontal Direction (m/s)
	Quinoa Grains	Long Stems	Short Stems
15	1.76	1.45	1.29
30	0.795	0.956	0.648
45	0.713	1.42	0.764
(b)
Opening Angle (°)	Amplitude of Average Velocity Changes in the Vertical Direction (m/s)
	Quinoa Grains	Long Stems	Short Stems
15	1.53	1.437	1.04
30	1.287	0.626	0.678
45	1.163	0.688	0.424

a, and the amplitude variation data in the vertical direction are organized in Table 4b.

It can be seen from Table 4a,b that when the herringbone screen opening is 15°, the changes in velocity in both the horizontal and vertical directions are relatively large. This is because the screening performance is lower when the opening is smaller. Meanwhile, the angle between the normal of the herringbone screen surface and the longitudinal vertical plane is small, resulting in a larger ejection angle of the straw and grain. As the herringbone screen opening increases to 30° and 45°, the amplitude of the average velocity changes for each material is significantly reduced.

4.2.3. Analysis of Screening Performance of Vibrating Screen

The herringbone screen openings were set at 15°, 30°, and 45°, respectively, and the separation effects of the vibrating screen on quinoa grains and long and short stalks were analyzed using the coupled RecurDyn and EDEM simulations. After the simulation calculations were completed, three particle number sensors were established at three locations: above the herringbone screen, below the herringbone screen, and below the woven screen, to count the number of particles passing through the vibrating screen. The data from these particle sensors are instructive for the qualitative analysis of screening performance. The velocity contour maps of threshed straw and grain at different moments under the three opening angles of the herringbone screen were obtained. To highlight the trends, the velocity contour maps of the straw and grain at 0.33 s for the 15°, 30°, and 45° openings, and at 0.33 s, 0.7 s, and 1 s for the 45° opening were plotted in

Table 5. Velocity clouds for three opening degrees over time.

Angle	Time	Velocity Distribution Map
15°	0.33 s
30°	0.33 s
45°	0.33 s
	0.7 s
	1 s

to analyze and compare the screening performance of the herringbone vibrating screen under different opening conditions.

As shown in Table 5, the opening size of the herringbone screen is positively correlated with the screening performance of quinoa grains, long stalks, short stalks, and other materials. When the opening of the herringbone screen is small, the screening performance of quinoa is low, and a large amount of straw and grain accumulates on the top of the herringbone screen. Under the action of vibration, the straw and grain move to the tail screen, resulting in low cleaning efficiency and easy blockage of the vibrating cleaning device. As the opening of the herringbone screen increases, the degree of ejection decreases, and the probability of quinoa threshing material passing through the screen increases. Both quinoa grains and long and short stalks fall into the woven screen to complete the cleaning of the threshing mixture. However, the impurity content increases, and the accumulation of grains in the first-stage conveying screw and the second-stage re-threshing screw becomes more severe, leading to an increase in cleaning load.

After the simulation calculations were completed, the straw and grain quantities detected by each sensor were exported. These data were then analyzed to determine the number of particles of threshed material passing through the herringbone screen and the woven screen under different opening angles. When the total pass rate was set to 250%, the pie chart would complete a full circle. Pie charts showing the passing rate of quinoa material through the herringbone screen and the woven screen at opening angles of 15°, 30°, and 45° for each screen are presented in Figure 12a,b.

Similarly, as shown in Figure 12a,b, when the herringbone screen has a small opening angle, the summated value of the cleaning efficiency of the straw and grain is less than 125%. This low screening efficiency results in reduced cleaning efficiency and an increased likelihood of straw and grain congestion due to the limited passage of straw and grain through the screen. As the herringbone screen opening increases, the screening performance is significantly enhanced, and more straw and grain enter the woven screen for cleaning. The woven screen performs a secondary screening of the threshing mixture, increasing the cleaning efficiency but also raising the impurity content. When the herringbone screen opening reaches 45°, the cleaning efficiency of quinoa material is the highest. However, the increase in impurity content leads to more severe grain accumulation in the second-stage re-threshing screw and an increased cleaning load. It can also be seen from Figure 12b that as the herringbone screen opening increases, the permeability of the woven screen to quinoa grains first increases and then decreases. Thus, the optimal herringbone screen opening for straw and grain cleaning is between 15° and 45°. Combined with the analysis of the displacement and acceleration of the center of mass of the vibrating screen using multi-body dynamics, the herringbone screen opening angle should be selected between 15° and 30°. From a commercial perspective, the ultimate design direction of the screen should be to achieve a certain harvesting efficiency while ensuring that the impurity content meets the technical requirements for quinoa harvesting, thereby guaranteeing economic benefits.

5. Materials and Methods

5.1. Test Subjects and Equipment Description

In October 2024, the experimental prototype of the quinoa combine harvester was tested in field trials in Dongxiang County, Linxia Autonomous Prefecture, China. The quinoa variety used in the trials was Longqi No. 5, developed by the Institute of Animal Husbandry, Grassland and Green Agriculture of Gansu Academy of Agricultural Sciences in Gansu, China. This variety exhibited an average plant height of approximately 1620 mm, with an average of 18 tillers per plant and a mean panicle height of 355 mm. The planting density was 4~7 plants/m², with a seed moisture content of 14% and a stem moisture content of 26%. The plant spacing was 320 mm, and the row spacing was 400 mm.

