Tire Model Research Articles

An Advancement in Truck-Tire–Road Interaction Using the Finite Element Analysis

This paper aimed to investigate the cornering characteristics of a Regional Haul Steer II, RHS 315/80 R22.5 truck tire traveling on a dry, hard surface using the Finite element analysis (FEA). This research was carried out using commercial Finite Element software and Pam-Crash in an Explicit Environment. A finite element truck tire model was developed to apply the tire terrain cornering condition. The concentrated loads and boundary conditions for the rim and wheel were applied to the model. The rubber material was defined using the Mooney–Rivlin model. The truck tire cornering operating conditions, including three different speeds with respect to various positive slip angles, were investigated. Several simulations were repeated at various operating conditions, including three different inflation pressures and three different vertical loads. Subsequently, the tire lateral force was computed using the local and global frame coordinates. Additionally, the self-aligning moment was extracted from the tire cross-section at each operating condition. Finally, a comparison between the simulation results showed that the tire lateral force was highly sensitive to the variation of the slip angles at the higher domain, and also that the tire inflation pressure, regardless of the speed, was considered to be one of the main parameters directly affecting the tire-cornering properties.

Thermomechanical Modeling of Aircraft Tire–Runway Contact for Transient Maneuvers

ABSTRACT The aircraft tire is the link between the aircraft and the runway and transmits forces and moments within the contact area. During ground maneuvers, the tire is exposed to a wide range of operating conditions. The tires support the weight of the aircraft, they ensure safe rolling during taxiing, and they transfer the required forces to the runway during takeoff and landing. Temperature development during these maneuvers is of great importance because temperature can affect both material stiffness and friction behavior as well as wear characteristics. Heat is generated inside the tire due to energy dissipation caused by the cyclic loading of the tire during rolling. In addition, heat is generated due to friction in the tire–runway contact. Experimental measurements of the temperature distribution in the entire tire are not yet possible. The tire temperatures can only be determined at selected critical spots. Simulation models can help to obtain a better understanding of the overall tire temperature distribution during transient maneuvers. In this work, the transient thermomechanical processes of a rolling aircraft tire, e.g., directly following the touchdown process or during taxiing, are modeled based on a simple physical tire model. An extended brush model is used to simulate the contact forces. The tire temperature is determined via the transient heat conduction equation in radial and circumferential directions. The mechanical and thermal models are coupled via the coefficient of friction and the sliding velocities in contact. The free model parameters are parameterized using experimental data, and the overall model is validated by measurements on the whole tire. The validated thermomechanical tire model is used for simulations or the analysis of different driving maneuvers to get a better understanding of the temperature development in the aircraft tire.

A novel hyperbolic tangent sliding mode observation of vehicle lateral force fed back by longitudinal force error

AbstractThe tyre lateral force control is crucial to vehicle lateral stability. Vehicle side slip and out of control can be prevented effectively by observing accurately the lateral force. Thus, a novel quasi‐sliding mode observer (QSMO) is proposed. The algorithm adopts the longitudinal tyre force error as feedback considering vehicle parameter uncertainties and without a complex tyre model. First, the on‐line verification of the algorithm was carried out by dSPACE for using the experimental data of the real vehicle linear acceleration and deceleration conditions, and comparison of experimental output with different observation algorithms. Further, the simulation under emergency obstacle avoidance conditions and the double‐line shifting conditions were conducted to verify the accuracy of the algorithm respectively. Simulation results show that the percentage errors between the tyre lateral forces from the proposed QSMO and the actual data are less than 5.35%, and the prediction accuracy of the QSMO by 38.78% is higher than that of the conventional first‐order SMO (FSMO), which indicates that the QSMO is superior to the FSMO.

