Simulation-based optimization and field validation of a tobacco transplanting earth auger using DEM–MBD coupling

Abstract

Efficient and consistent formation of transplanting holes (pits) is essential for the mechanized transplanting of tobacco plants, but the design of earth auger devices has traditionally relied on empirical selection and repeated trials. In this study, a systematic approach based on a combination of kinematic derivation, DEM–MBD coupled simulation, and orthogonal regression analysis was applied to optimize the geometry and operating parameters of an earth auger bit. Simulation results showed that the geometry of the bit primarily determined the depth of the transplanting hole, while the rotational speed exerted a significant quadratic effect on the hole’s diameter. Diameter and depth correction factors were also found to influence the stability of pit formation. Field experiments confirmed the feasibility of the optimized parameters, with an average diameter for the transplanting hole of 303 mm, an average depth of 127 mm, and a qualification rate of 98.2%, exceeding the 95% threshold set out in agronomic requirements. The close agreement between the simulation and experimental results validated the reliability of the DEM–MBD model. This study not only provides a theoretical reference for the design of tobacco transplanting using earth auger devices but also offers a practical methodology for improving agricultural engineering equipment involving interaction between soil and tools.

Keywords:
tobacco transplanting; earth auger; orthogonal experimental design; DEM–MBD coupling simulation

Introduction

Tobacco plays a significant role in China’s national economy, and is an important cash crop (Li et al., 2016; Wang, 2019). In 2022, the area used for tobacco planting in the country reached 1000.52 thousand hectares, with a yield of 213.4 thousand tons (Zou, 2022), accounting for approximately one-third of the global tobacco cultivation area. As the tobacco industry continues to develop both domestically and internationally, improvements to the efficiency and quality of tobacco transplanting have become critical. The “da tang” process (i.e., formation of the transplanting hole) in tobacco transplanting is particularly important in terms of ensuring the growth and yield of tobacco seedlings.

Research into tobacco transplanting machinery began outside of China; for instance, the PF2R ride-on fully automatic transplanting machine manufactured by Yanmar in Japan and the PZP-80 fully automatic transplanting machine sold by Iseki in Japan are known for their high technical standards, stable performance, and high degree of automation. However, although research into the mechanized transplanting of tobacco plants in China began later, it has progressed rapidly, and several achievements have been made. For example, Zheng Meiying and others from Yunnan Agricultural University developed a tobacco field cultivator and ridger with an earth auger mechanism for pre-transplanting operations (Zheng et al., 2022), while Yuan et al. (2019) developed a similar machine at Southwest Forestry University. With a focus on the transplanting process, other researchers from Southwest Forestry University developed a duckbill-type hole-digging mechanism for tobacco transplanting (Xiong et al., 2020). Chen et al. (2021) from the Nanyang City Tobacco Company, Neixiang County Branch, Henan Province, also studied the automation of tobacco planting and transplanting. However, there is a lack of research on the use of an earth auger for tobacco transplanting machines, both domestically and internationally. Traditional designs for earth augers often rely on the designer’s experience or are selected through numerous unsystematic trials, meaning that there is either a failure to ensure consistency in the depth and spacing of the transplanting hole or the process is time-consuming and labor-intensive, and does not provide guidance for future designs.

The development of a rational and generalizable design methodology for an earth auger for tobacco transplanting machines would therefore be an effective way to improve the design efficiency and enhance the transplanting quality. In recent years, the discrete element method (DEM) and coupling methods with multibody dynamics (MBD) and computational fluid dynamics (CFD) have been widely applied in studies of soil–tool interactions and the optimization of tillage and trenching equipment. Aikins et al. (2023) provided a comprehensive review of DEM applications in soil tillage and furrow opening, while 3D DEM models were applied by Ucgul et al. (2014) to predict soil disturbance and draft force, and to optimize the tool geometry and operating conditions. In research that was more closely related to this study, Wang et al. (2022) conducted numerical simulations and parameter optimization of earth augers in hilly areas using EDEM (Altair Engineering Inc., 2023), and confirmed the existence of a nonlinear optimum between the rotational speed and feed rate. Studies of earth augers for forestry planting have also begun to employ DEM–MBD coupling to evaluate the stability of the hole and the soil response under special terrain conditions (Wang et al., 2024).

Building on this foundation, the present study combines theoretical derivation with force analysis, DEM–MBD coupled simulation, and orthogonal experiments to determine the theoretical rotational speed of an earth auger and the relationships between the bit geometry and agronomic requirements. General formulae are also established for the rotational speed of the bit and the geometric parameter design, thereby providing a reference framework for the design of earth auger devices for tobacco transplanting machines.

