Tire-road Forces Research Articles

Tire–road contact modelling for multibody simulations with regularised road and enhanced UA tire models

AbstractMultibody simulations play an important role in the study of the dynamic behaviour of road vehicles, being one of the key aspects the modelling of the tire-road interaction. The tire-road contact modelling is required to detect the contact between the tire and road and to obtain the tire contact forces from the tire-road relative motion. The first part of the problem is solved by a contact detection algorithm, whereas the second part is handled by a tire model. In both cases, the trade-off between accuracy and computational cost needs to be addressed in the road dynamics scenario. For the contact detection problem, this work proposes a methodology in which the road is described by a mesh of triangles while the tire is described by a toroid. The triangular mesh road input can be directly extracted from any CAD model. To avoid the geometric discontinuities due to the transition between triangular patches, a set of auxiliary points is used to obtain a continuous variation of the road surface normal, based on the method proposed by Rill (Multibody Syst. Dyn. 45:131–153, 2019. In the process of contact detection, all kinematic quantities required by the tire-road contact model are evaluated. The tire–road forces are evaluated using the enhanced UA tire model, which is a numerically stable and efficient development of the original tire model proposed by Gim and Nikravesh (Int. J. Veh. Des. 12, 1991; Int. J. Veh. Des. 12:19–39, 1991; Int. J. Veh. Des. 12:217–228, 1991). Both the contact and tire models have smooth transitions between their internal transitions, thereby reducing the need for the variable-step ODE integrators to unnecessarily decrease time steps. The advances on contact detection and the tire–road contact models, proposed here, are demonstrated with a set of road vehicle simulation scenarios in which the influence of various modelling parameters on the stability and efficiency of the simulations is addressed. The novelties of the work consist not only in the demonstration of the enhanced UA tire model in practical situations but also in the description of the new tire–road contact methodology that employs a simple description of the road geometry, to achieve smooth tire–road contact forces.

Model Construction and Numerical Simulation for Hydroplaning of Complex Tread Tires

Euler-Lagrange coupling method is used to establish the fluid-structure interaction model for tires with different tread patterns by obtaining the grounding mark and normal contact force between tire and the road surface during tire rolling. The altering of load force, tire pressure, and water film thickness in relation to the effect on tire-road force during both constant speed and critical hydroplaning speed was analyzed. Results show that the critical hydroplaning speed and normal contact force between tire and the road surface are positively correlated with vehicle load and tire pressure and negatively correlated with water film thickness. Python language is used to develop the pre-processing plug-ins to achieve parametric modeling and rapid creation of Finite Element Analysis (FEA) model to reduce time costs, and the effectiveness of the plug-ins is verified through comparative tests.

Estimation of tire-road contact forces through a model-based approach employing strain measurements

The employment of intelligent tires to test the vehicle performances is ever-increasing in the last years. Many research activities have been made to correlate measurements provided by sensors to the tire dynamics. In this paper, a novel tire-road forces estimation technique is presented. The developed estimator is based on an approximation of the well-known Flexible Ring Tire Model (FRTM) and therefore, it is suitable for real-time normal and tangential forces identification. Only the tread band strain measurements are employed in the developed algorithm which can estimate the tire-road forces at every wheel revolution. The tool is validated through both numerical and experimental tests. The results indicate that the developed estimation algorithm, obtained by a mathematical inversion of the FRTM, can be employed as a monitoring tool for tires and vehicles.

Robust Set-Invariance Based Fuzzy Output Tracking Control for Vehicle Autonomous Driving Under Uncertain Lateral Forces and Steering Constraints

This paper is concerned with a new control method for path tracking of autonomous ground vehicles. We exploit the fuzzy model-based control framework to deal with the time-varying feature of the vehicle speed and the highly uncertain behaviors of the tire-road forces involved in the nonlinear vehicle dynamics. To avoid using costly vehicle sensors for feedback control while favoring the simplest control structure for real-time implementation, a new fuzzy static output feedback (SOF) scheme is proposed. In particular, though the robust set-invariance property and Lyapunov-based arguments, the physical constraints on the steering input saturation and the vehicle state can be taken into account in the control design to improve the driving safety and comfort. The theoretical development relies on the use of fuzzy Lyapunov functions and the non-parallel distributed compensation control concept to reduce the design conservatism. Exploiting some specific convexification techniques, the control design is reformulated as an optimization problem under linear matrix inequalities with a single line search, which are efficiently solved via semidefinite programming techniques. The proposed fuzzy path tracking controller is evaluated through various dynamic driving tests conducted with high-fidelity CarSim/Matlab co-simulations. Moreover, to emphasize the advantages of the new fuzzy SOF controller, a performance comparison with the CarSim driver model is also performed.