Coordinated Longitudinal and Lateral Stability Improvement for Electric Vehicles Based on a Real-Time NMPC Strategy

Under extreme conditions, such as low friction surfaces, violent steering and urgent acceleration/deceleration, vehicle states change rapidly and are influenced by nonlinear and coupled vehicle dynamics. To improve vehicle stability under extreme conditions, a hierarchical control strategy is proposed for DDEVs. In the upper layer controller, a combined-slip tire model is adopted to improve the model accuracy under extreme conditions. A nonlinear model predictive control based controller is then designed to generate the desired tire slip ratios with the main objectives of tracking the desired yaw rate and suppressing the lateral velocity and tire slip ratios. In the lower layer controller, the disturbance on the driver’s torque requirement, which is disregarded by existing studies, is taken into account. Next, a linear predictive controller is designed to track the desired tire slip ratios by adjusting the motor torques. To improve the computational efficiency of the nonlinear predictive controller, a PMP-based, fast solving algorithm is proposed. The effectiveness of the proposed solving algorithm is checked by comparing the control performance with IPOPT. The proposed control strategy is evaluated by a series of HIL experiments. The HIL results show better performance in overall stability improvement and minimize the disturbance on the driver’s torque requirement.

Soft Soil, Hard Problem

To help engineers with simulating off-road tyre applications, Mechanical Simulation Corporation has added a terramechanics-based tyre model to its CarSim and TruckSim vehicle dynamics simulation software

Slip Ratio Adaptive Control Based on Wheel Angular Velocity for Distributed Drive Electric Vehicles

In order to solve the adaptability problem of acceleration slip regulation for distributed drive electric vehicles, a slip ratio adaptive control strategy based on wheel angular velocity is proposed. The principle of road estimation algorithm based on the Burckhardt tire model is analyzed, and an improved estimation principle for optimal slip ratio is designed to improve the speed and accuracy of optimal slip ratio estimation. A slip ratio control strategy based on a conditional integral sliding mode control is designed, and its stability is proven. To make the slip ratio control strategy have better practicability, the slip ratio control strategy is combined with the road estimation algorithm, and the control variable of the slip ratio adaptive control strategy based on a conditional integral sliding mode control is redesigned to obtain a faster vehicle dynamic response. Finally, the effectiveness of the designed road estimation algorithm and the slip ratio adaptive control strategy is verified by simulation of acceleration on joint road and split road. Results show that the designed road estimator can obtain the road adhesion coefficient and optimal slip ratio quickly and accurately; the slip ratio adaptive controller, based on a conditional integral sliding mode control, can maintain the wheel slip ratio near the optimal slip ratio and reduce the steady-state error of the wheel slip ratio.

An Energy Efficient Control Strategy for Electric Vehicle Driven by In-Wheel-Motors Based on Discrete Adaptive Sliding Mode Control

This paper presents an energy-efficient control strategy for electric vehicles (EVs) driven by in-wheel-motors (IWMs) based on discrete adaptive sliding mode control (DASMC). The nonlinear vehicle model, tire model and IWM model are established at first to represent the operation mechanism of the whole system. Based on the modeling, two virtual control variables are used to represent the longitudinal and yaw control efforts to coordinate the vehicle motion control. Then DASMC method is applied to calculate the required total driving torque and yaw moment, which can improve the tracking performance as well as the system robustness. According to the vehicle nonlinear model, the additional yaw moment can be expressed as a function of longitudinal and lateral tire forces. For further control scheme development, a tire force estimator using an unscented Kalman filter is designed to estimate real-time tire forces. On these bases, energy efficient torque allocation method is developed to distribute the total driving torque and differential torque to each IWM, considering the motor energy consumption, the tire slip energy consumption, and the brake energy recovery. Simulation results of the proposed control strategy using the co-platform of Matlab/Simulink and CarSim® demonstrate that it can accomplish vehicle motion control in a coordinated and economic way.

