A review on traction prediction equations

A variety of methods, ranging from theoretical to empirical, which have been proposed for predicting and measuring soil-vehicle interaction performance are reviewed. A single wheel tyre testing facility at Indian Institute of Technology, Kharagpur, India, was used to check the applicability of the most widely used traction models, for tyres used in Indian soil conditions. Finally, the coefficients of traction prediction equations developed by Brixius [16] were modified to fit traction data obtained from the testing of the tyres in the Indian soil conditions.     

Development of a tyre traction testing facility

An experimental setup comprising up of an indoor soil bin, a single wheel tester (SWT), a soil processing trolley, a drawbar pull loading device and an instrumentation unit was developed to perform traction tests in the soil bin to study the effect of soil, tyre and system parameters on the performance of tyres. The design of the single wheel tester was such that the dynamic weight reaction force is equal to that measured statically. It is a simple wheeled device, capable of testing tyres of up to 1.5 m in diameter, vertical force up to 19 kN, net pull up to 7.2 kN, torque up to 5.5 kN m, and speed up to 3.5 km/h.     

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.     

Motion resistance measurements on large lug tyres

Motion resistance of tyres directly contribute to the operational costs of all vehicles. Advances in the design and simulation of large off-road vehicles (construction, mining, agriculture etc.) have increased the need for accurate models of large off-road tyres. Vehicle OEMs use coast down and drawbar pull tests to determine the motion resistance of tyres used. Drum test rigs and motion resistance test trailers can also be used to determine motion resistance. Most research on motion resistance to date have been conducted on passenger car tyres with on-road truck tyres coming into focus. Motion resistance studies on agricultural tyres traversing over deformable terrain have been conducted in the past. However as more off-road vehicle are being used on-road OEMs of off-road vehicle are infesting in motion resistance measurements on non-deformable terrain. This paper compares different methods used to measure the motion resistance of a large lug tyre, as used in agricultural applications, on non-deformable terrain. Some basic considerations that need to be taken into account are the very low longitudinal forces that need to be measured compared to the large vertical load carried by the tyre and tyre operating conditions.     

Effect of test method on winter traction measurements

Traction on winter surfaces was measured using three instrumented vehicles, each designed to measure traction for a different purpose: vehicle mobility research (CRREL instrumented vehicle), commercial tire testing (Uniroyal-Goodrich traction tester), and airport runway safety (Saab friction tester). The traction measured with each method is comparable but there are systematic differences due to the effects of the surface materials and test and analysis techniques. This comparison serves as the basis for collaboration between the various traction testing communities and illustrates the need for well documented, standard test and analysis procedures for traction testing and evaluation.     

Tractive characteristics of radial ply and bias ply tyres in a California soil

Four tyres (18.4-38, 18.4R38, 14.9-28, 14.9R28) were tested using the UCD single wheel traction tester. Each tyre was tested at two different inflation pressures and three different vertical loads at each inflation pressure. All tests were conducted in a well tilled Yolo loam soil. A dimensional analysis procedure was used to design and analyse the experiment. Two models were considered: (A) using inflation pressure as a variable, and (B) using tyre deflection as a variable. The effect of tyre type, tyre size, tyre inflation pressure and dynamic load on (1) net traction ratio at 20% slip and (2) average tractive efficiency in the 0–30% slip range were investigated using an ANOVA technique. An estimate of the possible energy savings due to the use of radial ply tyres instead of bias ply tyres in California agriculture was made.     

