Sowing depth stability analysis and test verification of no-tillage planter parallel 4-bar row unit

Abstract

The sowing depth stability and consistency of the no-tillage planter, particularly the high-speed operation, are poor. A reason for this is that the structure and parameter selection of no-tillage planter row unit profiling mechanism are unreasonable. The stability and consistency of sowing depth is beneficial when the upper and lower links of the parallel 4-bar profiling mechanism (PFPM) are parallel to the ground, but this principle is not satisfied on the uneven no-till soil. To improve the stability of gauge wheels downforce (GWD) and sowing depth of no-tillage planter row unit. The variation law of spring additional downforce (SAD) with tilt angle of parallel 4-bar profiling mechanism (PFPM) and connection offset of spring is discussed by constructing the steady state analysis matrix equation of PFPM. Additionally, the influence of tilt angle of PFPM and SAD on the stability of the sowing depth was analyzed. Based on the single factor control variable test method, bench and field tests were conducted. The test results show that the SAD increases nonlinearly with the increase in the degree of tilt of PFPM from downward to upward. Under the condition that four springs are installed and the tilt angle of PFPM is between (−20°–20°), the maximum SAD is 485.95 N, 1236.64 N, and 2258.05 N when the spring connection offset is 44 mm, 79 mm, and 115 mm, respectively. When the tilt angle is 8° upward, the GWD increases by 429 N, 575 N, and 984 N, GWD stability increases by 42.31 %, 56.16 %, and 50.29 %, and ditching depth stability increases by 30.00 %, 12.50 %, and 30.00 % compared with that of the control group at the sowing speed of 8, 10, and 12 km/h, respectively. At the sowing speed of 10 km/h, when the PFPM is operated with spring-free and additional springs, the average GWD increases by 353 N, and the stability of GWD and ditching depth increases by 34.38 % and 20.00 %, respectively. The results showed that the tilt upward of PFPM and SAD were beneficial to improve the stability of the GWD and sowing depth of the no-tillage planter row unit. The results not only verify the correctness of theoretical analysis, but also provide theoretical basis for the design and application adjustment of high-speed no-tillage planter.

1. Introduction

The stability and consistency of sowing depth are important indicators that affect the quality of sowing. Stable and consistent sowing depth can ensure the uniformity and evenness of seedlings, which is conducive to field management, yield and quality improvement in the later stage of crops [[1], [2], [3]]. Presently, a problems of no-tillage planter, particularly the high-speed (≥10 km/h) operation of no-tillage planter, is that its sowing depth stability and consistency are poor. This is because in addition to the usual surface fluctuation factors, the complex and changeable soil physical environment, such as the surface covered by straw, root stubble planted into the soil, soil moisture, and soil penetration resistance, are inconsistent. The abovementioned reasons result in inconsistency of sowing depth for no-tillage planter, and instability problems become particularly prominent [[4], [5], [6], [7]]. The current research on the sowing depth stability of no-tillage planter focuses on two control technologies to improve the sowing depth stability: using semi-active control for stability control [8,9] and using sensors to directly or indirectly measure the sowing depth in real time, and using the active executive component to actively control the downforce of the no-tillage planter row unit to stabilize the sowing depth, including pneumatic control and electro-hydraulic control [[10], [11], [12], [13], [14]]. However, the abovementioned control methods have some problems, such as complex structure, high cost, and poor reliability.

As for the theoretical problems of the influence of PFPM on the stability of sowing depth, there have been many studies by scholars, such as Zhang et al. [15] and Hu [16], who provided the mathematical model of precision planter row unit with PFPM without the spring, and described the relationship between the ditching depth and the geometric characteristics of the surface, structural parameters of row unit, and soil properties. Bao et al. [17] simplified the PFPM into a rigid connection system for the stress analysis of no-tillage planter row unit. Zhao et al. [18] designed a bidirectional profiling mechanism of wheat planter row unit and established a mechanical model of the spring-free. Using Lagrange equations, Bai et al. [19]and Zhang [20] analyzed the stability of the no-tillage planter row unit with tension spring and no spring, respectively. Hao et al. [21], Qian [22], and Fan [23] performed the simulation and optimization analysis of the PFPM, and determined the parameters of each link rod size, traction angle, etc. Chen et al. [24] designed an electro-hydraulic sowing depth adjustment device to adjust the sowing depth, aiming at the problem that the row unit is raised when the corn no-tillage planter works on the ground with large fluctuations, resulting in unqualified sowing depth. Hou et al. [25] designed a two-degree of freedom multi articulated profiling precision row unit to solve the problem of unsatisfactory consistency of seeding depth, and established a mathematical model of seeding trench depth by applying the conservative Lagrange equation. Lv et al. [26] analyzed and designed the PFPM, configuration of gauge wheels, and the ditching device of potato planter and established the mathematical model of the stability of the ditching depth through the dynamic analysis of the sowing depth control device. In summary, there have been many studies on the design, analysis, and seeding depth stability control for no-tillage planter row unit profiling mechanism, from theoretical and simulation analysis to experimental verification. In the theoretical analysis, there are two kinds of methods, one is the classical theoretical mechanics modeling analysis, the other is the analytical mechanics method established by Lagrange. These studies have given the research methods and conclusions of referential significance. However, with the continuous improvement of sowing speed, some problems need to be further analyzed and improved in the models, analysis processes, discussions and conclusions established in the existing literature. For example, in the process of analyzing the installed spring of the PFPM, the tilt and traction angle are not clearly differentiated. Although some literature analyses the special case of spring hanging on the diagonal of PFPM, but it has some limitations. Additionally, the stability and consistency of sowing depth is beneficial when the upper and lower links of the parallel 4-bar profiling mechanism (PFPM) are parallel to the ground, but this principle is not satisfied on the uneven no-till soil.

