Study on Soil Throwing Performance and Ditch Depth Stability of Ditching Device in Sandy Orchards in Southern Xinjiang

Abstract

In order to solve the problems of serious soil reflux and poor stability of ditch depth in the existing ditching organic fertilizer fertilization device in grey desert and loess orchards, rotary tillage theory and software simulation were used to conduct kinematic analysis of soil particles and ditching blade in the ditching process, and meanwhile, modeling and simulation are carried out for sand soil particles by using EDEM software, so as to determine the action mechanism of soil, blade and fairing in ditching process of grey desert and loess. The abstract on this basis, the quadratic orthogonal regression-rotation combination experiment was designed. The soil bin test was carried out by taking the cutter wheel speed, ditching depth and inclination of curved surface as the influencing factors, and the throwing distance and the stability of ditch depth as the test indexes. And it was concluded that the order of the influence of the operating parameters of the ditching device on the soil throwing distance is ditching depth > inclination of curved surface > cutter speed, and the order of the influence on the stability of the ditch depth is ditching depth > cutter speed > Inclination of curved surface. Finally, the optimized operating parameters of the ditching device are as follows: the cutter wheel speed is 119.61 r·min⁻¹, the inclination of curved surface is 30.07°, the ditching depth is 35.52 mm, the soil throwing distance is 57.31, and the stability of ditch depth is 87.43. With these parameters as test objects, 10 groups of single factor tests were carried out to obtain that the soil throwing distance is 58.33, and the stability of ditch depth is 86.51, which were basically consistent with the expected results of the optimization test, and also in line with the relevant agronomic standards.

1. Introduction

At present, the area of fruit cultivation in China has reached the top of the world [1], In case of application of organic fertilizers in orchards, it has also been shown that in addition to improving the physical and chemical properties of the soil, organic fertilizers can also improve the yield and quality of crops to a certain extent [2]. In China, inorganic fertilizer deep application in the orchard appeared mechanical fertilization, while organic fertilizer trenching and fertilization operations are still mainly dependent on manual completion, Intensive operation, low efficiency, low standardization, and easy to delay the farming time, has not adapted to the requirements of modern orchard fertilization management links [3]. And mechanical device operation, due to the large amount of organic fertilizer fertilization, narrow planting rows, in addition to poor cohesion of grey desert and loess, resulting in fertilization in the soil backflow serious, ditching depth stability is poor, power consumption and other outstanding problems.

The core of the research and development of organic fertilizer deep application ditching device for orchards is the ditching device, the structure and working parameters of the trenching device directly affect the stability of the depth of the trench and the distance of the throwing soil. Related scholars use smooth particle flow fields [4], discrete Element Simulation [5], image processing [6,7,8], experimental studies [9] and other methods were used to study the soil spreading pattern and the stability of ditching depth during the trenching operation in progress. Upon the analysis of II S245 rotary colter’s structural parameters and its mechanism of plowing and throwing, Luo Haifeng established a mathematical model of colter’s transverse throwing and pointed out that the main influencing factors of the distance of transverse throwing were the colter’s bending angle and the friction coefficient between the colter and earth [10]; in order to track the earth’s displacement distance, Fang Huimin established a model of plowing and throwing of earth based on discrete elements and concluded that the distance of horizontal and lateral throwing of earth was increased with the higher rotation speed of colters [11]; after analyzing the plowing, smashing and throwing of earth by colters, Ren Shuguang established a differential equation of earth particles’ movement and verified the plowing and throwing process through Matlab simulation and field test, thus obtaining the optimal parameter portfolio for plow colters’ motion during throwing of earth [12]; Professor Jun Sakai from Kyushu University of Japan believed that the earth may only be throwed horizontally or with slight skewness, as the bent colters were influenced by the anti-shear force between the upper layer of soil and the other earth within the colters’ maximum turning radius; and proposed that the relief angle formed with colter’s concave surface and the trajectory curve may affect the colters’ performance in throwing earth [13]; Given the clayey soil environment in Bangkok, Thai professor V.M.Salokhe made a clear observation of earth throwing trajectory with a simulation model, conducted theoretical analysis of its motion process and verified the colters’ performance in throwing earth and weed by changing the forward velocity of machine [14]; Kang Jianming designed a plow colter with sinusoidal exponential curve and determined its optimal portfolio of working parameters through analysis of tractor’s forward velocity, colter disc’s rotation speed and the influence of their interaction to power consumption and plowing depth stability [15]. Mainly for trenching blade drag reduction research as well as operational parameters and power consumption research. However, so far, for grey desert and loess organic fertilizer ditching device exists backflow serious, ditching depth stability is poor and other soil spreading mechanism research has not seen.

