Vertical Tire Forces Research Articles

Numerical analysis on tractor axle suspension for steering instability induced by bump disturbances

In Japan, small agricultural tractors without axle suspensions used on bumpy farm roads experience severe vibrations. Excessive vibrations often cause tyres to lose contact with the supporting ground or decrease the vertical tyre force such that the cornering force exceeds the static friction limit. The resulting bouncing and sliding motions induce steering instability, resulting in overturning accidents. This study investigated the effectiveness of axle suspension in alleviating bump disturbance-induced steering instability in small tractors. A step lane change test involving bump disturbances was newly proposed for the steering stability testing of small tractors. The numerical experiments compared four axle suspension structures: no-, front-, rear-, and full-suspensions. The results showed that bump disturbances induce steering instability in the no- and rear-suspension tractors. In contrast, the front- and full-suspension structures significantly improved the steering stability of the tractor by keeping the steering wheel in contact with the ground. The proposed testing method helped evaluate improvements in the steering stability brought about by increasing the ground contact of the steering wheel. Our results can aid in designing and testing suspension systems for small tractors.

Model predictive control for three-axle trucks during tire blowout on expressway based on equivalent chassis

Unexpected tire blowout on expressway is one of the most dangerous scenarios for heavy load multi-axle trucks, especially under the inexperienced driver’s improper intervention. To this end, this paper proposes an autonomous tire blowout controller for three-axle trucks based on model predictive control (MPC) method. First of all, aiming at balancing the computing load and the path-tracking accuracy, an equivalent chassis is transformed based on the stable two-dimensional vehicle dynamic model. Second, a tire blowout–oriented vehicle high-fidelity dynamic model is established based on the equivalent chassis, in which the vehicle lateral, yaw, and roll motions are all considered at the same time. Then, an MPC-based dynamic control strategy is proposed to achieve effective tire blowout suppression with the consideration of vehicle rollover stability. Afterward, a transient vertical tire force shock is employed to simulate the real tire blowout behavior, on which two typical scenarios are constructed based on the TruckSim–Simulink co-simulation platform. The simulation results illustrate the feasibility and effectiveness of the proposed method. In two different dangerous tire blowout conditions, the lateral load transfer rate (LTR) value of the vehicle is reduced by 3.45% and 40.87%, respectively, while the trajectory tracking error is reduced at the same time.

From the material behaviour to the thermo-mechanical long-term response of asphalt pavements and the alteration of surface drainage due to rutting: a sensitivity study

ABSTRACT In this contribution, a simulation chain for the thermo-mechanical and hydromechanical analysis (surface drainage) of a pavement structure during its whole service life is applied to a typical asphalt pavement (Bk100) used for motorways in Germany. Transient load signals for each tyre position of a truck-trailer combination (vehicle) are generated from a multibody analysis of the vehicle driving on a motorway with rough pavement surface. Material model parameters are derived from experimental identification tests of asphalt materials. The model parameters are used together with a continuum-mechanical description of the asphalt material representing the thermo-mechanical material behaviour at the material scale. The material response of the pavement layers is integrated on the structural scale by using the finite element method (FEM) in combination with an arbitrary Lagrangian-Eulerian (ALE) formulation and equivalent tyre loads of a representative, finite element (FE) discretised truck tyre rolling on an FE discretised pavement section. Different scenarios of rut formation are computed by varying different influence factors (climate temperature, vertical tyre force, type of asphalt material of the surface layers etc.). During the subsequent hydromechanical analysis of the pavement, the simulated deformed geometry of the pavement surface is used to numerically compute surface drainage characteristics.

Instantaneous optimum wheel slip estimation of anti-lock braking system based on extremum seeking algorithm and fuzzy method

The anti-lock braking system (ABS) adjusts the longitudinal wheel slip at its optimum value to achieve the maximum braking forces. The highest braking force capacity happens at a specific slip value and depends on the friction coefficient between the tire and the road, vertical tire force, and vehicle speed. Hence, using a fixed value for the desired longitudinal slip is not appropriate. To solve this problem, the instantaneous optimum wheel slip is determined via the sliding mode-based extremum seeking algorithm in combination with the fuzzy method to achieve the maximum possible brake deceleration. Then the nonlinear prediction-based controller is designed to find the braking torque by adjusting the longitudinal slip in the calculated desired value. In addition, a nonlinear half-vehicle model considering pitch dynamics is developed and validated with the Carsim software. The main contribution of the present work involves the combination of the optimal nonlinear predictive control method with the fuzzy extremum seeking algorithm to design a wheel slip controller. Additionally, the pitch dynamics has been taken into account in the design of the control system. The performance of the designed control system is investigated through conducted simulations in Matlab/Simulink software environment. The obtained results show an enhancement in the braking performance along with a considerable reduction in the stopping distance.