In this study, we analyze and discuss the variation law of spring additional downforce (SAD) with tilt angle of PFPM and connection offset of spring, and the influence of tilt angle of PFPM and SAD on the stability of the sowing depth through constructing the steady state analysis matrix equation theoretical analysis. Additionally, the single factor control variable test method was used to conduct the bench test and field test for verification. The research objective and contribution of this study is to explore the effect of the structural and application parameters of PFPM on the steady-state characteristics of no-tillage planter to provide a theoretical reference for the design of PFPM of row unit under the condition of no-tillage high-speed operation and the control technology of sowing depth consistency and stability.

2. Materials and methods

2.1. Row unit structure of no-tillage planter

Fig. 1 shows the row unit structure of 2BMG-2 no-tillage planter. The row unit consists of PFPM, frame of row unit, and earth-touching unit (including stubble breaker, disc opener, gauge wheels and closing wheels etc.). The earth-touching unit is installed on the frame of row unit. The frame is installed on the PFPM, forming the rear link rod of the PFPM. The front link rod of the PFPM is firmly connected with the main beam of the planter, and the planter is connected with the tractor.

Fig. 1.

Structure of the no-tillage planter row unit.

1. Main beam of planter row unit 2. Stubble breaker 3. Row Cleaner 4. Disc opener 5. Gauge wheels 6. Closing wheels 7. PFPM 8. Spring 9. Frame of row unit

2.2. Force analysis of no-tillage planter row unit

The tractor, the main beam of the planter, the row unit, and the soil interact to form a complex mechanical system. Fig. 2 shows the force analysis diagram of no-tillage planter row unit. Points A, B, C and D are the four hinge pairs of the PFPM on the row unit. The frame of row unit is connected under the link rod DC of the PFPM and the earth-touching unit is connected under the frame of row unit. The x-axis is the horizontal reference line of the row unit, and the direction is opposite to the forward motion of the planter. Traction force and self-gravity are the main forces of the mechanical system. The friction force of the hinge pairs is not considered in the model. The force of soil on earth-touching unit can be regarded as the binding force in the mechanical system.

Fig. 2.

Force analysis diagram of no-tillage planter row unit

Note: T_x is the horizontal reaction force on the stubble breaker and row cleaner, N; T_z is the vertical reaction force on the stubble breaker and row cleaner, N; R_x is the horizontal reaction force on the disc opener, N; R_z is the horizontal reaction force on the disc opener, N; Q_x is the horizontal reaction force on the gauge wheels, N; Q_z is the vertical reaction force on the gauge wheels, N; U_x is the horizontal reaction force on the closing wheels, N; U_z is the vertical reaction force on the closing wheels, N; G is the self-gravity of the row unit, N.

2.2.1. Analysis of traction angle of no-tillage planter row unit

As shown in Fig. 2, the traction angle is between the direction of traction force exerted by the main beam of the planter and the direction of forward motion of the planter [27], expressed by γ. When the direction of traction is upward biased from the direction of forward motion of the planter, the traction angle is positive, otherwise negative. The steady state mechanical equation of the planter row unit is established based on the uniform motion state of the planter row unit, as expressed using Eq. (1).

$$\{\begin{array}{c}{P}_x=P_{Ax}+P_{Bx}=T_x+R_x+Q_x+U_x\\ P_z=P_{Az}+P_{Bz}=G-T_z-R_z-Q_z-U_z\end{array}$$ (1)

$$\tan \gamma =\frac{P_z}{P_x}=\frac{G-T_z-R_z-Q_z-U_z}{T_x+R_x+Q_x+U_x}$$ (2)