Driving force coordinated control of an 8×8 in-wheel motor drive vehicle with tire-road friction coefficient identification

Because of the complexities of tire-road interaction, the wheels of a multi-wheel distributed electric drive vehicle can easily slip under certain working conditions. As wheel slip affects the dynamic performance and stability of the vehicle, it is crucial to control it and coordinate the driving force. With this aim, this paper presents a driving force coordination control strategy with road identification for eight-wheeled electric vehicles equipped with an in-wheel motor for each wheel. In the proposed control strategy, the road identification module estimates tire-road forces using an unscented Kalman filter algorithm and recognizes the road adhesion coefficient by employing the recursive least-square method. According to road identification, the optimal slip ratio under the current driving condition is obtained, and a controller based on sliding mode control with a conditional integrator uses this value for acceleration slip regulation. The anti-slip controller obtains the adjusting torque, which is integrated with the driver-command-based feedforward control torque to implement driving force coordination control. The results of hardware-in-loop simulation show that this control strategy can accurately estimate tire-road forces as well as the friction coefficient, and thus, can effectively fulfill the purpose of driving force coordinated control under different driving conditions.

Investigating the lateral stability of three-wheeled scooter taxi due to tyre-road forces

Three-wheeled scooter taxi (TWST) that is currently prevalent in developing countries, is fuel efficient and cheap. It is used mainly for commercial purposes, also as a means of reducing unemployment and tackling poverty. However, the vehicle is unstable and prone to accidents due to its design configuration. The aim of this research work is to investigate the lateral stability of TWST due to Tyre-Road Forces. Therefore, lateral stability equations for three-wheeled vehicle (TWV) were developed and used in the analysis of TWST based on parametric values obtained from static test. The results showed that the vehicle is stable with respect to lateral stability, which is in line with what was obtained from literature, thereby validating the models with the driver alone. However, with two or more occupants the vehicle became unstable. Possible ways of eliminating this instability were discussed. The static test procedure, if adopted and legislated upon, would significantly enhance safety of life and properties of stakeholders in developing countries.
 Keywords: Three-wheeled scooter Taxi, Stability Analysis, Safety of life and properties, Legislation.

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.

Development of a neuromuscular driver model with an estimation of steering torque feedback in vehicle steer-by-wire systems

In this paper, a neuromuscular driver model for sensing torque feedback or haptic interaction between the vehicle equipped with steer-by-wire (SBW) system and the driver has been developed. The proposed driver model consists of a preview model and a neuromuscular model. The preview driver model calculates the desired angle of the steering-wheel to follow the path, and the neuromuscular driver model, with the ability of perceiving real-time torque feedback, determines the real angle of the steering-wheel angle according to muscular system transfer functions to follow the desired steering-wheel angle. In order to calculate torques on the steering-wheel, the lateral tyre-road forces are estimated by Kalman filter designed using a linear 2-DOF vehicle model. So, the design of the neuromuscular driver model combined with torque feedback estimation is the main contribution of this paper. The simulation results from TruckSim and Simulink software indicate that the novel designed driver model with torque feedback estimation has an important role in the controlling and steering vehicle to follow the desired paths.

Nonlinear Model Predictive Lateral Stability Control of Active Chassis for Intelligent Vehicles and Its FPGA Implementation

The rapid development of intelligent vehicles has paved the way for active chassis lateral stability, which is a novel issue and critical to vehicle stability and handling performance. To obtain active chassis lateral stability for intelligent vehicles, a nonlinear model predictive control (NMPC) method integrating active front steering and an additional yaw moment is proposed. It adopts the tire sideslip angle to express vehicle lateral stability, and addresses the actuator and security constraints and the nonlinear properties of the tire-road force effectively. Moreover, the hardware implementation, based on the field programmable gate array (FPGA), is presented to satisfy miniaturization and to discuss the computational efficiency of the proposed NMPC method. To verify the effectiveness of the presented NMPC method, offline simulations comparing the NMPC method with the direct yaw moment control (DYC) method under various running conditions and a real-time implementation experiment are carried out. The results indicate that the proposed NMPC method controls better than the DYC-based method. In addition, the presented NMPC method exhibits good robustness when the longitudinal velocity and tire-road friction coefficient vary within a suitable range. Moreover, the computational time of the proposed NMPC controller, implemented using the FPGA, is only 4.994 ms during one sampling period, which can satisfy the real-time requirement of active chassis lateral stability control.

