Tire Response Research Articles

Finite element modeling and analysis of tire creep test

Abstract The tire is one of the most complex components of the vehicle, which justifies strict standards and regulations set by governments worldwide to ensure the performance, durability, and reliability of tires approved for use in the transport sector. Among these requirements, tire durability testing involves the assessment of short-and long-term tire response to determine optimum conditions of use and service life. Therefore, this paper focuses on the creep performance of tires using the finite element method in ABAQUS. As a case study, a selected tire with visco-hyperelastic rubber compounds and linear elastic reinforcements is subjected to a constant prescribed force for a period of time, and the resulting strain evolution is recorded till the release of the applied load. Several parameters are accounted for, such as the inflation pressure, material characteristic times, and load amplitude. The post-processing of results enabled the prediction of the overall creep response of the tire over time with respect to the prescribed load. The knowledge gained in this study can be exploited to predict tire failure caused by excessive strain and pinpoint the areas of the tire that are the most exposed to creep failure.

A numerical study of the influence of the choice of rubber material behavior on the static response of tires

A numerical study of the influence of the choice of rubber material behavior on the static response of tires

Influence of Tire-Enveloping Model Complexity on High-Frequency Simulations

ABSTRACT Race tires are subject to high speeds and high vertical loads during cornering. They are also subject to extreme stress when they are driven over high-frequency and low-amplitude curbs, often leading to tire failures. Research and development by D. C. Davis and P. W. A. Zegelaar has shown that when the tire moves over high-frequency, low-amplitude, and short-wavelength obstacles, it exhibits obstacle-enveloping properties. Tire response over such obstacles includes vertical force variation, longitudinal force variation, and rotational speed variation. Additionally, such road inputs excite tire belt dynamics that include high-frequency modes. Therefore, a single-contact-point model is no longer sufficient to predict tire response over such obstacles. To better capture the tire obstacle-enveloping behavior, advanced contact patch models such as the tandem-cam model by P. W. A. Zegelaar, the radial–interradial spring model by J. M. Badalmenti and G. R. Davis Jr., and the flexible ring model by S. Gong have been developed. To capture high-frequency tire belt dynamics, the rigid-ring model has been developed by P. W. A. Zegelaar. Previous work combines the rigid-ring model with the tandem-cam model to capture obstacle-enveloping behavior and tire belt dynamics up to 60–100 Hz. This paper presents a comparative study of different tire–road contact models to simulate high-frequency curbs typically found at racetracks. The curb profile of the Singes corner at the Paul Ricard racetrack is chosen for simulations as it is known to be extremely demanding on the tires, often causing failures. An advanced four-wheel model is used to simulate a race car at high speeds. Metrics to quantify the tire response over these high-frequency curbs are created and an investigation is conducted to quantify the influence of tire model complexity on the metrics.

Tire Performance and Testing under Longitudinal and Combined Slip States: Induced vs Resultant Wheel-Related Slip

ABSTRACT Tires influence many overall vehicle characteristics, including safety, performance, comfort, and handling. Testing is needed to characterize tires for the selection of original equipment manufacturers submissions as well as for the development of other suspension and chassis components. The reality that tire responses are highly nonlinear and change significantly with temperature, wear, and surface pairing makes testing to adequately characterize tires for vehicle development difficult. Furthermore, achieving robust, repeatable braking and driving measurements is particularly challenging. Unlike cornering tests, the test rig input is directly opposed to the tire response vector. Moreover, using an estimated parameter (e.g., slip ratio) as a control value prohibits a clear distinction between the linear test rig input and the nonlinear tire response. In this paper, the influence of the wheel-related slip control on tire performance under longitudinal and combined slip conditions is investigated. Two different tire types are measured in a laboratory environment on an MTS Flat-Trac CT+ tire test rig. A variety of test procedures are used to consider the influence of slip and torque rates under different operating conditions (e.g., wheel loads). A recommendation is given for a low-wear and cost-efficient testing methodology for an improved assessment of tire longitudinal and combined slip characteristics by using a linear test rig input.