Material and Methods

Mechanical analysis of the pit-forming device

Physical characteristics of the soil and agronomic requirements for tobacco transplanting

Honghe Prefecture in Yunnan Province is one of the top 10 tobacco-producing areas in China (Lu, 2016). The transplanting period runs from approximately late April to early May each year. The agronomic requirements for tobacco seedling transplantation are shown in Table 1 (Huang, 2016; Li, 2019; Yunnan Tobacco Standardization Technical Committee, 2021).

Table 1
Agronomic requirements for the transplanting of tobacco seedlings.

Measurement object	Units	Value(s)
Tobacco seedlings	Stem height (mm)	60–90
	Plant spacing (mm)	500–550
Tobacco ridge	Ridge height (mm)	250–300
	Row spacing (mm)	1,200
Transplanting hole	Hole depth (mm)	120–150
	Hole diameter (mm)	250–350
Irrigation	Irrigation amount (ml)	2,000–3,000

Structure and operational principle of the machine

The machine described in this study is based on the 2ZBZ-2 type of handheld tobacco transplanter. It mainly consists of a frame, a diesel-engine drive system, an hole-forming module based on an earth auger, a seedling separation and delivery device, and a control steering system. The structure is shown in Figure 1, and the main technical parameters are listed in Table 2. During operation, the diesel engine transmits power to the driving shaft through a chain-reduction system; the driving shaft then delivers power via a chain drive and a cam-linkage mechanism to the seedling separation and delivery device, the hole-forming and transplanting module, the irrigation system, and the ground wheel simultaneously. The seedling separation device consists of multiple hanging cups; when the delivery duckbill reaches its highest position, the hanging cups open under the compression of the block on the frame, and the tobacco seedlings fall into the seedling receiving funnel due to gravity and are fed into the duckbill planter. The hole-forming and transplanting module performs a complex motion composed of circular and forward movements under the drive power. During formation of the transplanting hole (pit), the conical blades below the pit-forming device rotate under the drive of the motor to excavate soil and form the pit openings. When the pit-forming and transplanting device reaches its lowest position, the duckbill planter opens to place the tobacco seedlings into the formed pits. The irrigation system is controlled by the cam linkage mechanism to achieve intermittent irrigation. During the pit-forming, transplanting, and irrigation processes, the driving shaft simultaneously transmits power to the movement output shaft, driving the transplanter forward. Due to the single degree of freedom of this mechanism, uniformity of operation is achieved for variable-speed planting.

Figure 1
Schematic diagram of the complete machine structure.

Table 2
Technical parameters of the machine.

Parameter	Value
Matching power (horsepower)	9
Travel speed (km/h)	0.5–2.0
Wheel spacing (mm)	900–1,100
Plant spacing (mm)	500–600
Planting speed (plants/h)	2,500
Irrigation per plant (ml)	2,000–3,000

Structural design of key components

The hole-forming and transplanting module is one of the core components of the tobacco transplanter. Its structure, as shown in Figure 2, consists of an earth auger, connecting rods, counterweight blocks, and a duckbill transplanter, forming a parallel four-bar mechanism. During operation, the rocker arm within the mechanism rotates counterclockwise, enabling the earth auger and the duckbill transplanter to move up and down in a periodic and reciprocating manner. Over each cycle of movement, the spacing between the earth auger and the duckbill transplanter is a precise integer multiple of the forward distance of the machine, thus achieving accurate transplanting. In addition, when the linear velocity of the end of the duckbill transplanter is equal to the forward speed of the machine at the moment the seedlings are inserted, ‘zero-speed transplanting’ can be achieved; in other words, at the moment the seedlings re released, the duckbill planter has zero horizontal velocity component relative to the ground. During this process, the earth auger is rotated by an independent motor to cut and remove soil effectively.

Figure 2
Diagram of the hole-forming and transplanting module.

Kinematic and dynamic analysis of the hole-forming and transplanting mechanism

A simplified kinematic diagram of the four-bar linkage assembly is shown in Figure 3, where α₁ represents the angle between rod AB and the x-direction, L₁ is the length of rod AB, α₂ denotes the angle between rod BC and the x-direction, L₂ is the length of rod BC, α₃ indicates the angle between rod CD and the x-direction, L₃ is the length of rod CD, and β is the angle between the BD line and the x-direction. All angles are defined as positive in the counterclockwise direction from the x-axis. The properties of a parallel four-bar mechanism mean that α₁ = α₃ and α₂ = 2π . Points 1, 2, 3, 4, and 5 correspond to rods AB, BC, CD, BE, and CF, respectively. Rods AB, BC, and CD are assumed to have uniform mass distributions, with their centers of mass located at the midpoints, and the friction between components is neglected.

