Analysis of handling performance based on simplified lateral vehicle dynamics

In this article, the analysis methods for vehicle handling performance are studied. Using simple models, dynamic characteristic parameters such as yaw, natural frequency, and the damping coefficient of a vehicle can be theoretically formulated. Here, the vehicle is simplified by a bicycle (single-track) model, and the tire is modeled by an equivalent cornering stiffness and first order lag. From the experimental road data, the tire model parameters (equivalent cornering stiffness and time lag constant) are extracted. These parameters are then inserted into the theoretically formulated equations of dynamic characteristic parameters. For the purpose of validating the efficiency of the suggested methods, experimental road tests (where the cars have different handling performances) are performed. The results show that vehicle handling performance can be sufficiently represented by the suggested dynamic characteristic parameters. So, it is concluded that the proposed method has practical use for the development of new cars or for the comparison of similar cars since the evaluations of the vehicle handling performance can be efficiently determined by the suggested dynamic characteristic parameters.     

A new flatness-based control of lateral vehicle dynamics

This paper presents a new concept for vehicle dynamics control (VDC). The control of the longitudinal vehicle dynamics is not discussed, since we are assuming that it is much slower and weakly coupled to the lateral and yawing dynamics. The actuators are considered to be the traction and the braking torques of the individual wheels and only the standard sensors of the common VDC system are used. A modular interface to the subordinate wheel control system is provided by choosing the yaw torque as a fictitious control input. The VDC system is designed by means of a two degrees-of-freedom control scheme. It comprises a flatness-based feedforward part and a stabilising feedback part. The reference trajectory generation is introduced for the flat output which is given by the lateral velocity of the vehicle. Thus an advantageous kind of body side-slip angle control is provided with the standard VDC system hardware. Extensive simulation studies show excellent performance of the designed control concept.     

Tire wear estimation based on nonlinear lateral dynamic of multi-axle steering vehicle

This paper presents a novel nonlinear dynamic model of a multi-axle steering vehicle to estimate the lateral wear amount of tires. Firstly, a 3DOF nonlinear vehicle dynamic model is developed, including dynamic models of the hydropneumatic suspension, tire, steering system and toe angle. The tire lateral wear model is then built and integrated into the developed vehicle model. Based on the comparison of experimental and simulation results, the nonlinear model is proved to be better than a linear model for the tire wear calculation. In addition, the effects of different initial toe angles on tire wear are analyzed. As simulation results shown, the impact of the dynamic toe angle on the tire wear is significant. The tire wear amount will be much larger than that caused by normal wear if the initial toe angle increases to 1° - 1.5°. The results also suggest that the proposed nonlinear model is of great importance in the design and optimazation of vehicle parameters in order to reduce the tire wear.     

Road profile input estimation in vehicle dynamics simulation

Vehicle motion simulation accuracy, such as in accident reconstruction or vehicle controllability analysis on real roads, can be obtained only if valid road profile and tire-road friction models are available. Regarding road profiles, a new method based on sliding mode observers has been developed and is compared with two inertial methods. Experimental results are shown and discussed to evaluate the robustness of our approach.     

Sliding mode-based lateral vehicle dynamics control using tyre force measurements

In this work, a lateral vehicle dynamics control based on tyre force measurements is proposed. Most of the lateral vehicle dynamics control schemes are based on yaw rate whereas tyre forces are the most important variables in vehicle dynamics as tyres are the only contact points between the vehicle and road. In the proposed method, active front steering is employed to uniformly distribute the required lateral force among the front left and right tyres. The force distribution is quantified through the tyre utilisation coefficients. In order to address the nonlinearities and uncertainties of the vehicle model, a gain scheduling sliding-mode control technique is used. In addition to stabilising the lateral dynamics, the proposed controller is able to maintain maximum lateral acceleration. The proposed method is tested and validated on a multi-body vehicle simulator.     