Set:

$$\{\begin{array}{c}\sum W_z=T_z+R_z+Q_z+U_z\\ \sum W_x=T_x+R_x+Q_x+U_x\end{array}$$ (3)

Then:

$$\tan \gamma =\frac{G-\sum W_z}{\sum W_x}$$ (4)

$$\sum W_z=G-\tan \gamma \sum W_x$$ (5)

where $\sum W_z$ is the algebraic sum of the vertical (z-direction) binding force of soil on the earth-touching unit of the row unit (that is the downforce of row unit), and $\sum W_x$ is the algebraic sum of the horizontal (x-direction) binding force of soil on earth-touching unit of the row unit. In the sowing operation, there are constraints of $\sum W_x\ge 0$ and $\sum W_{\mathrm{z}}\ge 0$.

When the self-gravity of the row unit is constant (not considering the change in the gravity of seed and fertilizer in the sowing operation for the time being), Eqs. (4), (5) show that γ, $\sum W_x$, and $\sum W_z$ are interrelated, and the change in any one parameter will lead to the change in the other two parameters. The traction angle of the row unit during the sowing operation is only determined by $\sum W_x$ and $\sum W_z$. When $G＞\sum W_z$, the traction angle is upward biased and greater than zero; when $G=\sum W_z$, the traction angle is equal to zero; when $G＜\sum W_z$, the traction angle is downward biased and less than zero.

2.2.2. Analysis of tilt angle of PFPM

The tilt angle of PFPM is between the upper or lower link rod and the x-axis, which is expressed by α, as shown in Fig. 2. For the convenience of analysis, the no-tillage planter row unit is divided into two parts: PFPM and earth-touching unit. The geometric relationship and force of each component of the PFPM are shown in Fig. 3. The tilt angle is the angle between the link rod BC and x-axis. When the rear of the link rod BC tilts downward, the tilt angle is positive, otherwise negative. β is the angle between the spring and link rod AD. The spring is connected to the E and F points of the PFPM, and the force on the E and F points is F_k and −F_k, respectively.

Fig. 3.

Force analysis diagram of the PFPM

Note: $F_C$, $F_C^{\prime }$ is the pair of action and reaction forces at the hinge point C, N; $F_D$, $F_D^{\prime }$ is the pair of action and reaction forces at the hinge point D, N; H is the length of the link rod AB, mm; L is the length of the upper or lower link rod, mm; L₁, L₂ are the lengths from the hinge points E, F of the spring and the upper and lower link rod of the PFPM to the hinge points A, B of the frame (mm), respectively.

2.2.2.1. (1) force analysis of PFPM

The matrix equation of steady state force analysis of PFPM is shown in Eq. (6) [28].

$$\left[\begin{array}{ccccccc}0& 0& 0& L\sin \alpha & L\cos \alpha & 0& 0\\ 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0\\ 1& H& 0& 0& 0& H& 0\\ 0& 1& 0& 1& 0& 1& 0\\ 0& 0& 1& 0& 1& 0& 1\\ 0& 0& 0& 0& 0& L\sin \alpha & L\cos \alpha \\ 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}M\\ F_x\\ F_z\\ F_{Dx}^{\prime }\\ F_{Dz}^{\prime }\\ F_{Cx}^{\prime }\\ F_{Cz}^{\prime }\end{array}\right]=\left[\begin{array}{ccccccc}0& -L_1\sin \alpha & -L_1\cos \alpha & 0& 0& 0& 0\\ 0& -1& 0& -1& 0& 0& 0\\ 0& 0& -1& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 1& 0& 0& 0& 0& 0& 0\\ 0& L_2\sin \alpha & L_2\cos \alpha & 0& 0& 0& 0\\ 0& 1& 0& 0& 0& -1& 0\\ 0& 0& 1& 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{G}_1\\ F_{kx}^{\prime }\\ F_{kz}^{\prime }\\ P_{Ax}\\ P_{Az}\\ P_{Bx}\\ P_{Bz}\end{array}\right]$$ (6)

where M denotes couple moment of earth-touching unit on the link rod CD, N·mm; F_x denotes x-direction force of earth-touching unit at point C of PFPM, N; F_z denotes z-direction force of earth-touching unit at point C of PFPM, N; G₁ denotes self-gravity of PFPM, N; L denotes the length of upper or lower link rod of PFPM, mm; H denotes the length of AB or CD, mm; L₁ denotes the length of AE, mm; L₂ denotes the length of BF, mm; α denotes the tilt angle, °; $P_{Ax}$, $P_{Bx}$, $F_{Cx}^{\prime }$, and $F_{Dx}^{\prime }$, are the component force of A, B, C, and D in the x directions, respectively, N; and $P_{Az}$, $P_{Bz}$, $F_{Cz}^{\prime }$, and $F_{Dz}^{\prime }$, are the component force of A, B, C, and D in the z directions, respectively, N.