Static Stiffness Properties of High Load Capacity Non-Pneumatic Tires with Different Tread Structures

A high load capacity non-pneumatic tire (HC tire) was designed and manufactured to solve the problems of air leakage, puncture, blowout, shoulder void, and delamination, which occur in traditional high load capacity tires, as well as significantly increase the unit load of tires. Experiments and numerical simulations were conducted to investigate the static stiffness properties of the HC tire. Additionally, the manufacturing process of the tire was highlighted. The tire mainly comprised polyurethane and silicon manganese steel, and a ‘π’-shaped support substructure was adopted. The tread structure was made up of a built-in spiral steel ring and a non-steel ring. The uniaxial tensile mechanical properties of the used metal and elastomer materials were tested, and the linear elastic constitutive model and Marlow constitutive model, respectively, were used to describe their mechanical characteristics. The stiffness properties of the HC tire, including torsional, longitudinal, vertical, and lateral stiffnesses, were evaluated using a tire comprehensive stiffness tester. Nonlinear finite element models of the HC tire were established, and their accuracies were verified through vertical stiffness tests. The stiffness properties of the HC tire in other directions were simulated as well. An in-depth comparative analysis of the simulation and experimental data was performed. The results demonstrated that the unit load of the unreinforced HC tire was 2.972 times and 1.615 times higher than that of the solid tire and pneumatic tire, respectively. The spiral steel ring embedded in the tread increased the vertical and longitudinal stiffness but reduced the torsional stiffness of the HC tire, thus reversing the variation trend of the lateral stiffness at the 0° and 5° test points. The findings can serve as a reference for theoretical research on, and the structural optimization of, non-pneumatic tires with a high load capacity.

Linear Stability of Reversing a Car-trailer Combination

In this paper, we investigate the reverse motion of a car-trailer combination. The single track model of the vehicle is used with quasi-static tire model to design a simple linear feedback controller that can achieve stable reversing motion along a straight path. The linear stability of the closed-loop system is analyzed by constructing stability charts in the plane of the control gains. The effect of the reversing speed of the vehicle on the stability is also shown. In order to validate the theoretical results, laboratory experiments are carried out using a small-scale vehicle and a conveyor belt.

A fusion estimation of tire vertical forces using model-based tire state estimators for a dual-sensor intelligent tire

Estimating tire vertical forces is essential to vehicle state estimation and stability control. Intelligent tires can be used to estimate tire vertical forces, but functional safety and extensive tests are issues to consider during intelligent tire development. This paper proposes a fusion estimation approach using model-based tire state estimators (TSEs) to estimate the tire vertical forces of a dual-sensor intelligent tire, which can output the circumferential strain, radial, and circumferential acceleration signals with a strain sensor and an accelerometer mounted at different positions on the inner liner. The mutual conversion between strain and acceleration signals is indicated in this paper for the first time; therefore, the internal relationship between different signals is revealed. Each measurement signal of the two sensors corresponds to a TSE composed of a signal processing algorithm, a mathematical model, and a Kalman filter. The mathematical model is proposed in this paper based on the flexible ring tire model (FRTM). The final estimated value of the tire vertical force is obtained by weighting and summing the outputs of the three TSEs. The weighting factors are determined using the genetic algorithm to study the fusion estimation effect. An integrated CarSim model is built in this paper to validate the estimation performance under various driving conditions, including driving straight at a constant speed, driving on an S-shaped road, and performing a double lane change at a high vehicle speed. For all driving conditions, the mean error rates of the fusion estimation are less than 2%. The model-based tire state estimators can avoid the extensive tests needed in the data-based methods. Furthermore, the fusion of the outputs of three TSEs can further improve the estimation performance compared with the situation when a single TSE is used. Therefore, the studies in this paper have guiding significance for intelligent tire development.

