Three-dimensional Tire Research Articles

A THREE-DIMENSIONAL TIRE REF MODEL IN ROLLING CONTACT WITH APPLICATION TO INTELLIGENT TIRES

ABSTRACT A new three-dimensional tire REF (ring on elastic foundation) model in rolling contact has been proposed and verified in this paper. The motivation is to apply this new physical model to the three-dimensional forces estimation for intelligent tires, which is currently a research hotspot in the automotive industry. The core contribution is the analytical solution of the three-dimensional tire deformation, stress, and forces in complex rolling contact. This new physical model is universal and efficient in linking intelligent tire signals with the solution results, which provides a powerful theoretical tool for intelligent tire modeling. Furthermore, the results have been validated by sensitivity analysis of key structural parameters on tire performance. In summary, through the modeling, verification, and application in case studies, it has been shown that the proposed methodology can be used for real practical three-dimensional forces estimation, which has the potential to simplify the vehicle state observer and benefit autonomous vehicles.

A THREE-DIMENSIONAL TIRE RING ON ELASTIC FOUNDATION MODEL IN ROLLING CONTACT WITH APPLICATION TO INTELLIGENT TIRES

ABSTRACT A new three-dimensional tire ring on elastic foundation model in rolling contact has been proposed and verified. The motivation is to apply this new physical model to the three-dimensional forces’ estimation for intelligent tires, a current research challenge in the automotive industry. The core contribution is the analytical solution of the three-dimensional tire deformation, stress, and forces in complex rolling contact. This new physical model is universal and efficient in linking intelligent tire signals with the solution results, thereby providing a powerful theoretical tool for intelligent tire modeling. Furthermore, the results have been validated by sensitivity analysis of key structural parameters on tire performance. In summary, through modeling, verification, and application in case studies, it has been shown that the proposed methodology can be used for real, practical three-dimensional forces estimation, offering the potential to simplify the vehicle state observer and benefit autonomous vehicles.

Structural analysis of a 3D dry-stack tyre wall by finite-discrete element method

This paper adopted a combined finite and discrete element method to investigate the structural performance of tyre walls built with tyre-encased-soil elements (TESEs). A full-scale three-dimensional tyre wall was simulated using Abaqus/Explicit, and the detailed procedures were discussed. The numerical model was verified against the experimental results, and the wall’s quasi-static structural responses under monotonic and cyclic loading were examined. Numerical modelling provided a deeper understanding of the tyre wall behaviour that was not captured experimentally due to time and equipment-related constraints, i.e., forces at the boundaries, wall permanent deformation profile, change in size of the gap openings during loading and unloading, as well as the stress distributions during different stage of loadings. From laboratory experimental observation, the tyre wall had a rotational gap opening mostly located at the mid-height portions due to the lateral loading, and this mechanism has been well replicated by the numerical modelling. The tyre wall was found similar to masonry walls regarding the force–displacement mechanism, however, tyre walls were distinct from masonry walls as the compressive crushing of a wall unit is an unlikely failure mechanism. The numerical modelling also showed that the forces at the boundaries enhanced the lateral load resistance of the wall. The results will encourage built environment professionals to adopt tyre walls in low-rise building constructions, which can assist in solving tyre recycling/storage problems and promote a more sustainable construction practice.

An approach for assessing the effects of porous materials on controlling the tire cavity resonance noise

Pasting porous material on the inner surface of a tire is an effective means to mitigate the tire cavity resonance noise. However, its performance is highly related to the material properties and geometry. This paper proposes an eigenvalue analysis approach based on the multi-domain boundary element method (MBEM) to evaluate this performance and further help determine the optimal parameters of the porous material lining in a tire. In this approach, the porous material is equivalent to a fluid, and the MBEM is used to model the sound fields in the air and equivalent fluid domains inside the tire cavity, based on which the eigenvalue analysis is conducted and the associated nonlinear eigenproblem is solved by using a contour integral method. The accuracy and validity of the proposed method are first verified by using a two-dimensional tire model with analytical solution, and then testified by comparing with the experimental results of a real tire lined with porous materials with different flow resistivities, thicknesses and widths. Furthermore, the effects of porous materials with different parameters are investigated based on the proposed method and the optimal parameters are suggested for a typical three-dimensional tire model.

