Soil deformation and slip relative to grouser shape and spacing

The development of soil deformation patterns and failure status behind grousers in the production of drawbar pull is examined in relation to grouser shape, size, and spacing (between grousers). The kinds of deformations, slip conditions, and patterns of soil displacement can be usefully examined to provide the input required for optimizing track performance.     

Shape effects of wheel grousers on traction performance on sandy terrain

This paper presents the effects of different wheel grouser shapes on the traction performance of a grouser wheel traveling on sandy terrain. Grouser wheels are locomotion gears that allow small and lightweight exploration rovers to traverse on the loose sand on extraterrestrial surfaces. Although various grouser shapes have been analyzed by some research groups, a more synthetic and direct comparison of possible grousers is required for practical applications. In this study, we developed a single wheel testbed and experimentally investigated the effects of four grouser shapes (parallel, slanted, V-shaped, and offset V-shaped) on the traction performance of linear movement on flat sand. The wheel slip, sinkage, traction and side force acting on the wheel axle, the wheel driving torque, and the efficiency of each wheel were examined. Thereafter, the effects on the lateral slope traversability of a small and lightweight four-wheeled rover with different grouser shapes were also examined. The traversability experiment demonstrated the vehicle mobility performance in order to contribute to the design optimization of rover systems. These experimental results and their comparisons suggested that, of the shapes studies herein, the slanted shape was the optimal grouser design for use in wheeled rovers on lunar and planetary soil.     

Effect of open spaces between grousers on the gross traction of a track shoe for lightweight vehicles analyzed using 2D DEM

The purpose of this study is to investigate the effect of open spaces between grousers on gross traction using the discrete element method (DEM). We used a quasi-2D track shoe model in which we could control the open spacing between track shoes to observe the tractive performance experimentally. The gross traction and the sinkage of the grouser were measured on artificial sand. Moreover, we applied a 2D DEM analysis to the interaction between the open-spaced track shoes and the model soil. We confirmed the accuracy of the DEM analysis using the experiments. The analysis with the model dry sand could recreate the characteristic region of the soil under the shearing action, which depends on the track shoe spacing. The DEM also showed that the gross traction decreased with the increase in open spacing of the grousers. From the result of a 2D DEM analysis of a grouser for a prototype mesh crawler for the Japan Aerospace Exploration Agency, we estimated a thrust coefficient of approximately 0.4 for a wider grouser pitch-to-height ratio of 4.0–7.75 because of the constant sinkage of the grouser, neglecting the role of the meshed belt.     

Traveling and abrasion characteristics of wheels for lunar exploration rover in vacuum

This paper investigates the traveling and abrasion characteristics of rigid wheels for a lunar exploration rover at atmospheric pressure and in a vacuum. For this investigation, a traveling test system that enables the wheel to continuously travel over a long distance was developed. Using this system, tests on traveling performance and abrasion were conducted with the wheel on a lunar regolith simulant surface. In the initial tests, various wheels traveled over different ground conditions and their performances were evaluated based on the relationship between the drawbar pull and slippage. In the later tests, a wheel with grousers traveled a distance of 3 km and the abrasion was analyzed at various intervals. From the traveling performance tests, it was found that for a soft ground condition, the traveling performance of the wheels in vacuum was slightly lower than that in atmosphere. This indicates that ground tests performed in atmosphere overestimate the actual performance on the lunar surface. The abrasion tests suggested that the scratching of wheels occurs more easily in vacuum than in atmosphere. These experiments confirmed that the abrasion of the wheels do not cause any critical problem for a traveling distance of up to 3 km in a simulated lunar environment.     

A dynamic terramechanic model for small lightweight vehicles with rigid wheels and grousers operating in sandy soil

This paper presents a validated dynamic terramechanic model for rigid wheels with grousers that may be used for planetary and terrestrial mobile robots operating in loose sandy soil. The proposed model is based on established analytical terramechanic theories and incorporates two new dimensionless empirical coefficients. The additional terms in the model are based on existing soil mechanic theories that vary as a function of soil properties, slip conditions, and vehicle loading. The proposed model was able to capture and predict the dynamic oscillations observed in experimental data from a single-wheel testbed for the sinkage, drawbar pull and normal load. For the operating conditions tested in this research the simulation results using the proposed model show an improvement over traditional terramechanic models for capturing the dynamic effects of grousers.     