“Wheels vs. tracks” – A fundamental evaluation from the traction perspective

The issue of wheeled vehicles vs. tracked vehicles for off-road operations has been a subject of debate for a long period of time. Recent interest in the development of vehicles for the rapid deployment of armed forces has given a new impetus to this debate. While a number of experimental studies in comparing the performances of specific wheeled vehicles with those of tracked vehicles under selected operating environments have been performed, it appears that relatively little fundamental analysis on this subject has been published in the open literature, including the Journal of Terramechanics. This paper is aimed at evaluating the tractive performance of wheeled and tracked vehicles from the standpoint of the mechanics of vehicle–terrain interaction. The differences between a tire and a track in generating thrust are elucidated. The basic factors that affect the gross traction of wheeled and tracked vehicles are identified. A general comparison of the thrust developed by a multi-axle wheeled vehicle with that of a tracked vehicle is made, based on certain simplifying assumptions. As the interaction between an off-road vehicle and unprepared terrain is very complex, to compare the performance of a wheeled vehicle with that of a tracked vehicle realistically, comprehensive computer simulation models are required. Two computer simulation models, one for wheeled vehicles, known as NWVPM, and the other for tracked vehicles, known as NTVPM, are described. As an example of the applications of these two computer simulation models, the mobility of an 8 × 8 wheeled vehicle, similar to a light armoured vehicle (LAV), is compared with that of a tracked vehicle, similar to an armoured personnel carrier (APC). It is hoped that this study will illustrate the fundamental factors that limit the traction of wheeled vehicles in comparison with that of tracked vehicles, hence contributing to a better understanding of the issue of wheels vs. tracks.     

Parameterization and modelling of large off-road tyres for ride analyses: Part 2 – Parameterization and validation of tyre models

Every mathematical model used in a simulation is an idealization and simplification of reality. Vehicle dynamic simulations that go beyond the fundamental investigations require complex multi-body simulation models. The tyre–road interaction presents one of the biggest challenges in creating an accurate vehicle model. Many tyre models have been proposed and developed but proper validation studies are less accessible. These models were mostly developed and validated for passenger car tyres for application on relatively smooth roads. The improvement of ride comfort, safety and structural integrity of large off-road vehicles, over rough terrain, has become more significant in the development process of heavy vehicles. This paper investigates whether existing tyre models can be used to accurately describe the vertical behaviour of large off road tyres while driving over uneven terrain. [1] Presented an extensive set of experimentally determined parameterization and validation data for a large off-road tyre. Both laboratory and field test are performed for various loads, inflation pressures and terrain inputs. The parameterization process of four tyre models or contact models are discussed in detail. The parameterized models are then validated against test results on various hard but rough off-road terrain and the results are discussed.     

Overview of cold regions mobility modeling at CRREL

Over the last several decades, the Cold Regions Research and Engineering Laboratory (CRREL) has extensively tested and analyzed issues related to vehicle performance in winter. Using this knowledge and the experimental database, models were developed to capture the important elements for cold regions mobility performance. These models span a range of resolutions and fidelities and include three-dimensional finite element models of tire–terrain interaction, vehicle dynamics models of vehicles on winter surfaces, semi-empirical cold regions algorithms for winter performance within the NATO reference mobility model (NRMM), all-season vehicle performance in force-on-force war-gaming simulations, and vehicle–surface interaction for real-time vehicle simulators. Each of these types of models is presented along with examples of their application.     

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.     

Laboratory experimental study of tire tractive performance on soft soil: Towing mode,traction mode,and multi-pass effect

Tire tractive performance, soil behavior under the traffic, and multi-pass effect are among the key topics in the research of vehicle off-road dynamics. As an extension of the study (He et al., 2019a), this paper documents the testing of a tire moving on soft soil in the traction mode or towing mode, with a single pass or multiple passes, and presents the testing results mainly from the aspects of tire tractive performance parameters, soil behavior parameters, and multi-pass effect on these parameters. The influence of tire inflation pressure, initial soil compaction, tire normal load, or the number of passes on the test data has been analyzed; for some of the tests, the analysis was completed statistically. A multi-pass effect phenomenon, different from any phenomenon recorded in the available existing literature, was discovered and related to the ripple formation and soil failure. The research results of this paper can be considered groundwork for tire off-road dynamics and the development of traction controllers for vehicles on soft soil.     

Modelling power requirement for traction tyres with zero sinkage

A model was developed by dimensional analysis to predict the gross traction at zero net traction for traction tyres (11.2–28, 12.4–28, 13.6–28) on a hard surface. Different parameters that affect the torque requirement, namely tyre size, tyre deflection, axle load, and rolling radius, were considered for the analysis. Experiments were conducted to study the effect of various wheel and system parameters on torque and energy consumed per unit distance travelled. The model developed predicts the torque requirement in an acceptable range and can be used as a reference for further traction studies of these tyres in various soils.     