Figure 3
Simplified kinematic diagram of the hole-forming and transplanting mechanism (angles defined as positive in the counterclockwise direction from the x-axis)

An analysis of the kinematics of the mechanism shows that the center of mass of AB is moving at (x₁, y₁):

$\{\begin{array}{c}{x}_1^{\prime }=-\frac{1}{2}{\alpha }_1^{\prime }{L}_1\sin {\alpha }_1\\ y_1^{\prime }=\frac{1}{2}{\alpha }_1^{\prime }{L}_1\cos {\alpha }_1\end{array}$ (1)

Owing to the properties of a parallel four-bar linkage, the center of mass of rod CD has a velocity with the same magnitude and direction. The angular velocity of rod BC is:

${\alpha }_2^{\prime }=\frac{2x_1^{\prime }\cos {\alpha }_3+2y_1^{\prime }\sin {\alpha }_3}{L_2\sin ({\alpha }_2-{\alpha }_3)}$ (2)

The speed of the center of mass of rod BC (x₂, y₂) can then be obtained as:

$\{\begin{array}{c}{x}_2^{\prime }=-{\alpha }_1^{\prime }{L}_1\sin {\alpha }_1-\\ \frac{-{\alpha }_1^{\prime }{L}_1\sin {\alpha }_1\cos {\alpha }_3+{\alpha }_1^{\prime }{L}_1\cos {\alpha }_1\sin {\alpha }_3}{2L_2\sin ({\alpha }_2-{\alpha }_3)}{L}_2\sin {\alpha }_2\\ y_2^{\prime }={\alpha }_1^{\prime }{L}_1\cos {\alpha }_1+\\ \frac{-{\alpha }_1{L}_1\sin {\alpha }_1\cos {\alpha }_3+{\alpha }_1^{\prime }{L}_1\cos {\alpha }_1\sin {\alpha }_3}{2L_2\sin ({\alpha }_2-{\alpha }_3)}{L}_2\cos {\alpha }_2\end{array}$ (3)

The centers of mass of rods BE and CF, which are pinned to rod BC, have the same velocity as the centroid of rod BC. Hence, the velocities of the centers of mass of rods BE (x₄, y₄) and CF (x₅, y₅) are the same as for rod BC.

If $\chi =\frac{3\pi }{2}+2\pi n$ (where n is a positive integer) and the forward velocity of the whole machine is v = -x'₂, then ‘zero-speed transplanting’ can be achieved. The structure of the whole machine dictates that the forward velocity at this point is 0.4375 m/s.

During the operation of the mechanism, the fixed support point A is subjected to a planar couple moment of magnitude M. A force analysis using the method of virtual work is conducted as shown in Figure 4. The masses of rods AB, BC, CD, BE, and CF are 𝑚₁, 𝑚₂, 𝑚₃, 𝑚₄, and 𝑚₅, respectively, and there is an additional torque M at the fixed support point A. The external force system acting on the earth auger can be equivalently represented by the forces F_Ex and F_Ey along the x- and y-directions at its endpoint E, respectively; the fixed support point A is subjected to the external force on the frame, with components F_Ax and F_Ay; and the fixed support point D is subjected to the external force on the frame, with components F_Dx and F_Dy. Since the external force acting on the duckbill transplanter during its operation is much smaller than that acting on the earth auger, the equation of virtual work can be established as follows:

Figure 4
Force analysis diagram for the earth auger.

$M\delta {\alpha }_1-m_{1}g\delta h_1-m_{2}g\delta h_2-m_{3}g\delta h_3-m_{4}g\delta h_4-m_{5}g\delta h_5-F_{Ex}\delta x_E-F_{Ey}\delta y_E=0$ (4)

From the torque balance at points A and D and the geometric relationship between them, we can obtain

$M+F_{Ey}{L}_1\cos {\alpha }_1-F_{Ex}(L_4-L_1\sin {\alpha }_1)-F_{Dy}{L}_2=0$ (5)

$M+F_{Ey}(L_3\cos {\alpha }_1+L_2)-F_{Ex}(L_4-L_3\sin {\alpha }_1)-F_{Ay}{L}_2=0$ (6)

Performing a force balance on the system, since rods AB and CD are two-force members, it can be deduced from the geometric relationship that:

$F_{Ay}+F_{Dy}+F_{Ey}=0$ (7)

$F_{Ax}+F_{Dx}+F_{Ex}=0$ (8)

