Tire Simulation Research Articles

High fidelity nonlinear finite element tire modeling for dynamic analysis: Total Lagrangian formulation in rolling contact

Tire design with respect to vibrational behavior and noise emission is a challenging task due to the large number of parameters and their coupling. Therefore, accurate high fidelity nonlinear Finite Element (FE) models are needed to aid in the design process. The widely used Arbitrary Lagrangian Eulerian (ALE) models, despite their computational efficiency, are limited to rib-slicked tires and require significant effort to consider inelastic material behavior and frictional phenomena. To overcome these limitations a novel nonlinear FE tire model is presented based on the Total Lagrangian (TL) formulation. The TL model is compared to the reference ALE model for the case of stationary rolling on a smooth and a rough road surface. The observed match of the TL model with respect to the hub and contact forces proves the feasibility of using the TL formulation in the context of rolling contact tire simulations. Therefore, the TL model can be seen as a valid alternative to the frequently used ALE models.

Cyclic Testing of Polymer Composites and Textile Cords for Tires.

This paper is oriented toward the specific testing of polymer composites and textile PA66 cords used as reinforcement for composites. The aim of the research is to validate the proposed new testing methods for low-cyclic testing of polymer composites and PA66 cords for the characterization of material parameters useful as input data for computational tire simulations. Part of the research is the design of experimental methods for polymer composites and test parameters such as load rate, preload, and other parameters such as strain for the start and stop of cycle steps. The DIN 53835-13 standard is used for the conditions of textile cord during the first five cycles. A cyclic load is carried out at two temperatures of 20 °C and 120 °C. The testing method includes a hold step for 60 s between each loop. The video-extensometer technique is used for testing. The paper evaluated the effect of temperatures on the material properties of PA66 cords. The true stress-strain (elongation) dependences between points for the video-extensometer of the fifth cycle of every cycle loop are the data results from composite tests. The forcestrain dependences between points for the video-extensometer are the data results from tests of the PA66 cord. These dependencies can be used as input material data of textile cords in the computational simulation of tire casings using a custom material model definition. The fourth cycle in every cycle loop of polymer composites can be considered a stable cycle because the change in the maximum true stress between the fourth and fifth cycles is 1.6%. Other results of this research include a relationship between stress and the number of cycle loops as the second-degree polynomial curve for polymer composites and a simple relationship to describe the value of the force at each end of the cycles for a textile cord.

Rolling Tires on the Flat Road: Thermo-Investigation with Changing Conditions through Numerical Simulation

A crucial material comprising a pneumatic tire is rubber. In general, the tire, or more specifically, the hysteresis effects brought on by the deformation of the part made of rubber during the procedure, heat up the part. In addition, the tire temperature depends on several factors, including the inflation pressure, automobile loading, car speed, road tire, the environmental conditions, and the tire geometry. This work focuses on using simulations to calculate the temperature and generated heat flow distributions of a rolling tire with constant velocity using the finite element method. For the sake of simplicity, it is assumed that the only components of the tire are rubber, body-ply, bead wire, and the rim. While the other components are believed to be made of a linear elastic material, the nonlinear mechanical behavior of the rubber is characterized by a Mooney–Rivlin model. Investigations are conducted into the combined effects of vehicle loads and inflation pressure. Hysteresis energy loss is used as a bridge to link the strain energy density to the heat source in rolling tires, and their temperature and heat flow distributions may be determined by steady-state thermal analysis. Thanks to the state-of-the-art computing method, the time required for connected 3D dynamic rolling tire simulations is reduced. The simulation outcomes demonstrate that the maximum temperature in this paper is attained with high weights, high velocities, and low inner inflated pressures. Overall, the maximum temperature is increased with the rise of all three variables. Moreover, the rise of the friction coefficient between the tread and road surface moves the high-temperature area towards the tread/sidewall connection area.

Experimental-cum-numerical approach for directional skid resistance measurement of grooved pavements

Currently there is no standard procedure for measuring the directional skid resistance of grooved pavements using the British pendulum tester (BPT). This study shows that BPT measured directional British pendulum numbers (BPNs) could over-estimate the actual directional BPN values of grooved pavements by more than 10 BPN at test angle of 90° to the grooves. The present study develops an experimental-cum-numerical procedure to provide corrections to measured directional BPNs of grooved pavements. Based on a single directional BPN measured in any test direction, the procedure permits one to calculate the full range of corrected directional BPNs at test angles between 0 and 90°. Corrected BPNs are derived from rubber-pavement friction coefficients back-calculated from measured BPNs. This was achieved through the application of two numerical skid resistance simulation models: a finite-element BPT simulation model and a finite-element sliding tire simulation model. The validity of the proposed approach was verified experimentally.