Experimental observations of tyre deformation characteristics on heavy mining vehicles under static and quasi-static loading

Due to large sidewall and bead thicknesses, multi-piece rims are necessary for use with large off-the-road (OTR) tyres. This paper presents the testing protocol and observed load/deflection and vertical/sidewall deflection characteristics of three Goodyear OTR tyre assemblies, namely, (1) a radial 29.5R29 (2) a bias-ply 29.5-29, and (3) a bias-ply 26.5-26. Localized tyre deformations and rim displacements were measured using optical displacement transducers and post-processing high-speed camera images using digital image analysis software. A validation analysis illustrated a maximum difference of 4.05% of vertical wheel displacements between the aforementioned methods. Quasi-static tests show the maximum values of vertical rim displacement and lateral tyre deflection are in the range of 72.2–78.9 mm and 23.3–27.1 mm, respectively, for a severe excitation condition. Differences ranging from 0.2% to 21.5% for maximum vertical and lateral tyre deflections were found between static load tests and engineering data provided by the tyre manufacturer. Linear relationships were observed for both vertical wheel displacement and lateral tyre deflection versus load for all tests. This study demonstrates a thorough methodology to study deflection characteristics of heavy duty OTR tyres and the collected data could be very useful in the development of numerical models of wheel and tyre assemblies for mining vehicles.     

Comparing the NRMM (VCI), MMP and VLCI traction models

A military vehicle’s ability to traverse soft soil is a significant aspect of its performance. It is therefore important to be able to accurately predict and compare the soft soil performance of wheeled and tracked vehicles. The paper compares the vehicle cone index (VCI) model used in the NATO Reference Mobility Model (NRMM) with the mean maximum pressure (MMP) and vehicle limiting cone index (VLCI) models. The wheeled vehicle models compare reasonably well but the VLCI model for tracked vehicles indicates markedly higher limiting go/no-go soil strengths compared to the VCI and MMP models. Some of the relationships used in the VCI model appear rather irrational and could be significantly simplified. There is a considerable lack of reliable experimental data for tracked vehicles especially in the low traction region.     

Tyre Wear Model: Validation and Sensitivity Analysis

Due to their many economic and ecological implications the possibility to predict tyre wear is of major importance to tyre manufacturers, fleet owners and governments. Based on these observations, in 2000 a three-year project named Tyre and Road Wear and Slip assessment (TROWS) was started. One of the TROWS objectives was to provide a tool able to numerically predict tyre global wear as well as to qualitatively determine the wear distribution. The proposed methodology combines a mathematical model of the tyre with an experimentally determined local friction and wear law. Thus, tyre abrasion due to each single manoeuvre can be determined. Full-scale experimental tests were carried out with two Peugeot 406 cars on a public road course in Italy. Each car was equipped with a different set of tyres: one car was equipped with four all-season tyres (from now on called A tyres) and the other car was equipped with four winter tyres (from now on called B tyres). Both sets of tyres had a 195/65 R15 size. The collected data was used to validate the model. The methodology proved to give qualitatively good tyre wear predictions.     

Analytical approach for the prediction of steady state tyre forces and moments under different normal pressure distributions

In general, all primary as well as disturbing forces acting on a vehicle (with the exception of aerodynamic forces) are generated at the tyre–road interface. The small size pneumatic tyres presented in this work are mostly used in lightweight vehicles like scooters, motor cycles and 3-wheelers that are extensively used for intercity transportation applications in India and other developing countries. Analytical approach is more advantage than experimental work due to many factors like it involves less cost, minimum time and little effort. Hence, Analytical tyre models are developed based on various normal pressure distributions with tyre contact patch as rectangle at the middle with part of circles at the ends. The tyre longitudinal and lateral force characteristic equations for proposed tyre models are developed. In addition, the equations for self – aligning moment and overturning moment characteristics for all tyre models are also derived. Results of proposed tyre models in the present study are compared with well-established earlier tyre models [4], [5], [6]. From the force and moment characteristics of all tyre models, unsymmetrical trapezoidal pressure distribution tyre model gives better performance than other models due to which better lateral stability of the vehicle can be obtained.     