Discrete element modelling for wheel-soil interaction and the analysis of the effect of gravity

The discrete element method (DEM) is widely seen as one of the more accurate, albeit more computationally demanding approaches for terramechanics modelling. Part of its appeal is its explicit consideration of gravity in the formulation, making it easily applicable to the study of soil in reduced gravity environments. The parallel particles (P²) approach to terramechanics modelling is an alternate approach to traditional DEM that is computationally more efficient at the cost of some assumptions. Thus far, this method has mostly been applied to soil excavation maneuvers. The goal of this work is to implement and validate the P² approach on a single wheel driving over soil in order to evaluate the applicability of the method to the study of wheel-soil interaction. In particular, the work studies how well the method captures the effect of gravity on wheel-soil behaviour. This was done by building a model and first tuning numerical simulation parameters to determine the critical simulation frequency required for stable simulation behaviour and then tuning the physical simulation parameters to obtain physically accurate results. The former were tuned via the convergence of particle settling energy plots for various frequencies. The latter were tuned via comparison to drawbar pull and wheel sinkage data collected from experiments carried out on a single wheel testbed with a martian soil simulant in a reduced gravity environment. Sensitivity of the simulation to model parameters was also analyzed. Simulations produced promising data when compared to experiments as far as predicting experimentally observable trends in drawbar pull and sinkage, but also showed limitations in predicting the exact numerical values of the measured forces.     

Re-examined principles of thrust generation by a track on soft ground

Dr. Bekker’s first book Theory of land locomotion offers in fact two different concepts of thrust generation on soft ground with respect to the slip: (a) as the push of grousers causing horizontal soil “distortion” and (b) as the shear force in the failure plane linked with the shear deformation. Bekker preferred the second concept and backed it up by the unique shear-ring measuring technique. To clear up the matter, the author decided to re-examine the thrust generation by a track plate experimentally in field conditions. The tests have shown that the initial stage of thrust generation in compressible ground is always horizontal soil compression by grousers, which divides the soil under a track into separate blocks initially at rest. This compression increases at least to the transition point, when a block is sheared off simultaneously at the bottom and in both lateral planes and starts sliding along the channel formed by the preceding grouser. The analysis of these measurements enabled to define the compressive displacement of the face of the soil block (travel of the grouser) appurtenant to the mentioned transition point, useful to define the thrust–slip curve. The case may also be described by the conventional shear stress–shear displacement relationship, imagined to take place in the bottom failure plane, however, namely the “shear displacement” is rather an unusual quantity.     

Evaluation and prediction of energy losses in track-terrain interaction

The interaction between an aggressive track with a soil substrate is examined with a view to development of a better knowledge of the manner in which energy is transferred and dissipated in the bearing soil substrate. The test tracks are tested in the laboratory tow bin. In addition substrate soil deformation and distortion are measured during multiple grouser motion in separate experiments for determination of the specific participants contributing to the expenditure of the energy transmitted by the track or multiple grouser test system. Application of the principle of energy transfer and conservation, using measured soil deformations and distortions for computations of energy expenditure in the soil due to track loading compares well with the measured values of drawbar pull when energy loss is subtracted from input energy. Application of this method of evaluation of track-terrain interaction allows for a better means of understanding the basic issues involved in the development of tractive efficiency.     

Analysis of Mars Exploration Rover wheel mobility processes and the limitations of classical terramechanics models using discrete element method simulations

A previous three-dimensional discrete element method (DEM) model of Mars Exploration Rovers (MERs) wheel mobility demonstrated agreement with test data for wheel drawbar pull and sinkage for wheel slips from 0.0 to 0.7. Here, results from the previous model are compared with wheel mobility data for non-MER wheels that cover the range of wheel slip from 0.0 to 1.0. Wheel slips near 1.0 are of interest for assessing rover mobility hazards. DEM MER wheel model predictions show close agreement with weight-normalized wheel drawbar pull data from 0.0 to 0.99 wheel slip and show a similar trend for wheel sinkage. The nonlinear increase in MER wheel drawbar pull and sinkage for wheel slips greater that 0.7 is caused by development of a tailings pile behind the wheel as it digs into the regolith.Classical terramechanics wheel mobility equations used in the ARTEMIS MER mobility model are inaccurate above wheel slips of 0.6 as they do not account for the regolith tailings pile behind the wheel. To improve ARTEMIS accuracy at wheel slips greater that 0.6 a lookup table of drawbar pull, wheel torque, and sinkage derived from DEM mobility simulations can be substituted for terramechanics equation calculations.     