$\frac{F_{Ay}}{F_{Ax}}=\frac{F_{Dy}}{F_{Dx}}=\tan {\alpha }_1$ (9)

By solving the simultaneous equations in eqs (1) to (9), an expression for F_Ex can be obtained as follows:

$F_{Ex}=\frac{\frac{1}{2}g2(m_1+m_3+2m_2+2m_4+2m_5)(2L_1\cos {\alpha }_1+L_2)-2M\cos {\alpha }_1}{\sin {\alpha }_1(2L_1\cos {\alpha }_1+L_2)-2\cos {\alpha }_1(L_4-L_1\sin {\alpha }_1)}$ (10)

A ring-shaped cross section for the bar is not only superior to other cross sections in terms of its mechanical properties but also saves material and is easy to machine (Zhao, 2020), and was therefore adopted in this design. If the large diameter of the ring is r₀ and the small diameter is r₁, the formula for the stress in the critical section can be obtained as follows:

${\sigma }_{max}=\frac{4L_4{r}_0[\frac{1}{2}g(m_1+m_3+2m_2+2m_4+2m_5)(2L_1\cos {\alpha }_1+L_2)-2M\cos {\alpha }_1]]}{\pi (r_0^4-r_i^4)[\sin {\alpha }_1(2L_1\cos {\alpha }_1+L_2)-2\cos {\alpha }_1(L_4-L_1\sin {\alpha }_1)]}$ (11)

It can be seen from this formula that when the sizes and materials of the various rods of the four-link mechanism are determined, a linkage rod diameter can be obtained that meets the strength requirements for the mechanism. After calculation, when r₀ = 14.763mm, r₁ = 11.433mm meet the strength conditions, for ease of processing design.

r₀ = 14.763mm, r₁ = 11.433mm

A force analysis of an infinitesimal element of soil on the helical blade of the earth auger is shown in Figure 5, where F₂ is the frictional force between the soil and the helical blade, with a magnitude of (Xu et al., 2020):

Figure 5
Diagram of the forces on the soil block

$F_2=K+fP$ (12)

Where:

f is the friction coefficient of the soil against the bit, according to the soil properties in the test area, with a value of 0.3; K is the adhesion coefficient,$K=6\mathrm{KN}/m^2$ and

P is the spiral blade pressure on the soil block, in units of N.

To satisfy the conditions for creating a hole, the upward force from the soil block along the helical blade during the hole-making process should be less than the sum of the downward forces along the blade, that is:

$F_2\cos \alpha +P\sin \alpha \le F_1$ (13)

$N=G\cos \alpha +F\sin \alpha$ (14)

Where:

α is the helix lead angle, in radians;

F₁ is the rolling friction force of the soil block microelement along the hole wall, calculated as:

$F_1=f_2{F}_3$ (15)

Where:

F₃ is the centrifugal force of soil element rotation:

$F_3=\frac{G{\omega }_r^2(R-r)}{g}$ (16)

f₂ is the rolling friction coefficient of the soil block relative to the hole wall, with a value of 0.4 based on the soil properties of the test area; R is the radius of the opening of the transplanting hole, in mm; r is the radius of the soil element, in mm; and ω is the angular velocity of the soil block relative to the hole wall, in rad/s.

By solving eqs (12) to (16) simultaneously, we obtain:

${\omega }_r^2\ge \frac{g(\frac{K}{G}+f_1\cos \alpha +\sin \alpha )}{f_3(R-r)(\cos \alpha -f_1\sin \alpha )}$ (17)

The equation satisfies [eq. (13)] for the angular velocity, meaning that the minimum angular velocity of the earth auger should be:

$\frac{g(\frac{K}{G}+f_1\cos \alpha +\sin \alpha )}{f_3(R-r)(\cos \alpha -f_1\sin \alpha )}$ (18)

The minimum rotational speed of the earth auger is calculated as 14.45 rad/s. In view of factors such as soil backflow, it is necessary to multiply the minimum speed by a constant value η, which typically ranges from 1.2 to 1.5 (Gao, 2018). The final designed speed is 17–21 rad/s.

SIMULATION OF THE CROSS SECTION OF THE EARTH AUGER

To select values for the cross section and rotational speed of the earth auger to best meet the agronomic requirements, a DEM scheme coupled with MBD (DEM–MBD) simulation was employed (Chen et al., 2024). An orthogonal experimental design was used to analyze the hole-forming process by simulating the earth auger device. The effects of different models, maximum diameters, hole depths, and rotational speeds on the hole-forming performance were compared and quantified. The resulting regression equation provides guidance for subsequent designs for auger bits.