Modeling of rubber-cord layers under quasi-static loading

Modeling a pneumatic tire with a strong change in shape causes the problem of choosing an adequate model for rubber-cord plies. Generally, the classical method of asymptotic homogenization is not suitable due to physical and geometrical nonlinearity for the strain up to 15 %. The known models used for simulation the entire tire as well as rubber-cord plies are analyzed. A choice is made in favor of modeling the plies using the stress anisotropic potential, which is an anisotropic function of the strain tensor invariants. The relationship of such a constitutive law with a quasi-linear constitutive equation in terms of stress and strain differentials is indicated. A convenience of these two types of constitutive equations in terms of numerical implementation is also given. A modification of the effective properties definition for an inhomogeneous layer is explained. The difference from the standard effective moduli definition is clarified. The arrangement of the cords is supposed to be approximately periodic and all cords to be equivalent to the effective fiber. Two models of a rubber-cord plies are described under such assumption. These are a model of an orthotropic material and a model of a transversely isotropic material. Computational experiments, which make it possible to determine the material parameters of anisotropic potentials, are pointed out. Real tests with a sample of rubber ply under slow quasi-static loading were conducted. Significant hysteresis was detected. It is shown that an additive model combining a hyper elastic material with Maxwell viscoelastic model provides good accuracy in stress dependence on the strain rate. The numerical procedure developed to calculate solution to the quasi-static problem of tire deformation is described. It is implemented in home-made computer code. A numerical example on the tire simulation is given. That is so-called breaking test, in which strong deformation is achieved and the developed model is applied to.

Study on the Stability Control of Vehicle Tire Blowout Based on Run-Flat Tire

In order to study the stability of a vehicle with inserts supporting run-flat tires after blowout, a run-flat tire model suitable for the conditions of a blowout tire was established. The unsteady nonlinear tire foundation model was constructed using Simulink, and the model was modified according to the discrete curve of tire mechanical properties under steady conditions. The improved tire blowout model was imported into the Carsim vehicle model to complete the construction of the co-simulation platform. CarSim was used to simulate the tire blowout of front and rear wheels under straight driving condition, and the control strategy of differential braking was adopted. The results show that the improved run-flat tire model can be applied to tire blowout simulation, and the performance of inserts supporting run-flat tires is superior to that of normal tires after tire blowout. This study has reference significance for run-flat tire performance optimization.

Isogeometric Analysis for Tire Simulations: From Mesh Generation to High Precision Results

ABSTRACTIsogeometric analysis (IGA) has become an alternative to standard finite element analysis (FEA) in many areas of engineering. Its powerful tools for model generation and flexibility of basis functions make this relatively new approach attractive for tire analysis and its computational challenges.This contribution summarizes the benefits of IGA for complex tire simulations starting from model generation and the subsequent transition to the environment of numerical analysis without losing accuracy at the parametrizing stage. It presents results of further development work on earlier pioneering examples of the application of IGA in pneumatic tire analysis. In addition to the analysis of vertical stiffness, for the first time, velocity and acceleration fields are addressed and compared with experimental results and standard FEA simulations, with a focus on benefits of the continuity of basis functions within the contact patch. The numerical issues that arise in IGA at the enforcement of contact and the application of inelastic materials with inclusions of reinforcing layers are studied. Moreover, the important advantages of the possibility to use higher order functions for simulations of tire maneuvers are addressed within the steady-state framework. Numerical examples are provided to illustrate the capabilities of IGA. Concluding remarks on the results close the publication.