Modeling and Verification of Tire Nonlinearity Effect on Accuracy of Vehicle Yaw Rate Calculation

<div class="section abstract"><div class="htmlview paragraph">The desired yaw rate is a vital target parameter for vehicle stability control, which is currently determined as a steady-state yaw rate by the linear single-track vehicle model. Tire nonlinearity deteriorates the effect of vehicle stability control at larger lateral acceleration. This paper proposes a new calculation method of the steady-state yaw rate considering the tire nonlinearity based on the brush tire model. To validate and verify the proposed method, step steering tests of the target vehicle under different lateral accelerations are carried out on a real proving ground. The results show that when the lateral acceleration is relatively small, the difference between the calculation results of the proposed method and the traditional one is not apparent, and both methods can provide a good estimation for the steady-state yaw rate; however, when the lateral acceleration is relatively large, the difference becomes apparent. It can be shown that the linear tire model cannot be able to calculate the steady-state yaw rate accurately, while the brush tire model agrees well with the observation. This difference shows the importance of considering tire nonlinearity in vehicle stability control, especially in extreme driving conditions. By analyzing the existence of the solution of the yaw rate equation, this paper finds that the vehicle speed upper limit under which the vehicle can be able to achieve steady-state steering is also affected by the tire nonlinearity. A Simulink vehicle model is built to verify the steady-state vehicle speed upper limit for vehicles with different steering characteristics. The results of the modeling and tests provide certain guidelines for developing a vehicle stability control system.</div></div>

Trajectory Planning and Tracking for Four-Wheel Independent Drive Intelligent Vehicle Based on Model Predictive Control

<div class="section abstract"><div class="htmlview paragraph">This paper proposes a dynamic obstacle avoidance system to help autonomous vehicles drive on high-speed structured roads. The system is mainly composed of trajectory planning and tracking controllers. The potential field (PF) model is introduced to establish a three-dimensional potential field for structured roads and obstacle vehicles. The trajectory planning problem that considers the vehicle’s and tires’ dynamics constraints is transformed into an optimization problem with muti-constraints by combining the model predictive control (MPC) algorithms. The trajectory tracking controller used in this paper is based on the 7 degrees of freedom (DOF) vehicle model and the UniTire tire model, which was discussed in detail in previous work [<span class="xref">25</span>, <span class="xref">26</span>]. The controller maintains good trajectory tracking performance even under extreme driving conditions, such as roads with poor adhesion conditions, where the car’s tires enter the nonlinear region easily. The innovation of this paper lies in introducing a high-fidelity vehicle model and a muti-conditions UniTire tire model with high precision obtained after parameter identification through tire test data. In addition, the nonlinear relationship between tire lateral force and slip angle is expressed as a linear function. This method updates the equivalent cornering stiffness in the linear function by solving the slope of the secant of the tire cornering characteristic curve at the current moment online, which solves the problem of high computational complexity caused by applying complex tire models in the control system. The co-simulation results of Simulink and CarSim show that the designed system has good dynamic obstacle avoidance and driving stability performance under driving conditions with high speed and poor road adhesion.</div></div>

Deep Reinforcement Learning-Based Torque Vectoring Control Considering Economy and Safety

This paper presents a novel torque vectoring control (TVC) method for four in-wheel-motor independent-drive electric vehicles that considers both energy-saving and safety performance using deep reinforcement learning (RL). Firstly, the tire model is identified using the Fibonacci tree optimization algorithm, and a hierarchical torque vectoring control scheme is designed based on a nonlinear seven-degree-of-freedom vehicle model. This control structure comprises an active safety control layer and a torque allocation layer based on RL. The active safety control layer provides a torque reference for the torque allocation layer to allocate torque while considering both energy-saving and safety performance. Specifically, a new heuristic random ensembled double Q-learning RL algorithm is proposed to calculate the optimal torque allocation for all driving conditions. Finally, numerical experiments are conducted under different driving conditions to validate the effectiveness of the proposed TVC method. Through comparative studies, we emphasize that the novel TVC method outperforms many existing related control results in improving vehicle safety and energy savings, as well as reducing driver workload.