Recent years, for the organic fertilizer ditching device researched by the group, theoretical analysis is made on the operation trajectory and operation flow of disc-type ditchers, combined with the phenomenon of grey desert and loess backflow, the mechanism of ditching grey desert and loess throwing is studied, the critical conditions of starting throwing are analyzed, the collision between the thrown up grey desert and loess particles and the guide hood is simulated by using EDEM software to explore its collision characteristics, and finally the operating parameters of the ditching device are optimized according to the soil bin test to improve the operation quality.

2. Materials and Methods

2.1. Structure and Working Principle of Organic Fertilizer Trenching Device

The organic fertilizer ditching device is mainly composed of a driving device, a transmission device, a fertilizer device, a ditching knife, a ditching knife, a deflector, and a plug, as shown in Figure 1.

The main function of ditching and fertilizer distributing machine is to dig a ditch and distribute organic fertilizer into it. Before operation, an appropriate amount of organic fertilizer is added into its fertilizer tank. The tractor is linked to draft gear through trifilar suspension, while the fertilizer distributing machine is aligned to the line along which fertilizer will be distributed. Then, start up the tractor. By connecting the power take-off shaft of the tractor, the cardan shaft will drive the gearbox of ditching machine. After the cutter wheel of ditching machine reaches the rated rotation speed, the hydraulic handle of tractor may be maneuvered to place the cutter wheel into the earth until it reaches the desired depth. The ditching operation may be continued at such depth and rotation speed. At the same time, the organic fertilizer in the tank is distributed into the ditch through a fertilizer guide plate, marking the completing of entire ditching and fertilizer distribution.

2.1.1. Main Parameters of Ditching Cutter

The ditching cutter mainly consists of front cutting plane, front cutting blade, side cutting plane, side cutting blade, bent plane, bent blade and earth throwing plate. As shown in Figure 2. According to the design requirements under the Manual for Agricultural Machine Design [16] and Rotary Tiller-Rotary Blades and Blade Holders (GB/T 5669-2008), the specific design parameters are as follows:

The parameter of front cutting plane is mainly the working width b which is mainly dependent on the desired ditch width. As excessive working width will reduce the rigidness of blade and earth crushing effect, the appropriate width b is 90~190 mm; the included angle of front cutting plane determines the sharpness of blade. According to the Manual for Agricultural Machine Design and based on the ditching demand, the included angle i of front cutting plane is 10°; the bending angle α refers to the included angle between front cutting plane and side cutting plane. Since the bending angle will directly affect the operation resistance of ditching wheeling and the power consumption thereof, a bending angle α of 50° is adopted in this design; the bending radius r is related to whether the cutter is easily stuck with soil, which will affect the power consumption; in this design, r is determined as 55 mm based on the ditching demand; the tilted cutting angle t is related to whether the cutter is easily tangled with roots of plants, which will affect the crushing of earth; in this design, t is 15°; the maximum turning radius R is dependent on ditching depth and in this design, R is 550 mm.

2.1.2. Kinematics Analysis of Ditching Blades

Based on the requirements on ditching operation, the travelling of cutting wheel during ditching is divided into three stages: soil cutting stage, soil removal stage and soil throwing stage. In the ditching operation, the ditching blade cuts the soil from the bottom of the trench to the surface, the direction of rotation of the ditching blade is opposite to the forward direction of the tractor wheel, and the corresponding horizontal force is also opposite to it, the trenching disc rotates and cuts the soil while moving forward together with the tractor, so its absolute motion is the synthesis of rotation and movement, and the trajectory is a cosine motion [17]. As shown in Figure 3,With the center of rotation of the cutter as the origin, X axis for the unit forward direction, the Y-axis is perpendicular to the X-axis in the positive direction to establish a right-angle coordinate system, let the forward speed of the unit be $V_m$, cutter rotation angular velocity is ω, the beginning of trenching, the blade end point is located at point A, in time t, the center of rotation of the cutter moves from point O to point P, at the same time, the blade end point from point A to point B, then the trajectory of point B equation is:

$$\{\begin{array}{c} x=V_{m}t+Rcos\omega t\\ y=Rsin\omega t\end{array}$$

(1)

where x, y is the trajectory coordinates of the ditching blade at any moment, m; R is the blade rotation radius, m; $V_m$ is the forward speed of the trencher, km/h; ω is the angular speed of the blade rotation, rad/s; t is the moving time, s; The absolute velocity of the end point of the ditching blade can be obtained by deriving the trajectory equation as:

$$\{\begin{array}{c}{V}_x=\frac{dx}{dt}=V_m-R\omega sin\omega t=V_m-R\omega sin\theta \\ V_y=\frac{dy}{dt}=R\omega cos\omega t=R\omega cos\theta \end{array}$$

(2)

where θ is the angle of blade rotation in time T.

