ANALYSIS AND EXPERIMENTATION OF THE CRUSHING AND SEPARATION PROCESS OF THE ROOT-SAND COMPLEX OF HARVESTED AND EXCAVATED Cyperus esculentus L. IN DESERTS

ABSTRACT

The aim of this study is to simplify the difficult excavation that is caused by the root-sand complex in the process of harvesting Cyperus esculentus in the desert of Xinjiang by performing mechanical tests and analysis of the interaction between the vibrating excavation shovel and the rotary blade on the root-sand complex. The rotary blade number, rotary blade speed and digging depth were used as the test parameters, and the Cyperus esculentus breakage rate, root-grass crushing rate, and soil carrying rate were used as the test indicators. The characteristics of the influence of various factors and their interaction on the crushing and separation of the root-sand complex were explored. A parameter combination optimization model is verified by experimental data. The test results showed that the optimal combination was as follows: the number of rotary blades was 20, the rotational speed of the rotary blade was 373 r/min, and the digging depth was 12 cm. At this time, the Cyperus esculentus breakage rate, root-grass crushing rate, and soil carrying rate were 2.62%, 63.68% and 55.40%, respectively. This study can support the development of a Cyperus esculentus harvester suitable for deserts in Xinjiang.

Cyperus esculentus; excavation; root-sand complex; rotary tillage; vibrating shovel

INTRODUCTION

Cyperus esculentus is a perennial herb of the Cyperaceae family that can be used as grain, oil and feed. This herb is an important oil crop with the characteristics of drought resistance, waterlogging resistance, barren resistance and strong adaptability ( Yang, 2017 ; Zhang et al., 2019 ; Wang, 2020a). Cyperus esculentus can maintain and restore the ecosystem in sandstorm areas and thus increase the profitability of farming to improve people's living standards (Wang, 2022). Therefore, some desert areas in Xinjiang use oil bean as the main crop variety. Cyperus esculentus has been planted on a large scale in Xinjiang. For example, in Xing'an town, Tumushuke city, alone, the planting area reached more than 13 km² in 2020. Moreover, the harvesting process of Cyperus esculentus plants is labor intensive and expensive ( Wang et al., 2019 ; Yang & Zhu, 2020 ; Lu et al., 2019 ; Huang et al., 2013) , especially considering the climate characteristics of Xinjiang, which has a large temperature difference between the day and night, extremely low precipitation and higher requirements for harvest timeliness ( Jing et al., 2014) . In harvesting Cyperus esculentus, the objects that are being handled are Cyperus esculentus, the roots and the sandy soil. In particular, the network-like fibrous root system of Cyperus esculentus is developed and intertwined with sandy soil to form a complex composite structure (hereafter referred to as the root-sand complex), which makes the binding strength of the composite higher than that of ordinary sandy soil and leads to problems such as difficulty in excavation during harvesting. In response to the above problems, this paper applied a Cyperus esculentus excavation device using rotary tillage technology and vibratory digging technology. The process of crushing and separating the root-sand complex of Cyperus esculentus was studied and tested.

Due to the characteristics of good soil cutting and strong soil breaking, rotary tillage technology has been widely used ( Lin et al., 2016 ). In the early 1970s, Hendrick and Gill conducted a series of studies on the design parameters and working parameters of rotary blades, which laid a theoretical foundation for research on the optimization of rotary blades (Hendrick & Gil, 1978). Using classical mechanics theory, Ahmadi et al. deduced the dynamic torque calculation model of a rotary blade. Compared with the test results completed by Chertkiattipol et al., the torque calculation result has an error of approximately 5% (Ahmadi, 2017; Chertkiattipol & Niyamapa, 2010) . Matin et al. analyzed the torque, power and energy consumption characteristics of C-shaped machetes, half-width knives and straight knives at four rotational speeds and recorded the entire process of the rotary cultivator during excavation with the help of a high-speed camera (Matin et al., 2015). Marenya, Salokhe et al. studied the traction force during the working process of a rotary blade (Marenya, 2009; Salokhe & Ramalingam, 2003) . Iwasaki et al. divided the rotary blade into the curved knife and the straight knife and analyzed the working resistance of each part (Iwasaki et al., 1992). Asl and Singh established the dynamic and static soil cutting resistance formulas of the rotary blade and analyzed the soil cutting energy consumption by means of computer and numerical methods ( Asl & Singh, 2009) . Moreover, the vibration excavation method is a common excavation method. According to the vibration form of the soil-contacting parts, this method is divided into self-excited vibration and forced vibration. Self-excited vibration does not require additional power input and is due to the change in excavation resistance exciting elastic soil-contacting components to generate vibration. The research shows that the self-excited vibration soil-contacting member has a certain drag reduction effect ( Soeharson & Radite, 2010 ; Wang et al., 2016 ; Berntsen et al., 2006) ; the forced vibration excavation method requires external energy and a vibration mechanism to drive the soil-contacting parts to vibrate at a fixed frequency and amplitude. Many scholars have carried out related studies on the above two methods, different component structures and their application conditions ( Rao et al., 2019 ; Rao et al., 2018 ; Razzaghi & Sohrabi, 2016 ; Niyamapa & Salokhe, 2000 ; Shahgoli et al., 2010 ; Shahgoli et al., 2009 ; Koc et al., 2017) , but due to the different structural types of soil-contacting components and soil working conditions, the excavation effects are different.

