ABSTRACT A new theoretical tire model considering two-dimensional contact patch for the relaxation length is developed by extending the theoretical model for force and moment of a tire in the steady state. Because models in many studies use first-order differential equations, they are only valid for small slip angles and slip ratios, and they cannot account for the effects of tire construction, profile, or pattern on the relaxation length. The proposed model can be applicable up to high slip angle, slip ratio, and combined slip conditions. Furthermore, it can consider the tire construction, profile, and pattern. The results of the effects of belt angle, lateral spring rate of a tire, load, slip angle, and slip ratio on the relaxation length qualitatively agree with those of previous experiments and finite element analysis. Because the shear stress distribution in a contact patch of a quasi-statically rolling tire can be predicted in this model, it is easier for engineers to understand the mechanism of the relaxation length and to find ways to control the relaxation length.
ABSTRACT Effects of height, thickness, and formula of the bead filler in 205/55R16 car tires on rolling resistance coefficients, indoor noise, handling, and ride comfort were examined. Height, thickness, and formula of the bead filler have an impact on the rolling resistance performance, indoor noise, static performance, handling, and ride comfort. The thickness of the bead filler showed a bigger sensitivity to rolling resistance coefficients than did formula and height. The formula of the bead filler showed a bigger sensitivity to indoor noise than did thickness and height. The height, thickness, and formula of the bead filler are sensitive to static, handling, and ride comfort performance.
ABSTRACT Experimental and simulation studies were conducted on the phenomenon of premature fatigue failure of a certain type of tire on mountainous roads. A representative vehicle was selected for the test, and the test was conducted in a mountainous area in southwestern China. The testing system was built using a mobile phone global positioning system and a MEMSIC acceleration sensor to record the position, speed, acceleration, altitude, and other data of the vehicle. After processing and analyzing the experimental data, the longitudinal, lateral, and vertical acceleration signals of the vehicle are obtained. Thereby, the validity of the test data is demonstrated. A MATLAB/Simulink simulation model of the representative vehicle is established. The vehicle’s tire forces on mountainous roads are calculated and statistically analyzed. The results indicate significant disparities in lateral, longitudinal, and vertical forces between the right front and right rear tires of the vehicle. The absolute maximum values of lateral, longitudinal, and vertical forces of the right rear tire are significantly greater than those of the right front tire. This research provides a reference for further exploration of tire fatigue failure under driving conditions on mountainous roads.
ABSTRACT Unlike the contact between tires and paved road, the tire–deformable terrain interaction is more complex, often involving traction, compaction resistance, slip sinkage, and other factors. This study introduces a novel “constant-sinkage” finite element analysis framework to decouple the effects of slip and sinkage and obtain clearer tire–terrain contact mechanisms. High-fidelity simulations of rigid and flexible tires under longitudinal slip reveal a key insight: the contact contour remains largely invariant with slip when sinkage is fixed and is only affected by the relative strength of the tire and the terrain. This discovery enables the systematic investigation of stress distribution, characterized by three distinct stages corresponding to increasing slip. Based on these findings, a new stress distribution model applicable across all slip stages is developed, incorporating soil parameters obtained from penetration and shear tests. This stress model is integrated with an improved contact contour model based on a surrogate circle, forming the basis of the accurate prediction of tire forces such as drawbar pull. Validation confirms that the model can effectively represent the in-plane characteristics of tires on deformable terrain and provide a robust foundation for off-road vehicle simulation.
Tire cords are critical not only for the structural integrity of tires but also for influencing vehicle noise, vibration, and harshness (NVH) performance. However, their dynamic behavior is often oversimplified to elastic behavior in finite element analysis (FEA) simulations, and this oversimplification can lead to inaccurate modal vibrations predictions. This study shows how proper viscoelastic characterization of the storage and loss moduli of a polyester polyethylene terephthalate 1500/2 cord in terms of frequency and mean cord strain about which they are measured gives correct predictions of the steady-state vibration response of cord-rubber laminates. Dynamic properties of the polyester cord were used in FEA simulations of the polyester cord–rubber laminates in tension and dual cantilever beam bending vibration modes and compared with that obtained via experimental predictions. Storage and loss moduli of the rubber properties were also characterized in terms of frequency and mean strain and incorporated into the FEA simulation. Simulations using the viscoelastic cord properties were within 3 and 13% of experimental results in tension and combined tension and bending, respectively. By contrast, modeling the cord with only hyperelastic properties led to underpredictions of 100 and 34% with experimental results in tension and combined tension and bending, respectively. This finding underscores the importance of the proposed cord viscoelastic modeling for accurate NVH predictions.