In order to study the soil throwing performance, The variable “$\mu$” is introduced here, and “$\mu$” is the ratio between the blade speed $V_k$ and the unit forward speed $V_m$, so that $\mu =\raisebox{1ex}{$\omega R$}\!\left/ \!\raisebox{-1ex}{$V_m$}\right.$, then the absolute speed of the blade end point can be obtained as follows:

$$V=\sqrt{V_x^2+V_y^2}=\sqrt{R^2{\omega }^2+V_k{}^2+2V_{k}R\omega cos\omega t}$$

(3)

Let the instantaneous angle between the velocity and the X-axis be φ.

$$\phi =\arctan \frac{v_x}{v_y}=\frac{v_m-R\omega sin\theta }{R\omega cos\theta }$$

(4)

Further deformation of the horizontal fractional velocity yields

$$V_x=V_m\left(1-\mu \sin \theta \right)$$

(5)

From the above equation, we can see that when $\mu <1$, that is, $V_k<V_m$, then no matter what position the ditching blade rotates to, there is always $V_x>0$, the soil particles on the blade have to move in the direction of the advance of the unit, a large amount of soil will be thrown into the ditch and cannot be thrown well out of the ditch. When $\mu >1$, $V_k>V_m$, The blade end point trajectory is a residual cycloid, and the horizontal velocity of the end point is opposite to the forward direction of the unit, so the soil will have the tendency to be thrown backward and reduce the soil return flow.

Similarly, the acceleration equation of point B is obtained by deriving

$$\{\begin{array}{c}{a}_x=\frac{d{v}_x}{dt}=-R{\omega }^{2}cos\theta \\ a_y=\frac{d{v}_y}{dt}=-R{\omega }^{2}sin\theta \end{array}$$

(6)

where the direction of acceleration is always directed to the center of the cutter.

2.1.3. Motion Analysis of Soil Particles under the Action of Fairing

Soil particles crushed by the blade collided with the fairing, and their trajectories changed due to the collision. Therefore, the rectangular coordinate system was established to study the influencing factors of throwing distance and reduce the soil backfilling rate. As shown in Figure 4, When the end point of the ditching blade was located at the front horizontal position, the axis center was the coordinate origin, and the X-axis was the forward direction of the unit, The Z-axis was positive and vertical upward, and the Y-axis was perpendicular to the forward direction of the unit and facing the soil throwing direction. Because the fairing and the blade rotation center moved in a straight line $V_m$ together, a $O_1{X}_1{Y}_1{Z}_1$ spatial coordinate system was established with the lowest point $O_1$ of the fairing as the coordinate origin, in which the tangent direction of the fairing at the point $O_1$ was consistent with $Y_1$. The included angle between the plane $O_1{Y}_1{Z}_1$ and the plane $\mathrm{OXY}$ was α. The distance between the lowest points $O_1$ of the fairing between $O$ were respectively $L_x, L_y, L_z$.

The equation of motion of soil particle Q before collision with the deflector is

$$S=\left(\begin{array}{c}x\\ y\\ z\end{array}\right)=\left(\begin{array}{c}{v}_{0x}t\\ v_{0y}t\\ v_{0z}t-\frac{1}{2}g{t}^2\end{array}\right)+\left(\begin{array}{c}{x}_0\\ y_0\\ z_0\end{array}\right)=\left(\begin{array}{c}{v}_{0x}t+x_0\\ v_{0y}t+y_0\\ v_{0z}t-\frac{1}{2}g{t}^2+z_0\end{array}\right)$$

(7)

where:$X_0$, $Y_0$, $Z_0$ are the initial positions of the blade and the throwing starting point of soil particles, and $V_{0x}$, $V_{0y}$, $V_{0z}$ are the initial velocities of soil particles.

