Lateral Tire Forces Research Articles

Physical Understanding of Transient Generation of Tire Lateral Force and Aligning Torque

ABSTRACT Increasing vehicle performance requirements and virtualization of the development process require more understanding of the physical background of tire behavior, especially in transient rolling conditions with combined slip. The focus of this research is the physical description of the transient generation of tire lateral force and aligning torque. Apart from tire force and torque measurements, two further issues were investigated experimentally. Using acceleration measurement on the tire inner liner, it was observed that the contact patch shape of the rolling tire changes nonlinearly with slip angle and becomes asymmetric. Optical measurement outside and inside the tire has clarified that carcass lateral bending features both shear and rotation angle of its cross sections. A physical simulation model was developed that considers the observed effects. The model was qualitatively validated using not only tire force and torque responses but also deformation of the tire carcass. The model-based analysis explained which tire structural parameters are responsible for which criteria of tire performance. Change in the contact patch shape had a low impact on lateral force and aligning torque. Variation of carcass-bending behavior perceptibly influenced aligning torque generation.

Real-time estimation and prediction of tire forces using digital map for driving risk assessment

This work aims to develop a driving risk warning system to enhance the road safety. Different from the existing lane departure warning system, speed limit warning system or collision warning system, the warning system proposed in this work focuses on the safety regarding vehicle's dynamics states. Many road accidents are caused by losing control of vehicle dynamics, such as the rollover, car drift and brake failure. First of all, the importance of monitoring vehicle dynamics states, especially the tire forces, is explained. Then the driving risk assessment criteria based on tire forces are developed in this work. The main contribution of this paper is the development of vehicle dynamics models and observers to estimate and predict individual tire forces using only low-cost sensors and ADAS (Advanced Driver Assistance Systems) map. The major new techniques developed in this study can be summarized in three aspects: (1) development of new vehicle dynamics models to estimate vertical, longitudinal, and lateral tire forces, (2) development of new nonlinear observers to minimize the estimation errors caused by sensor noises and model uncertainty, and (3) development of the tire forces prediction algorithm by taking advantage of digital map. The proposed warning system is validated by real vehicle experiments.

Integrated yaw and rollover control based on differential braking for off-road vehicles with mechanical elastic wheel

Aiming at the issue of yaw and rollover stability control for off-road vehicles with non-pneumatic mechanical elastic wheel (MEW), an integrated control system based on fuzzy differential braking is developed. By simplifying the structure of the MEW, a corresponding fitting brush tire model is constructed and its longitudinal and lateral tire force expressions are set up, respectively. Then, a nonlinear vehicle simulation model with MEW is established to validate the proposed control scheme based on Carsim. The designed yaw and rollover control system is a two-level structure with the upper additional moment controller, which utilizes a predictive load transfer ratio (PLTR) as the rollover index. In order to design the upper integrated control algorithm, fuzzy proportional-integral-derivative (PID) is adopted to coordinate the yaw and rollover control, simultaneously. And the lower control allocator realizes the additional moment to the vehicle by differential braking. Finally, a Carsim-simulink co-simulation model is constructed, and simulation results show that the integrated control system could improve the vehicle yaw and roll stability, and prevent rollover happening.

Chassis integrated control for 4WIS distributed drive EVs with model predictive control based on the UKF observer

Four-wheel independent steering (4WIS) system and direct yaw moment control (DYC) have an important influence on vehicle lateral stability. However, DYC has a great effect on the longitudinal velocity, and the capability of 4WIS is limited to stability. To decrease the influence on the longitudinal velocity and improve the stability of electrical vehicles, a chassis controller integrated with a 4WIS system and a DYC system with model predictive control (MPC) is designed. The framework consists of an unscented Kalman filter (UKF) observer and an MPC that contains three blocks: supervisor blocks, upper blocks and lower blocks. First, the sideslip angle, longitudinal velocity and lateral tire forces are estimated by the UKF observer; second, a bicycle model is utilized in the supervisor to calculate the desired values; third, the upper blocks are designed with the MPC to optimize the target steering angles and longitudinal tire forces under the constraints of subsystems; to facilitate the design of the MPC, a nonlinear tire is simplified based on the Taylor expansion method; finally, the target steering angles and longitudinal tire forces are achieved by the lower blocks. The integrated controller is simulated on the co-simulation platform of MATLAB-Carsim. The results show that the proposed integrated controller has less impact on longitudinal velocity and could effectively improve vehicle stability.