Analysis of Contact Stresses and Rolling Resistance of Truck-Bus Tyres under Different Working Conditions

In this work, to analyse the changing characteristics of contact stresses in the tyre–pavement interface and the functional relationship between rolling resistance and the working conditions of truck-bus tyres, a three-dimensional tyre–pavement model is established and used to predict the distribution of contact stresses and rolling resistance under different working conditions of the tyre, comprising various tyre loads, inflation pressures, and velocities. Results show that the magnitude relationship between transverse and longitudinal contact stresses is related to rolling conditions, and overload and low tyre pressure are important contributors to the wear of the tyre shoulder. In addition, the proposed exponential equation presents a method that can be used to forecast rolling resistance related to the working conditions of the truck-bus tyre, and a similar method can be used to predict the rolling resistances of other types of tyres.

A rolling resistance estimate using nonlinear finite element numerical analysis of a full three-dimensional tyre model

In accordance with the worldwide trend for developing energy-efficient vehicles and meeting environmental regulations, there exists a large potential for decreasing energy losses due to tyre rolling resistance and significantly reduce fuel consumption and greenhouse gas emissions and also improve tyre tread durability. To achieve a quantitative estimate of tyre rolling resistance force, in the present paper, we carry out rolling resistance modelling in order to introduce a comprehensive relation for predicting rolling resistance force variations with speed taking into account the most influential parameters. To accomplish this goal, full three-dimensional finite element modelling of a visco-hyperelastic inflated rubber tyre under the deformation of vertical loading is performed and validated by making use of available test data. Free rolling simulations are performed and rolling resistance diagrams at various vehicle speeds and inflation pressures are extracted by analysing the results. According to the simulation results, a general formula is suggested to predict the tyre rolling resistance force in terms of the influential factors such as velocity, inflation pressure and tyre load. Results obtained using the proposed equation compared with recorded coast down test data clearly indicate excellent agreement between the results, confirming the validity of the relation. The presented solution can be built into models for comprehensive techno-economic evaluation of vehicle performance and fuel economy where changes in velocity, load and inflation pressure can be considered.

Efficient experimental identification of three-dimensional tyre structural properties

Modal testing is routinely applied to tyres for the identification of structural parameters and prediction of their vibration response to excitations. The present work focuses on the more demanding case of modal testing with the aim of constructing a full mathematical model of a tyre, appropriate for use in a generic time-based simulation. For this purpose, the less common free–free boundary condition is employed for the wheel, while the tyre belt is excited in all three directions, namely radial tangential and lateral. To improve efficiency, a novel partial identification method is developed for the mode shapes, whereby measured and predicted frequency responses are matched around distinct resonance peaks, while eliminating the effect of out-of-band modes. Axial symmetry of the tyre requires high purity mode shapes to avoid angular dependency of the tyre’s response. For this reason, experimental mode shapes are digitally filtered and combined with their orthogonal counterparts. Processed data reveal apparent repetition of selected mode shapes, and this is attributed to rim deflection.

Optimal tread design for agricultural lug tires determined through failure analysis

Agricultural lug tires, commonly used in tractors, must provide safe and stable support for the body of the vehicle and bear any additional load while effectively traversing rough, poor-quality ground surfaces. Many agricultural lug tires fail unexpectedly. In this study, we optimised and validated a tread design for agricultural lug tires intended to increase their durability using failure analysis. Specifically, we identified tire failure modes using indoor driving tests and failure mode effects analysis. Next, we developed a threedimensional tire model using the Ogden material model and finite element method. Using sensitivity analysis and response surface methodology, we optimised the tread design. Finally, we evaluated the durability of the new design using a tire prototype and drum test equipment. Results indicated that the optimised tread design decreased the tire tread stress by 16% and increased its time until cracking by 38% compared to conventional agricultural lug tires.