In summary, problems such as the difficulty of excavation due to the root-sand complex arise during the harvesting of Cyperus esculentus in the desert areas of Xinjiang. This paper investigates the process of crushing and separation of the Cyperus esculentus root-sand complex in excavation operations. The Cyperus esculentus root-sand complex was taken as the research objective, and crushing and separation tests were performed with a self-developed Cyperus esculentus digging device using rotary tillage technology and vibratory digging technology. The breakage and separation characteristics of the root-sand complexes were studied through orthogonal tests of related parameters. Through the application of the above technology and experimental research, the crushing and separation of the Cyperus esculentus complex was accomplished while harvesting Cyperus esculentus in an extremely dry desert environment. This study provides support for the development of a Cyperus esculentus harvester suitable for the Xinjiang desert area.

MATERIAL AND METHODS

Analysis of the breakage and separation process of the root-sand complex

Analysis of the rotary blade operation process

When the rotary blade is working, it will cut and throw the sand and the root-sand complex. The tangential surface of the blade enters the soil and compresses and deforms the sand to form a shear plane. Then, the blade forms a soil ridge, part of which slides down to both sides of the tool, with the remainder sliding along the tangential surface. The force analysis is shown in Figure 1 .

FIGURE 1
Sandy soil force analysis schematic. Notably, O is the rotation center of the rotary blade shaft, R_q is the outer radius of the tangent, AB is the tangential plane of the rotary blade, ε’ is the tangent front inclination angle, R_p is the distance from the simplified centerpoint C of the force to the center of rotation when the sand is thrown on the tangent surface, ε is the angle between R_q and the tangent plane, ω is the rotary blade speed, θ_p is the angle that R_p has turned from the vertical position, and θ_q is the angle that R_q has turned from the vertical position. Simplified calculations are performed here without considering the tangential surface effects.

When the rotary blade is working (the force analysis is shown in Figure 1 ), in addition to cutting and throwing sand and soil, the blade cuts, crushes and throws the Cyperus esculentus root-sand complex. For the rotary blade to effectively cut sand and root-sand complexes, satisfying [ eq. (1) ] is necessary:

$\left\{\begin{array}{l}\frac{F_T-F{t}_f}{M_t}>{\tau }_s=\tan {\phi }_s+c_s\\ \frac{F_T-F{t}_f}{M_t}>{\tau }_{gst}=\sigma \tan {\phi }_{gst}+c_{gst}\end{array}\right.$ (1)

Where:

F_t is the shear force on the material, N;

F_tf is the shear resistance of the material, N;

M_t is the shearing surface area of the rotary blade, mm²;

τ_s is the shear strength of sand, Pa;

τ_gst is the shear strength of the Cyperus esculentus root-sand complex, Pa;

σ is the normal stress during shearing, Pa;

φ _s is the internal friction angle of sand;

φ _gst is the internal friction angle of the root-sand complex;

C_s is the cohesion of sand, Pa, and

C_gst is the cohesion of the root-sand complex, Pa.

Due to the special physical properties of sand, its cohesion can be ignored here. The cohesion c of the Cyperus esculentus root-sand complex of oleifera can be selected as 10~20 kPa with reference to the complex characteristics of other plants ( Yan et al., 2022 ; Yang et al., 2021 ; Wang, 2020b). Due to the constant shearing surface area of the rotary blade during work, according to [ eq. (1) ], the size of the shear force is the main factor that affects the cutting operation. In actual work, the rotational speed of the rotary cutter shaft determines the magnitude of the shear force, so the rotational speed of the rotary cutter shaft will affect the cutting operation of the root-sand complex.

At the same time, during the throwing operation, to avoid generating friction so that the sand and the root-sand complex can be thrown out, the resultant force perpendicular to the tangent plane on the material must be less than 0 (consider the action of centrifugal force F_o ); that is,

$\sum F(X)<0$ (2)

The following equations can be obtained from [ eq. (2) ] and Figure 1:

$\begin{array}{r}\sum F(X)=mg\sin \left({\theta }_p+\epsilon \right)+F_o\sin \epsilon +a{M}_Y+F_k\\ \sum F(X)=mg\sin \left({\theta }_p+\epsilon \right)+m{\omega }^2{R}_p\sin \epsilon +a{M}_Y+2m\omega v_h\end{array}$ (3)

Where:

∑ F ( X ) is the resultant force perpendicular to the tangent plane on the material, N;

m is the material quality, g;

g is the acceleration of gravity, m∙s^-2;

a is the adhesion factor;

M_y is the leaf area, mm²;

F_o is the centrifugal force of the material, N;

F_k is the inertial force of the material, N, and

𝒱_h is the relative velocity of the material moving along the tangential plane (as shown in Figure 3 , 𝒱_e is the implicated velocity of the material moving along the tangential plane, and 𝒱_o is the absolute velocity of the material moving along the tangential plane).