A Study on Self-Sustained Vibrations of a Tire Operating above Peak Friction

ABSTRACT When a tire operates at a side slip level above peak friction, large vibrations in the produced forces and moments are observed. In the lateral direction, these vibrations are typically centered at frequencies close to 50 Hz and significantly affect the force that is produced by the tire. As an example, high dynamics vehicle maneuvers with an electronic stability program control system in the loop can be affected by this behavior. To accurately reproduce the tire response in these operating conditions, it is important to employ a model that can capture this phenomenon. Based on analysis of nonlinear, unstable systems and limit cycle phenomenon, a theory is presented that provides a physical background for the source of vibrations. The theory also gives insight in how the frequency and amplitude of the vibrations are influenced by the tire physical characteristics and the operating conditions. It is found that the most dominant characteristics are the shape of the steady-state force response of the tire around peak friction, the contact patch mass, the carcass damping and stiffness. Simulations with physical models of different complexity levels, as well as with the commercial Simcenter Tire MF-Tyre/MF-Swift tire software model, validate the theory and demonstrate how the vibrations can be reproduced in a simulation environment. The simulation results are compared with tire measurements in different operating conditions, validating the exposed theory and employed models.

Implementation of a finite element modelling strategy for the prediction of aircraft tyre response

This paper presents the finite element modelling (FEM) strategy to identify the structural response of aircraft tyres under quasi-static and taxiing load conditions. The tyre FEM was developed to simulate the aircraft tyre/ground interaction for a range of inflation pressures under vertical, lateral, longitudinal, torsional, yawed and un-yawed rolling. A thorough comparison for validation purposes is made between the test and simulation data extracted from the FEM. The reinforcement plies of the tyres are modelled in a computationally efficient manner whilst also considering the variable fibre volume fractions and ply discontinuities within the tyre. The accurate material characterisation at coupon level combined with the overall modelling approach allowed most simulated responses to match the experimental stiffness within 12% against best fit curves of similar tyre types and within 5% for the majority of test comparisons.

A novel theoretical model of tire in-plane dynamics on uneven roads and its experimental validation

The dynamic response of tires directly affects the handling stability and ride comfort of a vehicle, which in turn determines the vehicle ride, handling, and driver perception. Modeling and simulation of tire dynamics typically require a reasonable computational cost while ensuring proper accuracy. In this study, a novel theoretical model, the coupled rigid–flexible ring model, is presented to analyze the characteristics of the in-plane dynamic responses of tires on uneven road surfaces. The proposed new method consists of three primary sub-models: an elastic contact algorithm featured by a flexible ring model, rolling/vibration dynamics represented by a rigid ring model, and an internal-force transmission algorithm linking the rigid and flexible ring models. In this way, the proposed new method has the merits of both high accuracy up to 150 Hz and low computing cost. A contact algorithm based on the two-dimensional flexible ring provides a pressure distribution on the tire–road contact patch and the length of the footprint under different vertical loads. The transient dynamic response is then estimated by combining the rigid ring model with the flexible ring model. The accuracy of the contact algorithm and the transient responses are validated against experimental radial stiffness and the over-cleat tests respectively. The results show that the in-plane dynamics of the tire can be predicted well. In addition, this model is extended to the analysis of the low-speed uniformity of tires with geometric defects and is validated experimentally. It indicates that the novel proposed model offers many application scenarios and extension possibilities.

The Unsteady-State Response of Tires to Slip Angle and Vertical Load Variations

The tire is the only part that connects the vehicle and the road surface. Many important properties of vehicles are related to the mechanical properties of tires, such as handling stability, braking safety, vertical vibration characteristics, and so on. Although a great deal of research on tire dynamics has been completed, mainly focusing on steady-state tire force and moment characteristics, as well as linear unsteady force characteristics, less research has been conducted on nonlinear unsteady characteristics, especially when the vertical load changes dynamically. Therefore, the main purpose of this paper is to improve the tire unsteady-state model and verify it by experiment. To achieve this goal, we first study the nonlinear unsteady tire cornering theoretical model and obtain clear force and torque frequency response functions. Then, based on the results of the theoretical model, a high-precision and high-efficiency semi-physical model is developed. Finally, model identification and accuracy verification are carried out based on the bench test data. The model developed in this paper has high accuracy, and it significantly improves the expression of the aligning torque, which helps to improve the virtual simulation of transient conditions, such as vehicle handling and dynamic load conditions.

