Tire Model Research Articles

Analytical solution of vehicle phase-plane equilibria through the Root-Rational tyre model

Passenger vehicle steady-state behaviour has been investigated for a long time. Among the existing methods, the phase portrait is rather popular and useful. However, the computation of vehicle equilibria may only be done numerically. Furthermore, the numerical procedure must be repeated in case of changes in the inputs (e.g. steering angle). This paper proposes a new methodology to obtain an analytical solution of vehicle equilibria. The key is the definition of a new tyre model, denoted as Root-Rational (RR) tyre model, which allows inverting the vehicle dynamics equations in closed form. Using the proposed tyre model reduces the equilibria location problem to finding the roots of a third-order polynomial. After describing the procedure in detail, comparisons are made between the analytical solution and a classical numerical approach, either using the same RR tyre model or a more classical one. Results show great accuracy when locating the equilibria coordinates and a significantly reduced computational time, paving the way for innovative vehicle stability control algorithms based on the real-time identification of the stability region in the phase plane.

Research on Lateral Stability Control of Four-Wheel Independent Drive Electric Vehicle Based on State Estimation.

This paper proposes a hierarchical framework-based solution to address the challenges of vehicle state estimation and lateral stability control in four-wheel independent drive electric vehicles. First, based on a three-degrees-of-freedom four-wheel vehicle model combined with the Magic Formula Tire model (MF-T), a hierarchical estimation method is designed. The upper layer employs the Kalman Filter (KF) and Extended Kalman Filter (EKF) to estimate the vertical load of the wheels, while the lower layer utilizes EKF in conjunction with the upper-layer results to further estimate the lateral forces, longitudinal velocity, and lateral velocity, achieving accurate vehicle state estimation. On this basis, a hierarchical lateral stability control system is developed. The upper controller determines stability requirements based on driver inputs and vehicle states, switches between handling assistance mode and stability control mode, and generates yaw moment and speed control torques transmitted to the lower controller. The lower controller optimally distributes these torques to the four wheels. Through closed-loop Double Lane Change (DLC) tests under low-, medium-, and high-road-adhesion conditions, the results demonstrate that the proposed hierarchical estimation method offers high computational efficiency and superior estimation accuracy. The hierarchical control system significantly enhances vehicle handling and stability under low and medium road adhesion conditions.

Critical response analysis of asphalt pavement on concrete curved ramp bridge deck considering tire-bridge interaction

ABSTRACT This study developed a full-scale concrete curved ramp bridge deck finite element (FE) model, which considered the effect of tire-bridge interaction. In this full-scale FE model, an inflated tire model was developed to simulate the rolling tire load. The tire-bridge interaction equations were established based on the different interaction modes of the driving and driven wheels with the deck pavement. The effects of travel speed, curvature radius and load position on the critical response of bridge deck pavement was analysed. The results indicated that the deck pavement above the mid-span and flange cantilever panel exhibited greater critical tensile stress and strain values; whereas the bearing end diaphragm and the flange longitudinal diaphragm contributed the maximum critical shear stress. In the vertical depth direction, the damage induced by the traffic load mainly initiated at the deck pavement surface, and shear damage was more prone to occur between the layers of different paving materials. The reduced curvature radius and increased travel speed both promoted the appearance of unbalanced damage in the inner and outer tire loading zones. Besides, the smaller curvature radii and higher travel speeds would result in more severe local damage of deck pavement.

Analysis of coupled suspension lateral dynamics characteristics based on suspension moment centre and non-steady tyre model

This paper presents an analytical approach for developing a coupled suspension lateral dynamics model to investigate lateral vibration characteristics. The concept of the suspension moment centre was introduced. The direction of the constraint reaction force from the independent suspension control arm is perpendicular to the tyre contact speed. This arrangement leads to a larger lateral movement of the suspension hub as the height of the moment centre increases. According to the coupled suspension lateral dynamics model, experimental results were used to validate the relationship between wheel camber, lateral displacement of wheel centre and wheel travel. The non-steady state lateral suspension force was calculated based on the tyre slip ratio, defined as the lateral speed relative to the rolling speed, and the system dynamics characteristics was analysed. The results show that under excitation from an uneven road surface, the root mean square value of the suspension lateral force initially increases and then decreases as vehicle speed increases. Additionally, the root mean square value of the suspension lateral force increases with the increase in tyre relaxation length.

