Improving Agricultural Tire Traction Performance Through Finite Element Analysis and Semi-Empirical Modeling

Abstract

Optimizing agricultural tire traction is essential for improving field efficiency and minimizing soil degradation. This study examines the influence of lug spacing and vertical load on traction performance using Finite Element Analysis (FEA) in ANSYS and the semi-empirical Wong and Preston-Thomas tire model. Simulations were conducted on clay soil under vertical loads of 35 kN, 45 kN, and 55 kN, with varying lug spacings. The results indicate that a 130 mm lug spacing provides the best balance between traction, thrust, and motion resistance. Higher vertical loads intensify soil compaction, leading to reduced thrust generation at 55 kN despite decreased motion resistance. These findings emphasize the importance of optimizing lug configurations to enhance traction while mitigating soil compaction. The study contributes to improving tire designs for agricultural machinery, promoting efficiency and sustainability in soil management.

1. Introduction

The role of tires in agricultural vehicles extends far beyond merely supporting the weight of the vehicle [1]. Tires are fundamental in determining vehicle performance, particularly in terms of traction, motion resistance, and the overall impact on soil conditions [2,3,4]. Among various tire characteristics, lug design, including spacing, angle, and depth were shown to significantly affect tire–soil interactions, which, in turn, influence the operational efficiency of agricultural machinery [5,6,7]. Effective tire design not only ensures optimal traction but also minimizes soil compaction, thereby improving crop yields and contributing to sustainable farming practices [8,9]. Traction efficiency and reduced soil degradation are especially critical in modern agriculture, where minimizing environmental impacts is a growing concern. Understanding the influence of tire design parameters on traction performance is thus a crucial area of research for improving agricultural machinery.

The interaction between tires and soil has been extensively studied in terramechanics, through both experimental and numerical methods. Traditional semi-empirical models, such as those developed by [10] and later refined by Wong and Preston-Thomas [11,12], provide a fundamental understanding of terrain mechanics and traction performance. These models consider soil deformation, tire slip, and rolling resistance to predict tire performance [11,12]. More recent studies have incorporated Finite Element Analysis (FEA) to provide a more detailed understanding of stress distribution and deformation at the tire–soil interface [13,14,15,16,17,18,19,20,21]. Despite these advancements, optimizing tire design remains a challenge due to the complex interplay between soil properties, tire geometry, and loading conditions [3].

Tire–soil interaction is typically analyzed by examining factors such as tire load, inflation pressure, and soil properties, all of which influence key performance metrics, including soil thrust, motion resistance, and traction [3,4,7,22]. These interactions vary significantly with soil type and tire design, particularly in agricultural applications where clay soils present unique challenges [23]. The cohesive nature of clay can either hinder or enhance traction depending on the tire’s configuration [2,3,24]. Poor traction leads to increased fuel consumption, higher operational costs, and reduced field efficiency [25,26,27,28,29,30]. Given these challenges, optimizing lugged tire designs is essential, as they are widely used in agricultural applications for their ability to generate traction in soft soils [31,32,33].

Among the key design parameters, lug spacing plays a crucial role in traction performance [7,34,35]. Larger lug spacings can either reduce or increase motion resistance, but they may also contribute to greater soil compaction and energy loss. Conversely, smaller lug spacings increase the frequency of soil engagement, which can improve penetration and traction but may also elevate motion resistance, reducing overall efficiency. This trade-off highlights the complexity of tire design and the necessity for optimization tailored to specific soil conditions.

In addition to lug spacing, vertical load significantly influences tire–soil interactions [3]. Higher vertical loads increase contact pressure, leading to deeper soil penetration and potential soil compaction [3,36,37]. While moderate compaction can enhance traction, excessive compaction degrades soil structure, reducing water infiltration and root growth, thereby impacting long-term soil health. Balancing vertical load and tire design is, therefore, essential for optimizing performance while minimizing soil degradation.