Hybrid State Estimation in a Semitrailer for Different Loading Conditions

For state and parameter estimation in vehicles, Kalman filters, especially nonlinear extensions like the extended Kalman filter (EKF) and unscented Kalman filter (UKF), are very common. However, the estimation accuracy is highly dependent on the quality of the model used in the process update of the Kalman filter. Model errors can result from non-modeled dynamics that are either unknown or very difficult to describe. In recent years data-driven approaches for state estimation are the subject of research with promising results in estimation accuracy and reduced implementation effort. In this work, both a model-based method with an UKF and a data-driven approach based on recurrent neural networks (RNN) are implemented and combined to two hybrid methods for the application of state and parameter estimation in a truck-semitrailer for three different loading conditions. Hybrid estimation architectures promise to combine the advantages of model-based and data-driven methods to achieve better estimation accuracy than their standalone components. To the best knowledge of the authors, this work is the first to extend the field of hybrid state estimation to semitrailers estimating the truck steering angle, articulation angle, and the trailer's lateral and vertical tire forces. Four estimation architectures (an UKF, one purely data-driven method, and two hybrid methods) are optimized and compared to each other regarding estimation accuracy. The UKF is optimized with a particle swarm optimization (PSO) while the hyperparameters of the data-driven method are tuned with the asynchronous successive halving algorithm (ASHA) to result in a fair comparison. All methods are developed and compared based on an experimental data set from a test vehicle.

A Comprehensive Vehicle Stability Assessment System Based on Enabling Tire Force Estimation

This paper presents an enabling comprehensive vehicle stability assessment system covering vehicle longitudinal, yaw and roll stability. First, the longitudinal, lateral and vertical tire forces are separately estimated using the strong tracking unscented Kalman filter and the conventional Kalman filter based on low-cost on-board sensors. Then, a comprehensive vehicle longitudinal, yaw and roll stability space is established by utilizing the normalized tire friction ellipse and the Load Transfer Ratio value. Finally, the vehicle stability is determined and predicted based on current driver's inputs. The hardware-in-loop experimental results show that the proposed vehicle stability assessment system can accurately estimate the longitudinal, lateral and vertical tire forces with the normalized root mean square errors of 1.87 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> , 1.07 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> and 1.43 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> , and exhibits satisfying performance for vehicle longitudinal, yaw and roll stability evaluation and prediction. This bears significance for the efficient functioning of active control systems to improve vehicle safety under critical driving conditions.

Coordinated Attitude Control of Longitudinal, Lateral and Vertical Tyre Forces for Electric Vehicles Based on Model Predictive Control

A novel longitudinal, lateral, and vertical integrated stability control system is proposed for distributed electric vehicle in this paper. The integrated stability control system is based on model predictive control and takes advantage of its multi-objective optimization feature to takes manipulability, stability and comfort requirements into consideration at the same time, and realize the optimal longitudinal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$/$</tex-math></inline-formula> lateral <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$/$</tex-math></inline-formula> vertical forces distribution with constraints overall considered. The advantage of the proposed integrated control system is that it can solve the control objective conflict of the cooperative motion control subsystems and the interference of the actuators compared to distributed control system. Finally, the simulation and comparison analysis are given in several different driving conditions under Carsim and Matlab <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$/$</tex-math></inline-formula> Simulink environment. Results show that an improvement of over 80 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> in the pitch angle and roll angle is realized compared to the simple control strategy.

