Pressure-sinkage Model Research Articles

Development and validation of sloped ground pressure prediction model for a tracked tractor in hilly and mountainous environments

Tracked tractors are better suited for agricultural production in hilly environments because of their excellent stability and flotation. The ground pressure in these environments is highly irregular owing to the ground slope, which has led to a lack of theoretical foundation and data support for the development of hillside tracked tractors (HTTs). Therefore, accurate prediction of the ground pressure at the track-soil interface on inclined terrain is important. In this study, sloped ground pressure prediction model composed of sloped terrain soil pressure-sinkage model was developed to analyse the distribution characteristics of the ground pressure of tracked tractors in agricultural operations on hillside slopes. Considering the influence of the slope angle, soil conditions, operating conditions, and important parameters of the tracked tractors (including mass, centre of gravity, and track gauge), the ground pressure prediction model used harmonic oscillator functions and peak-valley control primitive functions. To validate the proposed model, ground pressure tests of the experimental tracked tractor were conducted at different slope angles and operating conditions in an experimental platform integrating a "soil-machine-crop" system. The results showed that the maximum error between the predicted results and the test data under various slopes and operating conditions was approximately 6.3%, with an average error of approximately 4.7%; the consistency between the test results and the simulated results indicate that the model established in this study is accurate and credible. Based on the ground pressure model, the developed tractive performance prediction model for HTTs had high prediction accuracy for the slip rate and traction force in the climbing traction test. The developed theoretical model and results provide practical guidance for the structural design of advanced HTTs and manoeuvrability optimization.

Parameter optimization and tractive performance evaluation of tracked miner

Enhancing the traction performance of the tracked miner is crucial for ensuring smooth seabed operation. In this study, an experimental device for the interaction between track and deep-sea sediments was designed, aligning with the walking process of the tracked miner. The primary and secondary order of the influence of the driving parameters on the mechanical properties of the undisturbed deep-sea sediments was determined by an orthogonal test, and the pressure-sinkage model and shear stress–displacement model were constructed. Building upon the shear model and the vehicle ground mechanics theory, the driving mechanics model of the tracked miner in the seabed environment was derived, and the track structure and parameter optimization method were proposed. The results show that the experimental factors significantly influence the mechanical properties of undisturbed deep-sea sediments, with the order of influence being grounding pressure > grouser height > shear rate > track shoe length > track shoe width; By optimizing the structural parameters of the “Kunlong 500” tracked miner, the drawbar pull increased by 29.1%, and the sinkage depth reduced by 12.8%. This study quantitatively analyzes the influence of structural parameters in driving performance on the sinkage and shear characteristics of deep-sea sediments, and proposes a new method for optimizing the tractive parameters. It provides new insights for achieving efficient and environmentally friendly movement of tracked miner on the seabed.

Study on the Pressure–Sinkage Process and Constitutive Model of Deep-Sea Sediment

The driving performance of subsea mining vehicles is greatly affected by the pressure–sinkage characteristics of deep-sea sediment. Therefore, it is of great importance to analyze the microscopic properties of deep-sea sediment and establish the corresponding pressure–sinkage model for the safe operation of subsea mining vehicles. Hence, the present paper focuses on the physical properties of deep-sea sediment to provide a preliminary understanding of its pressure–sinkage process and evolution according to the solid–liquid two-phase flow characteristics and particle flow mechanism. In addition, the stress loading time and the rheological theory are applied in order to introduce a four-element model that describes the various pressure–sinkage stages that correspond to each stage of deep-sea sediment evolution. On this basis, the parameters of the pressure–sinkage constitutive model are determined by a specific calculation method. Moreover, a new pressure–sinkage constitutive model of deep-sea sediment that considers the time-variable mechanical properties is established in order to describe the full sinkage process. Finally, research results from the existing literature and experimental data are used to verify the rationality and correctness of the model. The results show that the proposed pressure–sinkage constitutive model is in good agreement with experimental data and is effective in describing the evolution of the mechanical properties and the trend in the sinkage rate of deep-sea sediment at various stages. A comparison with the Kelvin model indicates that the proposed pressure–sinkage constitutive model provides superior accuracy with the use of fewer parameters. Consequently, this study can provide a theoretical basis and technical support for the design of subsea mining vehicles.