In the formula, the initial velocities $V_{0x}$, $V_{0y}$, $V_{0z}$ of soil particles are the combination of the involved rotation of the cutter wheel and the relative movement along the the positive tangent plane of the ditching cutter wheel, so the initial velocity is only related to the rotation speed of the cutter wheel and the forward speed of the machine.

On the Z-axis, the necessary condition for the collision between soil particles and the fairing is that the $Z_{max}$ value of throwing soil particles to the highest point must be greater than or equal to the Z value on the fairing, where Z ranges from the lowest point $l_z$ to the highest point $l_z+lcos\alpha$ of the fairing. In accordance with this condition, the length and installation height of the shroud on the Z-axis direction can be calculated. Similarly, in the Y-axis, the necessary condition for the collision between soil particles and the deflector is that $Y_{max}$ is greater than the transverse minimum point of the deflector and less than the transverse maximum point, so the collision condition that can be satisfied in the direction of soil throwing is:

$$l_y\le y_0+\frac{v_{0y}{v}_{0z}}{g}\le l_y+l\mathit{sin}\alpha$$

(8)

The width of the fairing in the throwing direction can be calculated as per the condition.

The velocity of soil particles before collision can be obtained by deriving the motion equation of the fairing before collision, After the collision, if the soil particles are regarded as elastic-plastic particles, on the basis of the collision theory [18], after the thrown soil particle P collide with the fairing, its tangential velocity is related to the friction coefficient of the fairing, while the vertical velocity is related to the recovery coefficient of the fairing, Therefore, assuming that the velocities of soil particles after collision are $V_{px}$, $V_{py}$, $V_{pz}$ respectively, after being thrown out, soil particles are still thrown horizontally and move in a uniform straight line in the throwing direction, and the throwing distance can be calculated by:

$$S=V_{oy}{t}_1+V_{py}{t}_2=V_{oy}\ast \frac{\sqrt{2g{h}_1+V_{oy}^2}-V_{oy}}{g}+V_{py}\ast \frac{\sqrt{2g\left(h_1+l_z\right)+V_{py}^2}-V_{py}}{g}$$

(9)

where, $t_1$ is the time when the soil particles rise to the collision point after being thrown out, and $t_2$ is the time when the soil particles fall from the collision point to the ground. $h_1$ is the displacement in the Z-axis direction of the soil particles rising to the collision point after being thrown out.

It can be seen from the above formula that the throwing distance of soil particles is related to the rotating speed of the cutter wheel and the positions of the cutter wheel blade and the soil particles in the z-axis direction. In addition, the velocity before collision is also affected by the dip angle α of the fairing. Thus, the throwing distance is also related to the dip angle of the fairing.

2.2. Discrete Element Simulation of Ditching Device

2.2.1. Simulation Parameters of Soil Particles and Ditching Cutter Wheel

The soil selected for the test is the common grey desert and loess in southern Xinjiang. According to the test and literature, it is known that the intrinsic parameters of grey desert and loess and steel are shown in

Table 1. Soil particle parameters.

Soil Name	Collection Depth/(cm)	Particle Density/(g·mm−3)	Shear Modulus/MPa	Firmness/MPa	Poisson’s Ratio	Internal Cohesion c/kPa	Internal Friction Angle/(°)	Water Content/%
Grey desert and loess	30	1.638	1.15 × 107	1.68	0.3	2.47	33.1	10.56
Steel		7.850	7.0 × 107		0.25

[19]. The model used in the simulation is SolidWorks. In order to simplify the computer simulation speed, only the fairing and ditching cutter wheel are retained, and their working parameters are shown in

Table 2. Simulation parameters for soil cutting dynamics with ditching blades.

Forward Speed/(m/s)	Cutter Speed/(r/min)	Turning Radius/mm	Grooving Width/mm	Grooving Depth/mm
1.3	120	550	380	35

.

2.2.2. Simulation Process

Solid modeling of the ditching device using the 3D drawing software Solidworks, imported into EDEM software in .igs format, Combined with soil particle parameters and trenching blade cutting soil dynamic simulation parameters for soil particles, guide hood, soil particles and soil particles, soil particles and guide hood set the relevant parameters between, The soil simulation model is defined as an uncovered rectangular body of 700 mm × 1800 mm × 2000 mm, generating 1 × 10⁷ particles, and the particle size is a round ball of 2 mm radius. Specific parameters are shown in

Table 3. Simulation variables parameters setting.

