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.     

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.     

Grousers improve drawbar pull by reducing resistance and generating thrust at the front of a wheel

Grousers are commonly used to increase wheel traction, though how grousers exactly influence wheel thrust and resistance, and thus drawbar pull, has continued to remain an open topic of research. This work explores rigid wheels with grousers traveling on homogeneous granular soil. Unique experiments that provide insights into what grousers are doing at various points on a wheel are presented. To perform these experiments, a novel wheel that enables grousers to extend and retract in various regions around the wheel is developed; specifically grousers can always be extended at the front of the wheel but retracted below the wheel, even as the wheel rotates. These experiments show that grousers are much more effective at increasing drawbar pull when they are interacting with soil ahead of the wheel, rather than below it. A wheel with grousers engaging soil only ahead of the wheel, and not below it, nonetheless achieves over 80% of the relative improvement in drawbar pull that a “full grouser” wheel achieves over a grouserless wheel. This reveals how thrust is generated primarily by the front-most grouser, and further suggests that the reduction of resistive forward soil flow also plays a key role in increasing drawbar pull.     

Visualization and analysis of wheel camber angle effect for slope traversability using an in-wheel camera

This paper visualizes and analyzes an effect of a wheel camber angle for the slope traversability in sandy terrain. An in-wheel camera developed in this work captures the wheel-soil contact phenomenon generated beneath the wheel through a transparent section of the wheel surface. The images taken by the camera are then analyzed using the particle image velocimetry. The soil flows with various wheel camber angles are analyzed with regard to the soil failure observed on the slope surface. The analysis reveals that the slope failure and soil accumulation in front of the wheel significantly affect the wheel forces and distributions of the wheel sinkage in the wheel width direction. Further, the side force of the wheel in traversing a slope decreases as the slip ratio increases because the shear stress in the slope downward direction decreases owing to the slope failure.     

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.     

Experimental study on wheel-soil interaction mechanics using in-wheel sensor and particle image velocimetry part II. Analysis and modeling of shear stress of lightweight wheeled vehicle

Wheeled vehicle mobility on loose sand is highly subject to shear deformation of sand around the wheel because the shear stress generates traction force of the wheel. The main contribution of this paper is to improve a shear stress model for a lightweight wheeled vehicle on dry sand. This work exploits two experimental approaches, an in-wheel sensor and a particle image velocimetry that precisely measure the shear stress and shear deformation generated at the interaction boundary. Further, the paper improves a shear stress model. The model proposed in this paper considers a force chain generated inside the granular media, boundary friction between the wheel surface and sand, and velocity dependency of the friction. The proposed model is experimentally validated, and its usefulness is confirmed through numerical simulation of the wheel traction force. The simulation result confirmed that the proposed model calculated the traction force with an accuracy about 70%, whereas the conventional one overestimated the force, and its accuracy was 13% at the best.     

Development of in-wheel sensor system for accurate measurement of wheel terrain interaction characteristics

Planetary rovers need high mobility on a rough terrain such as sandy soil, because such a terrain often impedes the rover mobility and causes significant wheel slip. Therefore, the accurate estimation of wheel soil interaction characteristics is an important issue. Recent studies related to wheel soil interaction mechanics have revealed that the classical wheel model has not adequately addressed the actual interaction characteristics observed through experiments. This article proposes an in-wheel sensor system equipped with two sensory devices on the wheel surface: force sensors that directly measure the force distribution between the wheel and soil and light sensors that accurately detect the wheel soil surface boundary line. This sensor design enables the accurate measurement of wheel terrain interaction characteristics such as wheel force distribution, wheel–soil contact angles, and wheel sinkage when the powered wheel runs on loose sand. In this article, the development of the in-wheel sensor system is introduced along with its system diagram and sensor modules. The usefulness of the in-wheel sensor system is then experimentally evaluated via a single wheel test bench. The experimental results confirm that explicit differences can be observed between the classical wheel model and practical data measured by the in-wheel sensor system.     

Evaluation of link-track performances using DEM

A two-dimensional discrete-element model for the interaction between link-track and soil is presented. The model was developed using commercial PFC2D code. Two different particles, sphere and clump of two spheres, were used to represent the soil. The soil parameters of the model were determined using Hertzian contact theory. Based on the model and soil parameters, simulations of biaxial tests and calculations of the internal angle of friction and cohesion were preformed. The simulation results showed that the internal angle of friction should not exceed the value of 0.65 when using the spherical particles. Based on the clumped particles model, simulations of shear tests with two grouser plates (lengths 100 and 150 mm) were performed under different soil conditions, normal pressures, and cleat heights. A curve fitting of the simulation results was performed using three semi-empirical models from Bekker, Janosi, and Wong for representing the shear stress–displacement relationship. The best fitting was achieved using Wong’s approach. The simulation results of the cleat effects were compared with Bekker’s grouser approach and McKyes’s formulation for soil–blade interaction. In most of the cases, the results of Bekker’s model were the lower bound and McKyes’s model, the upper bound of the DEM simulation results. The properties of the soil model for the DEM were determined using simulation results of shear tests by grouser plate. In the range investigated, the size of the shearing grouser plate is not significant in determining the soil model properties.     