Emergency obstacle avoidance control for X-by-wire-based intelligent vehicles considering tire-road friction coefficient

This study presents an emergency obstacle avoidance control (OAC) algorithm for intelligent vehicles equipped with X-by-wire (XBW) systems. A tire-road friction coefficient (TRFC) observer is developed based on vehicle and tire models. A multi-sensor fusion method, utilizing Kalman filter and Bayesian estimation, is proposed to improve perception accuracy by using Mahalanobis distance to match sensor measurements. OAC strategies are designed by dividing braking and steering areas based on relative longitudinal distance. The braking-based strategy generates a desired deceleration which will be realize by an electro-hydraulic braking system (EHBS) with a sliding mode controller. The steering-based strategy plans an optimal trajectory using a cost function, generating a desired steering angle to follow this trajectory. The algorithm is tested on a hardware-in-the-loop (HIL) system under various scenarios, demonstrating the adaptability and precision of the TRFC observer. Additionally, the proposed fusion method shows a significant improvement in the average perception accuracy of longitudinal distance and lateral velocity. Moreover, by considering TRFC, the algorithm is able to improve OAC performance while ensuring driving comfort and vehicle stability in emergency situations.

The Nonlinear Dynamic Response and Vibration Transmission Characteristics of an Unloading System with Granular Materials

The aim of this study is to research the flow property of granular materials under nonlinear vibration, which directly affects the stability of the unloading system and the motion state of granules. According to the mechanical constitutive relation, the coupled suspension–tire model with nonlinear ordinary differential equations is established and the kinematic equations of granules are derived. Furthermore, the amplitude–frequency responses of the coupled system and force transmissibility are obtained by the incremental harmonic balance method (IHBM) with high-order approximation, and then the flow characteristics of granular materials are investigated based on the approximate analytic solution under nonlinear vibration. The theoretical analysis and numerical simulation show that the coupled suspension–tire system presents a softening nonlinear feature and the peaks are significantly smaller than that of the linear system, which further affects the motion rules of granular materials. As a result, different sliding states and flow paths are observed under the same operating conditions. This research not only shows the unloading mechanism and vibration transmission characteristics between the continuum structure and granular material but also theoretically explains the control mechanism of the coupled continuum–granular system. The research is instructive in improving the unloading efficiency of granules in practical engineering.

Development of Robust Lane-Keeping Algorithm Using Snow Tire Track Recognition in Snowfall Situations.

This study proposed a robust lane-keeping algorithm designed for snowy road conditions, utilizing a snow tire track detection model based on machine learning. The proposed algorithm is structured into two primary modules: a snow tire track detector and a lane center estimator. The snow tire track detector utilizes YOLOv5, trained on custom datasets generated from public videos captured on snowy roads. Video frames are annotated with the Computer Vision Annotation Tool (CVAT) to identify pixels containing snow tire tracks. To mitigate overfitting, the detector is trained on a combined dataset that incorporates both snow tire track images and road scenes from the Udacity dataset. The lane center estimator uses the detected tire tracks to estimate a reference line for lane keeping. Detected tracks are binarized and transformed into a bird's-eye view image. Then, skeletonization and Hough transformation techniques are applied to extract tire track lines from the classified pixels. Finally, the Kalman filter estimates the lane center based on tire track lines. Evaluations conducted on unseen images demonstrate that the proposed algorithm provides a reliable lane reference, even under heavy snowfall conditions.

Passenger vehicle behavior modeled by Power Flow using different mathematical tire models

Ground Vehicles can be approached as a set of integrated subsystems, with cause-effect relationships. Through the Power Flow Modeling approach, each of these subsystems can be interpreted as a black box, and interrelated with the others in a modular way, as long as causalities are respected. This work aims to take advantage of the modularity of the automobile interpreted as a set of integrated subsystems and evaluate the influence of mathematical tire models on its acceleration and braking behavior. Each of the subsystems is mathematically modeled in individual blocks that are then integrated, without loss of causality, in MATLAB/Simulink® software. The purpose is to provide a fully modular vehicle model, taking advantage of this Power Flow feature, in an open-source code. Furthermore, Inverse Problems are applied to estimate parameter values of the Burckhardt and Dugoff mathematical models in order to obtain similar behaviors of the corresponding tire model by the Magic Formula.