Local Refinement in Isogeometric Analysis of Complex Tire Models

AbstractThe capability of Non‐Uniform Rational B‐Splines (NURBS) to exactly represent conic sections exactly makes Isogeometric Analysis (IGA) an attractive alternative to classical Finite Element Method (FEM) for tire simulation. Application of NURBS as basis functions for geometry representation simplifies the generation of the computational mesh that can be directly obtained from the software for graphical design. NURBS‐based approximations of the field variables lead to higher convergence rates and allow higher continuity across the element boundaries. Moreover, the tensor structure of these functions permits the usage of additional advanced refinement techniques.The contribution at hand focuses on the application of hierarchically nested basis functions in tire analysis. The developed framework is based on the introduction of the global multilevel Bézier extraction operator [1]. This approach allows local refinement in the existing isoparametric FEM code without violating its architecture. Within the introduced framework, material models developed for standard FEM can be retained.Special attention is paid to the modelling of rebar elements within the framework of IGA and local refinement in particular. The from standard FEM adopted unconventional method avoids the drawbacks of smeared formulations common in tire numerical analysis and does not require an explicit definition of the reinforcing bars [2]. An additional check of the volumetric content of rebar in the material allows the compatibility of the employed concept with locally improved meshes.Numerical simulations for rolling tires using IGA are presented. The complex multilevel composite structure of tire‐models is obtained by means of CAD‐software. All simulations are performed under the consideration of steady‐state rolling within the Arbitrary Lagrangian‐Eulerian (ALE) description including finite deformations. A benchmark study of IGA and FEM for tire analysis closes this presentation.

Prediction of Hydroplaning Potential Using Fully Coupled Finite Element-Computational Fluid Dynamics Tire Models

Abstract Hydroplaning is a phenomenon that occurs when a layer of water between the tire and pavement pushes the tire upward. The tire detaches from the pavement, preventing it from providing sufficient forces and moments for the vehicle to respond to driver control inputs such as breaking, accelerating, and steering. This work is mainly focused on the tire and its interaction with the pavement to address hydroplaning. Using a tire model that is validated based on results found in the literature, fluid–structure interaction (FSI) between the tire-water-road surfaces is investigated through two approaches. In the first approach, the coupled Eulerian–Lagrangian (CEL) formulation was used. The drawback associated with the CEL method is the laminar assumption and that the behavior of the fluid at length scales smaller than the smallest element size is not captured. To improve the simulation results, in the second approach, an FSI model incorporating finite element methods (FEMs) and the Navier–Stokes equations for a two-phase flow of water and air, and the shear stress transport k–ω turbulence model, was developed and validated, improving the prediction of real hydroplaning scenarios. With large computational and processing requirements, a grid dependence study was conducted for the tire simulations to minimize the mesh size yet retain numerical accuracy. The improved FSI model was applied to hydroplaning speed and cornering force scenarios.

Hardware-in-the-Loop Test of an Open-Loop Fuzzy Control Method for Decoupled Electrohydraulic Antilock Braking System

To verify the functionality of an intelligent open-loop fuzzy-logic-based antilock braking system control method for four on-board motor drive electric sport utility vehicle, a hardware-in-the-loop experiment is conducted in this article. The experimental facility includes a novel decoupled electrohydraulic brake test bed characterized by highly nonlinear dynamics and time-varying behavior. It reproduces real pressure dynamics of the brake circuit allowing for simulation of various tire–road adhesions conditions and brake blending scenarios. To cope with degradation of antilock braking system performance induced by unexpected changing environmental conditions, such as road surface, the developed fuzzy control features a very simple yet effective and robust road surface recognition tool with estimation of the peak braking demands. Thus, the fuzzy logic serves as a controller and road surface estimator simultaneously allowing for complex mathematical modeling and feedback control avoidance not sacrificing safety system's performance. The results indicate that the control method manages highly nonlinear and time-variant dynamics of the brake system and offers significant feasibility for optimal slip control at regenerative braking, ensuring fuzzy control's potentiality for real-time application.

DEM–FEM simulation of tire–sand interaction based on improved contact model

In the interaction between rubber tire and granular terrain, the dynamic behavior of granular terrain is significantly affected not only by the shape of soil grains, but also by the deformation contact of tread rubber. Therefore, the effect of these two factors should be considered in tire–sand interactions. In this study, an improved contact model including the effect of sand grain shape and tread rubber deformation is developed for dealing with the interaction between rubber tire and sand terrain. In sand–sand contact model, the interaction between sand grains takes the form of surface contact instead of conventional point contact, where the contact calculation contains four interactions, i.e., normal force, tangential force, rolling resistance and twisting resistance. And in tread–sand contact model, the contact between tread rubber and sand grains is surface contact, which includes the rolling resistance and twisting resistance on the grains caused by rubber deformation during contact. As a result, the complete and realistic evaluation of contact forces is accomplished. Next, a comparison of sandpile simulation of coarse particles and experiment is carried out to verify the effectiveness of the sand–sand contact model. Finally, the novel contact model is applied to tire–sand interaction simulations and compared with the single-wheel experiments. The results indicate that the proposed contact model can be a powerful tool to simulate the interactions between rubber tire and sand terrain.