FIGURE 3
Structural diagram of the Cyperus esculentus digging device. 1. Frame assembly; 2. Regulator of depth-limiting wheel; 3. Depth-limiting wheel; 4. Rotary tillage cutter shaft; 5. Rotary cutter; 6. Vibratory digging shovel; 7. Sprocket assembly; 8. Connecting rods of vibratory digging shovel; 9. Rollers; 10. Cam

Equation (3) can be substituted into [ eq. (2) ]. Since the adhesion factor of sand is small, the a M _y term is ignored. At the same time, because the rotating speed of the rotary blade is fast, the relative motion of the material along the tangential plane is not currently considered; thus, the F_k term is ignored. Then, the following formula can be obtained:

$n_m>\frac{30}{\pi }\sqrt{\frac{g\sin \left({\theta }_p+\epsilon \right)}{R_p-\sin \epsilon }}$ (4)

From [ eq. (4) ], when the rotary blade rotates so that the tangential plane is in a horizontal position, materials such as sand and soil are most likely to leave the tangential plane. In addition, in the independent construction of the Cyperus esculentus excavation device when the rotary tillage blade IT245 is selected, in the calculation that R_p = 245 mm, ε = 80 °; at this time, only when the rotary tillage blade speed n_m > 61 r/min can the throwing operation be complete. During the excavation process, the rotation speed of the rotary blade will affect the number of materials that are cut and the time to cut those materials, which in turn affects the amount and magnitude of the force on the material. Through the calculation and analysis of Eq. (1) and (4) , the magnitude of the relevant force will lead to changes in the degree of cutting and the degree of fragmentation of Cyperus esculentus and the root-sand complex. At the same time, the rotation speed of the rotary cultivator will affect the difference in the throwing position and the initial velocity of the throwing. According to the traditional rotary blade motion analysis, the number of rotary blades will also affect the number of times the material is cut, which will lead to changes in the degree of fragmentation of Cyperus esculentus and the root-sand complex.

Analysis of the vibration excavation process

During vibration excavation, the digging resistance and vibration resistance of the device will affect the magnitude of the force on the material. Thus, in the process of analyzing the vibration digging shovel, the influence of the resistance should be considered. According to the force of the vibrating excavation shovel during excavation and the force of the excavated sand, the vibration excavation shovel is divided into the vibrating excavation flat shovel and the vibrating grid screen for analysis ( Figure 2 )

FIGURE 2
Vibration excavation process force analysis schematic. Notably, CD is the vibrating digging plane shovel surface; DF is the arc-shaped vibrating grid screen (the cross section is circular); E is a point on the arc sieve; G is the gravity of sandy soil on the shovel surface; C_n is the cohesion factor of sandy soil; C₁ is the sand adhesion factor; F₁ is the acceleration force of the sandy soil moving along the shovel surface; F_N1 is the normal load on the front failure surface; F_No is the normal load of the shovel surface on the sandy soil; M_s is the shear area within the sandy soil; M_c is the area of the digging shovel; ϒ is the inclination angle of the front failure surface; δ is the tilt angle of the shovel surface; μ is the internal friction factor of the sandy soil; μ1 is the friction factor between the sandy soil and the excavation shovel; O_s is the center of the arc sieve circle; F_s is the arc screen traction force; F_so is the sticky resistance caused by the sandy soil to the arc sieve; F_sn is the normal positive pressure on the curved screen; R_s is the radius of the curved screen; θ _s is the angle of the DF section arc screen; and θ is the angle of deflection of a point E on the curved sieve.

Moreover, the resistance calculation formula of the vibration excavation plane shovel is as follows:

$\left\{\begin{array}{l}{w}_{cc}=\frac{G}{Z_c}+\frac{C_n{M}_s+F_1}{Z_c(\sin \gamma +\mu \cos \gamma )}+\frac{C_1{M}_c}{Z_c\left(\sin \delta +{\mu }_1\cos \delta \right)}\\ w_{ct}=\left(C_n{M}_s+\mu F_{N1}\right)\sin \gamma +\left(C_1{M}_c+{\mu }_1{F}_{No}\right)\sin \delta +F_1\cos \delta +G\end{array}\right.$ (5)

Where:

W_cc is the horizontal resistance of the vibratory digging shovel;

W_ct is the vertical resistance of the vibratory digging shovel, and

Z_c is a constant.

