Modeling motion resistance of rigid wheels

A mathematical model was developed to describe the motion resistance of rigid wheels under self-propelled conditions where no drawbar pull is developed. The modeling was based on the concept that the work required to overcome the motion resistance is equal to the energy dissipated in compacting the soil beneath the wheel. Slippage of the wheel was also considered in the modeling. Finally the validity of the proposed model was discussed.     

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.     

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.     

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.     

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.     

Draftability of a 8.95 kW walking tractor on tilled land

A 8.95-kW walking tractor was evaluated for draft and drawbar power on tilled land. Empirical equations were developed to correlate the relationship between draft and wheel slip, drawbar power and wheel slip and drawbar power and fuel consumption. The values of draft, drawbar power and specific fuel consumption were calculated at 25% wheel slip. The results indicated that the values of draft on tilled land with pneumatic wheels at engine speed of 2000 rpm were 803 and 773 N in second low and third low gears, respectively. The respective draft values at engine speed of 1500 rpm were 748 and 735 N in second low and third low gears under slightly loose soil conditions. Mounting of a 40-kg wheel ballast increased the value of draft to 901 and 921 N at an engine speed of 2000 rpm and 872 and 888 N at an engine speed of 1500 rpm in second low and third low gears. Replacement of pneumatic wheels by steel wheels further increased the draft readings to 1034 and 999 N at an engine speed of 2000 rpm and 913 and 935 N at engine speed of 1500 rpm in second low and third low gears, respectively, indicating significant increase in drawbar power both at 2000 and 1500 rpm in second low and third low gears with the use of steel wheels. The specific fuel consumption decreased by about 28% and 27% at engine speed of 2000 rpm and about 17% and 21% at engine speed of 1500 rpm in second low and third low gear with the use of steel wheels over pneumatic wheels without wheel ballast. The specific fuel consumption decreased by about 4% and 14% at engine speed of 2000 rpm and 7% and 23% at engine speed of 1500 rpm in second low and third low gears, respectively, with the use of steel wheels over pneumatic wheels with 40 kg wheel ballast.     

Experimental study and analysis on driving wheels’ performance for planetary exploration rovers moving in deformable soil

Planetary rovers are different from conventional terrestrial vehicles in many respects, making it necessary to investigate the terramechanics with a particular focus on them, which is a hot research topic at the budding stage. Predicting the wheel-soil interaction performance from the knowledge of terramechanics is of great importance to the mechanical design/evaluation/optimization, dynamics simulation, soil parameter identification, and control of planetary rovers. In this study, experiments were performed using a single-wheel testbed for wheels with different radii (135 and 157.35 mm), widths (110 and 165 mm), lug heights (0, 5, 10, and 15 mm), numbers of lugs (30, 24, 15, and 8), and lug inclination angles (0°, 5°, 10°, and 20°) under different slip ratios (0, 0.1, 0.2, 0.3, 0.4, 0.6, etc.). The influences of the vertical load (30 N, 80 N, and 150 N), moving velocity (10, 25, 40, and 55 mm/s), and repetitive passing (four times) were also studied. Experimental results shown with figures and tables and are analyzed to evaluate the wheels’ driving performance in deformable soil and to draw conclusions. The driving performance of wheels is analyzed using absolute performance indices such as drawbar pull, driving torque, and wheel sinkage and also using relative indices such as the drawbar pull coefficient, tractive efficiency, and entrance angle. The experimental results and conclusions are useful for optimal wheel design and improvement/verification of wheel-soil interaction mechanics model. The analysis methods used in this paper, such as those considering the relationships among the relative indices, can be referred to for analyzing the performance of wheels of other vehicles.     

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.     

Advantages of all-season versus snow tyres for off-road traction and soil stresses

Tractive performance, as well as soil stresses under a vehicle equipped with two types of tyres, was investigated in this study. All-season and snow tyres were installed in a 14 T 6 × 6 military truck and the vehicle was driven over sandy and loess soil for drawbar pull tests. Simultaneously, the stress state was determined in the ground surface under the driving wheels. Effects of tread pattern on both traction curves and soil stress were analyzed for three different levels of vehicle loading. All-season tyres provide slightly better traction for both terrain surfaces, at all three loading levels, or the differences between traction measures are not significant. Soil stress analysis showed that the difference between the two tread patterns is not significant. Generally, on soft surfaces all-season tyres performed no worse than snow tyres, while they are pronouncedly better for highway use.     