Intelligent tires that are equipped with tire-mounted sensors have emerged as a transformative force in the automotive industry. These sensors provide real-time data on tire health, road conditions, and vehicle performance; however, their efficacy is constrained by battery-life limitations. To address this challenge, a range of strategies has been proposed in the literature to enhance the reliability and accuracy of intelligent tire systems. These strategies encompass edge computing, event-driven sensing, selective sampling, sensor fusion, and adaptive algorithms. By synergistically integrating these approaches, the output of intelligent tire systems across diverse applications can be optimized. We introduce a novel load estimation methodology that leverages a combination of these strategies. Initially, we present static tire load estimation algorithms alongside tire auto-location techniques. Subsequently, we propose a fusion strategy that unifies both algorithms, thereby yielding simultaneous results for static tire load and tire auto-location. Furthermore, we extend this approach to incorporate vehicle inertial measurement unit data that enables dynamic load estimation for each tire. Remarkably, this extension obviates the need for ongoing inputs from tire-mounted sensors during extended periods of driving. Validation results underscore the effectiveness, reliability, and accuracy of our proposed methodology, positioning it as a promising advancement in the field of intelligent tire systems.
When exposed to air, the long polymer chains of a rubbery object react with oxygen molecules to form oxygenated functional groups that weaken the material and make it more susceptible to cracking. Higher temperatures accelerate the diffusion of oxygen and the mechanisms of the ensuing chemical reactions. The property degradation of the oxidative rubber is manifested by embrittlement of its stiffness, reduction of its maximum chain extensibility, and accelerated crack initiation and propagation. In this paper, a process is developed to measure oxygen permeability, solubility, and oxygen consumption rate to map the state of oxygen concentration. These properties are updated for elevated temperature generated by the structural dynamic deformation. The fracture energies ( T 0 , T c ) are also measured at the relevant aerobic and thermal conditions and updated into Endurica DD/DT modules to predict the overall durability and lifespan of the rubber components. To fully demonstrate this crucial multiphysics mechanism in material design and engineering applications, two tire types (passenger car radial [PCR], truck bus radial [TBR]) were analyzed using finite element (FE) models in Abaqus. The predicted performance and longevity are compared for aerobic and anaerobic conditions.
In tire production, the molding of the tread is one of the most intricate and opaque processes. However, it also plays a significant role in tire performance. During this step, the uncured tire tread is subjected to extreme conditions and undergoes massive deformations, posing considerable challenges to simulation frameworks that could aid in the design process. For example, traditional mesh-based simulations face extreme distortion of the elements, resulting in inaccurate and unstable behavior. This study lays the foundation for a framework based on the material point method (MPM) to address these challenges. The tire tread is discretized using particles called material points. To compute their interactions, the material points are projected onto a static background grid to solve the underlying differential equations, facilitating a fast and robust computation. The focus of this contribution is on the alleviation of volumetric locking, a typical problem for nearly incompressible materials, and the interaction between the green tire and the mold, taking the unique properties of the MPM into consideration. A novel locking mitigation scheme based on the subdivision of B-splines is presented and validated. Additionally, the approach is applied to tire molding examples to investigate its efficacy.
In this contribution, the mechanical properties of polyester cords are investigated in a series of experiments: monotonic, multistep relaxation, and cyclic loading-unloading tests. The nonlinear elastic behavior due to crimping of the fibers and the inelastic behavior appear in the test results. To represent this behavior, a constitutive material model is proposed by decomposing it into endochronic, viscoelastic, strain-hardening, stretch-induced stiffening, and matrix parts. The identified material parameters capture the experiments qualitatively well. The proposed model is validated with the additional experiments including the complex conditions and further evaluated through finite element simulations of the tire building process.