Modular scheme for four‐wheel‐drive electric vehicle tire‐road force and velocity estimation

The limited availability of vehicle state information, including tire-road forces and vehicle velocities, restricts the development of control strategies for intelligent vehicles and new energy vehicles. This study proposes a modular estimation scheme for tire-road forces and vehicle velocities that can effectively cope with the cyclic coupling of the vehicle dynamics. The longitudinal tire-road forces are estimated using a sliding mode observer. Then, an observer for the lateral tire-road forces that exist in a cascade structure with the longitudinal tire-road force observer is designed. Non-linear vehicle velocity observers that take the estimated longitudinal and lateral tire-road forces as inputs are designed. A genetic algorithm approach is employed to select the observer gains. Finally, experimental validations under normal conditions and offline simulations under critical conditions for verifying the robustness with respect to measurement noise are conducted. The results demonstrate that the proposed modular scheme for tire-road force and vehicle velocity estimation yields acceptable results and has potential value for real vehicle applications.

Direct‐yaw‐moment control of four‐wheel‐drive electrical vehicle based on lateral tyre–road forces and sideslip angle observer

Considering some technical and economic reasons, it is not easy to directly measure the vehicular moving parameters (such as tyre-road forces and vehicle sideslip angle) in electronic stability programme systems. This study proposes a method to estimate lateral tyre-road forces and vehicle sideslip angle by utilising real-time measurements, based on the unscented Kalman filter. Direct-yaw-moment control can effectively guarantee the stability of vehicle while steering at a high speed. This study proposed a hierarchical control strategy as the solution to the problem of the yaw-moment distribution. The overloop controller is designed to calculate the desired yaw moment based on the estimated lateral tyre-road forces and sideslip angle, using the sliding mode control. The servo-loop controller is designed to optimise the torque distribution using weighted-least-squares method based on the desired yaw moment obtained from the overloop controller. MATLAB/Simulink with Carsim is applied for the simulation experiment, the results demonstrate the effectiveness of the lateral tyre-road force and sideslip angle observer, and the optimal allocation controller could improve the handling stability and energy efficiency dramatically.

Estimation of tire forces, road grade, and road bank angle using tire model-less approaches and Fuzzy Logic.

This paper presents a modular observer structure to estimate the tire-road forces robustly, avoiding the use of any particular tire model, and using standard signals available in current passenger vehicles. The observer consists of a feedforward longitudinal force estimation block and a hybrid lateral force estimation module formed by an Extended Kalman Filter and a Static Neural Network Structure. Road grade and bank angle are estimated using sensor fusion, where a Fuzzy Logic controller combines the outputs from a Euler Kinematic model and a Recursive Least Squares block. The proposed observer is tested and verified using the simulation software IPG CarMaker® under realistic driving situations. Lastly, the feasibility of the longitudinal force block is proved with real-time experiments.

Estimation of vehicle sideslip angle and individual tyre-road forces based on tyre friction circle concept

The real-time information of vehicle sideslip angle and tyre-road forces of individual wheels can help advanced vehicle chassis control systems to enhance vehicle handling, stability and safety. But in practice, these states are difficult to measure directly for technical and economic reasons. In order to estimate these states, this paper proposes an observer based on Extended Kalman Filter (EKF) by using a 7-DOF vehicle model. According to the Dugoff's tyre model, the lateral force can be expressed by a function of the longitudinal force with the knowledge of tyre work condition. Based on this concept, the reference vehicle model is modified to identify the lateral forces of each braked wheel without the online information of vertical load and tyre-road friction coefficient. The simulation results indicate that the longitudinal and lateral forces of each wheel can be well estimated under combined cornering and braking condition.