Hierarchical MPM-ANN Multiscale Terrain Model for High-Fidelity Off-Road Mobility Simulations: A Coupled MBD-FE-MPM-ANN Approach

AbstractA new hierarchical multiscale terrain model is developed using the material point method (MPM) to enable effective modeling of large terrain deformation for high-fidelity off-road mobility simulations. Unlike the Lagrangian finite element (FE) model, MPM allows for modeling large deformation of a continuum without mesh distortion using material points as moving quadrature points for the background grid. This unique feature is extended to account for complex granular soil material behavior with the hierarchical multiscale modeling approach in the context of off-road mobility simulations. The grain-scale discrete-element (DE) representative volume element (RVE) and its neural network surrogate model (artificial neural network (ANN) RVE) are developed and introduced to the upper-scale MPM model through the scale-bridging algorithm. The DE RVE is used to generate training data for the ANN RVE, allowing for predicting the history-dependent grain-scale soil material behavior efficiently at every material point that moves through the upper-scale MPM background grid. A numerical procedure for modeling the interaction of the nonlinear FE tire model with the MPM-ANN multiscale terrain model is developed considering moving soil patches generalized for the upper-scale MPM terrain model. It is fully integrated into the general off-road mobility simulation framework by leveraging scalable high-performance computing techniques. The predictive ability of the proposed MPM-ANN multiscale off-road mobility model is examined and validated against the full-scale vehicle test data, involving large deformation of soft terrain. The computational benefit from the neural network surrogate model is also demonstrated.

A model-based method of tire-road friction estimation for articulated steering vehicles

Articulated steering vehicles (ASV) are widely used in many industries for their high efficiency and excellent maneuverability. The autonomous driving and intelligent control of ASV are extremely critical owing to the operation characteristics. As a very important parameter, the tire-road friction coefficient (TRFC) determines the extreme tire force directly in the process of intelligent control. However, it cannot be obtained with the existing methods for the harsh environment and special structure of ASV. This paper proposed a two-layer model-based method of tire-road friction coefficient estimation for ASV. The dynamic models of ASV in the XY plane, including the longitudinal and lateral models of frames, tire forces, and steering system models, are established first. The dynamic models are embedded into the upper layer with a Kalman filter (KF) to estimate the tire forces in longitudinal and lateral directions. During the process, some self-contained sensors, including the state sensors of frames and steering system, are used to provide the observation data. In the lower layer, a recursive least square (RLS) method with a forgetting factor is used to obtain the TRFC and tire stiffness parameters with the aid of the tire model. The simulation and field test are carried out to validate the method under comprehensive conditions, in which different steering commands, velocities, and roads are included. The simulation and field test results show that the forgetting factor has a significant influence on the convergence and robustness of the proposed method. The forgetting factor τ = 0.95 is used in the field test, the estimation result of dry concrete road friction coefficient is around 0.83. The results indicated that the proposed method can obtain the TRFC and tire parameters dynamically for ASVs.

Nonlinear model predictive control for autonomous vehicle drifting

In this paper, nonlinear model predictive control (NMPC) is proposed for autonomous vehicle drifting, that is, stabilizing the vehicle at a desired unstable equilibrium point. Firstly, a three-degree-of-freedom vehicle model with a nonlinear tire model is introduced, and the equilibrium points are calculated. The relationship between the desired unstable equilibrium point and the lateral stability region is analyzed based on the phase plane method. Secondly, NMPC is designed to force vehicle states to stay around the desired unstable equilibrium point, that is, to keep the vehicle in sustained drifting. The terminal region and terminal constraint of NMPC are determined off-line to guarantee stability. Thirdly, Koopman operator theory and dynamic mode decomposition with control are introduced to obtain an approximately linear model, by which the nonlinear optimization problem is converted to a quadratic programming problem. Finally, comparative experiments are conducted by simulation, in which various model uncertainties are considered. The effectiveness of the proposed approach to achieve sustained autonomous drifting and to ensure vehicle safety is illustrated, and the efficient implementation of the proposed approach is also shown.