Despite extensive research on traction mechanics, a knowledge gap remains regarding the combined effects of lug spacing and vertical load on traction performance in clay soils. Most studies have examined these factors independently rather than in an integrated framework that reflects real-world agricultural conditions. Addressing this gap is critical for developing more efficient tire designs that balance traction, motion resistance, and soil preservation.

This study investigates the effects of lug spacing and vertical load on agricultural tire traction, particularly in clay soils. By integrating Finite Element Analysis (FEA) in ANSYS with the semi-empirical Improved Tire Model by Wong and Preston-Thomas, this research provides a comprehensive numerical analysis of tire–soil interactions under various configurations and loading conditions. The primary objective is to identify optimal tire designs that enhance traction while minimizing soil compaction, ultimately contributing to the development of more efficient and sustainable agricultural tires.

By addressing the existing gap in understanding how lug spacing and vertical load interact, this study offers valuable insights into optimizing agricultural tire performance. The findings will aid in designing tires that improve operational efficiency while promoting soil health and sustainable agricultural practices.

2. Materials and Methods

This study employed Finite Element Analysis (FEA) in ANSYS to numerically model tire–soil interactions under various lug spacing configurations and vertical load conditions. The objective was to assess how lug spacing and load variations influence traction efficiency, stress distribution, and energy loss at the tire–soil interface. ANSYS simulations were used to evaluate stress distribution and energy dissipation, while a semi-empirical approach based on the improved tire model by Wong and Preston-Thomas was applied to predict traction performance using stress values obtained from FEA. The primary goal was to determine the optimal lug spacing and load conditions that maximize traction efficiency while minimizing motion resistance and energy loss in agricultural applications.

2.1. Finite Element Model Development

2.1.1. Tire Model and Geometry

For this study, a tire model was developed solely for research purposes and does not represent any specific commercial or agricultural tire design. The tire was modeled as a rigid steel structure in ANSYS to eliminate deformation effects and isolate the influence of lug spacing on traction performance. The structural parameters (

Table 1. The key geometric parameters of the tire and soil models.

Parameter	Tire
Width (mm)	760
Diameter (mm)	2228
Lug angle	45°
Lug height (mm)	64
Lug spacing (mm)	90, 130, 170

), including diameter, width, and lug height, were selected based on general agricultural tire characteristics to ensure a relevant but neutral baseline for analysis. Lug spacing values, ranging from 70 mm to 170 mm in increments of 20 mm, were chosen to cover a broad spectrum of configurations commonly found in agricultural tires. This range ensures a systematic analysis of traction performance across different spacing scenarios, balancing computational feasibility with practical relevance. Evenly distributed lugs were used to maintain uniform contact pressure across configurations, allowing for a controlled evaluation of lug spacing effects.

Three distinct 3D tire models with varying lug spacing configurations were developed using ANSYS Design Modeler (Figure 1 and Figure 2). A structured finite element mesh was applied to the tire, with refined elements at the lug edges and tire–soil interface to enhance the accuracy of contact force predictions. The tire–soil interaction (Figure 3) was simulated using a penalty-based frictional contact algorithm, effectively capturing slip and grip conditions during interaction.

2.1.2. Soil Model and Material Properties

The soil model (Figure 3) was developed as a deformable medium using the Mohr–Coulomb failure criterion, which is widely applied in terramechanics studies [38]. This model describes soil failure behavior using the shear strength equation:

$$\tau =c+\sigma \mathit{tan}\left(\varphi \right)$$

(1)

where τ is the shear stress, c is the cohesion, σ is the normal stress on the shearing surface, and ϕ is the angle of internal shearing resistance of the terrain material [3].

The soil’s cohesion, internal and external friction angles, and bulk density were obtained from laboratory experiments on clay soil samples (

Table 2. Soil properties.