The viscous drag principle can be applied in the force analysis of the vibrating grizzly screen. Meanwhile, to simplify the calculation, the vertical height of arc DF is approximated to be equal to the digging depth d. The formula for calculating the resistance of a vibrating grizzly screen can be obtained as follows:

$\left\{\begin{array}{l}{w}_{sc}={\int }_0^{\delta -\arccos \left(\frac{R_s\cos \delta -d}{R_s}\right)}\left[\frac{F_{sn}+Z_s\left(6\pi \eta v_m{r}_0\right)}{\sin (\delta +\theta )}+\frac{{\mu }_1{F}_{sn}}{\cos (\delta +\theta )}\right]d\theta \\ w_{st}={\int }_0^{\delta -\arccos \left(\frac{R_s\cos \delta -d}{R_s}\right)}\left[\frac{F_{sn}+Z_s\left(6\pi \eta v_m{r}_0\right)}{\cos (\delta +\theta )}+\frac{{\mu }_1{F}_{sn}}{\sin (\delta +\theta )}\right]d\theta \end{array}\right.$ (6)

Where:

W_sc is the horizontal resistance of the vibrating grizzly screen;

W_st is the vertical resistance of the vibrating grizzly screen;

η is the viscosity coefficient of the sandy soil;

𝒱_m is the forward speed of the device;

r_o is the radius of the circular cross section of the curved vibrating grizzly screen, and

Ζ_s is a constant.

The digging depth will first affect the sand quality on the shovel surface, which will affect the normal positive pressure on each area. According to the analysis of Figure 2 , eqs (5) and (6) , in addition to the physical properties of the sand and root-sand complex, the main factors that affect the stress of the sand and the root-sand complex are the digging depth and the inclination of the screen surface.

The inclination of the screen surface will mainly affect the positive pressure of the material and the forward resistance of the device. This paper focuses on the process of fragmentation and separation of the Cyperus esculentus root-sand complex at harvest. The inclination of the screen surface was not a major influence in this process, so the inclination of the screen surface was not considered an influencing factor in the subsequent tests. Due to the relatively fixed growth depth of Cyperus esculentus and the physical characteristics of sandy soil, the digging depth influences the action of the relevant forces on the material and the cutting position of the rotary blade. Excessive digging depth will prevent the rotary blade from cutting the material and affect the crushing and separation of the root-sand complex. A digging depth that is too small will lead to inadequate cutting of the material, which affects the vibration separation effect of the vibratory excavation shovel.

Test material

The test samples were randomly selected from the Cyperus esculentus planting test base of the 54th Regiment of the Third Division of the Xinjiang Production and Construction Corps. The variety was Zhongyousha No. 1, and the sampling period was October 2021. During the test, the national standard "GB/T5262-2008 General Provisions for Determination Methods of Agricultural Machinery Test Conditions" was referenced. A square box of 1 m² was used to select 1 m² of Cyperus esculentus in the field test area for harvesting Cyperus esculentus, and 1 m² of Cyperus esculentus plant and grain samples of Cyperus esculentus were collected according to the cutting height. Measurements, calculations and statistical tests of the characteristic parameters of Cyperus esculentus are shown in Table 1 . At the same time, the following characteristic parameters of sandy soil in the same experimental area were measured: the density was 1.638 g∙cm^-3; the surface moisture content was 2.59%; and the average moisture content of the sand that was entrained by the root-sand complex was 6.51%.

TABLE 1
Table of Cyperus esculentus characteristic parameters for testing.

Name	Parameter
Cyperus esculentus plant quantity of 1 m2 (g)	1582
Cyperus esculentus yield of 1 m2 (g)	664
Cyperus esculentus grass and root quantity of 1 m2 (g)	918
Yield (kg·km-2)	996.51
Cyperus esculentus grass to grain ratio	1.38
Cyperus esculentus moisture content of grain/%	25~40
Hundred grain mass (g)	104.33
The root depth (cm)	10.88
Cyperus esculentus growth depth (cm)	6.73
Plant stubble height (cm)	8.44
Cyperus esculentus grain size (mm)	8~12

Test equipment

The test equipment mainly included a self-built oil bean digging device, a 101-IB type electric heating blast constant temperature drying oven, an electronic scale JM-B5003 (range: 0~500 g, graduation value: 0.001 g), an electronic scale JSB15-05 (range: 0~15 kg, graduation value: 0.5 g), a 20 m tape measure, a Vernier caliper, scissors, and receiving bags.

The Cyperus esculentus excavation device mainly includes a frame, a depth-limiting wheel component, a rotary blade part and a vibration excavation part. The height of the depth-limiting wheel is controlled by a pair of rotating lead screws. The components of the rotary blade part use a detachable rotary blade to change the number of rotary blades. In addition, the shaft of the rotary blade is driven by a set of sprockets. During operation, the rotational speed of the rotary blade shaft is changed by changing the speed of the engine and the number of teeth in the sprocket at the end of the sprocket group. As a result, the vibration frequency of the vibrating shovel is guaranteed. A schematic diagram of the structure is shown in Figure 3 .