The field test was conducted using the 4LZ-4.0 quinoa combine harvester for hilly and mountainous areas, manufactured by Gansu Agricultural University in Gansu, China. Before the test, the working conditions of all components of the combine harvester were checked. The threshing drum speed was set at 720–750 r/min, the forward speed of the combine harvester was set at 0.75–1.5 m/s, and the opening angle of the herringbone screen was adjusted to 20°. The test site is shown in (Figure 13a).

5.2. Experimental Methodology

The experiments were conducted in accordance with the current Chinese national standard “Combine Harvesters—Test Methods” (GB/T 8097-2008) [47]. As required by the standard, five evenly distributed sampling points were established within a 100 m experimental area. The combine harvester traversed the entire 100 m area at full working width. A square sampling frame with an area of 1 m² was used to collect the lost seeds discharged by the cleaning device, which were then bagged and labeled (Figure 13b). After the experiment, the mass of the five samples was measured using an electronic scale, and the average value was calculated to determine the loss rate of the cleaning device. Simultaneously, samples were taken from the upper, middle, and lower layers of the grain tank to separate broken seeds, unthreshed seeds, and other impurities. The threshing efficiency, impurity rate, and seed damage rate of the quinoa harvester were determined based on these measurements.

6. Results and Discussion

In accordance with the domestic quinoa harvesting technology requirements in China and the agronomic practices of quinoa cultivation, the combine harvester for quinoa is required to meet certain standards for threshing efficiency, impurity content, and seed damage rate. The specific indicators are shown in

Table 6. Technical specifications and experimental results.

Experimental Indicators	Threshing Efficiency (%)	Impurity Content (%)	Seed Damage Rate (%)	Cleaning Loss Rate (%)
Indicator requirements	≥95	≤5	≤3	≤3
Experimental results	96.83	4.3	0.15	0.52

.

A comparison of the experimental results in Table 6 with the technical specifications reveals that when the herringbone screen opening angle is set at 20°, the vibrating screening mechanism achieves a high cleaning efficiency while maintaining a low loss rate. The experimental data meet the technical requirements, with the cleaning loss rate significantly lower than that of conventional quinoa harvesters. Moreover, the threshing efficiency, impurity content, and seed damage rate all meet the design requirements.

The results of the experimental study on the vibrating cleaning screen mechanism of the quinoa combine harvester for hilly and mountainous areas are presented. The model of the vibrating cleaning screen mechanism was simplified, and the vibration screen parameters were optimized using the MBD-EDEM coupling method. The relevant parameters were set in RecurDyn and EDEM to simulate and analyze the screening mechanism of the quinoa combine harvester’s vibrating screen. The field experiments conducted to verify the cleaning effect of the herringbone screen at the given opening angle of 20° demonstrated that the performance of the vibrating screen met the requirements for quinoa harvesting. The cleaning efficiency was found to be high, while the loss rate remained low, indicating that the optimized design of the vibrating screen is effective in improving the overall harvesting performance. The findings suggest that the proposed design and parameter optimization approach can be a valuable solution for enhancing the efficiency and effectiveness of quinoa harvesting in challenging hilly and mountainous terrains.

7. Conclusions

The analysis of the displacement and acceleration at the center of mass of the vibrating screen revealed that both displacement and acceleration in the horizontal and vertical directions exhibit regular periodic variations. Moreover, the amplitude range of displacement and force variation in the horizontal direction is larger than that in the vertical direction. In other words, the screen structure designed based on the selected K0 value can achieve forward sliding and stratified throwing of the threshing mixture, effectively preventing the accumulation of threshing materials and improving the threshing efficiency.

Single-factor coupling simulation experiments were conducted on herringbone screens with openings of 15°, 30°, and 45°, respectively. When the herringbone screen opening was 15°, the amplitude of velocity changes in both the horizontal and vertical directions was relatively large. As the herringbone screen opening increased, the amplitude of average velocity changes for each material was significantly reduced.

A comprehensive analysis of the screening performance of the two screen surfaces under the three different opening angles of the herringbone screen, as well as the displacement and acceleration curves of the center of mass of the vibrating screen, revealed that the screening and cleaning effects were optimal when the herringbone screen opening was between 15° and 30°. At this time, the pass rate of quinoa grains through the herringbone screen was 81.86%, that of long stalks was 35.4%, and that of short stalks was 64.4%. The pass rate of quinoa grains through the woven screen was 73.24%, that of long stalks was 9%, and that of short stalks was 41%. The permeability and cleaning efficiency of the vibrating screen system were the best.

The field experiments demonstrated that when the herringbone screen opening angle was set at 20°, the vibrating screening mechanism achieved a high cleaning efficiency while maintaining a low loss rate. The experimental data not only met the technical specifications but also outperformed conventional quinoa combine harvesters. This finding confirms that the cleaning performance of the herringbone screen at this angle is satisfactory and consistent with the results obtained from simulation studies.