Clay Soil	Moisture Content (MC)	Density (Kg/m3)	Cohesion (kPa)	Internal Friction Angle (°)	External Friction Angle (δ)
Sample	34.2%	869	1.78	28.4	17.8

), while Young’s modulus and Poisson’s ratio were sourced from literature reviews [39,40,41,42]. These material properties were incorporated into ANSYS Explicit Dynamics to define the soil’s mechanical response under loading [43,44].

For improved computational accuracy, the soil domain was discretized using a structured hexahedral mesh, with refined meshing at the tire–soil contact region to capture localized stress variations and deformation characteristics. The bottom boundary of the soil model was fully constrained to prevent displacement, while lateral boundaries were set to allow controlled deformation within the tire’s interaction zone.

2.2. Simulation Setup and Boundary Conditions

2.2.1. Load and Motion Conditions

To evaluate the impact of vertical load variations on the tire’s traction performance, three distinct vertical loads, 35 kN, 45 kN, and 55 kN were applied. These values represent typical weight distributions that a tractor equipped with the analyzed tire might encounter in real-world applications. The load conditions can be categorized as follows:

• 35 kN (Light Vertical Load): Represents conditions where the tire operates under minimal weight, such as during sowing or light harrowing, resulting in lower soil engagement.
• 45 kN (Moderate Vertical Load): Reflects standard farming tasks, including medium-depth plowing and standard harrowing, where moderate vertical force is exerted on the tire.
• 55 kN (Heavy Vertical Load): Simulates high-load conditions typical of deep plowing and subsoiling, where increased vertical force is required for deeper soil penetration and enhanced traction.

These vertical loads were chosen to isolate their effect on traction performance while ensuring practical relevance in agricultural applications [45,46]. In this study, the vertical loads were applied at the tire’s center of mass (Figure 3) to replicate realistic weight distributions encountered during agricultural tasks. This setup enabled the evaluation of traction performance across different lug spacing configurations by analyzing stress distribution, thrust, and motion resistance under varying vertical loads.

While this study focuses solely on vertical loading, the limitations of this approach are acknowledged. Real-world conditions often involve additional forces, such as longitudinal and lateral loads, especially when towing implements or maneuvering on uneven terrain. These forces were not considered in this study but could be included in future research for a more comprehensive understanding of tire–soil interactions.

2.2.2. Contact Definitions and Soil Deformation Constraints

The tire–soil interaction was modeled using a frictional contact algorithm, incorporating both normal and tangential stress components to accurately simulate force transmission at the interface [47]. The soil base layer was fully constrained to prevent displacement, while the side boundaries were allowed to deform naturally, replicating real-world soil behavior under dynamic loading conditions.

The contact friction coefficient was set based on experimental studies of steel–agricultural soil interfaces. A penalty-based contact formulation was employed to enhance computational stability and ensure realistic stress distribution at the contact zone. This method enforced contact constraints by applying a virtual spring force proportional to the penetration depth, where the normal contact pressure was computed as:

$${ p}_c={ k}_n{ \delta }_n$$

(2)

where ${ k}_n$ represents the normal penalty stiffness and ${\delta }_n$ denotes the penetration depth [48].

2.3. Mesh Sensitivity and Convergence Analysis

To ensure computational efficiency and accuracy, a mesh sensitivity study was conducted. The tire and soil domains were meshed with different element sizes (Figure 3), and stress results were compared until further mesh refinement did not significantly alter the results. The final element size was selected based on a trade-off between computational cost and accuracy.

2.4. Dynamic Simulation and Solver Configuration

Simulations were conducted using the ANSYS Explicit Dynamics solver, which is widely recognized for its effectiveness in modeling high-deformation scenarios, especially in soil mechanics [49]. This solver is ideal for capturing the transient loading conditions that significantly affect traction behavior under dynamic tire–soil [50]. To ensure stable and accurate contact calculations, explicit time integration was employed, a method known for handling complex interactions in contact and deformation problems [51]. The simulations were performed under a normal tire load and a speed of 2.78 m/s, a value representative of common operational speeds in agricultural settings [36]. This configuration facilitates a detailed analysis of tire performance under conditions that closely mirror real-world agricultural applications.