Tire Lateral Vibration Considerations in Vehicle-Based Tire Testing

ABSTRACT Vehicle-based tire testing can potentially make it easier to reparametrize tire models for different road surfaces. A passenger car equipped with external sensors was used to measure all input and output signals of the standard tire interface during a ramp steer maneuver at constant velocity. In these measurements, large lateral force vibrations are observed for slip angles above the lateral peak force with clear peaks in the frequency spectrum of the signal at 50 Hz and at multiples of this frequency. These vibrations can lower the average lateral force generated by the tires, and it is therefore important to understand which external factors influence these vibrations. Hence, when using tire models that do not capture these effects, the operating conditions during the testing are important for the accuracy of the tire model in a given maneuver. An Ftire model parameterization of tires used in vehicle-based tire testing is used to investigate these vibrations. A simple suspension model is used together with the tire model to conceptually model the effects of the suspension on the vibrations. The sensitivity of these vibrations to different operating conditions is also investigated together with the influence of the testing procedure and testing equipment (i.e., vehicle and sensors) on the lateral tire force vibrations. Note that the study does not attempt to explain the root cause of these vibrations. The simulation results show that these vibrations can lower the average lateral force generated by the tire for the same operating conditions. The results imply that it is important to consider the lateral tire force vibrations when parameterizing tire models, which does not model these vibrations. Furthermore, the vehicle suspension and operating conditions will change the amplitude of these vibrations and must therefore also be considered in maneuvers in which these vibrations occur.

Self-excited vibration of whole vehicle with multiple limit cycles induced by shimmy of front wheels

Front wheel shimmy may induce the self-excited vibration of whole vehicle with multiple limit cycles. This kind of shimmy is difficult to control and can do great harm to the vehicle. In order to obtain the mechanism of this phenomenon, a 7-DOF dynamic model of whole vehicle self-excited vibration induced by the shimmy of front wheels which take the nonlinear factor of tire lateral force and the dry friction force in suspension and steering system into consideration was established. By using Hopf bifurcation theorem and central manifold theorem, the existence and stability of limit cycles are qualitatively determined. By means of numerical analysis, the self-excited vibration with multiple limit cycles is found. The results show that in the speed range of 50–185 km/h, front wheels shimmy induced the self-excited vibration of whole vehicle and the amplitude of system’s vibration decreases with the increase of vehicle speed; in the speed range of 50–83 km/h and 149–185 km/h, the self-excited vibration with multiple limit cycles occurs; in the speed range of 83–149 km/h, the self-excited vibration with single limit cycle occurs.

Simultaneous estimation of tire side-slip angle and lateral tire force for vehicle lateral stability control

Knowledge of tire side-slip angle and lateral tire force is crucial to vehicle lateral stability control which can enhance vehicle handling and passenger safety. However, due to high costs of sensors and limitations to sensor technologies, ordinary automobiles cannot measure the tire side-slip angle and lateral tire force directly during vehicle operation. Therefore, the accurate, affordable monitoring of lateral vehicle motion is essential. This paper presents a unified observation algorithm to simultaneously estimate the tire side-slip angle and lateral tire force of all four wheels. Firstly, an adaptive-sliding-mode observer (ASMO) is utilized to estimate the lateral tire force of each wheel. Secondly, the tire side-slip angle of each wheel can be estimated by an adaptive compensation algorithm (ACA). Simulations and real car experiments are used to validate the effectiveness of the proposed approach, and extended kalman filter (EKF) is used to compare with our proposed algorithm. Results show that the designed observer can effectively estimate tire side-slip angles and lateral tire forces of all four wheels, and its performance is better than EKF.