Development of a New Pressure-Sinkage Model for Rover Wheel-Lunar Soil Interaction based on Dimensional Analysis and Bevameter Tests

A rover is a planetary surface exploration device designed to move across the ground on a planet or a planetary-like body. Exploration rovers are increasingly becoming a vital part of the search for scientific evidence and discoveries on a planetary satellite of the Sun, such as the Moon or Mars. Reliable behavior and predictable locomotion of a rover is important. Understanding soil behavior and its interaction with rover wheels—the terramechanics—is of great importance in rover exploration performance. Up to now, many researchers have adopted Bekker’s semiempirical model to predict rover wheelsoil interaction, which is based on the assumption that soil is deformable when a pressure is applied to it. Despite this basic assumption of the model, the pressure-sinkage relation is not fully understood, and it continues to present challenges for rover designers. This article presents a new pressure-sinkage model based on dimensional analysis (DA) and results of bevameter tests. DA was applied to the test results in order to propose a new pressure-sinkage model by reducing physical quantitative parameters. As part of the work, a new bevameter was designed and built so that it could be successfully used to obtain a proper pressure-sinkage relation of Korean Lunar Soil Simulant (KLS-1). The new pressure-sinkage model was constructed by using three different sizes of flat plate diameters of the bevameter. The newly proposed model was compared successfully with other models for validation purposes.

Research in mechanical model of bionic foot intruding into sands with different physical characteristics

In this study, a bionic foot with sand fixation and fluidization limitation functions was designed. Also a rectangular foot with the same sizes, named the common foot, was designed for comparison. Three kinds of quartz sands were selected to study how particle size, shape and compactness affected the intrusion performances of mechanical feet. The intrusion resistive forces and pressures of the bionic foot on these three kinds of quartz sands were all smaller compared with the common foot. Discrete element simulations showed particle disturbance areas were smaller and particle motion trends were more consistent under the bionic foot versus the common foot. The intrusion resistive forces of these two kinds of mechanical feet firstly increased and then decreased with the increasing particle sizes of quartz sands. Moreover, the intrusion resistive force on spherical particles was less than that of irregular particles for both the bionic foot and the common foot. The corresponding resistive forces of mechanical feet were characterized based on quartz sand compactness. The classic pressure-sinkage model was modified based on the intrusion tests, and the relationships between intrusion resistive force and mechanical foot depth were obtained.

A Modified Pressure–Sinkage Model for Studying the Effect of a Hard Layer in Sandy Loam Soil

The applicability of the typical pressure–sinkage models used to characterize the soil’s bearing properties is limited to homogeneous soils (infinite thickness) that have no hard layer. At a given depth, a hard layer can have a considerable impact on the soil’s load-bearing capacity. It is thus necessary to alter the pressure–sinkage equation by taking this condition into account when assessing the load-bearing capacity. The present paper aims to determine a simple, high-fidelity model, in terms of soil characterization, that can account for the hard layer affection. To assess hard layer affection in this paper, a plate sinkage test (bevameter) was conducted on sandy loam soil. To this end, the soil was prepared by considering three bulk densities and two soil thickness levels at 7–9% moisture content levels. According to the results, this paper put forth a new perspective and related equations for characterizing bearing performance. The sinkage modulus (k) is an intrinsic soil parameter that has a determined unit of N/cm2 and is significant for managing the bearing performance. The results showed that the new modulus sinkage model incorporates the main factor of the rigid layer effect involving high fidelity that the conventional models have failed to account for.