A Three-Dimensional Ring Model for Uncertainty Quantification in Natural Frequencies and Sound Radiation Characteristics of Tires

Material and geometrical parameters of tires involve some degree of uncertainty mainly related to production processes. Accordingly, the associated structural responses are affected by these uncertainties. In this study, a novel theoretical ring model is presented to describe the in-plane and out-of-plane vibrations as well as the steady-state response of tires, and then to evaluate the influence of the uncertainties in structural parameters on the natural frequencies and the sound radiation characteristics under uncertain excitations. The Hamilton principle is applied here to derive the governing equations. The modal superposition method is used to calculate the steady-state response of the tire. In the sound radiation analysis, the in-plane and out-of-plane bending and torsional vibrations under a set of harmonic unit forces and moments are treated as the source of noise generation. On this basis, the generalized polynomial chaos expansion method is then adopted to evaluate the influence of the uncertainty on the natural frequencies and the sound power. To obtain the unknown coefficients of the expansions, the nonintrusive probabilistic collocation method is employed. Moreover, considering the concept of linear independence of vectors, the number of collocation points is reduced. It is applied to investigate the impacts of the elastic and structural uncertainties on the natural frequencies of the tire. This yields an efficient simulation in terms of computational costs. Finally, the distributions of the sound power due to the forced vibration under the random concentrated line forces are given.

Effects of Different Tire Operating Conditions on Transient Lateral Tire Response

ABSTRACT The concept of the relaxation length is often used to describe a tire's transient response. This paper investigates how the transient response changes under different operating conditions. Through the measurement of tire forces and tire deformations during transient maneuvers performed on an indoor flat-belt tire test machine, experimental data were used to calculate various tire stiffnesses and the associated relaxation lengths using a novel method via optimization. With this methodology, the effects of tire load, inflation pressure, speed, and temperature on these stiffnesses and the relaxation length have been identified. The mechanisms behind these effects are discussed with a particular focus on the influence of temperature.

A novel brush-model with flexible carcass for transient interactions

In this investigation, a double brush model, which aims at predicting both the longitudinal and the lateral tyre characteristics during transient phases, is developed. The solution of the tyre-road contact equation is provided by using the method of characteristics and a time delay of the bristles deformation with respect to the time is also introduced by modelling both the tyre tread and the carcass by means of viscoelastic and elastic elements, respectively. The temporal trend of some quantities of interest such as the adherence length and the critical slip value is then obtained as explicit function of the time or, equivalently, of the travelled distance. A preliminary analysis is carried out with reference to the transition from a pure rolling condition to accelerating or braking ones. The tyre response to a constant lateral slip input is also comprehensively discussed. Finally, in the case of consecutive manoeuvre, the model shows that all the generalised forces exerted by the road on the tyre vary continuously by introducing a finite increase in the slip parameter. Several examples are presented in order to demonstrate the applicability of the proposed model to severe braking or handling dynamic scenarios.

Frequency Domain Analysis of Tractor Tyre Enveloping Properties

Main source of vibration excitation for off-road vehicles are ground profile undulations. Most unprepared terrains are characterized by wavelength of unevenness that is of the order of magnitude of the contact length between tire and ground, so that, due to its shape and elasticity, tire actually behaves as geometric low-pass filter transforming real road profile geometry into effective vehicle vibration excitation. Since this effective profile represents real vehicle excitation, it is of interest to study this filtering behaviour in more depth. In this work, investigation of this kind of tire response has been studied for agricultural tractor tire rolling quasistatically over singular road obstacle. Frequency analysis of road excitation and tyre response was carried out in order to obtain their spectra and frequency response function magnitude of the tyre as filter was obtained by dividing input by output spectra. Final assessment of frequency response function magnitude was obtained by averaging instances obtained for different dimensions of input obstacles.