An Integrated Approach for Friction and Wear Simulation of Tire Tread Rubber. Part II: Wear Test, Characterization, and Modeling

ABSTRACT: On the basis of Part I, Part II continues further research on the wear of tire tread rubber. A test scheme composed of various combined conditions that are widely ranged in energy dissipation is developed. The wear rate and temperature increase are described by exponential energetic models. Coupled with the unified friction model, a well-demonstrated wearing simulation of the rubber wheel is proposed. The wear rate for the rolling of axisymmetric structure is derived, and a nonequal wear increment is proposed according to the maximum allowable wear depth of the surface elements, which act as a criterion for calculating the increment size. In order to maintain high quality of the worn mesh, the boundary displacement method is employed to reposition the interior nodes of the finite element model as well as the surface elements. The computed wear rates are roughly in agreement with the test results. As a further illustration, the tread wear simulation of an axisymmetric tire containing only longitudinal grooves is conducted. For the first time, the evolution rules of wear contour of the axisymmetric tire are revealed, and the linear variation of worn mass with the rolling distance is consistent with the experimental results reported in literature.

Chassis Tire simulation and steer-by-wire systems

Chassis Tire simulation and steer-by-wire systems

Advanced Rebar Formulation within a Thermo‐Mechanically Coupled Tire Simulation

AbstractAs shown in various experiments, coupling between the thermal and the mechanical field of a rolling tire in contact with a rigid surface can be observed. An increase of its temperature over time when rolling with a constant velocity can be seen. This phenomenon is caused by the viscoelastic material properties, where the dissipated energy will lead to a heating of the rubber. Also the constitutive behaviour will change, when the temperature increases. A nonlinear viscoelastic material model is chosen to model an amplitude dependency of the time dependent behaviour of the rubber, proposed by Bergström and Boyce [1].Another important part of a tire are the reinforcements, which are embedded inside the rubber. These consist mostly of steel or polyester. These materials are not known for a dissipative behaviour and will not contribute to the heating of the tire. However, they also change their properties with increasing temperature and have a significant influence on the overall tire properties. Even without a contribution to the heating, the reinforcements will change its conductivity and have to be taken into account.For an accurate and efficient way to model the thermo‐mechanical coupling, an in‐house framework [2] will be presented, by use of the Arbitrary Langrangian Eulerian formulation and a commercial code. It is assumed, that the temperature in circumferential direction will stay constant and instant coupling effects are negligibly small. Therefore, the problem is split into a thermal and a mechanical part, and the coupling quantities (dissipated energy and temperature) are updated in a sequential manner.A common practise to model the reinforcements in tires is to use smeared layers, which leads to some difficulties. First of all, the modelling is only valid for a really small spacing between the bars. Another problem is, that the smeared layers have to fit with the nodes of the rubber matrix. Because of that, the mesh has to be refined, which leads to an increasing computation time and can cause numerical difficulties, due to too small elements.In this contribution, a different way of modelling the rebars within a thermo‐mechanical coupled algorithm is presented without the assumption of a smeared layer and treat them as single rebars. In numerical examples, the advantages of the proposed method are presented and the difference to the classical approach is shown. Also, the influence of the reinforcements on the stiffness, heat generation and rolling resistance of the tire, will be discussed. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Experimental Validation of Various Temperature Modells for Semi-Physical Tyre Model Approaches

With increasing level of complexity and automation in the area of automotive engineering, the simulation of safety relevant Advanced Driver Assistance Systems (ADAS) leads to increasing accuracy demands in the description of tyre contact forces. In recent years, with improvement in tyre simulation, the needs for coping with tyre temperatures and the resulting changes in tyre characteristics are rising significantly. Therefore, experimental validation of three different temperature model approaches is carried out, discussed and compared in the scope of this article. To investigate or rather evaluate the range of application of the presented approaches in combination with respect of further implementation in semi-physical tyre models, the main focus lies on the a physical parameterisation. Aside from good modelling accuracy, focus is held on computational time and complexity of the parameterisation process. To evaluate this process and discuss the results, measurements from a Hoosier racing tyre 6.0 / 18.0 10 LCO C2000 from an industrial flat test bench are used. Finally the simulation results are compared with the measurement data.