UPM indoor tyre traction testing facility

Universiti Putra Malaysia (UPM) tyre traction testing facility was designed and developed to spearhead fundamental research on traction mechanics with high-lug agricultural tyres on tropical soils. This available facility consists of a moving carriage with a cantilever-mounted tyre that moves in either forward or reverse directions on rails well above a soil tank. The present facility set-up was able to operate in either: (a) towing test mode for tyre motion resistance studies, or (b) driving test mode for tyre net traction and tractive efficiency studies. The test tyre on the moving carriage under the towing test mode was made to rotate and engage onto the soil surface in the tank through a chain drive system. Under the driving test mode, the test tyre on the moving carriage was powered to rotate by a motor and a gearbox system with an additional pull provided by a cable-pulley mechanism connected to a tower with hanging dead weights. All controls on the moving carriage were activated from the main control console. Respective transducers were positioned at various localities within and interfaced to a data acquisition system to measure tyre horizontal and vertical forces, tyre sinkage, tyre speed and motion carriage speed. The data acquisition system was able to receive the measured signals in real time, display on the monitor screen and record into its CPU storage memory. Static calibration tests on various associated transducers showed excellent linearity with coefficients of determination (r²) of close to 1. The developed facility was successfully tested to determine motion resistance and net traction ratios for high-lug agricultural tyre at the recommended inflation pressure on sandy clay loam soil.     

The tractive performance of a wide, low-pressure tyre compared with conventional tractor drive tyres

The NIAE single-wheel test vehicle was used to compare the tractive performance of a 67 × 34.00-25 tyre at 0.34 bar inflation pressure with that of 20.8–38 radial tyre at 0.6 bar inflation pressure and a similar 18.4–34 tyre at 0.8 bar inflation pressure. All tyres had similar tread patterns and were tested at the same vertical load of 2250 kg. The best performance was achieved by the 20.8–38 tyre. There was little difference in performance between the other two tyres. When compared with empirical predictions of performance derived from previous work, the two narrower tyres were found to perform approximately as predicted, but the performance of the wide, low-pressure tyre was considerably worse than predicted. This was thought to be due to bulldozing, because of the great width and increased wheel-slip caused by deformation of the soft side-wall and also due to the relatively short ground contact area. It was concluded that wide, low-pressure tyres are only suitable for fitting to vehicles requiring a very low draught capability.     

Traction data analysis in reference to a unique zero condition

The lack of a unique definition for the zero condition leads to innumerable zero conditions resulting in different amounts of net traction at the same value of slip. In this paper, an attempt has been made to discuss various aspects of different zero conditions and finally result in a unique definition of the zero condition. Based on this definition, a traction prediction model using mobility number approach has been developed to evaluate the performance of tractor tyres in sandy clay loam soils.     

Performance prediction of animal drawn vehicle tyres in sand

Four animal drawn vehicle (ADV) tyres of 5.00–19, 6.00–19, 7.00–19 and 8.00–19 sizes were tested in sand under various but controlled conditions in an indoor soil bin. A tyre test carriage with four-bar parallel linkage was developed for accommodating a single wheel of different sizes. Performance tests were conducted at five levels of inflation pressure and load. The sand compaction level was varied in the range of 3.4–4.5 MPa/m and forward speed of the test carriage was maintained at 3.1 km/h. Performance of the tyres 7.00–19 and 8.00–19 was identical and offered less rolling resistance as compared to other tyres. However, their use in camel carts may not be recommended beyond the payload of 6 kN on single wheel with inflation pressure and sand compaction range of 172–379 kPa and 3.4 –4.5 MPa/m, respectively. Based on the experimental results, empirical models were developed to predict the performance of tyres. The accuracy of prediction of the developed empirical models was compared with that of existing semi-empirical approaches. Model with sand mobility number considered relatively simple and convenient to use in the field and yields reasonably good prediction for rolling resistance and sinkage.