Item	Property	Value
Soil particles	Poisson ration	0.30
	Shear modulus/Pa	1.15 × 107
	density/(kg·m−3)	1638
Guide cover	Poisson ration	0.25
	Shear modulus/Pa	7.0 × 107
	density/(kg·m−3)	7850
Soil particle-soil particle	Coefficient of restitution	0.6
	Coefficient of static friction	0.6
	Coefficient of kinetic friction	0.4
Soil particles-guide cover	Coefficient of restitution	0.6
	Coefficient of static friction	0.6
	Coefficient of kinetic friction	0.05

.

2.2.3. Analysis of Simulation Results

The ditching depth was set to be 35 mm, the forward speed of the fairing to be 1.3 m/s, the cutter wheel speed and the forward speed of the ditching cutter to be 120 r/min and 1.3 m/s respectively, and Hertz–Mindlin with JKR built-in optimal model was used between soil particles [20]. The cutter head and the fairing cut the soil clockwise from the left to the right. At 0.60 s, the cutter head began to contact the soil (Figure 5a), and the straight section of the ditching cutter began to squeeze the soil; the tangent edge began to cut the soil (Figure 5b); under the action of the retaining plate and the side cutting edge, the soil was squeezed and deformed and lifted along with the ditching cutter to create a ditch in the forward direction (Figure 5c); as the cutter head rotated, the soil continued to lift with the cutter head (Figure 5d); at 1.34 s, some of the soil continued to move in a circle with the cutter head, and some was thrown out of the ditch; meanwhile, it can be seen that as soon as one blade crossed the soil, another blade came into contact with the soil, indicating that there was overlapping soil cutting section between adjacent ditching blades (Figure 5e); when the simulation reached 1.41 s, a large number of soil began to move in a circle with the cutter head. When it was lifted to a certain height, some soil particles were thrown out of the cutter head and collided with the fairing, and then were thrown out (Figure 5f).

2.3. The Soil Tank Test

2.3.1. Test Equipment and Conditions

The TC8.0 digitally controlled soil tank test system from the Institute of Mechanical and Electrical Engineering of Tarim University was utilized in this experiment [21]. The effective working length of the soil trough is 120 m and the width is 8 m. The electrical system of the soil trough truck consists of a large truck travel device, a small truck travel device, a hydraulic device and a control platform. The electrical system of the soil tanker consists of a large car travel device, a small car travel device, a hydraulic device and a control platform. The control platform can control the work of the big car, the small car and the hydraulic system, and also control the driving speed of the big car, the hydraulic system makes the ditching device move up and down, and the small car makes the ditching device move left and right, and the system can control the independent variables such as traction speed, power output, cutter speed and plowing depth of the big car separately and continuously.

In addition, it also needs ditching device, LZ-30 tachometer (produced by Shanghai Tachometer Factory, Shanghai, China, measuring range: 30~1200 r/min), 8219 tape measure (produced by Wanli Group, Chongqing, China, measuring range: 0.00~50.00 m), data acquisition card, etc. According to the requirements of JB /T 11908-2014 “agricultural disc trencher, the test site is the soil tank test bed of Tarim University, Soil moisture content at 30 cm depth was 10.56% and firmness was 1.68 MPa.

2.3.2. Selection of Test Factors

From the analysis of the movement of soil particles under the action of the deflector hood to Section 2.1.3, it is known that the throwing distance of soil particles is related to the cutter wheel speed of the cutter disc, the position of the Z-axis direction where the soil particles of the cutter disc blade are located, and the inclination of curved surface of the deflector hood, Therefore, the cutter wheel speed, ditching depth, and inclination of curved surface are selected as the test factors.

2.3.3. Test Indicators

(1)

the soil throwing distance

The soil throwing distance is the vertical distance from the outermost side of the soil block thrown down by the trencher to the center line of the ditch, Therefore, the soil throwing distance is a good indicator of the throwing performance, thus reducing soil backflow and improving the quality of trenching. When measuring, one point is measured every two meters along the forward direction of the unit, and the average value of the throwing distance is calculated according to the following formula.

$$R=\frac{{\displaystyle \sum _{j=1}^N{h}_j}}{N}$$

(10)

where R is the average value of throwing distance, cm; h_j is the measured value of soil throwing distance, cm; N is the total number of measuring points of soil throwing distance in trenching area, one.