Thermo-mechanical coupled finite element simulation of tire cornering characteristics—Effect of complex material models and friction law

This research work is devoted to the development of an advanced finite element model for the simulation of a rolling tire under cornering conditions. The main goal of this research is to investigate the effect of material and frictional models complexity on results accuracy. A finite element model based on a coupled thermo-mechanical procedure was developed using Abaqus and two specific in-house user subroutines called as FRIC and UMASFL were written. Simultaneous consideration of real frictional behavior in conjunction with temperature dependent hyper-viscoelastic materials properties was performed. The accuracy of simulations with different complexity levels were checked via comparison between simulation results and the obtained data from a tire tested on a flat-trac machine. The results showed that the frictional heat generation during tire cornering is really complicated and could not be described with available models. Parametric studies revealed that the generated lateral force was not affected considerably by model complexity, but the aligning moment and pressure distribution in footprint area were very sensitive to the model complexity level.

Method for virtual tyre and braking distance simulation

Method for virtual tyre and braking distance simulation

Rubber Composition–Properties Relationships during Tire Numerical Simulation and Design Optimization

ABSTRACT Numerical simulation based on finite element analysis is now widely used during the design optimization of tires, thereby drastically reducing the time investment in the design process and improving tire performance because it is obtained from the optimized solution. Rubber material models that are used in numerical calculations of stress–strain distributions are nonlinear and may include several parameters. The relations of these parameters with rubber formulations are usually unknown, so the designer has no information on whether the optimal set of parameters is reachable by the rubber technological possibilities. The aim of this work was to develop such relations. The most common approach to derive the equation of the state of rubber is based on the expansion of the strain energy in a series of invariants of the strain tensor. Here, we show that this approach has several drawbacks, one of which is problems that arise when trying to build on its basis the quantitative relations between the rubber composition and its properties. An alternative is to use a series expansion in orthogonal functions, thereby ensuring the linear independence of the coefficients of elasticity in evaluation of the experimental data and the possibility of constructing continuous maps of “the composition to the property.” In the case of orthogonal Legendre polynomials, the technique for constructing such maps is considered, and a set of empirical functions is proposed to adequately describe the dependence of the parameters of nonlinear elastic properties of general-purpose rubbers on the content of the main ingredients. The calculated sets of parameters were used in numerical tire simulations including static loading, footprint analysis, braking/acceleration, and cornering and also in design optimization procedures.

Study on the Acquisition Method of Tire Rubber Parameters Based on Simple Shear Test

Tire simulation gradually becomes an important mean to ensure the quality of the tires. In order to guarantee the reliability of the analysis, the study on the method of obtaining the material parameters is also increasing. According to tire force situation of actual work, the acquisition method of tire rubber parameters based on simple shear test and its application in finite element analysis were studied in this paper. In this research, the international advanced dynamic mechanical analyzer was used to test the tire rubber, and the experimental results were processed by Yeoh hyper-elastic model. The hyper-elastic parameters and thus obtained could be used for finite element analysis of tires, and the simulation results showed that these parameters could be used to simulate the tire performance. In addition, the results could also provide certain guidance for the design and manufacture of tire.

Experimental and Numerical Simulation of the Dynamic Frictional Contact between an Aircraft Tire Rubber and a Rough Surface

This paper presents a numerical simulation of an aircraft tire in contact with a rough surface using a variable friction coefficient dependent on temperature and contact pressure. A sliding facility was used in order to evaluate this dependence of the friction coefficient. The temperature diffusion throughout the tire cross-section was measured by means of thermocouples. Both frictional heating and temperature diffusion were compared to numerical two- and three- dimensional simulations. An adequate temperature prediction could be obtained. In future simulations, wear should be taken into account in order to have a more accurate simulation especially in the case of high pressures and slipping velocities. A 3D finite element model for a rolling tire at a velocity of 37.79 knots (19.44 m/s) and in a cornering phase was investigated using a variable friction coefficient dependent on temperature and pressure. The numerical simulation tended to predict the temperature of the tire tread after a few seconds of rolling in skidding position, the temperature of the contact zone increases to 140 °C. Further investigations must be carried out in order to obtain the evolution of the temperature observed experimentally. The authors would like to point out that for confidentiality reasons, certain numerical data could not be revealed.