2.5. Assumptions and Limitations

To simplify the analysis while ensuring practical applicability, the tire was modeled as a rigid body to focus solely on lug geometry effects. Only clay soil was considered in the analysis, which means the findings may not directly apply to sandy or silty soils. The study did not include the effects of varying soil moisture content, though it is acknowledged as an influential factor in real-world scenarios. External environmental factors, such as field irregularities and temperature variations, were also excluded from the analysis.

Friction was incorporated in the simulation using a penalty-based contact method to realistically capture the interaction at the tire–soil interface. However, this does not account for field irregularities such as bumps, depressions, or variations in soil compaction, which require additional terrain modeling beyond uniform soil conditions. While these irregularities are important in real-world applications, their effects were beyond the scope of this study. Future research should consider incorporating non-uniform terrain profiles to enhance the practical applicability of numerical simulations.

2.6. Performance Metrics Evaluation

2.6.1. Stress Distribution Analysis

The normal and shear stresses at the tire–soil interface were extracted from ANSYS simulations. This analysis provided insights into vertical stress distribution under different loads, shear stress variations along the tire footprint, and the impact of lug spacing on localized soil deformation.

2.6.2. Traction Performance Analysis

Traction performance is a critical factor in assessing the overall efficiency of agricultural tires. In this study, the Improved Tire Model (ITM) by Wong and Preston-Thomas was employed to predict essential performance parameters, including motion resistance, thrust, and traction, based on tire–terrain interactions. The ITM integrates both the normal and shear stress components, which were derived from Finite Element Analysis (FEA) simulations using ANSYS software (version: 2023 R1). These stress components are essential for accurately capturing the tire’s behavior as it interacts with different soil types.

Additionally, the Bekker Tire–Soil Interaction Model [10,52,53,54,55] was referenced as a foundational model for understanding the basic principles of tire–terrain interactions. This model assumes that the normal pressure beneath a tire is equivalent to the pressure under a sinkage plate, providing a simple estimate of tire sinkage and motion resistance. However, while the Bekker model offers valuable insights for steady-state conditions, it falls short in capturing dynamic terrain variations and shear stress interactions, which are crucial for more realistic predictions.

In Figure 4, $R_c$ is the motion resistance, W is the vertical load on the tire, $\sigma$ is the radial (normal) pressure on the tire–terrain interface, D is the tire diameter, and ${\theta }_{\mathrm{o}}$ is the contact angle of the tire.

$$z_r={\left({\displaystyle \frac{3W}{{b_{ti}(3-n)(k}_c/b+k_{\Phi })\surd D}}\right)}^{2/\left(2n+1\right)}$$

(3)

For rigid operating conditions on soft terrain, Bekker derived $R_c$ and W as,

$${ R}_c={ b}_{ti}{\int }_0^{{\theta }_0}\sigma r sin\theta d\theta$$

(4)

$$W={ b}_{ti}{\int }_0^{{\theta }_0}\sigma r cos\theta d\theta$$

(5)

where ${ b}_{ti}$ and r are the width and radius of the tire, respectively.

Bekker assumed that the radial pressure $\sigma$ on the tire–terrain interface is equivalent to the normal pressure p beneath a sinkage plate at the same depth z in the pressure–sinkage test. Thus,

$$\sigma r sin\theta d\theta =pdz$$

(6)

$$r cos\theta d\theta =pdx$$

(7)

From Bekker pressure–sinkage relation

$$p=\left({\displaystyle \frac{k_c}{b}} +k_{\mathrm{\Phi }}\right)z^n=k_{eq}{z}^n$$

(8)

$${ R}_c={ b}_{ti}{\int }_0^{z_r}\left({\displaystyle \frac{k_c}{b}} +k_{\mathrm{\Phi }}\right)z^{n}dz={ b}_{ti}\left({\displaystyle \frac{k_c}{b}} +k_{\mathrm{\Phi }}\right)\left({\displaystyle \frac{z_r^{n+1}}{n+1}}\right)$$

(9)

Equation (9) implies that the motion resistance of a rigid tire is completely defined by the work carried out in making a rut of width ${ b}_{ti}$ and depth $z_r$. Motion resistance is referred to as compaction resistance $R_c$.