The Hohenheim Tyre Model: A validated approach for the simulation of high volume tyres – Part II: Validation

This publication series describes the development of the Hohenheim Tyre Model – an approach that considers the properties of high volume, agricultural tyres. The research project was conducted in accordance with the V-Model, which proposes a standardised development methodology for mechatronic systems. The previous publication described amongst others the model structure and parameterisation. This paper elucidates the validation, which is an essential part of the V-Model. Validation received special attention and is divided into three parts. First, three-dimensional tyre behaviour on level surfaces was investigated. Within the second step, single tyre behaviour is validated during obstacle passages. Similar obstacles were then used in the final step that shows up the correlation between measured and simulated whole vehicle behaviour. Throughout the validation avery high level of accuracy is achieved.

Mechanics based model for predicting structure-induced rolling resistance (SRR) of the tire-pavement system

The structure-induced rolling resistance of pavements, and its impact on vehicle fuel consumption, is investigated in this study. The structural response of pavement causes additional rolling resistance and fuel consumption of vehicles through deformation of pavement and various dissipation mechanisms associated with inelastic material properties and damping. Accurate and computationally efficient models are required to capture these mechanisms and obtain realistic estimates of changes in vehicle fuel consumption. Two mechanistic-based approaches are currently used to calculate vehicle fuel consumption as related to structural rolling resistance: dissipation-induced and deflection-induced methods. The deflection-induced approach is adopted in this study, and realistic representation of pavement–vehicle interactions (PVIs) is incorporated. In addition to considering viscoelastic behavior of asphalt concrete layers, the realistic representation of PVIs in this study includes non-uniform three-dimensional tire contact stresses and dynamic analysis in pavement simulations. The effects of analysis type, tire contact stresses, pavement viscoelastic properties, pavement damping coefficients, vehicle speed, and pavement temperature are then investigated.

Three-dimensional global pattern prediction for tyre tread wear

A theoretical tyre model was developed analytically using the proposed middle plane for predicting the three-dimensional global tyre wear qualitatively and quantitatively as a function of the road roughness and the dynamic characteristics of the vehicle. Diagrams of the tyre wear pattern across the tyre width and along the tyre circumference were drawn for different road roughnesses, camber angles and vehicle dynamic characteristics. The numerical results show how the three-dimensional tyre wear pattern varied when these factors changed. Numerical calculations also reveal that a unique wear pattern may be caused by the system’s inherent dynamic features, e.g. the modal shape. In addition, a sensitivity analysis shows that the slip ratio, the longitudinal stiffness, the tyre width, the velocity and the vertical force have the greatest effects on the frictional dissipation energy, in that order. With the established wear model, good tyre wear distribution predictions can be given qualitatively and quantitatively for the rolling surface of the tyre. Moreover, guidelines for obtaining less tyre wear are provided for tyre and car manufacturers.

Analytical Approach for Predicting Three-Dimensional Tire–Pavement Contact Load

Three-dimensional tire–pavement contact loads of two truck tires–-a new-generation wide-base tire (WBT) and a dual tire assembly (DTA)–-were measured and analyzed. Extreme and typical values of tire inflation pressure (552, 690, 758, and 862 kPa) and tire loading (26, 35, 44, 62, and 79 kN) were considered in the experimental program. The measurements were performed with the stress-in-motion Mk IV system at the Council for Scientific and Industrial Research in South Africa. Peak values in three directions were compared, and the importance of tangential contact stresses was highlighted. In addition, characteristic variations of the measurements in the longitudinal, transverse, and vertical directions were identified. A function depending on two regression parameters, applied load, and distance along the contact length was proposed to represent the contact load in the vertical and transverse directions. An analysis was performed on the measurements to obtain the regression parameters, and a simplified procedure was proposed to determine tire–pavement contact loads. The contact area and contact length of the WBTs and the DTA were also compared.

Effect of Surface Friction on Tire–Pavement Contact Stresses during Vehicle Maneuvering

AbstractAccurate modeling of tire–pavement contact behavior plays an important role in the analysis of pavement performance and vehicle stability control. A three-dimensional (3D) tire–pavement interaction model was developed using the FEM to analyze the forces and contact stresses generated during vehicle maneuvering (free rolling, braking/acceleration, and cornering). A pneumatic radial-ply tire structure with rubber and reinforcement was simulated. The steady-state, tire-rolling process was simulated using an Arbitrary Lagrangian Eulerian (ALE) formulation. An improved friction model that considers the effect of sliding speed on friction coefficients was implemented to analyze the effects of pavement surface friction on contact stresses, friction forces, and cornering forces. The results showed that the magnitudes and nonuniformity of contact stresses are affected by vehicle-maneuvering conditions. As the pavement surface friction increases, the tangential tire–pavement contact stresses at various roll...