Vision-based tire deformation and vehicle-bridge contact force measurement

Accurate measurement of vehicle-bridge contact force is the promise of rapid vehicle-induced bridge impact testing. This paper proposed a cost-effective vertical tire force measurement method based on computer vision and the long and short-term memory (LSTM) neural network. The main contribution of this paper includes two aspects: (1) Circle Hough transform was adopted to monitor tire deformation and vehicle speed from videos of the tire sidewall. Besides, the perspective transformation was employed to eliminate vehicle-induced camera motion; (2) Using tire deformation, vehicle speed, and tire pressure as the input, vertical tire force is estimated through the LSTM neural network. Finally, a detachable vehicle-mounted computer vision system was developed. Experiments, including laboratory and field tests, were conducted. The estimated vertical tire forces show good agreement with the reference values, demonstrating the potential for applying the proposed method to rapid vehicle-induced bridge impact testing.

Vertical Tire Forces Estimation of Multi-Axle Trucks Based on an Adaptive Treble Extend Kalman Filter

Vertical tire forces are essential for vehicle modelling and dynamic control. However, an evaluation of the vertical tire forces on a multi-axle truck is difficult to accomplish. The current methods require a large amount of experimental data and many sensors owing to the wide variation of the parameters and the over-constraint. To simplify the design process and reduce the demand of the sensors, this paper presents a practical approach to estimating the vertical tire forces of a multi-axle truck for dynamic control. The estimation system is based on a novel vertical force model and a proposed adaptive treble extend Kalman filter (ATEKF). To adapt to the widely varying parameters, a sliding mode update is designed to make the ATEKF adaptive, and together with the use of an initial setting update and a vertical tire force adjustment, the overall system becomes more robust. In particular, the model aims to eliminate the effects of the over-constraint and the uneven weight distribution. The results show that the ATEKF method achieves an excellent performance in a vertical force evaluation, and its performance is better than that of the treble extend Kalman filter.

Optimisation strategy of torque distribution for the distributed drive electric wheel loader based on the estimated shovelling load

The drive torque for each motor can be performed independently for the distributed drive electric wheel loader (DDEWL). On the shovelling condition, the torque distribution can be optimised according to the tire load. Then the parasitic power and wheel slippage can be reduced, and the tractive force and efficiency are improved. In this study, the singular value decomposition unscented Kalman filter is adopted to estimate the shovelling load. Based on the estimated shovelling load, the vertical tire force is calculated. The tire load rate is used to build the optimisation objective. The drive antiskid is set as the boundary condition. And a modified particle swarm optimisation is applied as the optimisation algorithm. A wheel loader is utilised for the testing data acquisition. Based on the acquired testing data, the comparative study about the optimisation and un-control strategies is operated. The results show that the slippage occurs less in the optimisation strategy, and the tractive force and efficiency are higher than the un-control strategy. In this study, the feasibility of the shovel load estimator is verified. The advantages of the optimisation strategy of distributed drive electric wheel loaders in shovelling process are analysed.

State estimation and experimental verification of a robotic vehicle with six in-wheel drives using Kalman filter

In this research we present an algorithm for a six-wheeled robotic vehicle with articulated suspension (RVAS) to estimate the vehicle velocity and acceleration states, slip ratio and the tire forces. The estimation algorithm consists of six parts. In the first part, a wheel state estimator estimates the wheel rotational speed and its angular acceleration using Kalman filter, which is used to estimate the longitudinal tire force distribution in the second part. The third part is to estimate respective longitudinal, lateral, and vertical speeds of the vehicle and wheels. Based on these speeds, the slip ratio and slip angle are estimated in the fourth part. In the fifth part, the vertical tire force is then estimated. In the sixth part, the lateral tire force is then estimated. For a simulation test environment, the RVAS dynamic model is developed using Matlab and Simulink. The estimation algorithm is then verified in simulation using the vehicle test data and different test scenarios. It is found from simulation results that the proposed estimation algorithm can estimate the vehicle states, longitudinal tire forces efficiently. Moreover, a small prototype of the robotic vehicle is fabricated for experimental verification of the estimation algorithm. Various experiments are executed in pavement and off-road driving to estimate the wheel angular position, velocity and acceleration states and finally the slip ratio is estimated in these situations.