Vibration characteristics of vehicle-pavement coupled system with non-uniform dynamic tire model based on nonlinear Timoshenko foundation beam

Vibration characteristics of vehicle-pavement coupled system with non-uniform dynamic tire model based on nonlinear Timoshenko foundation beam

Analysis of Tire-Road Interaction: A Literature Review

This paper presents a comprehensive literature review of the most popular and recent work on passenger and truck tires. Previous papers discuss a huge amount of work on the modeling of passenger car tires using finite element analysis. In addition, recent works on tire–road interaction and the validation of tires using experimental measurements have been described. Moreover, the history of the tire-road contact algorithms is explained. In addition, friction modeling that is implemented in tire–road interaction applications are discussed. Also, a summary of current state-of-the-art research work definitions and requirements of the tread rubber compound are covered from previous studies using various literature reviews and hyper-viscoelastic material models that are implemented for the tread top and the tread base rubber compound. Furthermore, the effect of tire temperature from previous works is presented here. Finally, this literature review also highlights the shortcomings of recent research work and describes the areas lacking in the literature.

RBCKF-Based Vehicle State Estimation by Adaptive Weighted Fusion Strategy Considering Composite-State Tire Model

The acquisition of vehicle driving status information is a key function of vehicle dynamics systems, and research on high-precision and high-reliability estimation of key vehicle states has significant value. To improve the state observation effect, a vehicle sideslip angle estimation method adopting a robust bias compensation Kalman filter and adaptive weight fusion strategy is proposed. On the basis of the extended Kalman filter algorithm, and with the goals of estimation exactitude and robustness, considering the potential signal deviation, a vehicle state robust deviation compensation Kalman filter estimation algorithm considering bias compensation and residual covariance matrix weighting is proposed. Meanwhile, considering the adaptive and dynamic adjustment capabilities of the observation system in complex state-change scenarios, an estimation strategy based on adaptive weight fusion and a model-based estimator is proposed. The results confirm that the robust bias compensation Kalman filter can ensure estimation exactitude and robustness when the vehicle state fluctuates greatly, and the proposed fusion strategy can ensure that the vehicle maintains optimal estimation performance during operating condition switching.

A Novel Nonlinear Adaptive Control Method for Longitudinal Speed Control for Four-Independent-Wheel Autonomous Vehicles

As autonomous driving technology and four-independent-wheel chassis systems advance, four-independent-wheel autonomous vehicles have increasingly become a focal area of modern research. The longitudinal control problem for four-independent-wheel autonomous vehicles presents challenges such as complex models, high nonlinearity, and strong system uncertainties. This paper proposes a novel hierarchical control algorithm to address these challenges, innovatively combining the advantages of adaptive backstepping and dynamic sliding mode control algorithms in the upper controller, allowing it to effectively overcome the impact of uncertain system parameters and suppress the common chattering phenomenon in the output of typical sliding mode control methods. Based on the design of the upper controller, an innovative optimized longitudinal force distribution strategy and the construction of a tire reverse longitudinal slip model are proposed, followed by the design of a fuzzy PID controller as the lower slip ratio controller to achieve precise whole-vehicle longitudinal speed tracking and improve overall control performance. This method not only improves the accuracy of speed tracking but also enhances the robustness and adaptability of the control system. Finally, the effectiveness and superiority of the proposed hierarchical control method are verified through CarSim simulations.