Longitudinal skid model for wheels of planetary rovers based on improved wheel sinkage considering soil bulldozing effect

To successfully deploy a wheeled mobile robot on deformable rough terrains, the wheel-terrain interaction mechanics should be considered. Skid terramechanics is an essential part of the wheel terramechanics and has been studied by the authors based on the wheel sinkage obtained using a linear displacement sensor that does not consider soil bulldozing effect. The sinkage measured by a newly developed wheel via detecting the entrance angle is about 2 times of that measured by the linear displacement sensor. On the basis of the wheel sinkage that takes the soil bulldozing effect into account, a linear function is proposed to the sinkage exponent. Soil flow in the rear region of wheel-soil interface is considered in the calculation of soil shear displacement, and its average velocity is assumed to be equal to the tangential velocity component of the transition point of shear stress. To compute the normal stress in the rear region directly, the connection of the entrance and leaving points is supposed as the reference of wheel sinkage. The wheel performance can be accurately estimated using the proposed model by comparing the simulation results against the experimental data obtained using two wheels and on two types of sands.     

Measurement and modeling for two-dimensional normal stress distribution of wheel on loose soil

On the Moon or Mars, typical target environments for exploration rovers are covered with fine sand, so their wheels easily slip on such weak ground. When wheel slippage occurs, it is hard for the rover to follow its desired route. In the worst case, the rover gets stuck in loose soil and cannot move anymore. To reduce the risk of the rover getting stuck, analysis of the contact mechanics between the soil and wheel is important. Various normal stress distribution models for under the wheel surface have been proposed so far. However, classical models assume a uniform stress distribution in the wheel’s width direction. In this study, we measured the two-dimensional normal stress distribution of a wheel in experiments. The results clarified that the stress distribution in the wheel’s width direction is a mountain-shape curve with a peak located at the center of the wheel. Based on the results, we constructed a stress distribution model for the wheel’s width direction. In this paper, we report our measurements for the two-dimensional stress distribution of a wheel on loose soil and introduce our stress distribution model for the wheel’s width direction based on our experimental results.     

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.     

Experimental study on wheel-soil interaction mechanics using in-wheel sensor and particle image velocimetry Part I: Analysis and modeling of normal stress of lightweight wheeled vehicles

This study aims to develop a wheel-soil interaction model for a lightweight wheeled vehicle by measuring the normal stress distribution beneath the wheel. The main contribution of this work is to clarify the wheel-soil interaction using a wheel testbed that equips multiple sensory systems. An in-wheel sensor accurately measures the normal stress distribution as well as the contact angles of the wheel. Particle image velocimetry with a standard off-the-shelf camera analyzes soil flow beneath the wheel. The proposed model for the normal stress distribution is formulated based on these experimental data and takes into account the following phenomena for the lightweight vehicles that have not been considered in the classical model: (1) the normal stress distribution takes the form of a Gaussian curve; (2) the normal stress distribution concentrates in the front region of the wheel contact patch; (3) the distribution is divided into two areas with the boundary determined by the maximum normal stress angle; and (4) the maximum normal stress exponentially decreases as the slip ratio increases. Then, the proposed model is experimentally validated. Furthermore, a simulation study for the wheel driving characteristics using the proposed model confirms the accuracy of the proposed model.     

An experimental investigation of jet flows through a row of forward expanded holes into a mainstream over a concave surface

This study performed detailed measurements of jet flows through a row of forward expanded holes into a mainstream over a concave surface using digital particle image velocimetry. Each of ejected holes had a streamwise inclined angle of 35° bounded on a concave surface with constant radius of 382 mm. The spacing of adjacent holes is 1.5D. The density and the momentum flux ratio of the mainstream to the jet flow were 1.0. Results show detailed 2D mean velocity maps on several horizontal and vertical planes and a 3D streamline pattern of jet mean velocity. The streamlines of 3D mean velocity clearly display different flow characteristics of the ejected jet flow along the transverse direction. In addition, the particle trajectory of a ring enclosing an ejected jet above the injection hole was also presented to show movement of jet.     

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.     