The working principle of the Cyperus esculentus excavation device during the excavation operation is as follows: the harvester rotates the excavating device down, and the depth-limiting wheel contacts the ground to provide support at the front end, which limits the digging depth; the harvester transmits power to the vibration excavation part and the rotary blade part in turn through the sprocket; at the same time, the cam is driven to vibrate the vibrating digging part by hitting the roller that is connected to the vibrating screen; finally, the rotation of the sprocket will also drive the rotary blade to rotate and start the rotary tillage operation.

Experimental method

Cyperus esculentus excavation test

Before the test, the catch bag was attached to the back end of the excavation device to collect excavation samples for each set of tests. Prior to the relevant trials, a review of relevant references and standards did not reveal any harvesting standards that met the criteria for Cyperus esculentus. Therefore, the general standard for harvesters, "GB/T 8097-2008 Equipment for harvesting-Combine harvesters-Test procedure", as well as the harvesting standards for crops similar to Cyperus esculentus, “JB/T 11912-2014 Soybean combine harvester" and "NY/T 502-2016 Operating quality for peanut harvesters," were referred to during the test. Additionally, to evaluate the degree of plant fragmentation, the standard "JB/T 8401.2-2007 Rototill combine equipment-Rototill scarifying-paring-ridging machine " is also referred to here. Furthermore, the working length of each group of tests was set to 25 m, and each group of tests was repeated 3 times. The samples were processed according to the calculation method of the experimental data, and the average value was calculated to obtain the Cyperus esculentus breakage rate, root-grass crushing rate, and soil carrying rate of each group of experiments. The Cyperus esculentus excavation tests were completed in sequence according to the test serial numbers, and the test process is shown in Figure 4 .

FIGURE 4
Test process.

Test index calculation method

The mass of all the Cyperus esculentus, including the mass of the Cyperus esculentus that is damaged by the excavation, in the samples that are taken after excavation are determined. Equation (7) is used to calculate the breakage rate of Cyperus esculentus.

$P_d=\frac{m_1}{m_2}\times 100\mathrm{\%}$ (7)

Where:

P is the breakage rate;

m₁ is the quality of the Cyperus esculentus that is damaged due to excavation, g, and

m₂ is the quality of Cyperus esculentus, g.

Additionally, all Cyperus esculentus stubble and broken grass in the samples taken after excavation are determined. The total quality of the broken grass and root stubble and the quality of the broken grass and root stubble whose length is less than or equal to 50 mm (excluding the length of fibrous roots) are determined. The root-grass crushing rate is calculated according to [ eq. (8) ].

$F_g=\frac{M_h}{M_Z}\times 100\mathrm{\%}$ (8)

Where:

F_g is the root-grass crushing rate;

M_h is the quality of the stubble and grass with length ≤50 mm, g, and

M_s is the total stubble and grass quality, g.

Equation (9) is used to calculate the soil carrying rate of the root grass.

$T=\frac{m_3}{m_4}\times 100\mathrm{\%}$ (9)

Where:

T is the soil rate;

m₃ is the mass of the soil in the sample (Cyperus esculentus plant sample) that was taken after excavation, g, and

m₄ is the quality of the Cyperus esculentus plant sample, g.

RESULTS AND DISCUSSION

Orthogonal design of the experiments

According to the calculation method of the test index, the calculation and statistics of the breakage rate, the root-grass crushing rate and the soil carrying rate are completed. Considering the harvesting efficiency of Cyperus esculentus and the width of the device used, the operating speed was 0.2 m/s, the amplitude was 9 mm, and the vibration frequency was 12.4 Hz.

Refer to the theoretical study in section 2.1 of the article. The number of rotary tillage blades, rotary tillage blade speed and digging depth are important factors that affect the quality of operation of the device and material crushing and separation. Therefore, they were chosen as test factors. Through the project team's preliminary single-factor test, it was found that at a rotary tillage blade number of 18~22, a rotary tillage blade speed of 335~405 r/min and a digging depth of 10~14 cm, the breakage rate and soil carrying rate were very low and the root-grass crushing rate was very high. Based on the parameter ranges of these test factors, the levels of the three test factors for this experiment were determined, as shown in Table 2 . A total of 17 sets of experiments were carried out by using the orthogonal test method and the L(3⁴) orthogonal table. The design table and the statistics of the breakage rate, root-grass crushing rate and soil carrying rate are shown in Table 3 .

TABLE 2
Digging parameter level.

Code	Number of rotary blades	Rotary blade speed (r/min)	Digging depth (cm)
-1	18	335	10
0	20	370	12
1	22	405	14

TABLE 3
Experimental layout and results.