The response of two-wheeler tires to three-body wear phenomena by experimental simulation of off-road terrains

The operation of two wheelers frequently encounters off-road terrain comprising loose particles of sand and soil, which setup three-body abrasive wear phenomena affecting the tire life. To evaluate the response of two-wheeler tires on such terrains, the dry abrasive wear behavior of two-wheeler tires was experimentally determined using a three-body wear test apparatus. Three different mixtures of sand and granite dust of varying grit size, 100, 200, and 300 µm, were employed to represent the abrasive cluster, typical of the varying roughness on off-road terrains. Taguchi’s L27 (33) orthogonal array was applied to analyze the specific wear rate as a response to three parameters—load, speed, and road roughness—separately for front and rear two-wheeler tires. Variation of hardness and wear pattern observation for the front and rear tires were carried out to oversee the surface deterioration. A numerical model based on abrasive grit-tire surface interaction was developed for comparison with the experimental results.

Finite Element Based Analysis of Reinforcing Cords in Rolling Tires: Influence of Mechanical and Thermal Cord Properties on Tire Response

ABSTRACT Tires of passenger cars and other special tires are made of rubber compounds and reinforcing cords of different type to form a composite with distinct mechanical and thermal properties. One of the major load cases is the steady state rolling operation during the tire's service. In this contribution, attention is paid to the strain and force state as well as the temperature distribution in the carcass cord layer of a steady state rolling tire. A simple benchmark tire geometry is considered, which is made of one rubber compound, one carcass cord layer (textile), and two belt cord layers (steel). From the given geometry, two tire designs are derived by using two distinct types of reinforcing cords (polyester and rayon) for the carcass cord layer. Subsequently, the two tire designs are subjected to three load cases with different inner pressure, vertical force, and translational velocity. The strain and the force state as well as the temperature distribution in the cords are computed via a thermomechanically coupled finite element simulation approach for each tire design and load case. To realistically capture the thermomechanical behavior of the cords, a temperature- and deformation-dependent nonlinear elastic cord model is proposed. The cord model parameters can be directly derived from data of cord tensile tests at different temperatures. Finally, cord design parameters (minimum and maximum strains and forces in the cords, maximum strain and force range per cycle, and maximum cord temperature) are summarized and compared. Additionally, the global vertical stiffness and the rolling resistance for each tire design are addressed.

Design of Quarter Car Test Bench to Measure Forces on the Tire Contact Path

Suspension system that located between vehicle body and wheels are designed to absorb shock from road surface. The dynamic behavior of the suspension and tire is depends on many factors. Some of the main factors are the vehicle load, speed, steering angle and the magnitude of the elasticity of the tire. The position of the tire-road contact is also always changed when the vehicle running make it difficult to observe the dynamic response of tires. To overcome this problem, in this paper, an in-door test-rig model is designed and evaluated experimentally. This study was conducted by five methods, namely; design, simulation, production, and experimentally test. The dynamic response evaluated includes geometric change of tires and the change of camber angle. The model build consist of framework components, the sprung mass as a representation of aquarter car body and un-sprung mass which are components of the suspension system, wheels and tires. The results show that the proposed design construction is not only saved to handle all forces and moments but alsocan fulfilled functions to simulate the dynamic response of ¼ car model.

Pneumatic tyres interacting with deformable terrains

In this study, a numerical model of a deformable tyre interacting with a deformable road has been developed with the use of the finite element code ABAQUS (v. 6.13). Two tyre models with different widths, not necessarily identical to any real industry tyres, have been created purely for research use. The behaviour of these tyres under various vertical loads and different inflation pressures is studied, initially in contact with a rigid surface and then with a deformable terrain. After ensuring that the tyre model gives realistic results in terms of the interaction with a rigid surface, the rolling process of the tyre on a deformable road was studied. The effects of friction coefficient, inflation pressure, rebar orientation and vertical load on the overall performance are reported. Regarding the modelling procedure, a sequence of models were analysed, using the coupling implicit - explicit method. The numerical results reveal that not only there is significant dependence of the final tyre response on the various initial driving parameters, but also special conditions emerge, where the desired response of the tyre results from specific optimum combination of these parameters.