Region of attraction analysis for nonlinear vehicle lateral dynamics using sum-of-squares programming

In this study we will estimate the region of attraction (RoA) of the lateral dynamics of a nonlinear single-track vehicle model. The tyre forces are approximated using rational functions that are shown to capture the nonlinearities of tyre curves significantly better than polynomial functions. An existing sum-of-squares (SOS) programming algorithm for estimating regions of attraction is extended to accommodate the use of rational vector fields. This algorithm is then used to find an estimate of the RoA of the vehicle lateral dynamics. The influence of vehicle parameters and driving conditions on the stability region are studied. It is shown that SOS programming techniques can be used to approximate the stability region without resorting to numerical integration. The RoA estimate from the SOS algorithm is compared to the existing results in the literature. The proposed method is shown to obtain significantly better RoA estimates.     

Analysis of vehicle rollover dynamics using a high-fidelity model

Recent data show that 35% of fatal crashes in sport utility vehicles included vehicle rollover. At the same time, experimental testing to improve safety is expensive and dangerous. Therefore, multi-body simulation is used in this research to improve the understanding of rollover dynamics. The majority of previous work uses low-fidelity models. Here, a complex and highly nonlinear multi-body model with 165 degrees of freedom is correlated to vehicle kinematic and compliance (K&C) measurements. The Magic Formula tyre model is employed. Design of experiment methodology is used to identify tyre properties affecting vehicle rollover. A novel, statistical approach is used to link suspension K&C characteristics with rollover propensity. Research so far reveals that the tyre properties that have the greatest influence on vehicle rollover are friction coefficient, friction variation with load, camber stiffness and tyre vertical stiffness. Key K&C characteristics affecting rollover propensity are front and rear suspension rate, front roll stiffness, front camber gain, front and rear camber compliance and rear jacking force.     

Development of a generalised equivalent estimation approach for multi-axle vehicle handling dynamics

This paper devotes analytical effort in developing the 2M equivalent approach to analyse both the effect of vehicle body roll and n-axle handling on vehicle dynamics. The 1M equivalent vehicle 2DOF equation including an equivalent roll effect was derived from the conventional two-axle 3DOF vehicle model. And the 1M equivalent dynamics concepts were calculated to evaluate the steady-state steering, frequency characteristics, and root locus of the two-axle vehicle with only the effect of body roll. This 1M equivalent approach is extended to a three-axle 3DOF model to derive similar 1M equivalent mathematical identities including an equivalent roll effect. The 1M equivalent wheelbases and stability factor with the effect of the third axle or body roll, and 2M equivalent wheelbase and stability factor including both the effect of body roll and the third-axle handling were derived to evaluate the steady-state steering, frequency characteristics, and root locus of the three-axle vehicle. By using the recursive method, the generalised 1M equivalent wheelbase and stability factor with the effect of n-axle handling and 2M equivalent generalised wheelbase and stability factor including both the effect of body roll and n-axle handling were derived to evaluate the steady-state steering, frequency characteristics, and root locus of the n-axle vehicle. The 2M equivalent approach and developed generalised mathematical handling concepts were validated to be useful and could serve as an important tool for estimating both the effect of vehicle body roll and n-axle handling on multi-axle vehicle dynamics.     

Effect of vertical and lateral coupling between tyre and road on vehicle rollover

The vehicle stability involves many aspects, such as the anti-rollover stability in extreme steering operations and the vehicle lateral stability in normal steering operations. The relationships between vehicle stabilities in extreme and normal circumstances obtain less attention according to the present research works. In this paper, the coupling interactions between vehicle anti-rollover and lateral stability, as well as the effect of road excitation, are taken into account on the vehicle rollover analysis. The results in this paper indicate that some parameters influence the different vehicle stabilities diversely or even contradictorily. And it has been found that there are contradictions between the vehicle rollover mitigation performance and the lateral stability. The direct cause for the contradiction is the lateral coupling between tyres and road. Tyres with high adhesion capacity imply that the vehicle possesses a high performance ability to keep driving direction, whereas the rollover risk of this vehicle increases due to the greater lateral force that tyres can provide. Furthermore, these contradictions are intensified indirectly by the vertical coupling between tyres and road. The excitation from road not only deteriorates the tyres’ adhesive condition, but also has a considerable effect on the rollover in some cases.     