As illustrated in Figure 4, the Bekker model provides an initial approximation of the tire–terrain interaction by considering only the normal pressure distribution. This figure helps in visualizing the basic tire–soil interaction parameters, such as sinkage and pressure distribution, which are important for understanding motion resistance in simpler scenarios.

To address these limitations, the ITM was utilized, as it accounts for both the normal and shear stress interactions, thus providing a more comprehensive and dynamic representation of the tire–terrain interface. By combining these models, this study aims to improve the accuracy of tire performance predictions under various operational conditions, especially for agricultural vehicles operating on diverse terrains. Figure 5 shows the application of the Improved Tire Model, which integrates more complex tire–terrain interaction factors and provides a better prediction of traction performance.

• Prediction of Tire Motion Resistance

When a tire moves across terrain, it experiences various forms of motion resistance, primarily driven by the interaction between the tire and the soil. This motion resistance is generally composed of several components, including obstacle resistance (R_ob), internal resistance (R_in) from the running gear, and the most significant component, terrain interaction resistance (R_t), which is the focus of this study [2,3,52]. The terrain interaction resistance represents the force required to overcome the friction between the tire and the soil during movement.

To predict the terrain interaction resistance (R_t), the ITM employs the integration of the horizontal normal pressure across the tire’s contact patch. This integral considers the pressure distribution over the contact area, which plays a pivotal role in determining the resistance force generated as the tire moves through the soil. The calculation is represented by Equation (10), where the pressure distribution is modeled based on the tire’s contact patch geometry and the soil’s response to the tire’s load.

The normal pressure component in the longitudinal direction was obtained using ANSYS simulation software (version: 2023 R1), which allowed for a more detailed and accurate estimation of motion resistance. By incorporating both the lug pressure and the carcass pressure, the model can simulate the actual pressure distribution across the contact patch, accounting for variations in soil conditions and tire behavior.

$${ R}_t={\displaystyle \frac{{ b}_{ti}D}{2}}\left[{\int }_0^{{\theta }_1}p\left(\theta \right)sin\theta d\theta -{\int }_0^{{\theta }_2}p\left(\theta \right)sin\theta d\theta \right]$$

(10)

where ${ b}_{tr}$ is the tire width and $D$ is the tire diameter, W is the normal load on the tire, ${\theta }_1$ is the entry/front contact angle and ${\theta }_2$ is the exit/rear contact angle.

2.

Prediction of Soil Thrust (Tractive Effort or Propelling Force)

Thrust, also referred to as tractive effort or propelling force, represents the force required for a tire to move a vehicle forward. Wong and Preston-Thomas [12] highlighted that thrust generation is influenced by the tire’s ability to shear the soil and the mechanical limitations of the vehicle’s powertrain. The thrust force is determined by the horizontal shear stress between the tire and the terrain, which acts to propel the vehicle.

To predict thrust, the horizontal shear stress is integrated across the tire’s contact patch, considering both the lug-terrain shear and the internal shear within the terrain. The thrust force is mathematically expressed as the integral of the shear stress components, as shown in Equation (11). The integration accounts for the loading and unloading regions of the tire’s contact patch, providing an accurate estimate of the thrust generated under different operational conditions.