Code	Number of rotary blades A	Rotary blade speed B	Digging depth C	Breakage rate Pd /%	Root-grass crushing rate Fs /%	Soil carrying rate T /%
1	-1	-1	0	3.73	28.51	73.62
2	1	-1	0	4.97	55.00	163.7
3	-1	1	0	4.47	45.51	74.08
4	1	1	0	5.50	54.43	79.67
5	-1	0	-1	5.68	38.83	65.16
6	1	0	-1	7.57	58.33	94.44
7	-1	0	1	4.86	44.39	73.90
8	1	0	1	5.46	51.40	123.87
9	0	-1	-1	4.71	38.13	116.67
10	0	1	-1	8.46	25.87	71.92
11	0	-1	1	4.29	34.11	119.98
12	0	1	1	3.48	52.45	124.27
13	0	0	0	2.45	58.72	70.35
14	0	0	0	3.22	63.60	44.49
15	0	0	0	1.84	73.97	52.74
16	0	0	0	3.34	70.40	66.19
17	0	0	0	2.51	60.88	63.81

Establishment of the significance test of the breakage rate regression model

According to the analysis of the test data in Table 3 and the multiple regression fitting, the analysis of variance was performed on the breakage rate, and the results are shown in Table 4 .

TABLE 4
Analysis of the variance of the breakage rate.

Source	Sum of squares	d f	Mean square	F value	P value	Significance
Model	46.08/45.66	9/7	5.12/6.52	13.62/19.19	0.0012/<0.0001	significant
A	2.83	1	2.83	7.53/8.33	0.0287/0.0180	*
B	2.22	1	2.22	5.89/6.52	0.0456/0.0310	*
C	8.67	1	8.67	23.07/25.52	0.0020/0.0007	**
AB	0.011	1	0.011	0.029	0.8689
AC	0.42	1	0.42	1.11	0.3278
BC	5.20	1	5.20	13.83/15.30	0.0075/0.0036	**
A2	7.41	1	7.41	19.71/21.80	0.0030/0.0012	**
B2	1.88	1	1.88	5.01/5.55	0.0602/0.0430	*
C2	15.10	1	15.10	40.18/44.44	0.0004/<0.0001	**
Residual	2.63/3.06	7/9	0.38/0.34
Lack of fit	1.12/1.54	3/5	0.37/0.31	0.98/0.82	0.4846/0.5946	not significant
Pure Error	1.51	4	0.38
Cor Total	48.72	16
R2	0.9460/0.9372

• Note: The value following the slash is the result of removing the nonsignificant factors. * means significant (0.01< P <0.05), and ** means very significant ( P <0.01)

Table 4 shows that the primary and secondary order of the influence of each factor and the interaction between the factors on the breakage rate P_d are C², C, A², BC, A, B , B², AC , and AB . Among them, C², C, A² and BC have a very significant influence on the breakage rate P_d ( P < 0.01), while A, B and B² have a significant impact on the breakage rate P_d (0.01 < P < 0.05). After incorporating the regression sum of the squares and degrees of freedom of some insignificant interaction terms into the residual term, the analysis of the variance was performed, as shown in Table 4 . The regression equation P₁ of each factor on the breakage rate P_d was obtained as follows:

$P_1=2.67+0.60A+0.53B-1.04C-1.14BC+1.33A^2+0.67B^2+1.89C^2$ (10)

Establishment of the significance test of the root-grass crushing rate regression model

According to the analysis of the test data in Table 3 and the multiple regression fitting, the analysis of the variance was performed on the root-grass crushing rate, and the results are shown in Table 5 . Table 5 shows that the primary and secondary orders of the influence of each factor and the interaction between the factors on the root-grass crushing rate F_g are B², A, C², BC, A², AB, B, C, and AC.

TABLE 5
Analysis of variance of the root-grass crushing rate.

Source	Sum of squares	d f	Mean square	F value	P value	Significance
Model	2843.19/2640.72	9/6	315.91/440.12	8.46/9.49	0.0051/0.0012	significant
A	479.26	1	479.26	12.83/10.33	0.0090/0.0093	**
B	63.34	1	63.34	1.70/1.37	0.2341/0.2698
C	56.13	1	56.13	1.50/1.21	0.2600/0.6972
AB	77.18	1	77.18	2.07	0.1928
AC	39.00	1	39.00	1.04	0.3409
BC	234.09	1	234.09	6.27/5.04	0.0408/0.0485	*
A2	86.29	1	86.29	2.31	0.1724
B2	963.16/996.51	1	963.16/996.51	25.78/21.48	0.0014/0.0009	**
C2	684.42/712.21	1	684.42/712.21	18.32/15.35	0.0037/0.0029	**
Residual	261.54/464.01	7/10	37.36/46.40
Lack of fit	94.87/297.34	3/6	31.62/49.56	0.76/1.19	0.5727/0.4533	not significant
Pure Error	166.67	4	41.67
Cor Total	3104.73	16
R2	0.9158/0.8505