(2)

Stability of ditch depth

The stability of ditch depth is the stability degree of ditching depth when the trencher works under the given working conditions, which reflects the uniform degree of trenching of the ditching blade. When measuring, every two meters measurement one point, according to the following formula to calculate the average value of the depth of the stability of ditch depth.

$$U=1-V$$

(11)

$$V=\frac{S}{h}\times 100\%$$

(12)

$$S=\sqrt{\frac{1}{N-1}{\displaystyle \sum _{j=1}^N(h_j-\overline{h}}{)}^2}$$

(13)

$$\overline{h}=\frac{1}{N}{\displaystyle \sum _{j=1}^n{h}_j}$$

(14)

where S is the standard deviation of ditching depth, cm; h_j is the measured depth of trenching, cm; $\overline{h}$ is the average depth of trenching, and N is the number of ditching depth measurement points in the trenching area, one; V is the variation coefficient of ditching depth, %; U is the stability coefficient of ditching depth, %; N is the number of measured ditch depths, one.

2.3.4. Experimental Scheme

In order to verify and optimize the operating parameters of the ditching device, a field test was carried out by using the quadratic orthogonal regression rotation combination experiment method, with cutter speed, ditching depth and inclination angle of the fairing surface as the influencing factors, and the throwing distance and the stability of ditch depth as the test indexes. As shown in Figure 6, The test scheme is shown in

Table 4. Coding of factors and levels.

Code	Cutter Speed A/(r·min−1)	Inclination of Curved Surface B/(°)	Ditching Depth C/(mm)
1	100	20	25
0	120	30	35
−1	140	40	45

.

3. Results

3.1. Analysis of Experimental Results

Design-Expert 8.0.6 was used to perform multiple regression fitting analysis on the experimental results in

Table 5. Test plan and result of two orthogonal regression rotation combination test.

	Test Factors			Test Index
	A	B	C	The Throwing Distance	The Stability of Ditch Depth
1	−1	−1	0	54.2	84.3
2	1	−1	0	55.8	83.7
3	−1	1	0	54.9	82.9
4	1	1	0	57.3	80.7
5	−1	0	−1	51.7	84.2
6	1	0	−1	53.9	81.9
7	−1	0	1	55.6	82.8
8	1	0	1	54.8	80.4
9	0	−1	−1	51.9	84.7
10	0	1	−1	53.4	84.8
11	0	−1	1	54.1	83.5
12	0	1	1	56.6	80.5
13	0	0	0	56.1	87.1
14	0	0	0	57.6	89.6
15	0	0	0	57.3	87.4
16	0	0	0	57.2	86.9
17	0	0	0	58.1	86.4

, and the variance analysis of soil throwing distance and the stability of ditch dept was obtained as shown in

Table 6. Analysis of variance of variance.

Category	The Throwing Distance					The Stability of Ditch Depth
Source	Squares	df	F	p	Significance	Source	Squares	df	F	Significance
Models	57.08	9	12.81	0.0014	**	102.89	9	10.36	0.0028	**
A	3.65	1	7.36	0.0301	*	7.03	1	6.37	0.0396	*
B	4.81	1	9.70	0.0170	*	6.66	1	6.04	0.0437	*
C	13.01	1	26.26	0.0014	**	8.82	1	7.99	0.0255	*
AB	0.16	1	0.32	0.5875		0.64	1	0.58	0.4712	*
AC	2.25	1	4.54	0.0705	*	2.5	1	2.265	0.9634
BC	0.25	1	0.50	0.5004		2.4	1	2.18	0.1836	*
A2	3.08	1	6.21	0.0414	*	33.37	1	30.23	0.0009	**
B2	3.08	1	6.21	0.0414	*	13.12	1	11.88	0.0107	*
C2	24.35	1	49.17	0.0002	**	23.06	1	20.89	0.0026	**
Residuals	3.47	7				7.73	7
Lack of Fit	1.29	3	0.79	0.5572		1.58	3	0.34	0.7976
Error	2.17	4				6.15	4
Total	60.55	16				110.61	16

Note: “p ≤ 0.01” means highly significant (**); “0.01 < p ≤ 0.05” means very significant (*); “p > 0.05” means nonsignificant.

. The quadratic regression model was highly significant [19]. It can be seen from the table: (1) For the soil throwing distance, the p value of ditching depth is 0.0014, which has the greatest influence on the soil throwing distance. For the stability of ditch depth, the p value of ditching depth is 0.0255, which is smaller than the cutter wheel speed and inclination angle. Ditching depth also has the greatest influence on the stability of ditch depth. (2) The order of the influence of each factor on the soil throwing distance is ditching depth > Inclination of curved surface > cutter speed, and the order of the influence on the stability of the ditch depth is ditching depth > cutter speed > Inclination of curved surface.