Optimization of control allocation with ESC, AFS, ARS and TVD in integrated chassis control

This paper presents an optimization of control allocation in integrated chassis control with active front steering, active rear steering, electronic stability control and torque-vectoring device under the saturation of lateral tire forces on front wheels. After a control yaw moment is calculated in the upper-level controller, a weighted pseudo-inverse based control allocation is used for yaw moment generation in the lower-level controller. Variable coefficients of the weighted pseudo-inverse based control allocation are used to represent various actuator combinations and are optimized for each actuator combination to enhance control performances using simulation on vehicle simulation package, CarSim. Due to severe cornering on low friction road, the front lateral tire forces can be easily saturated. Under the condition, the active front steering has little effect on control performance and, consequently, the desired control yaw moment cannot be generated. So, the lateral force generated by AFS should be restricted to its maximum, and a constrained weighted pseudoinverse based control allocation with electronic stability control, active rear steering and torque-vectoring device is applied to compensate the loss of the control yaw moment. Variable coefficients of the constrained weighted pseudo-inverse based control allocation with electronic stability control, active rear steering and torque-vectoring device are also optimized using simulated-based tuning. To validate the proposed method, simulation was done on CarSim. From simulation, it was verified which actuator combination is effective for integrated chassis control if the lateral forces on front wheels are saturated.

Integrated chassis control with AFS, ARS and ESC under lateral force constraint on AFS

This paper presents an integrated chassis control with active front steering (AFS), active rear steering (ARS) and electronic stability control (ESC) under lateral force constraint on front wheels. The control yaw moment is calculated using sliding mode control. A weighted pseudo-inverse-based control allocation (WPCA) is used for yaw moment distribution. On low-friction road, AFS has little effect on control performance since the lateral tire forces of front wheels are easily saturated. To overcome the problem, the lateral force generated by AFS is limited to its maximum, and the braking force of ESC and the angle of ARS, obtained from WPCA, are applied. To check the effectiveness of the proposed method, simulation was performed on the vehicle simulation package, CarSim. From simulation, it was verified that the proposed method can enhance the maneuverability and lateral stability, if the lateral forces on front wheels are saturated.

Adaptive Unified Monitoring System Design for Tire-Road Information

Knowledge of the tire-road information is not only very crucial in many active safety applications but also significant for self-driving cars. The tire-road information mainly consists of tire-road friction coefficient and road-tire friction forces. However, precise measurement of tire-road friction coefficient and tire forces requires expensive equipment. Therefore, the monitoring of tire-road information utilizing either accurate models or improved estimation algorithms is essential. Considering easy availability and good economy, this paper proposes a novel adaptive unified monitoring system (AUMS) to simultaneously observe the tire-road friction coefficient and tire forces, i.e., vertical, longitudinal, and lateral tire forces. First, the vertical tire forces can be calculated considering vehicle body roll and load transfer. The longitudinal and lateral tire forces are estimated by an adaptive unified sliding mode observer (AUSMO). Then, the road-tire friction coefficient is observed through the designed mode-switch observer (MSO). The designed MSO contains two modes: when the vehicle is under driving or brake, a slip slope method (SSM) is used, and a recursive least-squares (RLS) identification method is utilized in the SSM; when the vehicle is under steering, a comprehensive friction estimation method is adopted. The performance of the proposed AUMS is verified by both the matlab/simulinkCarSim co-simulation and the real car experiment. The results demonstrate the effectiveness of the proposed AUMS to provide accurate monitoring of tire-road information.

Active camber system for lateral stability improvement of urban vehicles

A suspension system with the capability of cambering has an additional degree of freedom for changing camber angle to increase the maximum lateral tire force. This study investigates the effects of cambering on overall vehicle stability with emphasis on applications to urban vehicles. A full vehicle model with a reliable tire model including camber effects is employed to investigate the vehicle dynamics behavior under cambering. Besides, a linearized vehicle model is used to analytically study the effects of camber lateral forces on vehicle dynamics. Vehicle behavior for different configurations of camber angles in front and rear wheels is studied and compared. Then, an active camber system is suggested for improvement of vehicle lateral stability. Specifically, performances of active front camber, active rear camber, and their combination are investigated. The results show that a proper strategy for camber control can improve both yaw rate and sideslip angle, simultaneously. Finally, the active front camber system is compared with the well-known active front steering. It is shown that, utilizing more friction forces at the limits, active front camber is more effective in improving maneuverability and lateral stability than active front steering.