Among them, B², A and C² have a very significant influence on the root-grass crushing rate F_g (P < 0.01), while BC has a significant impact on the root-grass crushing rate F_g (0.01 < P < 0.05). After incorporating the regression sum of the squares and degrees of freedom of some insignificant interaction terms into the residual term, the analysis of the variance was performed, as shown in Table 5 . The regression equation P₂ of each factor on the root-grass crushing rate F_g was obtained as follows:

$P_2=63.61+7.74A+2.81B+2.65C+7.65BC-15.36B^2-12.99C^2$ (11)

Establishment of the significance test of the soil carrying rate regression model

According to the analysis of the test data in Table 3 and the multiple regression fitting, the analysis of the variance was performed on the root-grass crushing rate, and the results are shown in Table 6 . Table 6 shows that the primary and secondary order of the influence of each factor and the interaction between the factors on the soil carrying rate T are A, B², B, AB, C², C, BC, A² , and AC . Among them, A, B², B, AB and C² have a very significant influence on the soil carrying rate T ( P < 0.01), while C has a significant impact on the soil carrying rate T (0.01 < P < 0.05). After incorporating the regression sum of the squares and degrees of freedom of some insignificant interaction terms into the residual term, the analysis of the variance was performed, as shown in Table 6 . The regression equation P₃ of each factor on the soil carrying rate T was obtained as follows:

TABLE 6
Analysis of the variance of the soil carrying rate.

Source	Sum of squares	d f	Mean square	F value	P value	Significance
Model	15402.97/15295.95	9/8	1711.44/1911.99	15.84/17.72	0.0007/0.0003	significant
A	3824.63	1	3824.63	35.40/35.44	0.0006/0.0003	**
B	1922.93	1	1922.93	17.80/17.82	0.0039/0.0029	**
C	1100.51	1	1100.51	10.19/10.20	0.0152/0.0127	*
AB	1784.64	1	1784.64	16.52/16.54	0.0048/0.0036	**
AC	107.02	1	107.02	0.99	0.3528
BC	601.23	1	601.23	5.56/5.57	0.0504/0.0459	*
A2	395.52	1	395.52	3.66/3.67	0.0973/0.0919
B2	3434.29	1	3434.29	31.79/31.82	0.0008/0.005	**
C2	1706.94	1	1706.94	15.80/15.82	0.0054/0.0041	**
Residual	756.30/863.32	7/8	108.04/107.91
Lack of fit	304.25/411.27	3/4	101.41/102.82	0.90/0.91	0.5161/0.5354	not significant
Pure Error	452.05	4	113.01/113.01
Cor Total	16159.27	16
R2	0.9532/0.9466

$P_3=59.52+21.87A-15.50B+11.73C-21.12\mathrm{A}\mathrm{B}+12.26BC+9.69A^2+28.56B^2+20.13C^2$ (12)

Response surface analysis

The experimental data were processed by Design-Expert 8.0.6 statistical software. The response surfaces of the significant and relatively significant interactions among the rotary blade number A , the rotary blade speed B , and the digging depth C on the breakage rate, root-grass crushing rate and soil carrying rate were obtained as shown in Figure 5 .

FIGURE 5
Response surface diagram of the oil bean digging device.

Figure 5a shows that when the digging depth of the device is constant, the breakage rate first decreases and then increases with an increasing number of rotary blades A . The optimal number of rotary blades is 19~20. The breakage rate initially decreases and then increases with increasing rotary blade speed B . The optimal rotary blade speed is 335~384 r/min. When the number of rotary blades and the rotary blade speed are low, the rotary cultivator fails to fully throw out the material, and the number of times that the material is acted on by the rotary blade increases, which results in an increasing breakage rate P_d . However, when the number of rotating blades and rotating blade speed of the equipment are high, the force between the rotating blades and the material increases and becomes larger, which will also lead to an increase in the breakage rate P_d .

As shown in Figure 5b , when the number of rotary blades is 20, the root-grass crushing rate first increases and then decreases with an increasing rotary blade rotation speed and an increasing digging depth. The optimal rotary blade speed is 356~384 r/min because when the rotating speed of the rotary cultivator is low, the rotary blades cannot fully cut the material, which results in a reduction in the root-grass crushing rate F_g . When the rotating speed of the rotary blades of the device is high, the throwing effect of the rotary blades increases, which also leads to a decreasing root-grass crushing rate. Currently, when the digging depth is shallow, the rotary blade cannot completely cut the roots and grass, which results in a reduction in the root-grass crushing rate F_g . When the digging depth is deep, the working part of the rotary tillage blade crosses the growth range of some roots and grasses, which results in a decrease in the root-grass crushing rate F_g .