Investigation of Tire-Soil Interaction with Analytical and Finite Element Method#

This article is devoted to the modeling of tire–soil interaction with the analytical and finite element method (FEM). Different from the traditional tire–soil interaction models in which the contact between tires and soils is described by nonlinear springs in the normal direction, the new analytical model added dampers accounting for the soil damping effects. A nonlinear three-dimensional tire–soil interaction model with the FEM, which takes into consideration the tire treads and belt/carcass layers, was validated by measuring tire vertical stiffness and contact stress. The conversion of the Modified Drucker-Prager/Cap soil model to the analytical soil model was demonstrated as well. The simulations for investigating the dynamic behavior of a bias tire running on the soft soil were performed. Good agreement was observed based on the simulation results obtained from these two tire–soil interaction models. However, experimental validation is necessary before the models can be further applied in the prediction of off-road vehicle dynamics.

Combined Effect of Three-Dimensional Contact Load and Thermal Gradients on the Cracking Performance of Heavy-Duty Asphalt Pavements

Top-down cracking is well recognized as a major distress for heavy-duty asphalt pavements, yet the mechanism is not fully understood. Studies have indicated that nonuniform tire–pavement contact stress may play a significant role in the initiation of top-down cracking, and thermal stress caused by the temperature gradient may contribute to the initiation and development of top-down cracking. These relevant factors were evaluated with a sophisticated three-dimensional viscoelastic finite element model that was developed for studying the cracking performance of heavy-duty flexible pavements under combined three-dimensional tire–pavement contact stress and thermal stress induced by the temperature gradient. It was found that the stress distribution in asphalt concrete layers continuously changed as the pavement was loaded because of the rheological behavior of the asphalt concrete. Significant maximum principal tensile stresses are present at the tire edge at the asphalt concrete surface, which may result in an accumulation of dissipated creep strain energy over time (or with a cumulative number of loads) and may eventually lead to crack initiation. Additionally, near-surface pavement responses associated with top-down cracking under three-dimensional tire–pavement contact pressure are found to be more severe than those from uniform contact pressure. In a comparison with pavements without thermal effect, the negative temperature gradient increases the potential for top-down cracking, and the positive temperature gradient increases the potential for bottom-up cracking. The study provides insight into crack mechanisms, which may improve current heavy-duty asphalt pavement design procedures.

Toward Using Tire-Road Contact Stresses in Pavement Design and Analysis

ABSTRACT: Optimization of road pavement design, especially close to the surface of the pavement, requires a more rational approach, which will inevitably include modeling of truck tire-road contact stresses. Various road-surfacing failures have been recorded as evidence that the traditional road pavement engineering tire model idealized by a single uniformly distributed vertical contact stress of circular shape may be inadequate to properly explain and assist in the design against road surface failures. This article therefore discusses the direct measurement of three-dimensional (3D) tire pavement contact stresses using a flatbed sensor system referred to as the “Stress-In-Motion” (SIM) system. The SIM system (or device) consists of multiple conically shaped steel pins, as well as an array of instrumented sensors based on strain gauge technology. The test surface is textured with skid resistance approaching that of a dry asphalt layer. Full-scale truck tires have been tested since the mid-1990s, and results show that 3D tire contact stresses are nonuniform and that the footprint is often not of circular shape. It was found that especially the vertical shape of contact stress distribution changes, mainly as a function of tire loading and associated tire inflation pressures. In overloaded/underinflated cases, vertical contact stresses are the highest toward the edges of the tire contact patch. Higher inflation pressures at lower loads, on the other hand, result in maximum vertical stresses toward the center portion of the tire contact patch. These differences in shape and magnitude need to be incorporated into modern mechanistic-empirical road pavement design tools. Four different idealized tire models were used to represent a single tire type to demonstrate effects of tire modeling on the road pavement response of a typical South African pavement structure incorporating a relatively thin asphalt surfacing. Only applied vertical stress was used for the analyses. It was found that the fatigue life of the road surface layer can be reduced by as much as 94% and strain energy of distortion be increased by a factor of 2.8, depending on the characteristics of the tire model input selected for road pavement design and analysis.