Development of field test procedure to assess force performances of used tires

Based on United Nation Economic Commission for Europe (UNECE) regulations, there are no existing standard procedures to identify the force performance of used tire which can be physically degraded by time. In vehicle safety, these tire forces in lateral and longitudinal directions are the key factors to response the driver decision during the brake application and maneuver conditions. Therefore, the objective of this research is to develop the used tire performances based on three vehicle testing standards such as brake test, steady-state circular test and severe lane-change test respectively. To assess the tire force performances, two tire categories which are used in those tests with the driving and pedal robot for the sedan vehicle are classified as new tires from 2018 and used tires from 2015, 2014, 2013. To identify tire force performances, various indicators for each test are determined. For example, the standard brake test from UNECE R13H is used to investigate tire friction force in the longitudinal direction. The severe lane-change manoeuvre and steady state circular tests are used to identify the lateral tire force from ISO 3888-2 and ISO 4138 respectively. As a result, it can be concluded that the tire force performances from new and used tires are different based on various indicators.

전륜 횡력 포화 시 요모멘트 보상을 위한 통합 섀시 제어

In this paper, we present the integrated chassis control strategy with electronic stability control (ESC), active rear steering (ARS) and torque vectoring device (TVD) under the saturation of the lateral tire force on front wheels, caused by the excessive application of active front steering (AFS). The control yaw moment was calculated using sliding mode control. Contrary to the previously proposed method that uses the optimization-based method, the simple distribution method was adopted under the assumption that a single actuator of the chassis control system was used for yaw moment distribution. The lateral tire forces of front wheels were easily saturated by the excessive sole application of AFS. To cope with the situation, the corrective steering angle of AFS has been limited, and it compensated the loss of the control yaw moment with ESC, ARS and TVD in this paper. For verification of the effectiveness of the proposed control method, simulation has been performed via the vehicle simulation tool package, CarSim. From simulation, it has been verified that the proposed method can enhance maneuver performance and lateral stability if the lateral forces on front wheels are saturated.

Observer-based estimation of velocity and tire-road friction coefficient for vehicle control systems

A novel nonlinear observer for the estimation of vehicle velocity together with the tire-road friction coefficient is presented in this paper. The modular observer is designed based on a longitudinal tire force estimation approach and a lateral tire friction model. Compared to the state-of-art methods, the proposed observer design provides accurate estimation of the longitudinal velocity, lateral velocity, and the tire-road friction coefficient simultaneously. Particularly, the longitudinal tire forces are first estimated based on a filter observer. Then, according to the calculation of lateral tire forces, the nonlinear observer is proposed to estimate vehicle velocity and the tire-road friction coefficient. Moreover, the stability property of the observer is analyzed using a Lyapunov-based method. Simulation results validate the effectiveness of the proposed method.

Unknown-input observer for vehicle lateral dynamics using new sensor force technology

Robust estimation of important states for vehicles (steering angle and sideslip angle) is essential for vehicle handling and stability control. In the past, the estimation of vehicle lateral state with the measured steering angle has been proposed. In this paper, four unknown input observers are designed using lateral tyre force measurements based on a nonlinear vehicle model, to simultaneously estimate vehicle steering angle as unknown input and vehicle lateral state variables sideslip angle and yaw rate. All of the design conditions are formulated in terms of linear matrix inequalities (LMI) which can be solved efficiently. Simulation results through MATLAB/Simulink software based on data of the CALLAS vehicle simulator are used to evaluate the performance of observers based on nonlinear unknown input observer (ONEI).

Calculation of Tire Lateral Force under Time-varying Vertical Load Using Brush Model

Calculation of Tire Lateral Force under Time-varying Vertical Load Using Brush Model

Fuzzy Observer-Based Prescribed Performance Control of Vehicle Roll Behavior via Controllable Damper

This paper presents a novel observer-based control strategy to improve the vehicle roll behavior performance through magneto-rheological (MR) dampers under steering wheel input and various road excitation conditions. Since the vehicle roll with sudden steering input is an essential part of driving safety and possesses inherent nonlinearities, the full-car nonlinear Takagi-Sugeno (T-S) fuzzy model is first established to describe the vehicle roll dynamics considering nonlinear coupling dynamics of tire lateral force and MR damper force under road excitation input. Furthermore, a T-S model-based fuzzy observer is adapted to estimate the vehicle roll angle and roll rate. The stability conditions for the used T-S observer are calculated using linear matrix inequalities (LMIs), and the proposed observer is induced by solving the proposed LMI. Based on the Lyapunov function, sliding mode theory and prescribed performance function, a novel state observer-based prescribed performance control strategy is developed to constrain the controlled vehicle roll angle and roll rate state within the prescribed performance boundaries. Finally, the proposed techniques are validated through the J-turn and Fishhook tests conducted via a high-fidelity CarSim software platform.