Modeling,calibration and validation of tractive performance for seafloor tracked trencher

Shear stress–displacement model is very important to evaluate the tractive performance of tracked vehicles. A test platform, where track segment shear test and plate load test can be performed in bentonite–water mixture, was built. Through analyzing existing literatures, two shear stress–displacement empirical models were selected to conduct verification tests for seafloor suitability. Test results indicate that the existing models may not be suitable for seafloor soil. To solve this problem, a new empirical model for saturated soft-plastic soil (SSP model) was proposed, and series shearing tests were carried out. Test results indicate that SSP model can describe mechanical behavior of track segment with good approximation in bentonite–water mixture. Through analyzing main external forces applied to test scaled model of seafloor tracked trencher, drawbar pull evaluation functions was deduced with SSP model; and drawbar pull tests were conducted to validate these functions. Test results indicate that drawbar pull evaluation functions was feasible and effective; from another side, this conclusion also proved that SSP model was effective.     

Development of a data acquisition system for measuring the characteristics of real time forces by cage wheels

A new data acquisition system was introduced that could be used to monitor the real time wheel forces to solve the limitations of obtaining precise performance characteristics of actual cage wheels. Contrary to previous methods, in which the cage wheel forces were obtained by summing up the individual lug forces. The new method enables measurement of the components of lug force in three orthogonal directions simultaneously. A single unit dynamometer system, with two extended octagonal rings was designed and fabricated using a solid mild steel block, was able to measure force up to 5 kN in each direction. It was used in a soil-bin test rig to determine the characteristics of the forces produced by a cage wheel with opposing circumferential lugs. The characteristics of the pull and lift forces agreed with measured drawbar pull and calculated wheel forces respectively. The force signals fluctuated periodically with rotation angle and the corresponding period approximately equal to the interval of angular lug spacing. The side force fluctuated between positive and negative values and the average was closer to zero due to the balancing effect of opposing lugs. The new system showed better output compared to the previous attempts, confirming its applicability for accurate measurement of real time wheel forces.     

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.     

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.     

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.     

Bayesian calibration of Vehicle-Terrain Interface algorithms for wheeled vehicles on loose sands

The Vehicle-Terrain Interface (VTI) model is commonly used to predict off-road mobility to support virtual prototyping. The Database Records for Off-road Vehicle Environments (DROVE), a recently developed database of tests conducted with wheeled vehicles operating on loose, dry sand, is used to calibrate three equations used within the VTI model: drawbar pull, traction, and motion resistance. A two-stage Bayesian calibration process using the Metropolis algorithm is implemented to improve the performance of the three equations through updating of their coefficients. Convergence of the Bayesian calibration process to a calibrated model is established through evaluation of two indicators of convergence. Improvements in root-mean square error (RMSE) are shown for all three equations: 17.7% for drawbar pull, 5.5% for traction, and 23.1% for motion resistance. Improvements are also seen in the coefficient of determination (R²) performance of the equations for drawbar pull, 2.8%, and motion resistance, 2.5%. Improvements are also demonstrated in the coefficient of determination for drawbar pull, 2.8%, and motion resistance, 2.5%, equations, while the calibrated traction equation performs similar to the VTI equation. A randomly selected test dataset of about 10% of the relevant observations from DROVE is used to validate the performance of each calibrated equation.     