Establishment of the simulation model

To simulate the characteristics of the hole-forming operation after preparation of the soil for tobacco cultivation in the Yunnan region, a soil particle model was established to represent relatively loose soil, with elastic collisions, sliding friction, and rolling friction between particles. The Hertz–Mindlin model with bonding was chosen for this experiment. Current research (Xie et al., 2024) indicates that particles of sandy loam are mainly spherical, cylindrical, core-shaped, and blocky triangular particles. The soil model therefore consisted of particles with four different shapes: single spheres, cylinders, triangles, and cones, as shown in Figure 6, with specific parameters as given in Table 3 (Zhang et al., 2023a).

Figure 6
Soil particle shapes used in the model.

Table 3
Parameters for the EDEM simulation (Pan et al., 2025).

Parameter	Value
Density of steel (kg·m-3)	7810
Poisson’s ratio for steel	0.3
Shear modulus for steel (Pa)	2.07e+11
Soil density (kg·m-3)	980
Poisson’s ratio for soil	0.4
Shear modulus for soil	1.09e+06
Restitution coefficient between soil particles	0.2
Coefficient of static friction between soil particles	0.4
Coefficient of kinetic friction between soil particles	0.3
Restitution coefficient between soil and steel	0.5
Coefficient of static friction between soil and steel	0.5
Coefficient of kinetic friction between soil and steel	0.3

A soil bin model was established in EDEM with dimensions of 2,000×600×300 mm ((length×width×height). A particle factory was created above the soil bin to generate soil particles, which fell along the negative Z-axis under a gravitational acceleration of –9.81 m/s² until the soil bin was filled, forming the soil layer shown in Figure 7. The simplified three-dimensional model of the earth auger device was converted to STP format and imported into EDEM, as shown in the figure.

Figure 7
Soil bin simulation model.

Orthogonal experimental design

Before conducting the experiment, it was necessary to consider the factors that significantly affected the diameter and depth of the transplanting hole, and to determine the possible range of optimal values for these factors. The main parameters that influence the geometry of an earth auger are the maximum diameter and depth of the bit, as well as the working rotational speed, which affects the efficiency of soil displacement (Ba et al., 2022; Thomas et al., 2002; Wang et al., 2017; Yuan et al., 2019; Zhang et al., 2023b; Zheng et al., 2023). There are currently three main types of earth auger bit that are used for the formation of transplanting holes: cylindrical spiral augers, cylindrical spiral augers with conical sections, and conical intermittent spiral augers (Ge et al., 2019; Qu & Liu, 2009; Zhang et al., 2015), as shown in Figure 8. Preliminary calculations indicated that the rotational speed of the bit was constrained to the range of 17–21 rad/s. To refine the structural parameters, single-factor experiments were performed with a target diameter for the transplanting hole of 300 mm and a target depth of 130 mm. The results were expressed in terms of normalized correction factors, defined as the ratio between the designed bit geometry (diameter or depth) and the corresponding agronomic targets. In view of the physical constraint that the diameter of the transplanting hole could not be smaller than the diameter of the bit, trials were conducted for auger diameters in the range of 80–100% of the target value, yielding an optimal diameter correction factor in the range of 90–100%. Similarly, since the effective depth of the transplanting hole could not exceed the auger penetration depth, experiments were carried out for auger penetration depths of between 100–130% of the target value, and the optimal depth correction factor was determined to lie between 115% and 125%.

Figure 8
Current models for earth auger bits.

During the experiment, the forward speed of the mechanism was set to 0.4375 m/s, based on the forward calculation and the ‘zero-speed transplanting’ condition. To optimize the design parameters of the bit, the type of auger (A), its rotational speed (B), the diameter correction coefficient (C), and the depth correction coefficient (D) were chosen as the experimental factors. The types of auger considered were a cylindrical spiral, conical spiral, and intermittent conical spiral; the rotational speeds ranged from 17 to 21 rad/s; the diameter correction coefficients ranged from 90% to 100%; and the depth correction coefficients ranged from 115% to 125%. The diameter fitness and depth fitness were used as response indicators. To investigate the influence of these factors and their interactions on the evaluation indicators, and to obtain the optimal parameter combinations, a four-factor, three-level orthogonal experiment was conducted, with 29 groups of experiments in total. Each experiment was repeated three times, and the average of the three tests was taken as the test result for that group. The experimental factors and their codings are shown in Table 4. Based on these values, DEM–MBD coupled simulations were performed on the earth auger bit to obtain numerical results under different conditions.