Vehicle Sideslip Angle and Road Friction Estimation Using Online Gradient Descent Algorithm

Estimating vehicle sideslip angle and road friction in real time is of great significance for vehicle stability control and intelligent vehicle lateral control. These parameters are often difficult to obtain directly and the high cost of measuring instruments restricts their application in general vehicle control. Therefore, an estimation method based on online gradient descent (OGD) algorithm for vehicle sideslip angle and road friction is proposed. For the front-wheel-steer and front-wheel-drive vehicle, the vehicle's lateral dynamics model is established with smaller assumptions. And an unknown input observer is designed to estimate the tire's lateral force of the rear wheel. On the basis of this, the parameter estimation is transformed into the parameter optimization problem and the cost function is designed by using the nonlinear tire model, i.e., magic formula, and its gradient formula. Then, the OGD algorithm is used to estimate the sideslip angle and road friction, respectively. The effectiveness of the proposed method is evaluated via numerical simulation based on MATLAB/Simulink and CarSim software platform. The results show that the method can reliably and accurately estimate the vehicle sideslip angle and the road friction under a variety of test conditions. The proposed algorithm can effectively suppress the influences of sensor noise, longitudinal velocity change, and tire force nonlinearity on the estimation results.

On the handling performance of a vehicle with different front-to-rear wheel torque distributions

ABSTRACTThe handling characteristic is a classical topic of vehicle dynamics. Usually, vehicle handling is studied by analyzing the understeer coefficient in quasi-steady-state maneuvers. In this paper, experimental testsare performed on an electric vehicle with four independent motors, which is able to reproduce front-wheel-drive, rear-wheel-drive and all-wheel-drive (FWD, RWD and AWD, respectively) architectures. The handling characteristics of each architecture are inferred through classical and new concepts. The study presents a procedure to compute the longitudinal and lateral tire forces, which is based on a first estimate and a subsequent correction of the tire forces that guarantee the equilibrium. A yaw moment analysis is performed to identify the contributions of the longitudinal and lateral forces. The results show a good agreement between the classical and new formulations of the understeer coefficient, and allow to infer a relationship between the understeer coefficient and the yaw moment analysis. The handling characteristics vary with speed and front-to-rear wheel torque distribution. An apparently surprising result arises at low speed: the RWD architecture is the most understeering configuration. This is discussed by analyzing the yaw moment caused by the longitudinal forces of the front tires, which is significant for high values of lateral acceleration and steering angle.

Emergency steering control of autonomous vehicle for collision avoidance and stabilisation

ABSTRACTCollision avoidance and stabilisation are two of the most crucial concerns when an autonomous vehicle finds itself in emergency situations, which usually occur in a short time horizon and require large actuator inputs, together with highly nonlinear tyre cornering response. In order to avoid collision while stabilising autonomous vehicle under dynamic driving situations at handling limits, this paper proposes a novel emergency steering control strategy based on hierarchical control architecture consisting of decision-making layer and motion control layer. In decision-making layer, a dynamic threat assessment model continuously evaluates the risk associated with collision and destabilisation, and a path planner based on kinematics and dynamics of vehicle system determines a collision-free path when it suddenly encounters emergency scenarios. In motion control layer, a lateral motion controller considering nonlinearity of tyre cornering response and unknown external disturbance is designed using tyre lateral force estimation-based backstepping sliding-mode control to track a collision-free path, and to ensure the robustness and stability of the closed-loop system. Both simulation and experiment results show that the proposed control scheme can effectively perform an emergency collision avoidance manoeuvre while maintaining the stability of autonomous vehicle in different running conditions.