Modeling and validation of off-road vehicle ride dynamics

Increasing concerns on human driver comfort/health and emerging demands on suspension systems for off-road vehicles call for an effective and efficient off-road vehicle ride dynamics model. This study devotes both analytical and experimental efforts in developing a comprehensive off-road vehicle ride dynamics model. A three-dimensional tire model is formulated to characterize tire–terrain interactions along all the three translational axes. The random roughness properties of the two parallel tracks of terrain profiles are further synthesized considering equivalent undeformable terrain and a coherence function between the two tracks. The terrain roughness model, derived from the field-measured responses of a conventional forestry skidder, was considered for the synthesis. The simulation results of the suspended and unsuspended vehicle models are derived in terms of acceleration PSD, and weighted and unweighted rms acceleration along the different axes at the driver seat location. Comparisons of the model responses with the measured data revealed that the proposed model can yield reasonably good predictions of the ride responses along the translational as well as rotational axes for both the conventional and suspended vehicles. The developed off-road vehicle ride dynamics model could serve as an effective and efficient tool for predicting vehicle ride vibrations, to seek designs of primary and secondary suspensions, and to evaluate the roles of various operating conditions.

Finite Element Analysis of Performance for Radial Tires, Part I: Model, Material Constants

As an economical, resultful and direct method, finite element method has been used broadly to simulate tire performance. However, much of the published research shows few detail model or no material constants. It is difficult for readers to judge if the result is reliable. To ensure simulation results are credible, the material constants, simulation model and analysis method must be dependable. In the current work, the three-dimensional radial tire models, finite element models of free and ground-touching tires, were built and showed in detail. The material constants measured from experiments in a tire factory were published. Using the well-known finite element simulation software ANSYS, the current research found some interesting results which will be presented in Part II.

Evaluation of Near-Surface Stress States in Asphalt Concrete Pavement

A sophisticated three-dimensional (3-D) tire model was placed directly on a three-layer asphalt concrete (AC) pavement system to form a 3-D tire–pavement contact model. The model was then verified with measured contact stresses and was used to investigate near-surface stress states in the AC layer. When compared with the traditional uniform vertical loading model, the 3-D tire–pavement contact model produced stress states not only higher in magnitude but also more variable in distribution. The 3-D tire–pavement contact model produced much higher principal tensile stress and maximum shear stress near the tire edge; the increased stress was a possible explanation for instability rutting and associated top-down cracking. A critical shear plane was developed for the top 50 mm of the AC layer by using a p-q diagram, and the tire–pavement contact model produced a much higher shear yield percentage.

Estimation of a three-dimensional tyre footprint using dynamic soil–tyre contact pressures

A method for estimating the three-dimensional (3D) footprint of a 16.9R38 pneumatic tyre was developed. The method was based on measured values of contact pressure at the soil–tyre interface and wheel contact length determined from the contact pressures and the depths and widths of ruts formed in the soil. The 3D footprint was investigated in an area of the field where the pressure sensors of the tyre passed in a soft clay soil. The tyre was instrumented with six miniature pressure sensors, three on the lug face and the remaining three on the under-tread region between two lugs. The instrumented tyre was run at a constant forward speed of 0.27 m/s and 23% slip on a soft soil, 0.48 MPa cone index, 25.6% d.b. moisture content for four wheel load and tyre pressure combination treatments. The 3D footprint assessment derived from soil–tyre interface stress used in this research is a unique methodology, which could precisely relate the trend profile of the 3D footprint to the measured rut depth. The tyre–soil interface contact pressure distributions results showed that as inflation pressure increased the soil strength increased significantly near the centre of the tyre as a compaction increase sensed with the cone penetrometer.