The equation of z-direction force of earth-touching unit on point C of the PFPM can be obtained by deduction, as expressed in Eq. (7).

$$F_Z=G_1-F_x\tan \alpha +\frac{F_k\left(L_1-L_2\right)\sin \beta }{L\cos \alpha }$$ (7)

SAD is expressed in Eq. (8).

$$F_{kj}=\frac{F_k\left(L_1-L_2\right)\sin \beta }{L\cos \alpha }$$ (8)

The angle between spring and link rod AD is expressed in Eq. (9).

$$\beta ={\sin }^{-1}\frac{H\cos \alpha }{\sqrt{{\left(L_1-L_2\right)}^2+H^2-2\left(L_1-L_2\right)H\sin \alpha }}$$ (9)

The spring connection offset is expressed by Eq. (10).

$$\Delta L=L_1-L_2$$ (10)

$\Delta L$ is a fixed value in the sowing operation, then:

$$F_k=k\left(\sqrt{\Delta L^2+H^2-2H\Delta L\mathit{sin}\alpha }-S_0\right)$$ (11)

where k denotes spring stiffness coefficient, N/mm; S₀ denotes the length of the spring in the free state plus the length of the connector, its value is a constant value, mm.

By combining Eqs. (8), (9), (10), (11), SAD can be obtained:

$$F_{kj}=\frac{kH\Delta L}{L}\left(1-\frac{S_0}{\sqrt{\Delta L^2+H^2-2\Delta LH\mathit{sin}\alpha }}\right)$$ (12)

Then:

$$F_z=G_1-F_x\tan \alpha +\frac{kH\Delta L}{L}\left(1-\frac{S_0}{\sqrt{\Delta L^2+H^2-2\Delta LH\mathit{sin}\alpha }}\right)$$ (13)

Eqs. (12), (13) show that: the spring generates additional downforce on the planter row unit, the value of which is related to the spring parameters, the geometric parameters of the PFPM, and spring connection offset and the tilt angle of the PFPM. For a determined planter row unit, the spring parameters and the PFPM geometric size are fixed, then the additional downforce is only related to the spring connection offset and tilt angle of the PFPM.

2.2.2.2. (2) force analysis of row unit frame and earth-touching unit

The force analysis diagram of row unit frame and earth-touching unit is shown in Fig. 4. The earth-touching unit is subjected to the force transmitted by the PFPM and binding force of soil on it.

Fig. 4.

Force analysis diagram of the row unit frame and earth-touching unit.

The mechanical balance equation is established as follows:

$$\{\begin{array}{c}-F_x+T_x+R_x+U_x+Q_x=-F_x+\sum W_x=0\\ F_z-T_z-R_z-U_z-Q_z+G_2=F_z+G_2-\sum W_z=0\end{array}$$ (14)

where G₂ is the self-gravity of the earth-touching unit, N.

The total self-gravity of the planter row unit is:

$$G=G_1+G_2$$ (15)

The tangent value of the tilt angle of the PFPM is expressed by Eq. (16).

$$\tan \alpha =\frac{G+F_{kj}-\sum W_z}{\sum W_x}$$ (16)

Eq. (16) shows that when α = 0, any change in the horizontal binding force ($\sum W_x$) of the soil will not affect the vertical binding force ($\sum W_z$). If α ≠ 0, the influence of the horizontal binding force cannot be ignored. If α < 0, the rear of the link rod BC of the PFPM will tilt upward, and the larger tilt angle or larger the horizontal binding force, the larger the vertical binding force. Contrariwise, the value of the vertical binding force will decrease, even less than the row unit self-gravity.

Therefore, the downforce of the row unit can be adjusted not only by changing the spring parameters, but also by adjusting the initial tilt angle of PFPM. The adjustment characteristics of the two methods are different. During sowing operation, SAD is only related to the tilt angle, and the position adjustment is related to the horizontal binding force. For row unit with light weight or high penetration resistance, the downforce of the row unit can be increased by the PFPM being tilted up towards the rear appropriately to improve soil insertion and z-directional interference resistance.

From Eqs. (4), (16), we obtain:

$$\left(\tan \alpha -\tan \gamma \right)\sum W_x=F_{kj}$$ (17)

Eq. (17) shows that when F_kj = 0, the traction angle is equal to the tilt angle of the PFPM. When F_kj > 0, the traction angle is less than the tilt angle. However, the traction angle is greater than the tilt angle. This indicates that when SAD is not zero, the tilt angle is not equal to the traction angle. In fact, traction angle and tilt angle are two different concepts with different physical meanings. The traction angle reflects the angle between the traction force and direction of forward motion, which is a mechanical parameter. The tilt angle reflects the angle between the upper or lower link rod and the direction of movement, and is the geometric parameter of PFPM. The two angles should not be confused.