Potential Modulation on Total Internal Reflection Ellipsometry.

Electrochemical-total internal reflection ellipsometry (EC-TIRE) has been proposed as a technique to observe the redox reactions on the electrode surface due to its high phase sensitivity to the electrolyte/electrode interface. In this paper, we mainly focus on the influence of the potential modulation on the TIRE response. The analysis suggests that both dielectric constant variation of gold and the electric double layer transformation would modulate the reflection polarization of the surface. For a nonfaradaic process, the signal of TIRE would be proportional to the potential modulation. To testify the analysis, linear sweep voltammetry and open circuit measurement have been performed. The results strongly support the system analysis.

Development of a Simulink-CarSim Interaction Package for ABS Simulation of Discrete Tire Models

ABSTRACT Automotive and tire companies have to spend extensive amounts of time and money to tune their products through prototype testing at dedicated test facilities. This is mainly because of the limitations in the simulation capabilities that exist today. With greater competence in simulation comes more control over designs in the initial stages, which in turn lowers the demand for the expensive stage of tuning. This article aims at taking today's simulation capabilities a step forward by integrating models that are best developed in different software interfaces. An in-plane rigid ring tire model has been developed to understand the transient response of tires to various high-frequency events such as antilock braking and short-wavelength road disturbances. A rule-based antilock braking systems (ABS) model performed the high-frequency braking operation. The tire and ABS models were created in the Matlab-Simulink environment. A vehicle model was developed in CarSim. The models developed in Simulink were integrated with the vehicle model in CarSim, in the form of a design tool that can be used by tire as well as car designers for further tuning of the vehicle functional performances, as they relate to handling and braking maneuvers. The straight-line ABS performance was predicted using these models for a sample vehicle, and the results were substantiated through physical outdoor tests on the same vehicle to validate the developed integration package. The tool development, simulation results, and the objective test will be discussed.

Tire Transient Lateral Force Generation: Characterization and Contribution to Vehicle Handling Performance

ABSTRACT Tire force generation is often described in terms of a steady-state force response, which is considered independent of time and a function of the kinematic roll conditions such as slip angle. In addition to the steady-state response, the tire also exhibits a time-dependent transient force response, which in the lateral direction is a delay in the buildup of the cornering force. This delay is often characterized by the so-called tire relaxation length (RL) (Ly), a tire performance characteristic often thought to have a strong effect on handling performance. The definition and mechanistic interpretation of tire lateral RL is discussed, and different methods for measuring and interpreting lateral RL are compared. The measurement methods include different types of flat belt as well as static stiffness measurements. Because of different levels of measurement uncertainty, the repeatability and benefits of the different measurement methods are demonstrated. To determine the effect of including tire transient response in tire/vehicle system models, a handling study was performed. The study included a series of CarSim handling simulations with tires of different transient force and moment characteristics as well as an analysis of outdoor subjective handling ratings. The results show the relatively small contribution of tire transient characteristics to vehicle handling performance compared with the tire steady-state force response.

Finite element analysis of tires in rolling contact

AbstractIn this publication an overview on sophisticated modeling approaches for the finite element computation of rolling tires based on an Arbitrary Lagrangian Eulerian (ALE) formulation of the kinematic will be outlined. After a brief introduction into the ALE‐concepts special attention is laid onto the treatment of the tangential contact formulation. As the path‐lines of the material points are not computed directly within the relative kinematics framework, techniques for the treatment of inelastic material properties and the coupled thermo‐mechanical analysis with emphasis to rolling loss analysis will be given. Furthermore a modal superposition approach is suggested for the analysis of the high frequency response of rolling tires excited from the surface roughness of the road. Finally a mesoscopic modeling approach for the transient dynamic analysis of the tread rubber with the rough roads surface is presented. In summary these techniques enable for a broad bandwidth of tire specific behavior in rolling contact. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)