The mechanical properties of tire turn-slip primarily reflect the mechanical characteristics of tires operating at low speeds with yaw angular velocity. Acquiring such tire force data is beneficial for improving the accuracy of tire model expressions under conditions of low speed and large turning angles. Currently, mainstream tire test benches lack the capability to test the pure turn-slip of tires. In exploring virtual sampling methods for tires, tire suppliers rely on predictive and virtual data for tire model identification. The acquisition of turn-slip data can expand the applicability of tire models. Furthermore, no researchers have publicly published results on estimating the mechanical properties of tire turn-slip by using finite element analysis. Thus, this paper proposes a tire camber-turn slip combined simulation method based on implicit and explicit finite element algorithms. First, using a non-pattern tire model, implicit and explicit simulation methods for camber turn-slip combined conditions are developed based on ABAQUS software. Second, the mechanical characteristics of tire turn-slip under different loads and inclination angles are analyzed and the distribution of tire forces in the contact patch is obtained using two simulation algorithms. And third, the reliability of the linear characteristics in the simulation results is evaluated and the influence of inclination angles on turn-slip characteristics under the two algorithms is compared. The results indicate that the bias of both algorithms shows consistent trends in the effects of camber, demonstrating high data reliability. Additionally, the mechanical characteristics of tire turn-slip obtained through finite element simulation effectively estimate its mechanical properties.
To predict and prevent uneven tire wear in addition to a reduction of overall tire wear, it is essential to estimate not only the total amount of wear but also how the wear is distributed across the tire width. This requires knowledge of the frictional power distribution in the tire contact patch, which is the basis for calculating tire wear using a wear law. Usually, only 3D structural tire models can generate such distributed contact results. However, they involve high computational costs and cannot be used for comprehensive optimization of a vehicle's suspension system with respect to tire wear characteristics. Hence, this contribution presents a methodology on how to accelerate the prediction of the frictional power distribution using two components: The structural tire model is replaced by an empirical tire model that on its own is not able to generate distributed contact results. Therefore, an artificial neural network is trained to predict the desired contact results from the kinematic quantities calculated by the empirical tire model. In the initial training phase, both components are fitted to data generated by the original complex tire model. After training, the empirical tire model can replace the structural tire model in vehicle simulations, resulting in significantly shorter calculation times. The simulation results are fed into the artificial neural network, which predicts the frictional power distributions over the tire width with negligible additional effort. Overall, the methodology reduces calculation time for the prediction of tire wear based on virtual test drives to approximately 25% of the time needed when using structural tire models.
Understanding the complex interactions between rubber and snow is vital for enhancing tire traction in winter conditions; such interactions include the process that occurs during contact between the tire tread and snow, particularly during sliding. Recognizing the inherent complexities of these interactions, especially under varying applied loading rates, a dual methodology is used: detailed computational simulations and experimental validation. To capture the diverse behaviors exhibited by snow, an advanced elastoplastic constitutive model at finite strains is used. This model is enriched by an implicit gradient damage enhancement to replicate the brittle nature of snow under high loading rates. After calibration against established experimental benchmarks, the proposed material model is shown to demonstrate a suitable alignment with observed behaviors. Further computational simulations provide insights into different examples of the rubber–snow interaction, whereas experimental data are used to validate our approach. This affirms the potential of the proposed framework as a robust tool for modeling the intricate interaction between rubber and snow.
Rolling resistance has become one of the key parameters that the vehicle industry is focusing on in their efforts to make vehicles more energy efficient. Rolling resistance is generally measured in steady state on a test drum that results in a higher rolling resistance than flat track measurements for the same test settings due to the curvature of the drum, which deforms the tire more. Therefore, the drum steady-state rolling resistance is commonly converted with Clark's formula, as suggested in the rolling resistance measurement standards. Freudenmann et al. suggest an adjustment of Clark's formula, claiming that it would improve the accuracy for steady-state conversions. The aim of this work is to compare non-steady-state drum and flat track measurements, performed at the same inflation pressure and tire temperature, to investigate whether Clark's or Freudenmann's formula can be used to convert the drum measurement to a corresponding flat track level when not in steady state. Non-steady-state measurements have been performed on both a test drum and a flat track. As expected, Freudenmann's formula is not good for the conversion at non-steady-state settings because it was empirically developed for steady state. Clark's formula works for non-steady-state conversions of measurements performed at the same tire temperature and inflation pressure. However, the dependency of rolling resistance on temperature is not the same in the drum and flat track measurements, causing a difference between the results that increases as the tire temperature decreases. Further research to improve Clark's formula for nonsteady-state measurements by including the effects of tire temperature would be beneficial.
ABSTRACT To address the challenges of lengthy development cycles and high testing costs in matching tire and vehicle mechanical characteristics, a fast and efficient virtual sampling method for tire mechanical properties is proposed. First, a detailed finite element model is established according to the material distribution diagram and material properties of the tire. Second, under the premise of ensuring simulation accuracy, structural simplifications and friction simplifications are applied to the detailed finite element model. A finite element friction subroutine is incorporated to accurately express the dynamic friction characteristics between the tire tread and the road surface. Then, the pure cornering and pure driving/braking mechanical characteristics of the tire are obtained through finite element simulations. With a high-precision combined-condition tire mechanical property prediction method, fast and accurate predictions of combined-condition forces and torques are made. Finally, the MF tire model is identified based on the data obtained from the finite element model and the prediction method. The results show that the finite element model can accurately obtain the lateral force, longitudinal force, and aligning moment of the tire in pure cornering and pure driving/braking, with an average accuracy of 93.4%, 88.4%, and 80.7%, respectively. Based on the pure condition data obtained from the tire finite element model, the mechanical properties under combined conditions are predicted, with average prediction accuracies of 92.82% for longitudinal force and 91.38% for lateral force. The predicted aligning torque exhibits a trend consistent with experimental results. The MF model is identified using the data from the tire finite element model and prediction method, achieving good accuracy for both forces and torques. The fast and efficient virtual sampling method for tire mechanical properties not only effectively shortens development cycles and reduces testing costs but also, by combining finite element models with predictive methods, enables the advancement of tire mechanical property development to the design stage, further enhancing the efficiency of virtual sampling for tire models.
ABSTRACT To predict and prevent uneven tire wear in addition to a reduction of overall tire wear, it is essential to estimate not only the total amount of wear but also how the wear is distributed across the tire width. This requires knowledge of the frictional power distribution in the tire contact patch, which is the basis for calculating tire wear using a wear law. Usually, only 3D structural tire models can generate such distributed contact results. However, they involve high computational costs and cannot be used for comprehensive optimization of a vehicle’s suspension system with respect to tire wear characteristics. Hence, this contribution presents a methodology on how to accelerate the prediction of the frictional power distribution using two components: The structural tire model is replaced by an empirical tire model that on its own is not able to generate distributed contact results. Therefore, an artificial neural network is trained to predict the desired contact results from the kinematic quantities calculated by the empirical tire model. In the initial training phase, both components are fitted to data generated by the original complex tire model. After training, the empirical tire model can replace the structural tire model in vehicle simulations, resulting in significantly shorter calculation times. The simulation results are fed into the artificial neural network, which predicts the frictional power distributions over the tire width with negligible additional effort. Overall, the methodology reduces calculation time for the prediction of tire wear based on virtual test drives to approximately 25% of the time needed when using structural tire models.
A theory for multifield analysis of the consequences of sliding asperities on a rubber surface has been developed. The analysis considers (1) the multiaxial mechanical fields set up via the asperity contact, (2) the thermal field set up due to friction and heat generation, (3) the material property fields that evolve due to thermochemistry, and (4) the growth of crack precursors near the sliding interface. The theory considers two distinct Eulerian directions: the first direction considers strain history along streamlines oriented in the direction of sliding, and the second direction considers the progression of material toward the wear surface as material is removed. Considering the mechanical and thermal fields set up around an asperity, the theory simplifies what would otherwise be a large and complex analysis. The theory produces an estimate of the variation with depth of fatigue damage (residual life; as calculated via critical plane analysis), from which may be derived the wear rate for a particular surface sliding under a given set of conditions. Results of the calculation for two cases (two-dimensional sine wave and square wave asperity surfaces) with varying normal contact pressure are compared with Gent and Pulford’s blade abrader experiments.
This work addresses the challenge of modeling tire behavior for virtual vehicle development, particularly in untripped rollover scenarios where a vehicle rolls over solely due to the tire-road friction interface. Despite the existence of various models, limited attention has been given to tire testing methods that accurately represent rollover conditions. We propose a revised lateral tire testing method that uses data from rollover-critical driving tests to derive conditions for a flat-track test bench and that focuses on operational and thermal conditions. These data are used to parameterize empirical Magic Formula Tire 6.2 models, emphasizing the importance of accurate measurements for model parameterization. Component-level validation through comparison of measured and simulated tire reaction forces and moments demonstrates improved estimates of lateral forces, hence lateral friction coefficient, and overturning moments compared with models based on outdoor tire test data with limited operating conditions. At the full vehicle level, the proposed method significantly reduces the error in rollover key performance indicators based on wheel lift-off during Fishhook maneuvers. These findings are particularly relevant for battery electric sport utility vehicles with increased vehicle mass and wheel loads.
ABSTRACT Measuring normal and tangential forces on tires is crucial for enhancing tire performance under various road conditions and environmental settings. The measurement of these forces has been challenging because of limitations in sensing technology related to rigidity, durability, and sensitivity. This research introduces an innovative method that utilizes flexible sensors made of ionic liquid to address the limitations. Through the utilization of the distinctive properties of ionic liquids, such as their flexibility, enhanced sensitivity, and exceptional stability, a multilayer sensor has been manufactured. This sensor consists of carbon nanotube electrodes, ionic liquid dispersed in polymer creating a pressure-sensitive layer, and polymer insulating layers. The focus of this study is on the development of the sensor and understanding how its output changes under varying normal and tangential forces. Preliminary testing has shown that the sensor exhibits distinct and measurable responses to both force components, highlighting its potential for accurate force differentiation. The research evaluates the sensor’s performance and efficacy under varied force conditions, demonstrating its capability to accurately measure both normal and tangential forces. Such measurements are vital for the development of intelligent tires, offering deeper insights into critical tire parameters such as braking or traction force coefficients, contact patch characteristics, vehicle dynamics, and road surface conditions, leading to the improvement of safety, efficiency, and performance of tires.
Finite element analysis has become a standard tool in the engineer's toolbox for tire and vehicle development work, with the goal of simulations replacing early prototypes and tests becoming a reality. However, 50 years ago this was just a glimmer on the horizon, with most of the fundamental model features and solution methodologies used in today's tire simulations, which are now taken for granted as routine, not existing in the finite element codes. Hence, tire researchers in the early 1970s began developing and incorporating technologies into the codes so that basic tire mechanics could be represented, allowing increasing levels of tire performance simulations to be performed. The current model and simulation capabilities have been built upon this foundation of research and applications to give engineers a wide range of tire performance solutions that can be entrusted to virtually develop tires and vehicles for production. This article reviews the early years of the development and application of tire finite element analyses, giving current users of the method an understanding of the foundational work that was done and the main people involved in its development.
ABSTRACT This article aims to determine the excited volume and penetration depth in the theoretical friction model of rubber sliding on a corundum surface. The theoretical procedure of the Klüppel friction theory was implemented using the power spectral density of the corundum surface and viscoelastic model for rubber. The power spectral density was obtained with a power-law mode using the height difference correlation function parameters calculated from a surface measurement taken with a profilometer. Viscoelastic model parameters for the rubber were derived from a dynamic mechanical analyzer. Empirical law for friction coefficient obtained from the side force experiments and simulations of a laboratory abrasion tester (LAT 100) were used in this work. The friction coefficient from the theoretical procedure was matched with the empirical friction coefficient to estimate the penetration depth and excited volume of rubber. The correlation between the theoretical and empirical model was satisfactory. Estimating the penetration depth and excited volume of sliding rubber provides an insight into the contact conditions near surface asperities and the volume of rubber contributing to energy dissipation during the frictional process.