In this study, ANSYS simulations were employed to calculate the shear stress components in the axial direction. These simulations provided a detailed stress distribution, which allowed for a more precise assessment of the tire’s ability to generate thrust. By evaluating different lug designs and soil types, the model was able to predict the tractive effort across various terrain conditions.

$$F={\displaystyle \frac{{ b}_{ti}D}{2}}\left[{\int }_0^{{\theta }_1}s\left(\theta \right)cos\theta d\theta -{\int }_0^{{\theta }_2}s\left(\theta \right)cos\theta d\theta \right]$$

(11)

3.

Prediction of Traction/Drawbar Pull (F_d)

The primary goal of agricultural tractors is to generate sufficient traction or drawbar pull, the net force required to pull or push agricultural implements such as ploughs or earth-moving machinery. Traction is essential for the effective operation of tractors, as it dictates their ability to perform various tasks in agricultural and construction settings.

Wong [3] formulated a practical method for predicting the traction force, by calculating the difference between the thrust force (F) and the motion resistance (R_t) encountered during operation. The traction force is given by Equation (12), where the thrust is the force generated by the tire to move the vehicle forward, and the motion resistance represents the opposing force.

$$F_d=F-R_t$$

(12)

This relationship is critical for assessing the efficiency of tire designs, as it helps to predict how well a tractor will perform in various soil conditions and under different loading scenarios.

3. Results

The results from the numerical simulations using ANSYS software (version: 2023 R1) offer valuable insights into the interaction between tire and clay soil, emphasizing the impact of lug spacing and vertical load on stress distribution and traction performance. These findings underscore the complexity of tire–soil interactions, which play a vital role in optimizing traction efficiency for agricultural applications.

3.1. Stress Distribution Trends at the Tire–Soil Interface

The stress distribution analysis reveals that normal and shear stresses vary significantly with changes in lug spacing and vertical load. As shown in Figure 6 and Figure 7, increasing the vertical load results in higher normal and shear stresses at the tire–soil interface. The highest normal stress occurs at 110 mm and 170 mm lug spacing, while 130 mm lug spacing reduces stress levels compared to 110 mm. However, beyond 130 mm, stress levels increase again, peaking at 170 mm, indicating greater soil compaction, which could influence motion resistance and traction performance.

Shear stress follows a similar trend, increasing with higher vertical loads, with the 55 kN load exhibiting the highest shear stress values. A peak in shear stress is observed around 110 mm and 170 mm lug spacing, while 130 mm spacing maintains a relatively stable stress level, reinforcing its effectiveness in optimizing traction. These stress distribution patterns highlight the crucial role of lug spacing in balancing soil engagement and compaction, directly impacting the efficiency of force transfer at the tire–soil interface.

3.2. Effect of Lug Spacing on Traction Performance at Different Tire Loads

Figure 8, Figure 9 and Figure 10 depict the relationship between lug spacing and traction performance. At a smaller lug spacing of 70 mm, the tire lugs do not effectively engage the soil, resulting in lower thrust and traction. As the lug spacing increases, thrust and traction improve, reaching their maximum value at 130 mm. Beyond this optimal spacing, traction does not improve further, as the reduction in the number of lugs in contact with the soil reduces effective force transfer.

At 130 mm lug spacing, the tire lugs engage the soil more effectively, enhancing traction performance. This spacing optimizes the contact area, ensuring adequate force transfer while maintaining efficient soil interaction. However, at 170 mm, the wider spacing reduces the number of active lugs, leading to a decrease in traction efficiency. Motion resistance remains relatively low up to 130 mm, but beyond this point, it begins to rise, indicating increased soil displacement and deformation.

Interestingly, after 150 mm spacing, a slight increase in thrust is observed, but it remains lower than the maximum thrust achieved at 130 mm. This increase in thrust can be attributed to changes in the interaction dynamics between the tire lugs and the soil. At wider spacings, while the number of active lugs decreases, the redistribution of the vertical load across the fewer active lugs results in slightly more effective soil engagement. However, this minor increase in thrust is not enough to overcome the significant rise in motion resistance, which peaks at 170 mm. At this wider spacing, the reduced number of lugs causes a larger portion of the soil to deform and displace more significantly, resulting in higher motion resistance. This increase in motion resistance contributes to reduced traction at 170 mm, despite the slight rise in thrust.