Construction and Experimental Verification of Sloped Terrain Soil Pressure-Sinkage Model

The construction of a scientific and effective soil pressure-sinkage model under sloped terrain condition has important guiding significance for the investigation of the soil compaction effect. It is also important for the theoretical calculation of driving resistance and design optimization of the undercarriage structure of hillside metal-tracked tractors (HMTs). The classic Bekker’s pressure-sinkage model does not consider the influence of the soil water content, bulk density, slope angle, and other factors; therefore, it cannot be directly used to investigate the relationship between the soil compaction and its sinkage under sloped terrain conditions. To solve this problem, this study first verified that the soil water content and bulk density exert significant effects on the pressure–sinkage relationship under flat terrain condition. Secondly, a pressure-sinkage test was carried out using the quadratic rotation orthogonal combination design method, and the soil water content, density, and slope angle were considered. The pressure-sinkage curves of sloped terrain soils from Yangling and Yangxian in Shaanxi Province, and Huining and Jingning in Gansu Province were obtained. Then the pressure–sinkage parameters (sinkage exponent, cohesive modulus, and frictional modulus) were calculated using the weighted least-squares method. Thirdly, the mathematical relationship between the parameters and the soil water content, bulk density, and slope angle was obtained. Then Bekker’s model was modified to obtain the pressure–sinkage model of sloped terrain. Finally, the control variable method under slope angle of 10°, soil water content of 10%, and bulk density of 2 mg·m−3 were used to validate the model. The results revealed that the root-mean-square error between the calculated pressure value of the model and the measured value of the film pressure sensor was 1.614, 1.601, and 0.822, respectively. In the dynamic operation of a hillside tractor prototype, the calculated pressures between the supporting wheels were close to the measured values. It indicates that the modified soil pressure–sinkage model is more suitable for calculating the force at the bottom of the track between the supporting wheels. It can also provide an important theoretical basis for accurately calculating the pressure–sinkage parameters of sloped terrain soil. Additionally, this approach could provide theoretical and technical support for the rational arrangement of HMT undercarriages to reduce the soil sinkage and driving resistance.

Mechanical Performances of Typical Robot Feet Intruding into Sands

Four kinds of feet with typical structures, referred to as the hemispherical foot, the semicylindrical foot, the rectangular foot and the circular foot, respectively, were designed and manufactured to study the foot–terrain interaction mechanics for legged robots. Three kinds of quartz sand were selected to study how particle size, shape and compactness affected the physical properties of the substrate and the intrusion performance of mechanical feet. The media with smaller particle sizes had higher bulk densities and lower angles of stability, but no obvious rule was found for particle shapes of quartz sand with different sizes. The intrusion resistive forces and pressures of the hemispherical foot on these three kinds of quartz sand were all less compared with the other three mechanical feet. The particle disturbance areas and motion trends were compared under these four kinds of mechanical feet using discrete element method simulations. The intrusion resistive forces of these mechanical feet first increased and then decreased with the increasing particle sizes of the quartz sand. Moreover, the intrusion resistive forces of these mechanical feet on spherical particles were smaller compared with irregular particles. The corresponding resistive forces of the mechanical feet were characterized based on the compactness of the quartz sand. According to the intrusion test data, the classic pressure–sinkage model was modified, and the relationships between intrusion resistive force and mechanical foot depth were obtained.

A study of pressure-sinkage relationship used in a tyre-terrain interaction

The vehicle applies a normal load to the terrain, which causes sinkage and motion resistance. To forecast the normal pressure distribution on the interface of a vehicle–terrain and the tractive performance of a vehicle, the response of the terrain to normal load (which is characterized by pressure–sinkage relationship equations) must be measured. This paper presents the common conventional pressure sinkage models used in terramechanic and the modification that happened to this models. In addition the features of the new models.