According to the statistical analysis of soil throwing distance Y₁, p = 0.0014 < 0.01, while the p value of the lack of fit is 0.5572, which indicates that the regression model is extremely significant and has high fitting accuracy, where the coefficients of X₁, X₂, X₃, X₂X₃, X₁₂, X₂₂, X₃₂ are less than 0.05, indicating significant, and the rest are not significant. Similarly, according to the statistical analysis of Y₂ stability of ditching depth, the total model p = 0.0028 < 0.01, and the p value of the lack of fit is 0.7976, which means that the regression model is extremely significant. After removing the non-significant items, the relationship between the response values and the independent variables was expressed by the quadratic polynomial regression model as follows:

$$Y_1=57.26+0.67X_1+0.77X_2+1.28X_3-0.85X_1^2-0.85X_2^2-2.41X_3^2$$

$$Y_2=87.48-0.94X_1-0.91X_2-1.05X_3-2.81X_1^2-1.76X_2^2-2.34X_3^2$$

where Y₁ is the throwing distance; Y₂ is the stability of ditch depth, X₁ Cutter speed, X₂ is inclination of curved surface, and X₃ is the ditching depth.

At a certain ditching depth, the influence of both Inclination of curved surface and cutter speed on the throwing distance increases first and then decreases, and the trend of both influences is basically the same (Figure 7a); when the Inclination of curved surface is certain, the influence of cutter speed and ditching depth on the throwing distance increases first and then decreases, among which the influence on the throwing distance is greater when the cutter wheel speed is less than 124 r·min⁻¹ and the ditching depth is less than 40 mm (Figure 7b); When the speed is certain, the influence of ditching depth and Inclination of curved surface on the throwing distance also increases first and then decreases, and has no interactive effect, so when operating, it is not advisable to use a deeper ditching depth, and the installation angle of the guide cover should not be too large (Figure 7c).

When the ditching depth is certain, the influence of Inclination of curved surface and cutter speed on the stability of ditching depth are increasing first and then decreasing, and the influence of cutter speed is greater than the influence of Inclination of curved surface (Figure 7d); when the Inclination of curved surface is certain, the influence of cutter speed and ditching depth on the stability of ditching depth are increasing first and then decreasing, the influence trend is basically the same, and the two do not have interactive effect (Figure 7e). When the cutter wheel speed is certain, the influence of ditching depth and Inclination of curved surface on the stability of ditching depth also increases first and then decreases, in which the ditching depth is less than 40 mm and the Inclination of curved surface is less than 30° has a greater influence on the stability of ditching depth and the ditching depth has a greater influence, and the ditching depth affects the power consumption, so it has a greater influence on the stability of ditching depth (Figure 7f).

3.2. Experimental Optimization

When the rotating speed of the cutter is 100–140 r·min⁻¹, the inclination of curved surface is 20–40°, and the depth of trenching is 25–45 mm, the multi-objective optimization method is used to optimize the distance of throwing soil and the stability of ditching depth as the maximum optimization target, and the optimization results are: the rotating speed of the cutter is 119.61 r·min⁻¹, the inclination of curved surface is 30.07°, and the depth of trenching is 35.52 mm. At this time, the throwing distance is 57.31 and the stability of ditch depth is 87.43. With this parameter as the test object, 10 groups of single-factor tests are conducted, and the test result is that the throwing distance is 58.33 and the stability of ditch depth is 86.51, which are basically consistent with the expected results of test optimization and also meet the relevant agronomic standards.

4. Discussion

(1) Soil particle kinematics was analyzed, aiming to simplify the soil particles in the trenching process as mass points and establish their motion coordinate system, thus obtaining the collision mechanism between the soil and the deflector during the motion and the ideal soil throwing distance model. It can be seen from the soil throwing distance model that the throwing distance of soil particles is related to the rotating speed of the cutter wheel, the position of the cutter wheel blade, and the soil particles in the z-axis direction. In addition, the velocity before collision is also affected by the dip angle α of the fairing. Thus, the throwing distance is also related to the dip angle of the fairing. In this throwing distance model, the soil particles are deemed as plastic particles, without taking into account the formation of soil particles due to collision. In the future, researchers may consider the circumstance of crushing particles due to collision.