2.3. Analysis of the sowing depth stability of no-tillage planter

2.3.1. Analysis of the influence of tilt angle of PFPM on the stability of sowing depth

Under the influence of soil heterogeneity and sowing speed disturbance, the influence of the initial tilt angle of the PFPM on the stability of seeding depth is worth analyzing and discussing.

By taking the partial derivative of $\sum W_x$ from Eq. (16).

$$\frac{\partial \sum W_z}{\partial \sum W_x}=－\tan \alpha$$ (18)

Eq. (18) shows that when the initial tilt angle of PFPM is tilted downward (tilt down towards to the rear of the parallel arms, α ＞ 0), its value is always less than 0, indicating that the change trend of $\sum W_z$ is opposite to that of $\sum W_x$. In other words, if the row unit of planter encounters stubble or the soil penetration resistance increases (the row unit advance resistance and soil characteristic coefficient increase), the downforce of row unit will decrease accordingly, and the sowing depth will become shallow. Contrariwise, when the soil compactness decreases, the downforce of the row unit and the sowing depth will increase. Therefore, the initial tilt angle, which is tilted downward, is not conducive to the sowing depth stability.

When the initial tilt angle of PFPM is tilted upward (tilt up toward to the rear of parallel arms, α ＜ 0), its value is always greater than 0, indicating that the change trend of $\sum W_z$ is same with that of $\sum W_x$. In other words, if the row unit of the planter encounters the stubble or the soil compactness increases, the downforce of the row unit will increase accordingly. The change in sowing depth can be suppressed by proper uptilt of the initial tilt angle. However, when the soil compactness decreases, the downforce of the row unit will decrease.

To deal with the disturbance of stubble, soil heterogeneity, and sowing speed, the PFPM can be upward tilted properly, which is conducive to the stability of sowing depth.

2.3.2. Analysis of the influence of SAD on the stability of sowing depth

In the heterogeneity of soil property, especially in the no-tillage area with root stubble, the disturbance of individual advance constraint resistance is large, which makes the sowing depth unstable.

By taking the derivative of α from Eq. (12).

$$\frac{d{F}_{kj}}{d\alpha }=－\frac{k{H}^2\Delta L^2\sqrt{H^2+\Delta L^2}\cos \alpha }{L{\left(H^2+\Delta L^2-2H\Delta L\sin \alpha \right)}^{\frac{3}{2}}}$$ (19)

Eq. (19) shows that in the range of (−90°, +90°), the numerator term is greater than 0, and the denominator term is always greater than 0. Therefore, $d{F}_{ck}/d\alpha <0$, thus the change trend of SAD is opposite to the change trend of the initial tilt angle of PFPM.

Therefore, on a flat sowing area, when the sowing depth increases owing to the heterogeneity of soil property, the initial tilt angle of PFPM will be increased, and the SAD will be decreased, i.e., gauge wheels downforce (GWD) will be reduced. SAD inhibits the increase in sowing depth. However, when the soil disturbance makes the sowing depth shallow, SAD will be increased, i.e., the GWD will be increased. The depth of subsidence increases, such that SAD inhibits the shallower sowing depth. Therefore, in a plot with uneven soil quality, SAD is conducive to stable sowing depth.

2.4. Test for verification

Bench tests were conducted to study the variation law of SAD with tilt angle and connection offset of the PFPM. Field tests were conducted to study the effects of initial tilt angle of PFPM and spring factors on GWD and stability of sowing depth.

2.4.1. Bench test

2BMG-2 type maize no-tillage planter was used to test the variation of SAD with tilt angle and connection offset. It was implemented in the Engineering Training Center of the College of Engineering, Northeast Agricultural University.

2.4.1.1. (1) Instruments and equipment

The main instruments and equipment include the universal testing machine (WDW-100E), electric crane (CDZT-6M), force sensor (YZC-516), and hydraulic lift (0086), etc.

2.4.1.2. (2) Test method

The test includes two parts: the spring stiffness and SAD measurement. The SAD test method is shown in Fig. 5, and the test process is shown in Fig. 6(a). The spring stiffness was measured using the universal testing machine, as shown in Fig. 6(b). When SAD is measured, four springs are installed on the PFPM, and it is necessary to lubricate the articulation point of the PFPM to minimize friction resistance. The row unit was raised with an electric crane to allow sufficient clearance of the gauge wheels base floor to push the hydraulic lift and force sensors under the gauge wheels. When the hydraulic lift is adjusted to the required tilt angle of the PFPM, the row unit of the planter is made to fall on the load sensing pressure surface, and GWD is measured and recorded. Then, SAD is measured as GWD minus the body weight of row unit.