Studies on the sinkages of rigid plain wheels and lugged wheels on TRI-1 lunar soil simulant

This paper summarises the experimental work and analytical work carried out to determine the wheel sinkage of plain rigid wheels and lugged wheels, traversing on TRI-1 Lunar Soil Simulant (Plain and lugged wheels: small wheel- 160 mm × 32 mm and large wheel- 210 mm × 50 mm) with different number of lugs (N = 8, 12, 16) and lug height (h = 5, 10, 15 mm). Bekker and Reece pressure sinkage models are considered to determine the theoretical sinkage, and outlined in the present study. Comparisons of the analytical results with the experimental results are also carried out. The comparisons hold good for plain rigid wheels and in 2 cases, for lugged wheels (Small and Large), with 16 lugs of height, 5 mm. For all other combinations of lugged wheels (no. of lugs = 8, 12 and height of lugs = 5 mm, 10 mm and 15 mm), the predicted values are found to be less than the experimental values. For efficient functioning of the rover, optimization of wheel dimensions is a must.A new sinkage model accounting gravity effect and aspect ratio is developed, based on experimental results for wheel sinkages on TRI-1 simulant, the range of results obtained for different cases are examined.

Present situation and problems of soil pressure-sinkage model fitting method

The development history of soil pressure-sinkage relationship is briefly introduced. The soil pressure-sinkage model is classified after the research progress of soil pressure-sinkage characteristics at home and abroad was summarized. Several improved models of soil pressure-sinkage based on bekker formula and other models under different soil conditions, such as paddy field soil, desert sand and so on, ware introduced respectively. Analyzing the experimental conditions and the theoretical basis of the existing models of soil pressure-sinkage, it is concluded that the existing pressure-sinkage model of soil is established under the condition of the quasi-static loading, the unidirectional applied load, and the assumption that the bottom plate load is evenly distributed. The difference between the experimental conditions of the existing soil pressure-sinkage models and the interaction of pressure-sinkage characteristics between the track of tracked vehicle and ground is analyzed. Based on the finite element simulation analysis and the in situ test, a new idea which can be referenced is proposed to study the interaction of pressure-sinkage characteristics between the track of tracked vehicle and ground from the aspects of loading rate, plate bottom load distribution and cyclic loading and so on.

Performance evaluation of a wire mesh wheel on deformable terrains

Because of the unique lunar environment, a suitable wheel for lunar rover decides the rover’s trafficability on deformable terrains. The wire mesh wheel (hereinafter referred to as WMW) has the advantages of light weight and superior stability, been widely adopted for lunar rovers. But a comprehensive research on performance of WMW on deformable terrains has not been conduct. This paper would provide particular study on a type WMW, including quasi-static pressure-sinkage test and driving performance. A novel pressure-sinkage model for the WMW on deformable soils was presented. In order to investigate the sinkage characteristics of the WMW, tests were performed using a single-wheel testbed for the WMW with different loads and velocities. The effects of load and velocity on sinkage were analyzed, and the relationship between real and apparent sinkage was presented. The research on traction performance of WMW under different slip ratios (0.1–0.6) was also conducted, contrast tests were proceed by using a normal cylindrical wheel (hereinafter referred to as CW). The traction performance of WMW is analyzed using performance indices including wheel sinkage, drawbar pull, driving torque, and tractive efficiency. The experimental results and conclusions are useful for optimal WMW design and improvement/verification of wheel–soil interaction mechanics model.

New perspective on characterizing pressure–sinkage relationship of terrains for estimating interaction mechanics

Conventional pressure–sinkage models of characterizing bearing properties of terrains for vehicles are semi-empirical with poor adaptability and extrapolation ability; definitions of parameters are nonintuitive. The purpose of this paper is to provide more general and high-fidelity models for terrain characterization to satisfy the high requirements of autonomous wheeled vehicles, which should “understand” terramechanics in an accurate way on off-road terrains. Based on the analysis of conventional models and experimental results, new perspective and related equations on characterizing bearing performance are proposed. The stiffness modulus which is an intrinsic terrain parameter with determined unit of Pa/m has dominant role in governing the bearing performance. The sinkage exponent is variable as the function of various influential factors. Numerical analysis verifies that the new model with two meaningful parameters has high goodness of fit with Bekker’s model. Experimental results verifies that the new model using constant stiffness modulus and variable sinkage exponent reflects key factors such as dynamic sinkage, dimension effect, payload effect, and lug effect with high fidelity, which are not considered by the conventional models. This concept could be applied to various terrains and conventional vehicles.