Travelling performance of a wheel on a finite thickness ground

Off-road terrain can often be regarded as a finite thickness ground consisting of a soft soil layer on a rigid base. Experiments for the traveling performance of a wheel in a dense sand layer on a rigid base revealed that as the soil layer thickness decreases under the condition of high constant slip, the drawbar pull does not increase monotonically but increases gradually to a maximal value, then decreases to a minimal value, and thereafter again increases rapidly to the highest value at zero soil layer thickness. The mechanical interpretation of the relationship between the drawbar pull and the soil layer thickness is given qualitatively from the aspects of the shear characteristics of dense sand and the rigid-body friction between the wheel and the rigid base of the soil layer. It is indicated that the relationship takes the same form as van der Waals' state equation for the pressure and the volume of an imperfect gas with a phase transition between gas and liquid. The equation representing the relationship of the drawbar pull to the soil layer thickness is proposed in accordance with van der Waals' equation.     

Experimental analysis of soil reaction on a lug of a movable lug wheel

A movable lug wheel was tested in a soil bin test apparatus to determine its traction performance and to measure the soil reaction forces on its lugs. Similar tests were also conducted using a fixed lug wheel. The effects of the lug motion pattern, lug spacing and horizontal load on pull and lift forces were studied. From the experiments it is confirmed that the movable action of the lug plate could generate superior pull and lift forces in comparison with the fixed lug wheel. Among the test wheels, lug motion pattern-2 generated the highest pull and lift forces. Within the range of the test conditions, there was no significant difference in pull and lift forces of the lug plate between the test lug wheels with 12 lugs and 15 lugs at the same level of horizontal and vertical loads. The increase of horizontal load up to 200 N generally increased the pull force and generated smaller rolling resistance before the lug left the soil, but did not increase the lift force significantly. The patterns of pull force, lift force and drawbar pull generated under a constant slip were slightly different from those under a constant horizontal load. Finally, the results were also elucidated by their actual lug trajectories in soil.     

Soil flow analysis for grouser wheels based on a particle image velocimetry method

This paper presents an analysis, based on a particle image velocimetry method, of soil flow field beneath a grouser wheel traveling over loose soil. Although the grouser wheel is expected to have better traction and mobility over fine, loose soil, its interaction mechanisms with the soil remain to be elucidated. Thus, a particle image velocimetry-based soil flow analysis is conducted to directly observe soil behavior around the grouser wheel. In the experimental analysis, key parameters of the soil flow field, such as general shape, thickness, streamlines of the flow field, soil velocity on the streamlines, and soil failure angle are examined quantitatively. From the results, the soil flow shape periodically changes with wheel rotation, and this change appears, depending on wheel slip varying over time. Furthermore, the experimental result of the soil failure angle differs drastically from its typical theory. These results will contribute to modeling the mechanical interaction between the grouser wheel and soil.     

Experimental study of a tracked mobile robot’s mobility performance

This paper proposes an experimental method of predicting the traction performance of a small tracked mobile robot. Firstly, a track-terrain interaction model based on terramechanics is built. Then, an experimental platform of the tracked robot is established, on which the measurement methods of the parameters that influencing the accuracy of the prediction model are introduced and the data post-processing are improved, including drawbar pull, slip ratio, sinkage, track deformation and so on. Based on the experimental data, several key terrain parameters are identified. With the tracked robot platform, the drawbar pull-slip ratio relationship is tested, and the effects on drawbar pull considering different kinds of terrain and the influence of the grousers are analyzed as well. The research results provide a reference for the experimental study on the traction performance of small tracked robots.     

Precise measurement of soil deformation and fluctuation in drawbar pull for steel and rubber-coated rigid wheels

The travelling performance of rigid wheels on sand stratum is measured using two kinds of surface material, i.e. steel and steel coated with rubber. A new method for measuring the displacement of soil beneath the wheel has been developed using small polyester film markers. The trajectories of soil particles beneath the wheels are approximated by an exponential function and the fluctuations in the drawbar pull are represented by a sinusoidal function. The amplitude and basic wavelength of the fluctuation in the drawbar pull are discussed for both types of wheels.     

A calculation method of track shoe thrust on soft ground for splayed grouser

Thrust of track shoes on soft ground is affected by soil moisture content, shear rate and structure parameters of track shoes. A lack of comprehensive consideration of these factors exists for normal calculation methods. A method to predict thrust for track shoes on soft ground with splayed grouser was established based on experimental results and theoretical derivations. Model track shoe traction experiments were conducted for verification and correction of the thrust formula. It was observed that the thrust for the track shoes decreased with the increase in moisture content of the soil. Increases in shear rate, grouser height, and grouser splayed angle resulted in greater tractions. Effect of grouser thickness and grouser draft angle on tractions was not obvious. A corrected thrust formula allowed accurate prediction of thrust for a single track shoe on soft ground.     