Fig. 5.

Test method of SAD.

Fig. 6.

SAD and stiffness measurement test.

During the test, the GWD at 5 positions with different tilt angles of 20°, 10°, 0°, −10°, and −20° (positive values are PFPM with tilt down toward the rear and negative values are the opposite) and 3 different spring connection offsets were measured for each parameter combination thrice, and the average value was considered for statistical analysis.

2.4.2. Field test

2.4.2.1. (1) Test condition

As shown in Fig. 7, the field test was conducted at the Xiangyang Test Demonstration Base (126°55 ‘39 “E, 45°45′ 48″ N) of Northeast Agricultural University, Harbin, Heilongjiang Province, from May 6–9, 2023. The test plot was a field with corn stubble. The soil penetration resistance was 0.8–1.48 MPa at 5 cm depth, soil moisture content was (22.03 ± 1.03)%, and stubble coverage rate was (62.89 ± 6.71)%.

Fig. 7.

Field test condition and devices.

2.4.2.2. (2) Instruments and equipment

The 2BMG-2 type no-till planter used for the field test is shown in Fig. 1. The main instruments and equipment included the tractor (MF 604), soil penetration resistance meter (PV6.08), data acquisition device, and downforce sensor for GWD (along the X and Y directions, the sensitivity outputs are 0.6080 mV/V and 0.6090 mV/V, nonlinearity are 0.35 % and 0.50 %, and cross sensitivity are 0.0253 and 0.0251, respectively, at full scale [29]).

2.4.2.3. (3) Test method and scheme

Single factor control variable test method was adopted in the field test. Owing to the correlation between sowing depth and ditching depth and to ensure the accuracy of the measurement results, the closing wheels of the row unit were removed during the test. The influence of the test factor on the stability of the sowing depth was indirectly analyzed by measuring and processing the data of the ditching depth.

Three groups of comparative analysis tests were conducted at three sowing speeds of 8, 10, and 12 km/h. In each comparison test, the single factor variable of the test was the initial tilt angle of PFPM. The no-tillage planter used in the tests had two row units for simultaneous sowing operation, as shown in Fig. 7(b). The initial tilt angle of the PFPM of one row unit was adjusted to −8°(tilt up toward to the rear of parallel arms) by the connecting plate, and the other was maintained at 0° as the control group. Fig. 8 shows the structure and installation position of the connecting plate. Here, we assumed that all the other structural and application parameters of no-tillage planter row unit are completely consistent, and the influence of surface irregularity on the test is ignored. The test scheme is shown in run1–3 in Table 1.

Fig. 8.

Structure and installation position of the connecting plate.

Table 1.

Test scheme.

Run	Row unit	Factors
		Speed $x_1$/(km·h−1)	Initial tilt angle $x_2$/(°)	Spring $x_3$
1	Improvement row unit	8	−8	Yes
	Control row unit (CK)		0
2	Improvement row unit	10	−8	Yes
	Control row unit (CK)		0
3	Improvement row unit	12	−8	Yes
	Control row unit (CK)		0
4	Improvement row unit	10	0	Yes
	Control row unit (CK)			No

Note: If the row unit is installed with spring during the test, it means that 2 springs are installed, and the connection offset is 79.3 mm.

The influence of SAD on the stability of GWD and sowing depth was studied. A group of comparative analysis field test was conducted at 10 km/h sowing speed. During the test, the single factor variable of the test was whether the PFPM is installed with springs. One row unit of planter springs were removed, and the other row unit was installed with 2 springs. We also assumed that all the other structural and application parameters of row unit are completely consistent, and the influence of surface irregularity on the test was ignored. The test scheme is shown in run4 in Table 1.

2.4.2.4. (4) Evaluation indicators and calculation methods

The evaluation indicators were obtained as follows.

• 1)Downforce of the gauge wheels

The data were collected by the mechanical parameter and motion parameter measuring instrument in the stable speed interval, and then the real-time GWD was calculated according to the regression model obtained by the test calibration. By taking the sowing depth adjustment lever placed in the 6^th gear as an example, GWD was calculated using Eq. (20), and the regression model determination coefficient was 0.99.

$$F_w=0.2268\sqrt{x^2+y^2}$$ (20)

where x and y denote the X and Y -direction loads of the sensor, respectively.

• 2)Ditching depth

The ditching depth was manually measured by a laser rangefinder. Then the average of ditching depth was compared and analyzed.