(2) Cutter speed, ditching depth and the inclination of curved surface on the throwing distance and the stability of ditch depth were obtained through soil trough test. Gully depth had the most significant effect on both. At a certain ditching depth, the influence of both inclination of curved surface and cutter speed on the throwing distance and the stability of ditching depth increased first and then decreased, and the influence of cutter speed was greater than that of the inclination of curved surface. For the soil throwing distance, it has the greatest influence on the soil throwing distance. It further shows that the ditching depth has the most important influence on the soil throwing distance and the stability of the ditch depth of the trenching equipment.

(3) The soil bin test bed of Tarim University was selected for the experiment, the soil characteristics and working parameters of this test bed are easy to be adjusted, and this test bed can avoid uncontrollable factors in field trials. During the experiment, it was found that the trencher was subjected to a high resistance to trenching, Therefore, this group will use the existing grey desert and loess test bed to study the power consumption generated during trenching. In the experiment, it was found that in case of a significant increase of plowing depth, there would be increased vibration of the entire mechanical device with a significant increase of soil backflow and the colter disc’s rotation speed was also affected. Therefore, it can be seen that there is a great relation between soil backflow and the shape of the plowing colter.

5. Conclusions

(1)

Combined with the characteristics of sandy orchards cultivation in South Xinjiang. A ditching organic fertilizer fertilization device was designed, the relevant parameters of the ditching blade were set, and the kinematic analysis of the ditching blade and the motion analysis of soil particles under the action of the fairing were carried out, the theoretical soil throwing model of the test setup was obtained. It can be seen from the soil throwing distance model that the throwing distance of soil particles is related to the rotating speed of the cutter wheel, the position of the cutter wheel blade, and the soil particles in the z-axis direction. In addition, the velocity before collision is also affected by the dip angle α of the fairing. Thus, the throwing distance is also related to the dip angle of the fairing. This throwing distance model does not take into account the change of sandy soil particles’ speed due to their deformation caused by collision.

(2)

Discrete element simulation was carried out on the ditching device by EDEM simulation software, and the action mechanism between soil particles, ditching blade and fairing was obtained in simulating ditching operation. Make it clear that the trenching process. The movement of soil particles in the deflector hood under the action of the blade, the conclusion is consistent with the results of the theoretical analysis. When opening the trench, some of the soil continued to move in a circle with the cutter head, and some was thrown out of the ditch; meanwhile, it can be seen that as soon as one blade crossed the soil and continued the trenching, another blade came into contact with the soil, indicating that there was overlapping soil cutting section between adjacent ditching blades, a large number of soil began to move in a circle with the cutter head. When it was lifted to a certain height, some soil particles were thrown out of the cutter head and collided with the fairing, and then were thrown out. Furthermore, due to low viscosity and fineness of sandy soil, not all soil will collide against the fairing. Therefore, some soil will still escape from the seams of fairing.

(3)

Cutter speed, ditching depth and the inclination of curved surface on the throwing distance and the stability of ditch depth were obtained through soil trough test. For the stability of ditch depth, the ditch depth was smaller than the cutter wheel speed and the inclination angle. Ditching depth also has the greatest influence on the stability of ditch depth. The order of the influence of each factor on the soil throwing distance is ditching depth > inclination of curved surface > cutter speed, and the order of the influence on the stability of the ditch depth is ditching depth > cutter speed > inclination of curved surface. At a certain ditching depth, the influence of both inclination of curved surface and cutter speed on the throwing distance and the stability of ditching depth increased first and then decreased, and the influence of cutter speed was greater than that of the inclination of curved surface. For the soil throwing distance, it has the greatest influence on the soil throwing distance. It further shows that the ditching depth has the most important influence on the soil throwing distance and the stability of the ditch depth of the trenching equipment. The quadratic orthogonal regression rotation combination experiment method was designed. The device test was carried out by taking cutter speed, ditching depth and inclination angle of the fairing surface as the influencing factors, and the throwing distance and the stability of ditch depth as the test indexes, to obtain the optimized working parameters. the optimized operating parameters of the ditching device are as follows: the cutter wheel speed is 119.61 r·min⁻¹, the inclination of curved surface is 30.07°, the ditching depth is 35.52 mm, the soil throwing distance is 58.33, and the stability of ditch depth is 86.51, which were basically consistent with the expected results of the optimization test. The combination parameters were obtained by experimental optimization. This optimization method herein is quite effective in seeking the quantitative law between test indexes and each factor. It will help identify the optimal portfolio of factors that is close to theory.