Table 4
Experimental factors and coding levels

Code	A=Type of earth auger	B=Rotation speed	C=Diameter correction coefficient	D=Depth correction coefficient
−1	Cylindrical spiral	17	90%	115%
0	Conical spiral	19	95%	120%
1	Conical intermittent spiral	21	100%	125%

• Note: The coded levels (−1, 0, +1) in Table 4 were obtained by linear scaling from the corresponding nominal values; the actual (decoded) value can be recovered as follows: actual value = nominal center value + coded level × step size.

Simulation process

The total simulation time was set to 18 s, of which 12 s was allocated to generating the soil model and 6 s was allotted to the earth auger device to perform field operations. The time step was set to 20%, and the save interval was set to 0.1 s.

Based on the agronomic requirements for tobacco transplanting and the zero-speed transplanting condition, the working parameters of the auger device were set as follows: the forward speed of the device was 0.4375 m/s, and the rocker arm rotated at a speed of 4.99 rad/s in a counterclockwise direction. At the start of the simulation, the device was positioned at one end of the soil bin, as shown in Figure 7(b). During operation, as the device moved forward, the rocker arm underwent circular motion, driving the earth auger to perform periodic up and down movements. The earth auger rotated at the designed speed to displace soil and create transplanting holes. Upon completion of the simulation, the device left the soil bin, leaving a row of uniform transplanting holes, as shown in Figure 9.

Figure 9
DEM–MBD simulation results for the formation of transplanting holes.

Results and Discussion

Experimental results and analysis

An analysis of variance (ANOVA) can be used in an experimental design process to determine whether there are significant differences between different groups of experiments, and the coefficient P reflects whether these differences are statistically significant. Tables 5 and 6 show the results of ANOVAs for the diameters and depths of the holes, where items with P < 0.1 for the diameter fitness and depth fitness of the transplanting hole are all significant. After eliminating less important influencing factors, the regression equations for Y₁ and Y₂ were obtained as follows:

Table 5
Results of an analysis of variance for the quadratic polynomial model of the diameter of the transplanting hole.

Category	Transplanting hole diameter
	Sum of squares	DF	Mean square	F	P
Model	32,196.98	14	2,299.78	13.3	＜0.0001***
A	5,099.62	1	5,099.62	29.49	＜0.0001***
B	4,147.8	1	4,147.8	23.98	0.0002***
C	4,435.9	1	4,435.9	25.65	0.0002***
D	1,934.24	1	1,934.24	11.18	0.0048***
AB	406.41	1	406.41	2.35	0.1476
AC	57.8	1	57.8	0.3342	0.5724
AD	1,687.85	1	1,687.85	9.76	0.0075***
BC	261.97	1	261.97	1.51	0.2387
BD	0.0108	1	0.0108	0.0001	0.9938
CD	84.36	1	84.36	0.4878	0.4963
A2	1,796.73	1	1,796.73	10.39	0.0061***
B2	8,878.28	1	8,878.28	51.34	＜0.0001***
C2	819	1	819	4.74	0.0472**
D2	1,715.75	1	1,715.75	9.92	0.0071***
Residual	2,421.13	14	172.94
Lack of fit	2,421.13	10	242.11
Pure error	0	4	0
Cor total	3,4618.11	28

• Note: *** indicates extremely significant (P<0.01); ** indicates significant (0.01<P<0.05); * indicates relatively significant (0.05<P<0.10).

Table 6
Results of an analysis of variance for the quadratic polynomial model of the depth of the transplanting hole.

Category	Transplanting hole depth.
	Sum of squares	DF	Mean square	F	P
Model	8,058.42	14	575.6	3.93	0.0076***
A	35.88	1	35.88	0.2449	0.6284
B	3,064.48	1	3,064.48	20.91	0.0004***
C	3,103.12	1	3,103.12	21.18	0.0004***
D	936.95	1	936.95	6.39	0.0241**
AB	331.42	1	331.42	2.26	0.1548
AC	47.89	1	47.89	0.3268	0.5766
AD	1.99	1	1.99	0.0136	0.9089
BC	4.02	1	4.02	0.0274	0.8708
BD	0.3938	1	0.3938	0.0027	0.9594
CD	17.22	1	17.22	0.1175	0.7368
A2	0.9459	1	0.9459	0.0065	0.9371
B2	302.7	1	302.7	2.07	0.1726
C2	236.59	1	236.59	1.61	0.2246
D2	117.23	1	117.23	0.8001	0.3862
Residual	2,051.41	14	146.53
Lack of fit	2,051.41	10	205.14
Pure error	0	4	0
Cor total	10,109.83	28

• Note: *** indicates extremely significant (P<0.01); ** indicates significant (0.01<P<0.05); * indicates relatively significant (0.05<P<0.10).