eTS fuzzy driver model for simultaneous longitudinal and lateral vehicle control

In this paper, evolving Takagi-Sugeno (eTS) fuzzy driver model is proposed for simultaneous lateral and longitudinal control of a vehicle in a test track closed to traffic. The developed eTS fuzzy driver model can capture human operator’s driving expertise for generating desired steering angle, throttle angle and brake pedal command values by processing only information which can be supplied by the vehicle’s on-board control systems in real time. Apart from other fuzzy rule based (FRB) models requiring human expert knowledge or off-line clustering, the developed eTS driver model can adapt itself automatically, even ‘from scratch’, by an on-line learning process using eTS algorithm while human driver is supervising the vehicle. Proposed eTS fuzzy driver model’s on-line human driver identification capability and autonomous vehicle driving performance were evaluated on real road profiles created by digitizing two different intercity express ways of Turkey in IPG© CarMaker® software. The training and validation simulation results demonstrated that eTS fuzzy driver model can be used in product development phase to speed up different tests via realistic simulations. Furthermore eTS fuzzy driver model has an application potential in the field of autonomous driving.     

Bus mathematical model of acceleration threshold limit estimation in lateral rollover test

Vehicle safety is a major concerns for researchers, governments and vehicle manufacturers, and therefore a special attention is paid to it. Particularly, rollover is one of the types of accidents where researchers have focused due to the gravity of injuries and the social impact it generates. One of the parameters that define bus lateral behaviour is the acceleration threshold limit, which is defined as the lateral acceleration from which the rollover process begins to take place. This parameter can be obtained by means of a lateral rollover platform test or estimated by means of mathematical models. In this paper, the differences between these methods are deeply analysed, and a new mathematical model is proposed to estimate the acceleration threshold limit in the lateral rollover test. The proposed model simulates the lateral rollover test, and, for the first time, it includes the effect of a variable position of the centre of gravity. Finally, the maximum speed at which the bus can travel in a bend without rolling over is computed.     

Development and validation of a Kalman filter-based model for vehicle slip angle estimation

It is well known that vehicle slip angle is one of the most difficult parameters to measure on a vehicle during testing or racing activities. Moreover, the appropriate sensor is very expensive and it is often difficult to fit to a car, especially on race cars. We propose here a strategy to eliminate the need for this sensor by using a mathematical tool which gives a good estimation of the vehicle slip angle. A single-track car model, coupled with an extended Kalman filter, was used in order to achieve the result. Moreover, a tuning procedure is proposed that takes into consideration both nonlinear and saturation characteristics typical of vehicle lateral dynamics. The effectiveness of the proposed algorithm has been proven by both simulation results and real-world data.     

Road disturbance estimation for the optimal preview control of an active suspension systems based on tracked vehicle model

This research investigates stochastic estimation of a look-ahead sensor scheme using the optimal preview control for an active suspension system of a full tracked vehicle (FTV). In this scheme, wheel disturbance input to the front wheels are estimated using the dynamic equations of the system. The estimated road disturbance input at the front wheels are utilized as preview information for the control of subsequently following wheels of FTV. The design of optimal preview control is used as a classical linear quadratic Gaussian problem by combining dynamics of the original system and estimation of previewed road inputs. The effectiveness of the preview controller is evaluated by comparing the estimated information with the measured information for different road profiles, where Kalman filter is used for the state-variables estimation of the FTV. This research also considers the reduced order estimation using commonly available sensors in order to decrease the number of sensors and measurements. The simulation results’ using an active suspension system with different preview information shows that the proposed system can be beneficial for the improvement of ride comfort of tracked vehicles without using any specialized sensors for preview information calculation.     