An energy efficient intelligent torque vectoring approach based on fuzzy logic controller and neural network tire forces estimator

In electric vehicles (EVs) with multiple motors, torque vectoring (TV) control can effectively enhance the cornering response and safety. Moreover, TV systems can also improve the overall efficiency through an optimal torque distribution that also considers the power consumption. For such a complex control system with multiple objectives, intelligent control techniques have demonstrated to be one of the best alternatives. However, the works proposed in the literature do not handle both vehicle dynamics behaviour and energy efficiency, and generally do not consider the real-time implementability of the developed controllers. To overcome the aforementioned issues, in this work, a novel torque vectoring approach is proposed, which uses a neural network-based vertical tire forces estimator and considers the regenerative braking capabilities of EVs. Moreover, the implementability of the controller in a hetereogenous (FPGA and microcontroller) automotive suitable system on chip is addressed, ensuring its real-time capabilities. For the sake of validating the proposed approach, a set of experiments have been carried out in a hardware in the loop setup. The performance of the proposed TV approach has been compared with other two TV approaches from the literature, evaluating them in several challenging manoeuvres in high and low tire-road friction coefficient scenarios. Results show that the proposed approach not only is able to enhance the vehicle dynamics behaviour but also to decrease the energy consumption about 13%.

A hierarchical estimation scheme of tire-force based on random-walk SCKF for vehicle dynamics control

The estimation of vehicle dynamics states is crucial for vehicle stability control and autonomous driving, especially tire-force which governs vehicular motion. However, measuring tire-force directly needs expensive measurement instruments, moreover, vehicle non-linear characteristics, vehicle parameter uncertainties, unknown key variables, and sensor noise could cause great challenges in its observation. Therefore, this paper aims to develop an accurate, affordable tire-force estimator to tackle the above-mentioned issues. A novel hierarchical estimation scheme based on random-walk square-root cubature Kalman filter (SCKF) is proposed and it works without a complex tire model and considers vehicle parameter uncertainties. The estimator scheme contains three blocks. The first block estimates related key variables of tire force observation. The second block estimates both vertical tire-force and longitudinal tire-force. The longitudinal tire-force is observed based on effective tire radius identification, and a proportional integral differential (PID) method is derived based on the Lyapunov principle. Then, a random-walk SCKF algorithm is presented to estimates lateral tire-force. To validate the effectiveness of the proposed estimation scheme, CarSim & Matlab/Simulink joint simulation and real car tests are carried out. Results show that the proposed estimation scheme's accuracy performance and its potential as an affordable solution for the tire-force observation.

Experimental research on determining the vertical tyre force of a tractor semi-trailer

The vertical tyre force is crucial to the study of the dynamics of a tractor semi-trailer. The paper presents an experimental method for determining the vertical tyre force by determining the vertical acceleration of the un-sprung mass and the vertical acceleration of the sprung mass when the tractor semi-trailer moves. The results of this study form the basis for determining the dynamic tyre force without the installing of sensors on road.

Fail-Operation Control of In-Wheel Motor Drive Electric Vehicle Based on Wheel Isolation and Yaw Moment Compensation

To improve the trackability of in-wheel motor drive (IWMD) and wheel-individual steer electric vehicles (EVs) when steering actuators fail, the fail-operation control strategy was proposed to correct vehicles in a steering failure situation and avoid losing control of vehicle steering. A linear quadratic regulator (LQR) decides the additional yaw moment of the vehicle according to vehicle state errors. The tire force estimation module estimates the compensating resistance moment generated by the failed wheel according to the tire slip angle and the vertical tire force. By isolating the failed wheel, the optimal torque distribution (OTD) controller allocates the additional yaw moment and the compensating resistance moment to normal wheels to realize the fail-operation control of the IWMD vehicle. The control effect was verified through co-simulation of MATLAB/Simulink and Trucksim. Compared with the uncontrolled and direct torque allocation methods, the proposed OTD method reduces the lateral trajectory error of the vehicle by 86% and 60.5%, respectively, when failure occurs, and achieves better velocity maintaining ability, which proves the effectiveness of the proposed fail-operation control strategy.