Dynamic behaviour of an open lugged wheel under paddy soil conditions

Many experimental studies of open lugged wheel-soil interaction have been conducted, mainly based on the condition of constant slip and sinkage. As a result the reaction force to lugs seemed to be equal to the soil cutting resistance to a metal surface. However, analyses based on such methods do not appear to represent the actual behaviour of lugged wheel-soil interaction, especially when the lugs are spaced widely. The actual motion the wheel axle. In this study, an experimental device for a model lugged wheel was constructed to investigate the characteristics of the interaction between a lugged wheel and soil. Experiments were conducted under several test conditions of soil including paddy soil with a hard pan. The result of both theoretical and experimental data indicated that slip and sinkage of a lugged wheel showed a fluctuation with rotation angle of which the period is equal to the angular lug spacing. In each test soil condition used, the motion of the lugged wheel and the reaction forces acting on each lug from the soil for a free sinking wheel were different from that of the condition of constant slip and sinkage. It was found that the results obtained from this study could clarify the actual behaviour of lugged wheel-soil interaction.     

NUMERICAL SIMULATION OF ORIENTATION DISTRIBUTION FUNCTION OF CYLINDRICAL PARTICLE SUSPENSIONS

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Hummingbirds generate bilateral vortex loops during hovering: evidence from flow visualization

This article derives a method to estimate and correct the bias error of the shift vector’s absolute length in the presence of curved streamlines. The main idea is to identify the most likely streamline with constant curvature from the second-order shift vector and its gradient. The work establishes a theoretical framework including the systematic errors of the first-order and second-order shift vector’s absolute value and angle. Synthetic images of a stationary vortex are used to validate the proposed method. The curvature-correction is also applied to a synthetic flow field with non-constant curvature to demonstrate its potential for more realistic flow fields. The results reveal that second-order accurate vector fields suffer from a biased shift vector length depending on the streamline’s curvature and on the shift vector length. The bias error is negligible for vector fields with a shift vector length below the streamline curvature radius. For large shift vectors or strong curvatures, the bias error can be significantly reduced with the developed method. The approach is very general and can be applied to any vector field obtained from window-correlation particle image velocimetry (PIV), single-pixel ensemble-correlation PIV, particle tracking velocimetry or optical flow methods. It also works for all 3D extensions of the techniques, such as 3D-PTV or tomographic PIV.     

Prediction of wheel-soil interaction and performance using the finite element method

In this experimental-analytical study of wheel-soil interaction, a technique based on the finite element method is used for predicting continuous wheel performance and subsoil response behaviour. The evaluation of wheel-soil interaction performance at any degree of slip is performed using energy principles. The analytical technique utilizes experimentally determined wheel-soil particle path as displacement input for load simulation to predict the soil response beneath the wheel.

An incremental loading approach is adopted to satisfy as closely as possible the soil loading path. The solution requires initial conditions which establish the soil at zero energy level (no stress history) and proceeds to stationary wheel positions with wheel-soil penetration equal to its dynamic sinkage. The method of analysis then proceeds to the steady-state wheel travel mode. The predicted drawbar pulls and subsoil behaviour results are presented and shown to compare well with the experimentally measured values.     

Compression–Sliding approach: Dependence of transitional displacement of a driving element on its size and load

Every element of a pulling traction device (e.g. track shoe with grouser or tire section with lug) exhibits increasing rearward displacement during its engagement with soft ground. Compression–Sliding (CS) approach states in agreement with experimental evidence that on common soft ground this displacement starts due to longitudinal soil compression by the grouser or lug, which steadily increases up to the transitional displacement when the soil segment beneath a driving element fails in shear. Further displacement of a driving element is marked by forced slide of a sheared off soil block, which may eventually collapse. There was justified reasoning that the transitional displacement depends not only on the grouser (lug) contact pressure but also on the area and load of the respective traction element. The presented article reports on experiments designed to test this premise. The measurements applying the novel double plate (DP) meter technique were carried out in a laboratory soil bin containing loam charge of uniform bulk density and moisture content. Three sizes (proportions 1:2:4) and two mean vertical contact pressures (ratio1:2) of DP meter main plate were tested. The analysis of performed experiments confirmed the existence of dimensional and loading relationship “main plate – transitional displacement”, which bears upon the evaluation of thrust–slip relationship of any traction device by the CS approach or by any other method observing the existence of displacement.     

Traffic performance of a rubber-tracked vehicle travelling up and down a sloped pavement

The tractive and braking performances of a 40 kN rubber-tracked vehicle travelling up and down a sloped pavement depend on the grouser shape. The purpose of this paper is to find the most suitable grouser shape to obtain the maximum optimum effective tractive effort and the maximum optimum effective braking force and to clarify the several traffic performances of the vehicle travelling up and down sloped concrete and asphalt paved roads. As results, it is verified that the most suitable shape of rubber grouser is an equilateral trapezoid type of contact length 3 cm for concrete pavement and another of contact length 5 cm for asphalt pavement, respectively, and that the effective tractive effort and the effective braking force decrease with the increment of slope angle.