Simulation and experimental validation of a modified terramechanics model for small-wheeled vehicles

The ability to model and predict vehicle performance over deformable terrains, which is typically done using terramechanics, is important for planetary exploration, military operations, and off-road vehicle design. This paper details the development of a new vehicle-terrain model that specifically addresses some of the limitations of traditional terramechanics when applied to Unmanned Ground Vehicles (UGVs) with small wheel diameters. Assumptions and limitations of the classical Bekker terramechanics model for wheeled locomotion are discussed. A novel pressure-sinkage model that was recently developed by the authors is detailed and shown to improve sinkage and compaction resistance models significantly. These models are implemented in a numerical simulation, which is used to predict the tractive performance of an experimental UGV. Field tests carried out on sandy terrain are described, and the results are used to validate the simulated predictions.

Development and experimental validation of an improved pressure-sinkage model for small-wheeled vehicles on dilative, deformable terrain

This paper presents a novel pressure-sinkage model for small-wheeled vehicles operating on dilative, deformable soils. Dilative soils, such as sand and Martian regolith, undergo negligible compaction during deformation. The proposed model takes both wheel diameter and width into account and is established using results from over 120 pressure-sinkage tests on two soils and 35 wheel geometries. The model builds on the authors’ previously established diameter dependent pressure-sinkage relationship, which has been shown to be more accurate for small wheels than classical models. X-ray images of the sub-surface strain field during soil indentation are used to visually validate the model. Using this model, an improved terramechanics framework is developed, which is subsequently implemented in an A∗ path planning algorithm. The algorithm determines the optimal route for an unmanned ground vehicle based on distance, energy consumption, and mobility. Field tests performed using a four-wheeled experimental UGV on moist, sandy terrain validate the modified terramechanics framework and its usefulness in field operations.

A pressure-sinkage model for small-diameter wheels on compactive, deformable terrain

Traditional terramechanics theorems utilize pressure-sinkage models based on the assumption that the contact area between a tire and soil can be approximated as a flat plate. Examples include work by Bernstein–Goriatchkin, Bekker, Reece, and Ishigami. Recently, the authors have demonstrated that (1) this assumption does not hold for wheels with a diameter less than approximately 50cm and (2) an improved diameter-dependent pressure-sinkage model can yield more accurate results. Further improvements to the pressure-sinkage model for small diameter wheels are presented here that account for both wheel width and diameter on compactive soils. Results from 125 pressure-sinkage tests using 35 wheel geometries on a clay/silt mix are presented. X-ray images of sub-surface soil deformation are used to visually validate the model.

A modified pressure–sinkage model for small, rigid wheels on deformable terrains

Bekker’s semi-empirically derived equations allow the designers of off-road vehicles to understand and predict vehicle mobility performance over deformable terrains. However, there are several underlying assumptions that prevent Bekker theory from being successfully applied to small vehicles. Specifically, Bekker’s sinkage and compaction resistance equations are inaccurate for vehicles with wheel diameters less than approximately 50 cm and normal loading less than approximately 45 N. This paper presents a modified pressure–sinkage model that is shown to reduce sinkage and compaction resistance model errors significantly. The modification is validated with results from 160 experiments using five wheel diameters and three soil types.

Prediction of sinkage and motion resistance of a tracked vehicle using plate penetration test

The relationship between contact pressure and sinkage must be represented by a mathematical model to estimate the sinkage and the motion resistance due to a vehicle. In this study an approximate and simple pressure-sinkage model is proposed. This model takes into account the effect of the size of the penetration plate on soil response, and includes two soil values that can be obtained by a single plate penetration test. It is submitted that the sinkage and the motion resistance of a tracked vehicle can be estimated by means of the proposed model.