As shown in Figure 5c , when the digging depth is constant, the soil carrying rate T increases with an increasing number of rotary blades. The optimal number of rotary blades is 18~20 because the higher the number of rotary blades is, the greater the throwing action of the rotary blades. Thus, some root-sand complexes cannot be broken up, which results in an increasing soil carrying rate T . As shown in Figure 5d , when the number of rotary blades is 20, the soil carrying rate T first decreases and then increases with an increasing rotary blade speed B . The optimal rotary blade speed is 342~391 r/min because when the rotating speed of the rotary blade is low, the cutting action of the rotary blade decreases, the vibration decreases, and the root-sand complex cannot be effectively destroyed. When the rotational speed of the rotary blade of the device is high, the throwing effect of the rotary blade increases, and the root-sand complex cannot be effectively cut, which leads to an increasing soil carrying rate. Currently, the soil carrying rate T increases with an increasing digging depth C . The optimal digging depth is 10~12 cm because the increase in the digging depth reduces the direct effect of the rotary blade on the root-sand complex, which results in an increased soil carrying rate.

To obtain the best operating parameters, optimizing the working parameters and achieving a reasonable matching of parameters between factors are key. The objective is to have the lowest breakage rate and soil carrying rate and the highest root-grass crushing rate. The objective function and constraints are shown in [ eq. (13) ].

$\left\{\begin{array}{r}min{P}_1\\ max{P}_2\\ min{P}_3\\ 18\le A\le 22\\ 335\le B\le 405\\ 10\le C\le 14\end{array}\right.$

According to the actual working conditions and the abovementioned related model analysis, the solution result is as follows: the number of rotary blades is 19.74, the rotary blade speed is 372.92 r/min, and the digging depth is 12.19 cm. Currently, the breakage rate of the device is 2.58%, the root-grass crushing rate is 62.92%, and the soil carrying rate is 57.35%.

Experimental verification of the optimal excavation parameter combination for the Cyperus esculentus excavation device

To verify the reliability of the optimization model for the combination of parameters of the Cyperus esculentus excavator, a validation test of the excavator was conducted in the same Cyperus esculentus test area based on the solved optimal combination. Considering the actual working conditions, the optimal excavation parameter combination of the Cyperus esculentus excavation device was adjusted to the following field verification excavation test parameter combination: rotary blade number of 20, rotary blade speed of 373 r/min, and digging depth of 12 cm. A total of three field validation trials of the Cyperus esculentus excavator were completed utilizing the above combination. The mean values of the breakage rate, root-grass crushing rate and soil carrying rate were calculated for the three groups of field validation tests and were 2.62%, 63.68% and 55.40%, respectively, as shown in Table 7 . Using this table and the optimization results in Section 3.2.4 to calculate the error, the breakage rate, the root-grass crushing rate and the soil carrying rate are 1.55%, 1.21% and 3.40%, respectively, with small errors.

TABLE 7
Data of the validation test for the combination of an optimum Cyperus esculentus digging device for harvesting.

Serial No.	Breakage rate	Root-grass crushing rate	Soil carrying rate
1	2.16	65.38	60.12
2	2.97	63.25	52.26
3	2.73	62.42	53.82
Average value	2.62	63.68	55.40

CONCLUSIONS

1. In view of the excavation difficulties caused by the root-sand complex during the harvesting of Cyperus esculentus in the Xinjiang desert area, a series of studies was conducted in this paper. A mechanical analysis of the vibrating excavation shovel and the rotary blade on the root-sand complex was carried out. The rotary blade number, rotary blade speed and digging depth were used as the test parameters, and the Cyperus esculentus breakage rate, root-grass crushing rate, and soil carrying rate were used as the test indicators. Thus, the trends of the various influencing factors and their interactions on the fragmentation and separation of root-sand complexes were explored.

2. According to the principle of the response surface experimental design, the 3-factor 3-level response surface analysis method was used to conduct multifactor variance analysis on the factors that affect the experimental indicators. The results showed that the factors that affect the crushing rate of Cyperus esculentus were the digging depth, the rotary blade number, and the rotary blade speed, in descending order. The main factor that affected the root-grass crushing rate was the number of rotary blades. The factors that affect the root-grass carry rate were the rotary blade number, rotary blade speed, and digging depth, in descending order.

3. The regression model was optimally solved using the optimization module in Design-Expert 8.0.6 software and experimentally verified. The test results show that the optimal combination of excavation parameters is a rotary blade number of 20, a rotary blade speed of 373 r/min, and a digging depth of 12 cm. Moreover, the breakage rate, root-grass crushing rate and soil carrying rate were 2.62%, 63.68% and 55.40%, respectively. Thus, this paper provides support for the development of a Cyperus esculentus harvester applicable to the desert region of Xinjiang.

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• Funding: The work was supported by China's Central Government Guides Local Science and Technology Development Fund Projects (No. 2060404).

Edited by

Area Editor: Renildo Luiz Mion

Publication Dates

• Publication in this collection
  28 July 2023
• Date of issue
  July 2023

History

• Received
  29 July 2022
• Accepted
  14 June 2023