These results confirm that 130 mm is the optimal lug spacing, as it provides the best balance between traction, motion resistance, and thrust. The decline in performance beyond 130 mm suggests that excessive spacing reduces the frequency of soil engagement, diminishing overall traction efficiency. While thrust increases slightly at 170 mm due to changes in the interaction dynamics, the peak in motion resistance at this spacing leads to lower overall traction performance compared to the optimal 130 mm spacing.

3.3. Influence of Tire Load on Traction Performance at Optimal Lug Spacing

At the optimal 130 mm lug spacing, traction performance varies with tire load, as shown in Figure 11. At 35 kN vertical load, traction reaches its highest value, as the soil structure supports adequate grip without excessive deformation. At 45 kN, traction decreases slightly due to additional soil compaction, which marginally reduces grip efficiency. However, motion resistance increases only slightly, remaining within an effective range for traction performance.

At 55 kN, excessive soil compaction limits the tire’s ability to maintain effective ground engagement, leading to a further decline in traction. Despite the reduction in rolling resistance at this higher load, traction performance does not improve, reinforcing the idea that higher loads do not necessarily enhance traction but rather contribute to soil over-compaction and reduced thrust generation [3].

These findings highlight the trade-off between load-induced compaction benefits (reduced rolling resistance) and traction losses due to excessive soil deformation. An amount of 45 kN was identified as the optimal vertical load, as it provides a balance between traction efficiency and soil engagement while avoiding excessive compaction losses.

Overall, the results confirm that lug spacing and vertical load are critical parameters in optimizing tire traction performance on clay soils. The 130 mm lug spacing consistently achieves the best traction–thrust balance, while 45 kN is the optimal load, preventing excessive soil compaction that could reduce grip efficiency. These insights contribute to improving tire design for agricultural applications, enhancing traction performance while minimizing energy losses in field operations.

4. Discussion

The results underscore the critical influence of lug spacing and vertical load on optimizing traction performance in agricultural tires. Stress distribution analysis reveals that higher loads intensify both soil compaction and shear resistance, which can either enhance or hinder traction depending on the interaction between lug spacing and soil properties.

Lug spacing significantly affects traction performance, with 130 mm emerging as the optimal spacing where thrust and traction are maximized. At this spacing, the lugs maintain effective soil engagement, optimizing force transfer while minimizing excessive soil deformation. Beyond 130 mm, traction efficiency declines due to a reduction in the number of lugs actively engaging the soil, leading to decreased force transfer and increased soil disturbance.

Remarkably, thrust begins to increase slightly beyond 150 mm but remains lower than at 130 mm. This slight increase in thrust at 170 mm can be attributed to the redistribution of vertical load across fewer active lugs, which allows for deeper penetration and localized stress concentration. However, this effect is accompanied by a significant rise in motion resistance, which peaks at 170 mm. Larger spacing reduces the frequency of soil–lug interaction, leading to greater soil displacement and deformation, which in turn increases resistance to movement. As a result, overall traction remains low at 170 mm despite the minor rise in thrust, emphasizing the trade-off between lug spacing, soil engagement, and resistance.

The study further highlights how vertical load influences traction performance. As vertical load increases, soil compaction intensifies, affecting both rolling resistance and thrust generation. At moderate vertical loads (up to 45 kN), compaction enhances shear resistance and stabilizes soil–lug interaction, leading to improved traction efficiency. However, beyond this threshold, excessive compaction restricts soil displacement and limits thrust generation, leading to traction losses.

This trend aligns with Wong’s [3] findings, which emphasize that for a given vehicle configuration, the drawbar pull coefficient, thrust coefficient, and tractive efficiency decrease as vehicle weight increases. In our study, at 55 kN, excessive soil compaction prevents effective lug penetration, reducing the ability to generate thrust despite a concurrent reduction in motion resistance. This indicates that beyond an optimal load, additional weight does not necessarily translate into better traction performance.