A novel numerical method for quantifying the combined effect of tire on 13-degree impact test of automotive wheels made of lightweight materials

One of the technical challenges encountered for automobile wheels made of lightweight materials is whether they can successfully pass the 13-degree impact test. When optimizing the wheel impact resistance through finite element method, the combined effect induced by the tire on this performance can be fully included by introducing the tire model, whereas its strong nonlinear characteristics lead to high computational cost and convergence difficulty. Therefore, to introduce the quantification coefficient for combined effect instead of tire model into the impact simulation model can effectively address above problems. However, the inaccurate quantification coefficient leads to the deviation in the evaluation of wheel impact resistance, which may directly affect the optimization design results. Aiming at these problems, a novel numerical method combining the energy reduction and energy-scaling coefficients is proposed. Firstly, an equivalent simulation model of wheel impact test excluding the tire is obtained by calculating and including the energy reduction coefficient. Then, an adaptive energy-scaling coefficient is constructed and introduced to ensure that the wheel strain status remains unchanged. Finally, the effectiveness and practicability of the proposed method are demonstrated by investigating two types of wheels. The results show that the proposed method can serve as an efficient tool during optimizing the impact resistance, not only improving the computational efficiency and convergence by excluding the tire model, but also accurately evaluating the wheel impact performance by including the combined effect.

Методические аспекты создания рам маломощных транспортных средств (квадроциклов) на основе трубчатых профилей

The paper discusses the main methodological aspects of creating a carrier system (frame) of a lowpower vehicle (quad-cycle) based on tubular profiles. The basic requirements for the frame of the ATV, the issues of the layout of the ATV based on the basic three points are considered. The requirements for the ATV frame are proposed, taking into account the possibilities of unification of design elements and modernization of the structure in the future when creating other models of tires. The analysis of consumer properties for the ATV and the influence of these properties on the design of the designed machine is carried out. A simplified algorithm for the development of a low-power vehicle frame is proposed, and it is also proposed to extend the cubic shape method to the ATV design process. The accuracy requirements for various methods of assembly of tubular parts of the ATV carrier system are considered.

Truck tyre transient rolling resistance and temperature at varying vehicle velocities - Measurements and simulations

Rolling resistance is causing a significant part of the energy consumption in truck applications, especially at low-speed levels. To be able to better estimate the energy consumption or remaining driving range, the truck tyre rolling resistance must be understood well. Temperature is a vital parameter for rolling resistance estimations. This article shows truck tyre rolling resistance and temperature measurements in a climate wind tunnel and simulations of tyre temperature and rolling resistance. During the climate wind tunnel tests, tyre temperature at the shoulder and tread was measured. In addition, on-road driving was conducted with inner-liner infrared temperature measurements. Tyre temperature simulations were conducted using a thermal tyre model with speed-variable thermal inertia. The comparison of tyre temperature simulations with measured inner-liner and shoulder temperatures showed good agreement with the test data. The rolling resistance was simulated using the principle of time-temperature superposition, and a master curve for rolling resistance and a curve for tyre temperature shift were constructed. These curves were used to simulate rolling resistance at a wide range of speed levels with good agreement to the experimental results. The investigation showed that the tyre shoulder temperature is a better indicator of rolling resistance than infrared measurements from the tyre tread.

Study on Deflection-Span Ratio of Cable-Stayed Suspension Cooperative System with Single-Tower Space Cable

This study uses the wind–vehicle–bridge coupling vibration analysis method to investigate the bridge stiffness problem of a large-span cable-stayed-suspension cooperative system. On the basis of the particle-damping-spring vehicle model, the TMeasy surface contact tire model is introduced, and a set of universal wind–vehicle–bridge coupling analysis algorithm is built in the framework of the whole process iterative method. Based on the Latin supercube sampling principle, random traffic flow is generated and loaded onto bridge structures with different stiffness conditions to analyze the driving comfort and safety under each stiffness condition. Combining the specification requirements, engineering experience, and research results, the vertical stiffness limit applicable to the bridge of the highway cable-stayed-suspension collaborative system is proposed. Existing engineering experience shows that the vertical deflection-to-span ratio of a cable-stayed bridge under live load is distributed between 1/400 and 1/1600, and the vertical deflection span ratio under the action of lane load is recommended based on numerical analysis.