• 3)Variation coefficient of GWD and ditching depth

The coefficient of variation is expressed using Eq. (21).

$$CV=\frac{\sigma }{\mu }$$ (21)

where $\sigma$ denotes the standard deviation and $\mu$ denotes the average value.

• 4)Stability improvement rate of GWD and ditching depth

The stability improvement rate is expressed using Eq. (22).

$$\delta =\frac{\left|C{V}_a-C{V}_b\right|}{C{V}_b}\times 100\%$$ (22)

where $C{V}_a$ denotes the coefficient of variation after treatment, and $C{V}_{\mathrm{b}}$ denotes the coefficient of variation of the control group.

3. Results and discussion

The measurement results of spring and PFPM are shown in Table 2. The test results and theoretical calculation results of SAD are shown in Table 3. The results of relative and absolute errors between theoretical and test values are shown in Table 4. The change in SAD with the tilt angle and connection offset is shown in Fig. 9.

• (1)As observed from Table 3 and Fig. 9, SAD is related to the initial tilt angle and connection offset of the PFPM. When the connection offset is constant, SAD of the PFPM increases nonlinearly with the changes in the tilt angle. When the tilt angle is the same, SAD increases with the increase in the connection offset. This verifies the correctness of the theoretical analysis. The test values of SAD of each tilt angle are greater than the theoretical values. This is because even with sufficient lubrication is carried out before the test, there is friction between the articulation pairs of PFPM, which affecting the test results.
• (2)The test results in Table 3 show that under the conditions that four springs are installed and the tilt angle of PFPM is between (−20° and 20°), the maximum SAD is 485.95 N, 1236.64 N, and 2258.05 N when the spring connection offset is 44 mm, 79 mm and 115 mm, respectively.
• (3)According to the statistical analysis in Table 4, under different connection offset, the maximum absolute errors of test and theoretical values for each group are 31.85 N, 72.35 N, and 101.98 N, respectively, and the maximum relative errors of each group are 6.55 %, 5.85 %, and 5.61 %, respectively.

Table 2.

Measurement results of spring and PFPM.

Parameter	Value
Spring stiffness k/(N/mm)	26.6
Sum of spring free length and connector length S0/mm	190
Height and length of PFPM H × L/(mm × mm)	207 × 340

Table 3.

Test and theoretical calculation results of SAD.

SAD/N Tilt angle/°	Connection offset/mm
	44		79		115
	Test value	Theoretical value	Test value	Theoretical value	Test value	Theoretical value
20	97.77	92.36	131.48	124.42	365.53	349.12
10	209.04	196.34	478.84	454.03	1024.21	966.76
0	310.57	292.17	763.24	733.91	1517.94	1459.78
−10	398.79	378.33	1017.49	968.95	1956.65	1854.67
−20	485.95	454.10	1236.64	1164.29	2258.05	2171.14

Note: The theoretical and test values are SAD under the action of 4 springs in PFPM, where the theoretical value is calculated by taking the parameter values from Table 2 into Eq. (12).

Table 4.

Results of relative and absolute errors between theoretical and test values.

Tilt angle/°	Connection offset/mm
	44		79		115
	Absolute error/N	Relative error/%	Absolute error/N	Relative error/%	Absolute error/N	Relative error/%
20	5.41	5.53	7.06	5.37	16.41	4.49
10	12.7	6.08	24.81	5.18	57.45	5.61
0	18.4	5.92	29.33	3.84	58.16	3.83
−10	20.46	5.13	48.54	4.77	101.98	5.21
−20	31.85	6.55	72.35	5.85	86.91	3.85

Fig. 9.

Change in SAD with the tilt angle and the connection offset.

For field tests, data samples were collected from the speed stable section of each test. In each group of tests, 300 and 30 data samples of GWD and ditching depth of each row unit were collected, respectively. GWD is automatically obtained by the data acquisition device, and the ditching depth is obtained by manual measurement.

Dynamic change in GWD of tests groups 1−3 and group 4 are shown in Fig. 10, Fig. 11, respectively. The box distribution diagram of the ditching depth (tests groups of 1–3) at different speeds is shown in Fig. 12(a). The box distribution diagram of the ditching depth (tests group 4) is shown in Fig. 12(b).

Fig. 10.

Dynamic change in GWD of no-tillage planter row unit.

Fig. 11.

Dynamic change in GWD of no-tillage planter row unit.

Fig. 12.

Box distribution diagram of the ditching depth.

Through the skewness analysis, we can be seen that the samples data of the two evaluation indicators of GWD and ditching depth are between [−1,1], so descriptive statistical indicators can be used for comparative analysis. The results of statistical analysis of GWD and ditching depth are shown in Table 5, Table 6, respectively.