$Y_1=356.60-20.61A+18.59B+19.23C+12.70D+20.54AD+16.64A^2-37B^2-11.24C^2-16.26D^2$ (19)

$Y_2=121.94+15.98B+16.08C+8.84D$ (20)

These regression equations were subjected to lack-of-fit tests, which yielded values for Y₁ and Y₂ of less than 0.1; this indicates that there was no lack of fit, suggesting that the equations fitted well. The quadratic relationship of the regression equations is significant, making the analysis of the results reasonable.

Using Design-Expert 12.0 software, response surfaces were obtained for the interactions between the type of earth auger, rotational speed, diameter correction factor, and depth correction factor with respect to the diameter and depth of the hole (Stat-Ease Inc., 2019). To enable a more intuitive deduction of the patterns of influence of the experimental factors on the response variables, dimensionality reduction was applied by examining the relationship between any two factors while holding the others constant at their zero levels. As shown in Figures 10(a–c), changing the type of auger between Types 1, 2 and 3 resulted in a gradual reduction in the diameter of the hole. This indicates that the geometry of the auger directly determines soil fragmentation and discharge patterns, thereby influencing the cross-sectional size of the pit. From Figures 10(a, d, e), it can be seen that as the rotational speed was increased from 17 to 21 rad/s, the diameter of the hole first increased and then decreased, showing a significant quadratic effect (B²). Optimal performance was achieved at intermediate speeds; this is because at low speeds, insufficient cutting leads to pit collapse and smaller diameters, whereas at high speeds, excessive soil scattering and intensified wall disturbance reduce the effective diameter. This nonlinear behavior is consistent with the DEM–CFD simulations of strip-tillage tools reported by Yuan et al. (2023). Figures 10(b, d, f) show that the diameter of the hole increased steadily as the diameter correction factor rose from 90% to 100%, a trend consistent with its physical meaning. Figures 10(c, e, f) show that the diameter initially increased but then decreased as the depth correction factor was increased from 115% to 125%.

Figure 10
Response surface plots for dual-factor impacts on the hole diameter.

Although moderate increases in depth facilitated the formation of pits, excessive values caused wall disturbance and soil backfill, leading to reduced effective diameters. As illustrated in Figures 11(a–c), the depth of the hole underwent an progressive increase as the type of auger was changed from Type 1 to Type 3, due to the differences in the cutting angles and force transfer paths among the geometries of the earth auger. Similarly, Figures 11(b, d, f) show that the depth increased as the diameter correction factor rose from 90% to 100%. This finding can be attributed to the larger soil discharge volume and reduced wall collapse associated with larger diameters, which enhanced the effective depth of the hole. From Figures 11(c, e, f), it can be seen that the diameter increased as the depth correction factor was increased from 115% to 125%. This was not only due to the greater cutting coverage and increased soil discharge, but also because the forward motion of the machine caused the deeply embedded outer edges of the earth auger to exert an additional lateral expansion force on the pit walls. This observation is consistent with the conclusions of Wang et al.(2022) on the influence of the penetration depth on edge stability in auger simulations, thus further validating the reliability of the results presented here.

Figure 11
Response surface plots for dual-factor impacts on the hole depth.

Based on the target values of a diameter of 300 mm and a depth of 130 mm, the target values of Y₁ and Y₂ were set to 300 and 130, respectively, in Design-Expert Optimization, with Y₁ and Y₂ assigned equal weights. The final optimal solution obtained was:

$\{\begin{array}{c}{Y}_1=300.000\\ Y_2=127.373\\ A=1.000\\ B=-0.121\\ C=1.000\\ D=-0.995\end{array}$

It is important to note that the value of A should be an integer. By applying the encoding formula, it was determined that the most suitable hole-forming performance to meet the agronomic requirements would be achieved using a conical intermittent spiral auger with a speed of 18.785 rad/s, a diameter of 300 mm, and a depth of 150.375 mm. In this case, the diameter of the transplanting hole was 300 mm, and the depth was 127.373 mm.