Similarities Between Wheels and Tracks: A “Tire Model” for Tracked Vehicles

Similarities Between Wheels and Tracks: A “Tire Model” for Tracked Vehicles

Rollover prevention by designing a new fuzzy set solution for automotive active stabilizer bars based on a complex dynamic model

In this paper, the author introduces using active stabilizer bars (hydraulic anti-roll bars) for automobiles to improve the stability of rolling over when an automobile is steering. The car rollover oscillation is described by a complex dynamic model, a combination of the Pacejka tire model, the motion model, and the full oscillation model. A new fuzzy solution has been developed in order to control the active stability bars. This algorithm has three inputs related to the car’s rollover factor. The fuzzy rule (with 125 situations) and membership function are determined based on views related to the car’s stability and the antiroll system’s responsiveness. Numerical calculations and simulation are performed with two cases corresponding to two kinds of steering angles. Three situations correspond to three velocity values: v1, v2, and v3, and four scenarios are simulated in each situation to facilitate the comparison of results. According to the research findings, output values such as roll angle, rollover index, and load change are drastically reduced when the new fuzzy solution is applied to the active anti-roll bars. In the last case, the rollover occurs when the automobile does not use any stability bars or uses regular mechanical bars. The roll angle peak values reach 8.79° and 10.79°, while the maximum value belonging to the Active with Fuzzy situation is 10.94° without rolling over (corresponding to a rollover index of 0.64). The results obtained from this paper are the basis for developing more complex solutions for stabilizer bars in the future.

An Improved Adaptive Sliding Mode Control Approach for Anti-Slip Regulation of Electric Vehicles Based on Optimal Slip Ratio

To optimize the acceleration performance of independently driven electric vehicles with four in-wheel motors, this paper proposes an anti-slip regulation (ASR) strategy based on dynamic road surface observer for more efficient tracking of the optimal slip ratio and enhanced vehicle acceleration. The method uses the Unscented Kalman Filter (UKF) observer to estimate vehicle speed and calculate the actual slip ratio, while a fuzzy controller based on the Burckhardt tire model identifies road surfaces. The road’s peak adhesion coefficient and optimal slip ratio curve are fitted using a Back Propagation Neural Network (BPNN) optimized by Particle Swarm Optimization (PSO). The control strategy further refines torque management through an adaptive sliding mode control (ASMC) that integrates adaptive laws and a super-twisting sliding mode approach to track the optimal slip ratio. Joint simulations with MATLAB/Simulink and Carsim on low-adhesion, joint, and split road surfaces demonstrate that the strategy quickly and accurately identifies the optimal slip ratio across various road surfaces. This enables the tire slip ratio to approach the optimal value in minimal time, significantly improving vehicle dynamic performance. Compared to conventional sliding mode controllers, the optimized ASMC reduces chattering and improves control precision.

Winch Traction Dynamics for a Carrier-Based Aircraft Under Trajectory Control on a Small Deck in Complex Sea Conditions

When the winch traction system of a carrier-based aircraft works under complex sea conditions, the rope and the tire forces are greatly changed compared with under simple sea conditions, and it poses a potential threat to the safety and stability of the aircraft’s traction system. The accurate calculation of the rope and tire forces of a carrier-based aircraft’s winch traction under complex sea conditions is an arduous problem. A novel method of dynamic analysis of the aircraft-winch-ship whole system under complex sea conditions is proposed. A multiple-frequency excitation is adopted to describe the complex sea conditions and the influences of pitching amplitude, and the rolling frequency on the traction dynamics of a carrier-based aircraft along the setting trajectory under complex sea conditions are studied. The advantages and disadvantages of a winch traction system with trajectory control and without trajectory control in complex sea conditions are analyzed. For realizing the trajectory control of the aircraft, the vector difference between the center of mass for the carrier-based aircraft and the position on the predetermined Bessel curve is calculated, so as to obtain the azimuth vector in the aircraft coordinate system. This research is innovative in the modeling of the whole system and the trajectory control of a carrier-based aircraft’s winch traction system under the complicated sea condition of the multi-frequency excitation. ADAMS (Automatic Dynamic Analysis of Mechanical System) is used to verify the correctness of the theoretical calculation for the winch traction. The results show that the complex sea environment has a certain influence on the winch traction safety of the aircraft; in the range of 10–15 s for the traction, the rope force amplitude of complex sea conditions under the multi-frequency excitation is 29.5% larger than that of the single-frequency amplitude, while the vertical force amplitude of the tire is 201.1% larger than that of the single-frequency amplitude. This research has important guiding significance for the selection of rope and tire models for a carrier-borne aircraft’s winch traction in complex sea conditions.