• (1)As observed from Fig. 10 and Table 5 (test data of groups 1–3), GWD increases when the tilt angle of PFPM is upward. This is consistent with the theoretical analysis. Additionally, as observed from Table 5, at the speeds of 8, 10, and 12 km/h, the coefficients of variation of the GWD of row unit after the tilt angle was upward by 8° were 0.30, 0.32, and 0.31, respectively, which are smaller than the coefficients of variation of the control group under corresponding speeds. The stability of GWD was increased by 42.31 %, 56.16 %, and 50.29 %, respectively. The results show that PFPM with upward tilt can effectively improve the stability of GWD.
• (2)As shown in Fig. 12 (a), at all sowing speeds, after the PFPM of no-tillage planter with upward tilt, the interquartile spacing of the ditching depth box distribution is smaller than that of the control group, and no outliers appear. It observed from Table 6 (test data of groups 1–3) that when the tilt angle is upward by 8°, the coefficient of variation of ditching depth at each sowing speed was 0.07, which is smaller than the coefficient of variation at corresponding speeds of the control group. The stability of the ditching depth increased by 30.00 %, 12.50 %, and 30.00 %, respectively. The results indicate that the stability and consistency of the sowing depth can be effectively improved by the tilt upward of PFPM.
• (3)It can be seen from the test data of group 4 in Table 5, Table 6 that when PFPM is installed with springs compared with the row unit without spring, the average value of GWD increases from 752.40 N to 1105.13 N. Simultaneously, the coefficients of variation of GWD and ditching depth after installing springs were 0.42 and 0.12, respectively, which were less than those of the control group. The stability of GWD and ditching depth increased by 34.38 % and 14.29 %, respectively. The test results proved that the PFPM after installing springs is conducive to the stability of GWD and sowing depth.

Table 5.

Statistical analysis of GWD.

Run	Row unit	Average ± SD (N)	SE	Coefficient of variation	Stability improvement rate (%)
1	Improvement row unit	1392.30 ± 420.57	24.28	0.30	42.31
	Control row unit (CK)	963.10 ± 504.82	29.15	0.52
2	Improvement row unit	1364.72 ± 434.00	25.06	0.32	56.16
	Control row unit (CK)	789.72 ± 574.28	33.16	0.73
3	Improvement row unit	1840.87 ± 572.89	33.08	0.31	50.29
	Control row unit (CK)	856.99 ± 541.44	31.26	0.63
4	Improvement row unit	1105.13 ± 463.90	26.78	0.42	34.38
	Control row unit (CK)	752.40 ± 484.30	27.96	0.64

Table 6.

Statistical analysis of ditching depth.

Run	Row unit	Average ± SD (mm)	SE	Coefficient of variation	Stability improvement rate (%)
1	Improvement row unit	61.93 ± 4.39	0.80	0.07	30.00
	Control row unit (CK)	60.13 ± 6.25	1.14	0.10
2	Improvement row unit	57.90 ± 4.22	0.77	0.07	12.50
	Control row unit (CK)	56.43 ± 4.77	0.87	0.08
3	Improvement row unit	56.07 ± 4.08	0.75	0.07	30.00
	Control row unit (CK)	53.43 ± 5.46	1.00	0.10
4	Improvement row unit	53.23 ± 6.26	1.14	0.12	14.29
	Control row unit (CK)	51.07 ± 7.23	1.32	0.14

4. Conclusion

• (1)On a flat sowing area, the stability of sowing depth can be improved by increasing the SAD when the fluctuation in sowing depth is because of the heterogeneity of the soil property.
• (2)The initial tilt angle of PFPM is upward, which can not only increase the GWD but also effectively improve the stability and consistency of sowing depth. The research results can provide theoretical basis for the design and application adjustment of high-speed no-tillage planter.

Funding statement

This research was supported by State's Key Project of Research and Development Plan of China [2021YFD2000401], Heilongjiang Province Engineering Science and technology major project of China [2020ZX17B01] and National Modern Agricultural Industry Technology System Project [GARS-04].

Additional information

No additional information is available for this paper.

Data availability statement

Data included in article/supp. material/referenced in article.

CRediT authorship contribution statement

Jiajie Shang: Writing – original draft, Software, Formal analysis, Data curation, Conceptualization. Dongmei Liu: Writing – review & editing, Formal analysis, Data curation. Xingtao Song: Software, Formal analysis. Yibin Han: Formal analysis. Sitong He: Formal analysis. Ying Zhang: Formal analysis, Data curation. Liyi Liu: Supervision, Methodology, Conceptualization. Haitao Chen: Writing – review & editing, Project administration, Funding acquisition.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

The following is the Supplementary data to this article: