Enhancing Sustainable Afforestation through Innovative Earth Auger Design: A Simulation Study in Hilly Regions

Abstract

The objective of this study was to advance sustainable forestry development through the creation of mechanical equipment, taking into account forestry operational methods. A suspended automatic feeding and retracting excavation device for tree pits was engineered, and its interaction with soil was investigated by integrating the Discrete Element Method (DEM) with Multi-Flexible Body Dynamics (MFBD). Based on simulation results, the research explored the impact mechanisms of the machine on soil transportation, working load, and fatigue lifespan of the spiral blades for different terrains and operating conditions. The coupling simulation method demonstrated the potential for designing and testing forestry equipment in specific operating environments, reducing time and resource consumption for field testing. Terrain significantly influenced soil disturbance variability, while the effect of operating direction was minor. Operational parameters should consider soil and water conservation, favoring the formation of fish-scale pits. Field tests in forested areas validate the practicality of the apparatus, providing valuable insights for the operation and equipment design of earth augers in hilly regions.

1. Introduction

Afforestation is crucial for maintaining ecological balance, improving environmental quality, and promoting sustainable development. Although hilly and mountainous regions are prone to environmental damage, the level of forestry mechanization is relatively low. The tree-planting excavator (also known as the earth auger) is a typical and practical tool for afforestation. Still, there is less research on hilly regions, particularly on working principles and forestry processes. Tree planting in hilly regions usually requires attention to soil and water conservation. Many land preparation methods similar to fish-scale pits require mechanization to improve job efficiency. To adapt to slope operations, the verticality of the pit needs to be ensured. In hilly areas, digging operations mainly rely on manual labor. However, manual work on slopes exceeding 25° involves high labor intensity and poor safety. When designing and developing equipment for pit digging in hilly and mountainous regions, it is crucial to consider these challenges. This ensures that the equipment is capable of efficient operation and meets safety requirements in these challenging conditions [1,2,3].

The current research on earth augers mainly focuses on plain terrain. Many scholars have explored various aspects of earth augers, such as their vibration characteristics, cutting model, power consumption, and frame structure. The outcome of this approach is optimizing the mechanical structure, which consequently leads to an enhancement in work efficiency [4,5,6]. Ma et al. [7] designed an automatic feed mechanism with a half-nuts structure for a portable earth auger, which helps to achieve efficient pit-digging operations and reduce labor intensity. S. Engin et al. [8] established a mechanical and dynamic model that can describe different shapes of auger devices, as well as a dynamic model and mathematical expressions for predicting the digging process. This approach can be employed to optimize auger shape, spiral space, and other associated parameters. Although much research considers the effects of terrain and afforestation craft, little research focuses on the earth auger, especially in hilly terrains. Integrating craft with machinery is crucial for enhancing the practicality of research outcomes. Therefore, it is necessary to study the patterns of soil disturbance when terrain and equipment structure act simultaneously to further understand their impact on future slope afforestation. To consider both safety and efficiency, studying the load and fatigue characteristics of the auger becomes crucial. On the other hand, using a chassis-mounted digging machine will enhance the safety and efficiency of the slope operation. The aforementioned results do not specifically discuss the hitching device, but its mechanical structure is shown in the figures in their paper. However, research on sloped terrain has not been reported. Depending on the operating direction (uphill or downhill), the earth auger can be classified as front-mounted or rear-mounted relative to the chassis. The position of the working components during chassis slope operation can affect operational stability. Therefore, it is necessary to design a suspended digging machine and study the impact of its operating direction on performance. This is significant for the adaptability and safety of operations on sloped terrain.

As a result of the soil’s characteristics, spatial changes, and fluidity, the mechanical properties of the earth auger are complex and variable, especially in hilly regions with slopes [9]. However, after the earth auger enters the soil, the movement of soil and auger within the pit is difficult to monitor due to the obstruction of the surrounding soil and mechanical structures. In agricultural engineering research, the DEM can accurately model soil particles and analyze the intrinsic motion and force characteristics, which is an effective method to explore the dynamic behavior of soil [10]. MBD simulations of mechanical systems were widely used to analyze component motions and joint forces under various operating conditions [11,12]. MBD-DEM coupling can achieve the ideal simulation for analyzing the device motion and simulating the particle characteristics [13]. Wang and others have researched the mechanism of the straw burial and return machine during the ditching process. The MBD-DEM coupling method was used to conduct a simulation experiment for the ditching device [10]. Zhu et al. proposed a RecurDyn-EDEM-AMESim co-simulation that accurately characterizes the working loads in straight bulldozing conditions [14]. Yeon-Soo Kim et al. utilized the DEM-MBD coupling model for the draft force prediction according to the tillage depth. This study can gradually replace existing field tests with digital twin-based simulation tests. The approach can provide valuable insights for optimal design while minimizing the development time and cost of soil–machine systems [15]. Many types of forestry equipment also primarily involve soil as their primary target. However, the above-mentioned methods have seen limited application in forestry, lacking practical experience and parameter support. According to the literature, compared with the single directionally coupled simulation method using DEM-MDB, the bi-directionally coupled simulation method using DEM-MFBD can accurately simulate the process of interaction between geometric bodies and particles, more realistically reflect the actual working situation of the earth auger, and accurately obtain the movement and force conditions of the components [16,17].

In actual digging operations, numerous nonlinear mechanical behaviors, such as contact and collision, occur between the auger and the soil. The method of DEM-MFBD can analyze the contact and connection between particles and continuum structures, and the bidirectional coupling and data synchronous exchange between the continuum module and the discrete body module can be realized. The objective was to obtain the mechanical characteristics of the soil and the auger and their disturbance effects. During the process of pit digging on slopes and plains, factors such as the uniformity of force on the spiral blades, the shape of the soil collection peak, and the shape of the pit wall are different. Therefore, virtual simulations need to be conducted for different terrain types [14]. Cutting torque stands as a pivotal criterion for evaluating the efficiency of an earth auger. The predictive estimation of the auger’s cutting torque holds utmost significance, offering essential insights and references for dynamic characteristic investigations and reliability analyses, as well as structural design and enhancements. Monitoring the torque of the rotary joint can reflect the pattern of variation of the auger’s soil resistance [18,19].

In this study, a hanging type earth auger used in hilly terrain was designed. The machine features an adjustable auger angle and automatic feed and return functions. Subsequently, employing the bidirectional coupling simulation technique of DEM-MFBD, we explored the mechanisms underlying pit digging on slopes and optimized the operational mode of the apparatus. Based on the simulation results of the virtual prototype, the motion law of the soil and the load and fatigue characteristics of the auger were analyzed. The operational performance of the apparatus was assessed by conducting afforestation trials involving pit digging in forested areas. This equipment was designed to enhance the efficiency of constructing fish-scale pits in hilly regions. This endeavor serves as a reference for designing and developing equipment and essential components for pit digging operations in hilly and mountainous terrains. This study can provide experience for the research on ground-contact equipment for continuous forestry operations.

2. Design of Hanging-Type Earth Auger

2.1. Overall Structure and Forest Craft of the Device

A compact, versatile, easy-to-use pit digging device was proposed in response to the working conditions of slope planting operations. This device, installable on the chassis, allows for the rapid adjustment of the auger’s angle relative to the ground, accommodating various slopes within 45° for vertical digging operations. By manipulating the hydraulic system, the auger can perform automatic feed and return movements. The hanging-type earth auger consists of the relevant components, as indicated in Figure 1. The specific technical parameters are listed in

Table 1. Technical parameters of the device.

Parameter	Unit	Value
The dimensions of the overall machine	mm	1140 × 900 × 1590 (Length × Width × Height)
The dimensions of the hitch plate	mm	900 × 300 × 10 (Length × Width × Thickness)
The range of angle adjustment	°	±45°
The range of feed motion	mm	0–600
The range of lateral adjustment	mm	±250
The weight of the device	kg	≈380

.

A hybrid method combining hydraulic and mechanical techniques was utilized to accomplish the overall position and angle adjustment of the device system. The angle of the hitch plate can be adjusted through a hinge linkage mechanism with the swing cylinder, ultimately achieving the adjustment of the auger angle. The automatic feed and return movements of the auger are achieved through the retractable sleeve-type structure. The outer segment rod is a square tubular structure connected to the hitch plate using bolts. The inner segment rod is inside the outer rod, and its movement is adjusted through the longitudinal oil cylinder. The implementation of adjusting the transverse digging position of the auger using a slide-style structure was adopted. The slide rail is connected to the hitch plate. The slider is connected to the slide rail at both the front and end positions through the horizontal hydraulic cylinder to adjust the movement. The apparatus can conduct pit digging on upslope, downslope, and plain terrains, as illustrated in Figure 2.

The analysis of the advantages of this equipment in slope operations was as follows. Figure 2 is a comparative flowchart illustrating manual and mechanized methods for afforestation on slopes. For the original manual operation steps in hilly regions, the procedure involves felling forests and preparing land first, followed by digging circular pits on the slope. Afterward, the soil is reinforced to form fish-scale pits. In contrast, with mechanized operations, there is no need for excessive land preparation to ensure personnel safety. Instead, a simple soil reinforcement process is carried out directly on the slope after digging. According to the operational process, it can be observed that the terrain features and soil dynamic characteristics are crucial influencing factors in the construction of slope-scale fish-scale pits.

2.2. Design of Linkage Mechanism

The linkage mechanism for digging angle adjustment is shown in Figure 3a. The swing cylinder and the power mechanical frame are installed and fixed through the back-ear plate. The swing cylinder and the rotating arm are installed and fixed through the front-ear plate. The swing cylinder is hinged with the front and back-ear plates. The telescopic cylinder drives the connecting rod to move. The connecting rod mechanism is designed according to the principle of compact structure, and the size of each rod and the stroke of the cylinder will also be determined based on that principle. Figure 3b depicts the movement diagram of the linkage mechanism with a swing cylinder, wherein AB represents the cylinder, which is regarded as a telescopic rod. BD stands for the front-ear plate. CD signifies the distance between the rotating arm and the fixed position of the front-ear plate. CE represents the rotating arm, and OC is the length of the front end of the frame. AO corresponds to the back-ear plate. In the analysis, ΔBCD and ΔACO are regarded as rigid bodies, with their function being to elevate the auger relative to the ground when it is raised and prevent interference between the rod entities. Upon rotation, the positions of points B, D, and E are transformed into points B′, D′, and E′, respectively. For the sake of convenience in analysis, this mechanism can be simplified as a guide rod mechanism, as illustrated in Figure 3c. The oil cylinder was transformed into a slider, wherein AC represents the frame and BC denotes the crank. The distinctive feature of this design was that the slider serves as the driving component, capable of moving along the AB rod and simultaneously driving the crank BC to rotate clockwise. The slider rotates around point A while sliding linearly on the guide rod AB. The purpose of this design was to facilitate a 90° swing angle when the BC rod is positioned at BC′, allowing for respective upward and downward swings of 45°. The stroke of the slider is the expanded or contracted length of the cylinder. The relationship between the lengths of relevant components and their included angles is expressed by the following Equations (1)–(7).

$$AB=BC\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{\angle }6+CA\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{\angle }7$$

(1)

$$BC=\mathit{AC}·\sin (\epsilon ∕2)$$

(2)

$$\epsilon =\mathsf{\pi }/2-\mathrm{\angle }4$$

(3)

where ε represents the pole position angle of the guide rod mechanism.

$$\mathrm{\angle }5+\mathrm{\angle }6+\mathrm{\angle }7=\pi$$

(4)

$$\mathrm{\angle }1+\mathrm{\angle }5=3\mathsf{\pi }/4-\arctan (AO/OC)$$

(5)

To establish the relationship between AB and AB′ in the triangle ΔABC, there are the following numerical relationships.

$$A{B}^{\prime }=AB\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{\angle }9+\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{\angle }8\ast BC/\mathrm{s}\mathrm{i}\mathrm{n}(\mathsf{\pi }/4)$$

(6)

$$MB{B}^{\prime }=\mathrm{\angle }8,MBA=\mathrm{\angle }9,\mathrm{\angle }8+\mathrm{\angle }9=\mathrm{\angle }6+\mathsf{\pi }/4$$

(7)

In Figure 3b, EF stands for the telescopic inner and outer rods. It should be ensured that when the auger rises to its highest position and tilts to the maximum angle, EF does not interfere with other components. In other words, the upper vertex must not exceed point C in the horizontal direction. Based on its placement within the triangle, it can be inferred that the distance EC is equal to half of the height of h, i.e., EC = h/2.

Because the rotation space of the cylinder is limited by the front end of the frame, the BC rod cannot interfere with the movement of the CO rod. Consequently, when the cylinder AB′ is parallel to CO, it reaches the extreme position of motion, at which the rod length of AB is maximized. By adjusting the height of AO, the cylinder can swing at 45°, as illustrated in Figure 3d. This figure presents the design analysis diagram of the extreme position of the rod. The movable range of the BC rod is 0 to π/4 rad, and the maximum height is achieved at π/4 rad.

Under these conditions, the aforementioned formulas can be combined to yield the following values: the length of AC is 320 mm, ∠4 is 30°, and BC is 278 mm long. When the cylinder reaches the extreme position, the total length of AB is 424 mm. Conversely, when the cylinder bottoms to the extreme position, the full length of AB′ is 598 mm. The stroke of the cylinder is 174 mm, ∠1 is 15°, and the length of the rotating arm EC is 700 mm. The above-mentioned data can provide a reference for the design and selection of components, such as oil cylinders, ear plates, and other relevant components.

3. Methods and Materials

3.1. DEM–MFBD Coupling Simulation Model

To explore the impact of slope topography on the functionality of pivotal components in pit excavation, a rigid–flexible coupling body dynamics model was created using the RFlex method within the software. Subsequently, a bidirectional coupling simulation model encompassing DEM and MFDB was formulated. The hanging-type earth auger geometric model of the structure and terrain was created using three-dimensional drawing software and saved in “.x_t” format. In the discrete element software, two types of soil bins were created, one for a 30° slope and the other for a plain surface. The input parameters of Material properties used to characterize the DEM particles and tool are listed in

Table 2. Material properties of soil and tool.

Parameter	Soil	Tool
Diameter particle (mm)	7	-
Contact radius(mm)	8.5	-
Particle density (kg/m3)	1350	7860
Shear modulus (Pa)	1 × 106	7.9 × 1010
Poisson’s ratio	0.3	0.3
Coefficient of restitution of soil-	0.2	0.26
Coefficient of static friction of soil-	0.54	0.5
Coefficient of rolling friction of soil-	0.2	0.04

[20,21,22,23].

The contact model plays a pivotal role in exploring the adhesion between mechanical components and soil particles. Soils commonly exhibit elevated moisture levels in afforestation areas, resulting in cohesive and adhesive attributes between soil particles and tools. Consequently, a Hertz–Mindlin model, supplemented with the JKR model and an additional model-bounding contact model, has been employed as the primary contact model for both particle–particle and particle–tool interactions. This model is particularly suitable for simulating materials that exhibit conspicuous adhesion and aggregation among particles due to factors such as static electricity and moisture.

Table 3. Parameters of contact model.

Parameter	Unit	Value
Normal stiffness per unit area	N·m−2	2.1 × 108
Shear stiffness per unit area	N·m−2	8 × 107
Critical normal stress	Pa	1.5 × 106
Critical shear stress	Pa	8 × 105
Bonded disk radius	mm	2.5
Surface energy of soil–soil	J·m−3	7.46
Surface energy of soil–tool	J·m−3	5.5

delineates the requisite input parameters for the contact models [24,25].

MFBD was used to establish the earth auger device structure. It is then imported into the multi-flexible body dynamics software to define the fundamental physical properties of the earth auger device. Furthermore, to improve computational efficiency, simplification measures have been implemented in the model [26]. Simplify the supported cylinder as a linkage. Simplify the power-actuated cylinder as a motion pair. Using the finite element mesh generation technology, the nodes of the auger were divided and unitized. Three-node triangular shell 3 elements were used for discretization, the minimum mesh size was about 15 mm, the maximum mesh size was about 25 mm, and the number of meshes divided was 4918. A mesh quality check was performed in the software, and the results indicated that the mesh quality was good. In the simulation process, the structure matrix was calculated iteratively, and then the accurate analysis of the stress and strain information of the structure was realized [27]. The rigid body model was adopted, as the deformation of the hitch plate and the frame was negligible. After defining the mechanism and actuators, the model was saved in “. wall” format and imported into the DEM (EDEM V2.6) software [28]. In actual production, the feeding process of this device was most susceptible to causing auger damage [29]. The simulation was conducted with the operation parameters set in

Table 4. Structure and operating parameters of auger.

Parameter	Unit	Value
The length of the auger	mm	700
The diameter of the auger	mm	400
The helical angle of the auger	°	25
The speed of the feed	m/s	0.1
The rotation speed of the auger	r/min	150

. To investigate the operational performance of the hanging-type earth auger on slopes, three different operating methods were established, including upslope, downslope, and flat terrain. The specific modeling process of the digging process of the auger model is shown in Figure 4.

In summary, the modeling process of the earth auger device structure was divided into discrete element soil bin modeling and rigid–flexible device structure coupling modeling. In this study, the hanging-type earth auger was simulated by the rigid body and flexible body modules in RecurDyn (RecurDyn 2023) software, and the granular soil bin was simulated by EDEM (EDEM V2.6) software. The information for the two simulation environments was transmitted by the wall element. The modeling process software usage flow and methods are shown in Figure 5. By conducting comparative simulation experiments, several critical evaluation metrics, such as soil particle movement, the force exerted on the spiral blades, the torque of the auger, and the force applied to the auger rotary joint, were analyzed.

3.2. Field Test

To empirically assess the operational performance of the hanging-type earth auger, field tests were conducted in a forested area in April 2023, as shown in Figure 6. An experimental apparatus was assembled on the earth auger to facilitate the acquisition of critical data such as rotational speeds. To enhance the data collection process, a user interface was crafted using LabView (LabView 2018) software.

The digging tests in the forest area were divided into trials conducted on plain terrain and slopes. Considering the local conditions, slope digging experiments were conducted with a maximum slope inclination of 30°. Under these conditions, data were collected from excavated pits that represented optimal operating conditions. The tests were repeated six times, and the digging quality was assessed to calculate the average values. The operational performance of the equipment was evaluated according to the relevant standard (LY/T 1490-2006) [30].

4. Results and Discussion

4.1. Motion Law of Soil Particles

To enhance the visualization of soil movement patterns within the auger through cross-sectional views, a Clipping Plane was incorporated within the EDEM software analyst module. Furthermore, Motion-Vectors patterns were employed to visualize soil particles, facilitating the examination of their motion trends. The disturbance process of the soil by the auger is analyzed in Figure 7a. The primary region of soil disturbance was concentrated at the blade edge and auger tip position. The auger tip initially made contact with the soil, serving to position and loosen the soil. Due to the cutting action at the lower end of the spiral blade edge, the soil underwent displacement from its initial position. As the penetration depth increased, the range of disturbed soil particles increased, and the squeezing pressure was transmitted to adjacent particles. Subsequently, the soil rose along the surface of the spiral blade and tended towards the pit wall under the centrifugal force. This occurred until the soil reached the ground surface and formed a soil collection peak. When the earth auger was in operation, the instantaneous velocity of the soil could be expressed using Equation (8) [7]. The higher the pit wall, the greater the acceleration of soil velocity loss. This is because a taller pit wall implies a longer displacement for the soil, resulting in the mutual interaction force between soil particles and their initial velocity being more easily consumed.

$$\left\{\begin{array}{c}V=\frac{r\omega b}{2Pc\mathrm{c}\mathrm{o}\mathrm{s}\phi }\left[AB-\sqrt{{\left(AB\right)}^2-4P\left(A^2\phi -\frac{E}{f_1}\right)}\right]\\ a=\tan \phi \\ A=1-\frac{\tan \xi }{\tan \phi }\\ B=a+2b+0.4ab\\ P=b(1+0.4a+0.4b+0.16ab)+b\\ E=\frac{g}{r{\omega }^2}\end{array}\right.$$

(8)

where V is the soil movement velocity, m/s. r is the auger radius, m. ω is the rotational speed of the auger, r/min. c is the soil speed loss coefficient. φ is the auger elevation angle, °. f₁ is the friction coefficient between soil particles. ξ is the angle between the soil particle velocity and the horizontal plane at the auger radius. A, B, C, D, a, and b are coefficients. g is the gravitational acceleration, 9.8 m/s².

It can be seen from Figure 7a that the impact of the vehicle’s travel direction on soil disturbance law within the pit during slope digging was not significant. However, the impact of terrain on soil disturbance was more significant. When comparing the movement trajectory and trend of the soil, it can be observed that when the soil was conveyed to the pit mouth, the low-altitude side lost the constraint of the pit wall and was thrown downward, followed by downward movement along the slope. As a result, the collection of a soil collection peak, as shown in Figure 7b, was formed. The fan-shaped soil collection peak after digging on the slope had the same shape as the fish-scale pit. After shaping the soil shape, it only needed manual reinforcement. Based on the principles of soil dynamics, it can be found that implementing mechanized excavation on slopes is conducive to the efficient construction of fish-scale pits.

In the comparison of particle kinetic energy, the maximum value of velocity was observed at the cutting end of the auger and the contact position between the spiral blade and the pit wall in the context of plain land operations. In contrast, during slope operations, the maximum value of velocity occurs at the cutting end of the auger and when the soil is just ejected from the pit. Analyze the reason based on Equation (8). The presence of a slope leads to a lower time required for soil to reach the pit mouth on the low-altitude side. The slope is more favorable for removing soil from the pit, and the kinetic energy of the soil decreases as the soil weight per unit time decreases. This results in a greater disparity in soil velocity at the cutting-end position compared to other locations. The observation is consistent with the theoretical formula, demonstrating the effectiveness of the model.

4.2. Analysis of Working Load

The auger structure is predominantly comprised of spiral blades and a tip. The resistance factors encompass the auger’s cutting resistance in soil, the resistance encountered by the spiral blades during soil cutting, and the resistance related to soil transportation, among others. These resistances collectively manifest as the torque magnitude experienced by the auger during its operation.

As demonstrated in the simulation process, the auger must undergo a slope cutting process and a deep digging process to complete the pit digging, as shown in Figure 8a. The force distribution cloud diagram on the auger upon initial soil contact in different terrains is illustrated in Figure 8b. The distinction lies in slope cutting operations, where each sided spiral blade experiences alternating forces.

Figure 9 depicts a schematic diagram of the resistances and torque experienced by the auger during its operation. The total torque M₀ of the auger is composed of three parts, as described in Equation (9) [6]:

$$M_0=M_1+M_2+M_3$$

(9)

where M₁ is the torque required for the auger to perform its cutting operations. M₂ is the torque required for the spiral blades to cut through the soil. M₃ is the torque required for the soil to be uplifted and removed from the pit.

$$M_1=\left(q_1+k_{1}S\right)d^2$$

(10)

$$M_2=M_r+M_q+M_d=i\left[q_2\cos \beta +k_2\frac{S}{i}\sin \left(\delta +{\phi }_1\right)\right]{\int }_d^{r}rdr$$

(11)

$$M_3=fi\cdot F_a\cos \phi$$

(12)

where $q_1$ and $q_2$are the soil resistance proportion coefficients. $k_1$ and $k_2$ are the soil deformation resistance coefficients. S is the feed per revolution of the auger. d is the bottom circular radius of the auger. i is the number of spiral blades on the auger. $\delta$ is the nominal angle of the spiral blades. ${\phi }_1$ is the friction angle of the soil against steel. $F_a$ is the centrifugal force of the soil flow. $f$ is the friction coefficient between the soil and the auger. M_r and R_r (in Figure 9) are the soil deformation resistance and the torque it generates. M_q and R_q (in Figure 9) are the cutting resistance and the torque it generates for the spiral blades. M_d and R_d (in Figure 9) are the resistance and the torque generated by the soil’s kinetic energy.

Based on the simulation results, Figure 10 shows the normal force diagram of the feed device’s translational joint, the total force diagram of the auger rotary joint, and the total torque diagram of the auger rotary joint, respectively. The curves in Figure 10 demonstrate that during the cutting process of the sloping surface, the variations in force and torque of the device operation exhibit a regular fluctuation pattern. The reason for this phenomenon was that during the cutting process of the sloping surface, the two spiral blades alternate contact with the soil, causing soil particles to be thrown outside the pit as soon as they come into contact with the blades. However, as the feed depth increases, although the force is unstable, it shows a gradually increasing trend. The degree of disturbance experienced by soil particles within a unit of time was relatively large, as illustrated in Figure 7a. Upon completion of the slope cutting process, the deep digging process commences, and the variations in the force and torque experienced by the sloping surface operation tend to become more stable.

Compared to digging operations in plain regions, the normal force values of the translation joint were similar after completing the slope cutting process. However, the torque and force values of the rotary joint in slope surface operations were larger. The cause of this lies in the slope of the terrain; the backfill rate of the soil is smaller, resulting in greater kinetic and centrifugal forces of the soil due to the lack of restraint from the backfilled soil. Both phenomena are consistent with the conclusions of Equations (9)–(12), confirming the accuracy of the model. The torque and force generated during uphill operations with different operating directions were greater due to the presence of the hitch plate on the low-altitude side, which hindered soil slippage and increased the backfill rate of the soil. Therefore, downhill operations are more favorable for digging tree pits when conditions permit.

4.3. Analysis of Fatigue of the Auger

Following the rigid-flexible coupling simulation, the stress and displacement nephogram of the auger was obtained, as shown in Figure 11. The deformation of the spiral blades was warping which mainly occurred at the edges of the spiral blades. The main stresses in digging operations were bending and torsional stresses. The maximum stresses occurred at the welded joint between the spiral blades and the auger’s rod, as well as at the contact areas between the spiral blades and the pit wall. The simulated results were consistent with the areas prone to damage in actual scenarios.

The interaction between the auger and soil was characterized by low-stress amplitude, resulting in a higher number of fatigue cycles, and thus, the auger was subjected to high-cycle fatigue. In this study, the Manson–Conffin stress life equation, one of the stress life algorithm forms, as shown in Equation (13), was utilized to determine the fatigue life of the auger [31].

$$\frac{\Delta \sigma }{2}={\sigma }_f^{\prime }{\left(2N_f\right)}^{b_1}$$

(13)

where Δσ/2 is the cyclic stress amplitude, MPa. 2N_f is the fatigue life, and MPa. σ_f′ is the fatigue strength coefficient. b₁ is the fatigue strength index.

The most susceptible locations for fatigue failure of the auger were in the vicinity of the junction between the cutting end of the spiral blade and the rod (abbreviated as Position-A), as well as the connection between the auger and the motor (abbreviated as Position-B). Position-A initially came into contact with soil with a higher firmness and continuously contacted soil while applying compression and cutting forces throughout the entire digging process. The density of the soil in the whole pit decreased gradually from bottom to top, resulting in a diminishing micro-cutting property between the auger and the soil particles. Position-A served as both the root of the auger tip and the lower root of the spiral blades, resulting in a fulcrum effect. Furthermore, Position-A was where the interface of rapid shape changes occurred, resulting in stress concentration. Position-B was where the driving force was applied. The fatigue life of these two locations was relatively low, and the model conformed to the theoretical Equation (9).

According to the simulation calculation results, the minimum fatigue life of the auger was approximately 7.89 × 10¹⁵ times, 4.48 × 10¹⁶ times, and 2.88 × 10¹⁶ times under plain, downslope, and upslope field operation, respectively. In terms of the factor terrain, during slope operations, the uneven distribution of force on the auger arises from its intermittent contact with the soil and the non-uniform discharge volume of soil along the circumferential direction. The presence of an unbalanced torque can lead to rotational deviations and vibrations in the auger. The auger requires additional energy to overcome the unbalanced torque, thereby reducing equipment efficiency and increasing energy costs. Hence, the auger reliability was highest in flat terrain. In downslope operations, due to superior removal performance of soil, the fatigue lifespan was relatively extended.

4.4. Prototype Fabrication and Field Testing

The manufacturing of the equipment was completed based on the aforementioned analysis. A practical experiment involving pit digging was conducted in the afforestation area. The results of the collected data are presented in

Table 5. Test results of operation.

Parameter	Unit	Value in Plain Terrain	Value in Sloped Terrain
The depth of the pit	mm	500	500
The diameter of the auger	mm	400	400
The helical angle of the auger	°	25	25
The speed of the feed	m/s	0.1	0.1
The speed of return	m/s	0.15	0.15
The rotation speed of the auger	r/min	0–260	0–260
Efficiency	Num./h	110	90
The rate of soil discharge	%	70	60
The radius of soil collection peak	mm	550	600
The maximum radius of soil throwing	mm	850	2300

. In Figure 12, the data collected by the speed sensor and the damage that occurred during prolonged use of the auger are depicted. Different colors represent different input speeds in Figure 12a. From Figure 12, it can be observed that the auger speed is stable and adjustable, indicating good overall operational stability of the machine. The region of auger damage closely resembles the simulation results.

During the forestry field trials, one piece of equipment could replace the continuous work of 20 laborers for excavating tree pits measuring 400 × 500 mm. The forest field trials demonstrated that all the specified parameters of the designed hanging-type earth auger were within acceptable ranges. The device was capable of automatically adjusting the digging angle, lateral distance, and feed and return motion. The adjustable digging speed enhanced operational flexibility, resulting in a satisfactory excavation outcome. The equipment is particularly suitable for deep digging and slope operations in hilly and mountainous regions.

5. Conclusions

This study was aimed at advancing the sustainable development of forestry through the design of a suspended automatic feeding and retracting excavation device tailored for tree pits, with consideration given to forestry operation methods. To assess the efficacy of this device, the Discrete Element Method–Multi-Flexible Body Dynamics (DEM-MFBD) coupling method was utilized to simulate and analyze the interactions between the soil and the device across various terrain and operational conditions.

Based on the simulation results, the coupling simulation method can gradually be applied to designing and testing outdoor forestry equipment in specific operating environments. It can reduce the consumption and R&D time of field testing. The impact of terrain on variability in soil disturbance was exhibited to be more significant, while the influence of vehicle operating direction was found to be less pronounced. The slope digging operations need to consider soil and water conservation measures, and appropriate operational parameters will be advantageous for shaping fish-scale pits. The highest speed value of soil during plain terrain operations occurs at the positions where the auger cuts the soil and the blades contact the pit wall. On the other hand, this phenomenon mainly occurs during the soil-cutting end and the soil-throwing process in slope operations. During operations on inclined surfaces, the equipment experiences higher forces and torques during slope-cutting, showing regular fluctuations. Downslope operations result in lower torque and forces applied regarding the operating direction.

According to the analysis of the flexible body, the primary deformation of the auger occurs as bending deformation at the edges of the spiral blades. The maximum stresses of the auger occur at the welded joint between the spiral blades and the auger’s rod and at the contact areas between the spiral blades and the pit wall. The most susceptible locations for fatigue failure of the auger were in the vicinity of the junction between the cutting end of the spiral blade and the rod, as well as the connection between the auger and the motor. The minimum fatigue life of the auger under plain field operation was approximately 7.89 × 10¹⁵ times, 4.48 × 10¹⁶ times, and 2.88 × 10¹⁶ times under plain, downslope, and upslope field operation, respectively. The efficiency of soil discharge, the compactness of soil, the stability of soil movement speed, and the differences in pit wall shape contribute to the phenomena, as mentioned above, due to the disparities in terrains.

The results of the field tests in forested areas have demonstrated the practicality of the apparatus. This study provides valuable insights into the operation and equipment design of the earth auger in hilly regions.