Tractive performance of a bulldozer running on weak ground

To determine the tractive performance of a bulldozer running on weak ground in the driven state, the relations between driving force, drawbar pull, sinkage, eccentricity and slip ratio have been analysed together with each energy balance; effective input energy, sinkage deformation energy, slippage energy and drawbar pull energy. It is considered that the thrust is developed not only on the main straight part of the bottom track belt but also on parts of the front idler and rear sprocket, and the compaction resistance is calculated from the amount of slip sinkage. For a given vehicle and soil properties, it is determined that the drawbar pull increases directly with the slip ratio and reaches about 70% of the maximum driving force. The compaction resistance reaches about 13% of the maximum driving force. The sinkage of the rear sprocket, the eccentricity, and the trim angle increase with the increment of slip ratio due to the slip sinkage. These analytical results have been verified experimentally. After determining the optimum slip ratio to obtain a maximum effective tractive power, it is found that a larger optimum drawbar pull at optimum contact pressure could be obtained for a smaller eccentricity of vehicle center of gravity and a larger track length-width ratio under the same contact area.     

Experimental research on grouser traction of deep-sea mining machine

The traction characteristics of the grouser, cutting the simulative soil of deep-sea sediment, with different tooth widths, tooth heights, and ground pressures are studied with traction characteristic test apparatus. A traction-displacement model is obtained by combining the analysis of the cutting mechanism. The results show that the traction-displacement curves of grousers with different tooth widths, tooth heights, and ground pressures have the same changing trend, which matches the Wong traction model. Their sensitivity coefficient and shear modulus are slightly fluctuated. Therefore, the average values can be used as the traction model parameters. The maximum traction of the grouser with a two-side edge and a 10mm tooth width increment changing with the tooth height and ground pressure can be determined according to the grousers with different tooth widths. By combining the traction model parameters, the traction-displacement curve of the grouser with a certain group values of tooth width, tooth height, and ground pressure can be predicted. Therefore, the slip of the mining machine can be prevented to improve the mining efficiency.     

Study of the influence of vehicle parameters on tractive performance in deep snow

This paper describes an experimental study of tractive performance in deep snow, carried out with a new special skid steered tracked vehicle, developed by Bodin [1]. The vehicle design parameters studied include the influence of the ground clearance of the vehicle belly and the longitudinal location of the centre of gravity on tractive performance in deep snow, as well as the effect of initial track tension. The most important results from the test show that an increase in the ground clearance has a positive effect on the drawbar pull, originating from a greater increase in the thrust than in the track motion resistance and a slight decrease in the belly drag. Tests of the longitudinal location of the centre of gravity show that a location ahead of the midpoint of the track contact length is to be preferred. The drawbar pull increases with the centre of gravity moving forward. This is due to a reduced track motion resistance, a slight decrease in the belly drag and an almost constant vehicle thrust. The reason for the decreased track motion resistance and belly drag with the centre of gravity located ahead of the midpoint of the track contact length is a decreased vehicle trim angle.     

An indoor traction measurement system for agricultural tires

To reliably study soil–wheel interactions, an indoor traction measurement system that allows creation of controlled soil conditions was developed. This system consisted of: (i) single wheel tester (SWT); (ii) mixing-and-compaction device (MCD) for soil preparation; (iii) soil bin; (iv) traction load device (TLD). The tire driving torque, drawbar pull, tire sinkage, position of tire lug, travel distance of the SWT and tire revolution angle were measured. It was observed that these measurements were highly reproducible under all experimental conditions. Also relationships of slip vs. sinkage and drawbar pull vs. slip showed high correlation. The tire driving torque was found to be directly influenced by the tire lug spacing. The effect of tire lug was also discussed in terms of tire slip.     

Analysis of soil flow and traction mechanics for lunar rovers over different types of soils using particle image velocimetry

Grouser wheels have been used in planetary rovers to improve mobility performance on sandy terrains. The biggest difference between a wheel with and without grousers is the soil behavior beneath the wheel as the grousers shovel the soil. By analyzing the soil flow, we gain insight into the mechanics dominating the interaction between the wheel and the soil, directly impacting performance. As the soil flow varies depending on the soil properties, the effects of soil type on soil behavior and wheel-traveling performance should be studied. This paper reveals the difference in soil flow and wheel performance on cohesive and non-cohesive soils. We conducted a series of single wheel tests over different types of soils under several wheel-traveling conditions. Soil flow was visualized by using particle image velocimetry (PIV). The experimental results indicate that soil flow characteristics highly depend on the shear strength of the soil. The cohesive soil exhibited lower fluidity due to its higher shear strength. At the same time, the wheel displayed a higher traveling performance over the cohesive soil, that is, a lower slip ratio.