Estimation of vehicle sideslip angle and individual tyre-road forces based on tyre friction circle concept

Estimation of vehicle sideslip angle and individual tyre-road forces based on tyre friction circle concept

Longitudinal and Lateral Tire Road Forces Estimation for Electric Vehicle with Four in-wheel Motors

This study introduces an estimation process for longitudinal and lateral tire road forces, for that an electric vehicle with four in-wheel motors has been implemented. This structure permits to control independently each one wheel so that deals to torque’s control with fast response which represent the best advantage in this kind of vehicles with PMSM which take a dominant position in several systems with variable speed drive because of their, low inertia, high efficiency and no maintenance. The performance of this concept is tested and demonstrated using Matlab/Simulink. The simulation results show that the proposed approach is a promising technique to provide accurate estimations of vehicle dynamic states.

Ground Semi Active Damping Force Estimator (gSADE) for Magnetorheological Damper Suspension System Using Quarter Heavy Vehicle Model

This paper proposed semi active controller scheme for magnetorheological (MR) damper of a heavy vehicle suspension known as Ground Semi Active Damping Force Estimator (gSADE), where it was modified from Semi Active Damping Force Estimator (SADE) algorithm. A reported algorithm known as Groundhook (GRD) was developed where its aim to minimize tire road forces and hence reduce road damage. Thus, the objective of this paper is to investigate the effectiveness of the proposed gSADE algorithm compared to GRD and SADE. These algorithms are applied to a quarter heavy vehicle models and the simulation model was developed and simulated using MATLAB Simulink software. Ride test was conducted at three different speeds and three bump heights, and the simulation results of gSADE, SADE and GRD are compared and analysed. The results showed that the proposed controller is able to reduced tire force significantly compared to GRD control strategy.

Study on Vehicle Stability Control by Using Model Predictive Controller and Tire-road Force Robust Optimal Allocation

Study on Vehicle Stability Control by Using Model Predictive Controller and Tire-road Force Robust Optimal Allocation

Adaptive Nonlinear Tire-Road Friction Force Estimation for Vehicular Systems Based on a Novel Differentiable Friction Model

A novel adaptive nonlinear observer-based parameter estimation scheme using a newly continuously differentiable friction model has been developed to estimate the tire-road friction force. The differentiable friction model is more flexible and suitable for online adaptive identification and control with the advantage of more explicit parameterizable form. Different from conventional estimation methods, the filtered regression estimation parameter is introduced in the novel adaptive laws, which can guarantee that both the observer error and parameter error exponentially converge to zero. Lyapunov theory has been used to prove the stability of the proposed methods. The effectiveness of the estimation algorithm is illustrated via a bus simulation model in the Trucksim software and simulation environment. The relatively accurate tire-road friction force was estimated just by the easily existing sensors signals wheel rotational speed and vehicle speed and the proposed method also displays strong robustness against bounded disturbances.

Design of a Novel Nonlinear Observer to Estimate Sideslip Angle and Tire Forces for Distributed Electric Vehicle

For four-wheel independently driven (4WD) distributed electric vehicle (DEV), vehicle dynamics control systems such as direct yaw moment control (DYC) can be easily achieved. Accurate estimation of vehicle state variables and uncertain parameters can improve the robustness of vehicle dynamics control system. Various sensors are generally equipped to the acquisition of the vehicle dynamics. For both technical and economic reasons, some fundamental vehicle parameters, such as the sideslip angle and tire-road forces, can hardly be obtained through sensors directly. Therefore, this paper presented a state observer to estimate these variables based on Unscented Kalman Filter (UKF). To improve the accuracy of UKF, measurement noise covariance is also self-adaptive regulated. In addition, a nonlinear dynamics tire model is utilized to improve the accuracy of tire lateral force estimation. The simulation and experiment results show that the proposed observer can provide the precision values of the vehicle state.

IMM-based sensor fault detection and identification for a drive-by-wire vehicle

With the development of the embedded application and driving assistance systems, it becomes relevant to develop parallel mechanisms in order to check and to diagnose these new systems. This is particularly true in the case of partially and fully autonomous vehicles. In this paper, we focus our researches on a subpart of this issue dedicated to the detection and the identification of sensor faults for a drive-by-wire road vehicle. An Interacting Multiple Model approach has been implemented, based on a non-linear vehicle dynamics observer, including tire-road force and actuator modeling. Experimental validation tests, relying on real vehicle signals, show a fast and robust fault identification.