The observed motion resistance trends further distinguish lugged tires from tracked vehicles. Wong [3] reported that in tracked systems, motion resistance typically increases with vehicle weight due to greater ground penetration and energy dissipation. In contrast, our findings demonstrate that motion resistance decreases at 55 kN because soil compaction lowers rolling resistance. This discrepancy highlights fundamental differences in soil deformation mechanisms between continuous track systems and lugged tires, reinforcing the importance of optimizing lug spacing and load distribution for maximum efficiency in agricultural applications.

These findings underscore the trade-off between load-induced compaction benefits (such as reduced rolling resistance) and traction losses resulting from excessive soil deformation. Under the tested conditions, a vertical load of 45 kN appears optimal, as it balances traction efficiency and soil engagement while minimizing performance losses due to excessive compaction. This insight is particularly relevant for agricultural applications in clay soils, where optimizing load distribution can enhance overall traction performance.

While these results provide valuable insights, they are based on numerical simulations using ANSYS under controlled conditions. Real-world agricultural operations involve complex terrain variability and dynamic factors that may further influence tire performance. Thus, controlled field experiments using actual agricultural tires under diverse soil conditions are necessary to validate these findings. Field studies would facilitate direct measurements of traction forces, motion resistance, and soil deformation, providing a more comprehensive assessment of the interaction between lug spacing and vertical load in practical settings.

Future research should also explore a wider range of soil types, including sandy loam and loamy soils, to determine whether the optimal lug spacing of 130 mm and a vertical load of 45 kN are applicable across different terrains. Such experimental validation would contribute to refining semi-empirical models and improving the predictive accuracy of numerical simulations for real-world agricultural applications.

Furthermore, investigations into alternative lug designs, material compositions, and tire carcass flexibility could enhance the efficiency and adaptability of agricultural traction systems. Advancements in these areas may contribute to improved field performance, reduced energy consumption, and greater sustainability in agricultural mechanization, aligning with broader goals of optimizing resource use and minimizing environmental impact.

5. Conclusions

This study examined the influence of lug spacing and vertical load on the traction performance of agricultural tires using Finite Element Analysis (FEA) in ANSYS and the semi-empirical improved tire model by Wong and Preston-Thomas. The findings indicate that an optimal lug spacing of 130 mm and a vertical load of 45 kN provide the best balance between traction efficiency and motion resistance in clay soils. At 130 mm, thrust generation is maximized, while motion resistance remains controlled, ensuring effective soil engagement and force transfer.

Beyond 130 mm, traction efficiency declines due to reduced soil–lug interaction. Although thrust increases slightly beyond 150 mm, motion resistance peaks at 170 mm, counteracting any benefits from increased thrust and leading to overall traction losses. Similarly, increasing the vertical load beyond 45 kN results in excessive soil compaction, which restricts lug penetration and reduces traction, despite lowering rolling resistance. These results emphasize the importance of optimizing both lug spacing and load distribution for improved traction performance in agricultural applications.

Despite the limitations of this study, such as the need for real-world validation, the observed trends align with Wong’s findings [3], which highlight that for a given vehicle configuration, the drawbar pull coefficient, thrust coefficient, and tractive efficiency tend to decrease as vehicle weight increases. This study confirms this principle by demonstrating that beyond 45 kN, excessive soil compaction hinders thrust generation, leading to traction losses even as motion resistance decreases. The interplay between lug spacing, vertical load, and soil deformation underscores the complex nature of tire–terrain interactions, reinforcing the need for carefully optimized design parameters in agricultural mechanization.

By optimizing tire design and operational parameters, this study contributes to enhancing traction efficiency, improving fuel economy, and promoting sustainable mechanization practices, ultimately supporting more effective and environmentally responsible farming operations.