Torque vectoring system design for hybrid electric–all wheel drive vehicle

A torque vectoring system is designed for the hybrid electric–all wheel drive vehicle where the front and rear wheels are powered by the combustion engine and electric motors, respectively. The vehicle provides enhanced handling performance by a twin motor drive unit that can distribute the driving and regenerative braking torques to the rear-left and rear-right wheels independently. Based on the driver’s intention, a sliding mode controller is designed to calculate the desired traction force and yaw moment for the vehicle. The force distribution between the front and rear axles is investigated considering the principle of the friction circle, and characteristics of the engine and drive motors. The vertical tire force is estimated using the random walk Kalman filter for the proportional distribution between the front and rear longitudinal forces. For the torque distribution between the rear-left and rear-right wheels, an optimization problem is formulated by considering the constraints of the friction circle and motor characteristics. The proposed algorithm is evaluated in a simulation environment first by reflecting the characteristics of the hybrid electric–all wheel drive modules. Then, the test vehicle is utilized to validate the handling performance experimentally and to compare with the uncontrolled cases.

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.

Modular Estimation Strategy of Vehicle Dynamic Parameters for Motion Control Applications

The presence of motion control or active safety systems in vehicles have become increasingly important for improving vehicle performance and handling and negotiating dangerous driving situations. The performance of such systems would be improved if combined with knowledge of vehicle dynamic parameters. Since some of these parameters are difficult to measure, due to technical or economic reasons, estimation of those parameters might be the only practical alternative. In this paper, an estimation strategy of important vehicle dynamic parameters, pertaining to motion control applications, is presented. The estimation strategy is of a modular structure such that each module is concerned with estimating a single vehicle parameter. Parameters estimated include: longitudinal, lateral, and vertical tire forces – longitudinal velocity – vehicle mass. The advantage of this strategy is its independence of tire parameters or wear, road surface condition, and vehicle mass variation. Also, because of its modular structure, each module could be later updated or exchanged for a more effective one. Results from simulations on a 14-DOF vehicle model are provided here to validate the strategy and show its robustness and accuracy.

Dynamic Characteristics Analysis of Vehicle Incorporating Hydraulically Interconnected Suspension System with Dual Accumulators

A novel roll‐resistant hydraulically interconnected suspension with dual accumulators on each fluid circuit (DHIS) is proposed and dynamic characteristics of vehicle incorporating DHIS subsystem are studied in this paper. A 10‐degrees‐of‐freedom (DOFs) vehicle model coupled with DHIS subsystem is established and validated. Four physical parameters of DHIS subsystems which are crucial to vehicle responses are selected with prescribed variation ranges to explore their relationships with the vehicle performance. Simulations of vehicle conducting sine‐wave steering maneuvers are carried out to evaluate handling performance with roll angle and vertical tyre force for DHIS subsystem with the parameters varying, compared with the results for vehicle with the original spring‐damper suspension and conventional hydraulically interconnected suspension (HIS). On the other hand, ride comfort performance indicated by total weighted root mean square accelerations at the center of gravity is studied when vehicle is excited by three different types of road pavements when the four parameters vary in the prescribed ranges. Simulation results are compared to investigate the special merits of DHIS subsystem, and the parameters that influence the handling performance and ride comfort most are identified. Overall, the DHIS subsystem can effectively enhance the vehicle handling performance compared with the original spring‐damper suspension, and it can also benefit much to the ride comfort in contrast to the HIS subsystem.

Intelligent Torque Vectoring Approach for Electric Vehicles with Per-Wheel Motors

Transport electrification is currently a priority for authorities, manufacturers, and research centers around the world. The development of electric vehicles and the improvement of their functionalities are key elements in this strategy. As a result, there is a need for further research in emission reduction, efficiency improvement, or dynamic handling approaches. In order to achieve these objectives, the development of suitable Advanced Driver-Assistance Systems (ADAS) is required. Although traditional control techniques have been widely used for ADAS implementation, the complexity of electric multimotor powertrains makes intelligent control approaches appropriate for these cases. In this work, a novel intelligent Torque Vectoring (TV) system, composed of a neuro-fuzzy vertical tire forces estimator and a fuzzy yaw moment controller, is proposed, which allows enhancing the dynamic behaviour of electric multimotor vehicles. The proposed approach is compared with traditional strategies using the high fidelity vehicle dynamics simulator Dynacar. Results show that the proposed intelligent Torque Vectoring system is able to increase the efficiency of the vehicle by 10%, thanks to the optimal torque distribution and the use of a neuro-fuzzy vertical tire forces estimator which provides 3 times more accurate estimations than analytical approaches.