How well a single-track linear model captures the lateral dynamics of long combination vehicles

ABSTRACT

The effect of centre-of-gravity heights on the high-speed performance measures of long combination vehicles including truck with double centre-axle trailers, Nordic, and A-double combination vehicles is investigated. The high fidelity three-dimensional models, used in this research, are validated against physical test data. These models are often accurate in terms of the actual dynamic behaviours of the vehicle. On the other hand, the simple yaw-plane single-track models with linear tires require less number of vehicle parameters. In this paper, it is investigated how accurate the estimations of performance measures are at high forward speeds by such single-track linear (STL) models. The influence of load height is especially studied. The high-speed performance-based standard or PBS measures considered are rearward amplifications of both lateral acceleration and yaw velocity; lateral load transfer; yaw damping and high-speed transient offtracking. The results show that tire relaxation has a large effect and it is rather easy to add to an STL model, so it is assumed to be modelled in STL. With realistically high payload and a required accuracy of PBS measures of approximately 10%, only the accuracy of rearward amplification of yaw velocity calculated by the frequency response is fulfilled by the STL. With low payload, the same statement is valid, but with around 5% in required accuracy. The roll dynamics effects are more important than the tire non-linearities.     

Study on lateral dynamic characteristics of vehicle/turnout system

Based on Chinese No. 12 high speed, single-way swing nose rail concrete sleeper turnout, a comprehensive vehicle/turnout system coupling dynamic model has been established in this paper, and the lateral and vertical dynamic characteristics of vehicle/turnout systems have been simulated while the car passes through the turnout zone on divergence. These dynamic characteristics show that the lateral impact and vibration of the systems caused by the wheel/rail contact and irregularity are very intensive, especially at the switch zone and nose area of the turnout, and the lateral dynamics of the turnout system, such as lateral stability, vibrating responses, impacting and the allowable passing velocity force between the wheelsets and the switch rails are much more complicated than that of the vertical ones.     

Study on lateral dynamic characteristics of vehicle/turnout system

Based on Chinese No. 12 high speed, single-way swing nose rail concrete sleeper turnout, a comprehensive vehicle/turnout system coupling dynamic model has been established in this paper, and the lateral and vertical dynamic characteristics of vehicle/turnout systems have been simulated while the car passes through the turnout zone on divergence. These dynamic characteristics show that the lateral impact and vibration of the systems caused by the wheel/rail contact and irregularity are very intensive, especially at the switch zone and nose area of the turnout, and the lateral dynamics of the turnout system, such as lateral stability, vibrating responses, impacting and the allowable passing velocity force between the wheelsets and the switch rails are much more complicated than that of the vertical ones.     

悬架K&C特性对车辆操控性能影响的分析

悬架系统设计开发是底盘开发的重要环节,对于整车操控性能有至关重要的影响。本文以某A级车的大量KC数据为基础,利用面向总成特性的整车动力学仿真软件CarSim分析悬架KC特性变化对整车操控性能的影响,并运用试验统计学中的DOE试验设计方法计算各特性车辆操控性能指标的主效应,得到了悬架KC特性影响整车操控性能的规律,在设定悬架性能目标时重点关注,为整车开发早期的结构选择和后续的结构设计提供了依据。     

Effects of model response on model following type of combined lateral force and yaw moment control performance for active vehicle handling safety

This paper presents a comparison study of the effect of model response on the performance of the model following type combined lateral force and yaw moment control. The combined controls aim to maximize stability limit as well as vehicle responsiveness. In order to realize this aim, two types of model responses are proposed to introduce the required lateral force and yaw moment control. The model responses (a) is the side-slip angle and yaw rate vehicle response of the two degree of freedom vehicle motion (bicycle model). The model responses (b) is an intentional modification from the model responses (a) to the side slip angle converging to zero and first order yaw rate. Three different cases of combining lateral force and yaw moment control have been investigated using the two types of model responses. The effect of model responses is proved by computer simulations of the vehicle response to a single sine wave steering input with braking for the combined control methods proposed. It is found that the influence of the model response has a significant effect on the combined control performance.