Numerical analysis on tractive performance of off-road wheel steering on sand using discrete element method

This paper presents a numerical analysis on steering performance including tractive parameters and lug effects. To explore the difference between the turning and straight conditions of steering, a numerical sand model for steering is designed and appropriately established by the discrete element method on the basis of triaxial tests. From the point of mean values and variation, steering traction tests are conducted to analyze the tractive parameters including sinkage, torque and drawbar pull and the lug effects resulting from type, intersection and central angle. Analysis indicates that steering motion has less influence on the sinkage and torque. When the slip ratio exceeds 20%, the steering drawbar pull becomes increasingly smaller than in the straight condition, and the increase of steering radius contributes to a decline in mean values and a rise in variation. The lug effect of central angle is less influenced by the steering motion, but the lug intersection is able to significantly increase the steering drawbar pull along with the variation reduced. However, the lug inclination reduces the steering drawbar pull along with the variation raised in different degrees.     

Mobility algorithm evaluation using a consolidated database developed for wheeled vehicles operating on dry sands

A substantial number of laboratory and field tests have been conducted to assess performance of various wheel designs in loose soils. However, there is no consolidated database which includes data from several sources. In this study, a consolidated database was created on tests conducted with wheeled vehicles operating in loose dry sand to evaluate existing soil mobility algorithms. The database included wheels of different diameters, widths, heights, and inflation pressures, operating under varying loading conditions. Nine technical reports were identified containing 5253 records, based on existing archives of laboratory and field tests of wheels operating in loose soils. The database structure was assembled to include traction performance parameters such as drawbar pull, torque, traction, motion resistance, sinkage, and wheel slip. Once developed, the database was used to evaluate and support validation of closed form solutions for these variables in the Vehicle Terrain Interface (VTI) model. The correlation between predicted and measured traction performance parameters was evaluated. Comparison of the predicted versus measured performance parameters suggests that the closed form solutions within the VTI model are functional but can be further improved to provide more accurate predictions for off-road vehicle performance.     

Effects of reduced inflation pressure and vehicle loading on off-road traction and soil stress and deformation state

Field experiments on off-road vehicle traction and wheel–soil interactions were carried out on sandy and loess soil surfaces. A 14 T, 6 × 6 military truck was used as a test vehicle, equipped with 14.00-20 10 PR tyres, nominally inflated to 390 kPa. Tests were performed at nominal and reduced (down to 200 kPa) inflation pressures and at three vehicle loading levels: empty weight, loaded with 3.6 and 6.0 T mass (8000, 11,600 and 14,000 kg, respectively). Traction was measured with a load cell, attached to the rear of the test vehicle as well as to another, braking vehicle. Soil stress state was determined with the use of an SST (stress state transducer), which consists of six pressure sensors. Soil surface deformation was measured in vertical and horizontal directions, with a videogrammetric system. Effects of reduced inflation pressure as well as wheel loading on traction and wheel–soil interactions were analyzed. It was noticed that reduced inflation pressure had positive effects on traction and increased stress under wheels. Increasing wheel load resulted in increasing drawbar pull. These effects and trends are different for the two soil surfaces investigated. The soil surface deformed in two directions: vertical and longitudinal. Vertical deformations were affected by loading, while longitudinal were affected by inflation pressure.     

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.     

A method for predicting the internal motion resistance of rubber-tracked undercarriages,Pt. 3. A research on bending resistance of rubber tracks

Optimizing the efficiency of rubber-tracked undercarriages requires models for calculating external and internal motion resistance, including the resistance resulting from bending of rubber tracks. The experiments on the bending resistance of rubber tracks and a new model of this phenomenon are discussed in this article. An empirical model of friction in bearings typically implemented in driving and idler wheels of rubber-tracked undercarriages is also presented. According to the sample computations carried out on the basis of these models, the efficiency of rubber-tracked undercarriages might be improved by minimizing the number and maximizing the diameter of idler wheels. Furthermore, it has been shown that increase in the initial tension and driving force transmitted by rubber tracks does not significantly affect bending resistance of these tracks; however, it results in increased friction in the driving and idler wheels’ bearings. Nevertheless, the higher the driving force transmitted by the rubber tracks, the higher the efficiency of rubber-tracked undercarriages. Consequently, since track systems of vehicles operating at relatively small drawbar pull will manifest exceptionally low efficiency, there is a serious need for optimizing them in terms of energy consumption.