FIELD EXPERIMENT

To verify the reliability of the results, a field experiment was conducted on May 2, 2023, in Honghe Prefecture, Yunnan Province. The soil had an average moisture content of (20±1)% and a bulk density of 0.98 g/cm³, and was classified as clayey. The machinery was operated at a speed of 1.5 km/h, using a conical intermittent spiral auger with a speed of 18.8 rad/s, a diameter of 300 mm, and a depth of 150.375 mm. The qualified rate of the diameter and depth of the holes was taken as the indicator, and each ridge was operated on over 50 m, with a total of 10 ridges. The qualified rates were measured separately for the diameter and depth and then averaged. The measurements were conducted according to the Yunnan Tobacco Mechanized Transplanting Standard DB5305/T 50.14-2021. Photographs of the field harvest experiment are shown in Figures 12 and 13, and the results of the field validation test are presented in Table 7.

Figure 12
Photograph of the field test.

Figure 13
Photograph of transplanted tobacco seedlings in the field experiment.

Table 7
Experimental results for the diameter and depth of the transplanting hole.

Assay group	Number of plants (n)	Average hole diameter (mm)	Average hole depth (mm)	Diameter qualification rate
1	100	301.4	135.5	100%
2	100	305.3	125.7	99%
3	100	305.7	126	98%
4	100	298.2	121.6	100%
5	100	296.1	123.5	95%
6	100	311.5	129	97%
Average		303.0	126.6	98.2%
Min		294.0	120.0
Max		314.0	137.0
95%CI		297.3–308.7	121.7–131.5

The results of the field tests indicated that when the implement was operated at a forward speed of 1.5 km/h, the earth-auger-based hole-forming and transplanting device achieved an average qualification rate of 98.2%, exceeding the agronomic benchmark of 95% required for tobacco transplanting in Yunnan Province. In addition, the mean diameter and depth of the holes measured during field trials deviated from the simulation predictions by less than 1%, providing strong evidence for the reliability of the DEM–MBD simulation model and the associated regression equations.

Conclusions

The findings of this research can be summarized as follows:

1. Based on the structural characteristics of the earth-auger-based hole-forming and transplanting device for tobacco seedlings, the soil displacement conditions of the earth auger bit, and the requirements for zero-speed transplanting, formulae were obtained for the cross-sectional dimensions of the earth auger shaft, the zero-speed transplanting condition, and the range of rotational speeds.

2. Using a DEM–MBD coupled simulation, an orthogonal experimental analysis was conducted on the cross-sectional shape and size of the earth auger bit, and Design-Expert 12.0 software was used to solve the regression equations for the rotational speed and geometric parameters of the auger. The optimal cross-sectional parameters for the auger bit of the 2ZBZ-1 walk-behind tobacco transplanter were determined as follows: a conical intermittent spiral auger with a rotational speed of 18.785 rad/s, a diameter of 300 mm, and a depth of 150.375 mm. Some of the optimal results were close to the parameter boundaries, due to physical constraints on the geometry of the bit, and in future work, the tested ranges will be extended to further validate the robustness of these conclusions.

3. A field experiment was conducted to validate the simulation test results. The results showed that when the machinery was operated at a speed of 1.5 km/h, using a conical intermittent spiral auger with a speed of 18.8 rad/s, a diameter of 300 mm, and a depth of 150.375 mm, the average diameter of the hole was 303.0 mm, the average depth was 126.6 mm, and the qualification rate was 98.2%. These values met the agronomic requirements for the formation of tobacco transplanting holes, and verified the feasibility of the theoretical approach.

At present, DEM–MBD coupled simulation studies with a specific focus on earth-auger-based hole-forming modules for tobacco transplanters remain scarce, making it difficult to carry out a direct comparison of our results with similar international research. Nevertheless, the optimization approach proposed in this study offers methodological advantages over traditional empirical design. Furthermore, this approach was validated through field experiments, and the results not only met but exceeded current agronomic requirements, highlighting the feasibility and broader applicability of the method.

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• Data Availability Statement:
  The datasets generated and/or analyzed during the current study, including the DEM-MBD simulation outputs, experimental measurements, and related analytical data, are not publicly available because they are associated with a cooperative research project and contain technical details related to device development. However, the data are available from the corresponding author upon reasonable request.
• Funding:
  This research project was sponsored by the Honghe Branch of Yunnan Tobacco Company, with funding support from the Science and Technology Plan Project of Yunnan Tobacco Company (2023530000241020), China Tobacco Corporation.

Edited by

• Area Editor:
  Tiago Rodrigo Francetto

Data availability

The datasets generated and/or analyzed during the current study, including the DEM-MBD simulation outputs, experimental measurements, and related analytical data, are not publicly available because they are associated with a cooperative research project and contain technical details related to device development. However, the data are available from the corresponding author upon reasonable request.

Publication Dates

• Publication in this collection
  20 July 2026
• Date of issue
  2026

History

• Received
  18 Dec 2024
• Accepted
  2 Mar 2026