Hardware-in-the-Loop Simulations and Experiments of Anti-Lock Braking System for Cornering Motorcycles

This study focuses on developing an advanced anti-lock braking system (ABS) for motorcycles, specifically targeting the challenges associated with cornering. Significant roll angles during motorcycle turns can often lead to slipping and the loss of control, increasing the risk of accidents. Existing ABSs primarily address longitudinal dynamics and fail to provide optimal braking control during cornering. To address this gap, this study utilizes BikeSim and MATLAB/Simulink for simulations and experiments to design an ABS that adapts to varying roll angles by analyzing motorcycle dynamics during cornering. A tire model is constructed using the Magic Formula to examine both longitudinal and lateral characteristics under different conditions, which helps determine the current tire slip set-point. The controller, designed with a finite-state machine combined with bang-off-bang control, uses tire slip as the control variable. It adjusts the slip set-point based on changes in roll angle and sends control signals to the hydraulic actuator to regulate braking pressure, ensuring optimal braking performance without the loss of control. Finally, hardware-in-the-loop experiments are conducted, with real-time control commands sent to the hardware platform’s actuator via BikeSim RT. These experiments validate the effectiveness of the designed controller, significantly enhancing braking stability during cornering and improving safety for motorcycle riders.

Validation of a new road and contact model for vehicle–soft soil terrain interaction through an elaborate modelling of the FED-Alpha vehicle

Employing multibody dynamic simulations with semi-empirical tyre models is widely recognised as a cost-effective approach. A recent development introduces a novel road and tyre–soil contact model that is not only swift and memory-efficient but also addresses limitations in classical semi-empirical models. This study conducts a thorough validation of the new road and contact model by creating a detailed multibody model of the four-wheeled vehicle, Fuel Efficiency Demonstrator – Alpha, integral to NATO’s Next-Generation reference mobility model. The comprehensive model encompasses the chassis, suspension, tyres, engine, transmission and various other components. Through simulations of various driving scenarios, accounting for complex terrain geometries, spatially varying soil properties and multi-pass phenomena, the model’s performance is evaluated. The simulation results are compared with physical measurements, providing a detailed assessment of the tyre–soil model’s predictive accuracy for wheeled vehicle mobility on deformable terrains.

Mechanical properties analysis of non-pneumatic tire with gradient honeycomb structure

Non-pneumatic tires have the advantages of high safety and high load-carrying capacity, and have a broad potential for engineering applications. In this paper, the effects of different gradient angles on the static and dynamic performance of honeycomb spoke structure are studied. First of all, according to different gradient and gradient-free Non-Pneumatic Tires (NPTs) are designed and the corresponding finite element models of non-pneumatic tires are established respectively. Then, the static mechanical properties of NPTs are analyzed, including the bearing capacity of NPTs and the stress distribution of NPT components. Finally, the dynamic mechanical properties of gradient-free and gradient NPTs are simulated. The stress characteristics and rolling characteristics of the gradient to the key components of NPTs under dynamic load are analyzed. The results show that different gradients have effects on the radial stiffness of the tire, the maximum stress distribution position of spokes, tire rolling characteristics, and the stress characteristics of other parts of NPTs. The research results provide guidance for the structure design and optimization of non-pneumatic tires.

Investigating Tire Ground Contact Mechanics Under Partial Hydroplaning Conditions: A Multivariate Analysis Approach

Tire hydroplaning is one of the main causes of traffic accidents on slippery roads. In order to study the ground contact mechanical characteristics of tires under partial hydroplaning conditions, 205/55the R16 passenger car tire was taken as the research object, a tire hydroplaning CEL simulation model was established, and the test plan was created using the orthogonal experimental design method. Through range analysis, partial correlation analysis and multivariate linear regression analysis, a tire side slip UA model suitable for different working conditions on slippery roads was established. Comparative analysis shows that the model can accurately predict the tire ground contact mechanical characteristics on slippery roads, and provide a theoretical reference for studying the tire multi-condition hydroplaning performance.