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

ABSTRACT

The 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 tests are 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.     

Interaction of vehicle and steering system regarding on-centre handling

For the on-centre handling behaviour of vehicles the steering system is absolutely important. To investigate the interaction of the vehicle and steering system a validated, especially tailored simulation model was developed. Some meaningful vehicle and steering system parameters are altered to show the influence on steering wheel torque, steering feel and understeer. The results underline the importance of an accurate steering system model. Identified measures to improve the centre feel and steering response were a stiffer torsion bar, a higher cornering stiffness or a lower overall steering ratio. The steering response, however, suffers when the centre feel is improved by a higher trail. The steering rack friction reduces mainly the steering response while the steering column friction decreases the centre feel whereas a stiffer torsion bar lessens the understeer tendency.     

Interaction of vehicle and steering system regarding on-centre handling

For the on-centre handling behaviour of vehicles the steering system is absolutely important. To investigate the interaction of the vehicle and steering system a validated, especially tailored simulation model was developed. Some meaningful vehicle and steering system parameters are altered to show the influence on steering wheel torque, steering feel and understeer. The results underline the importance of an accurate steering system model. Identified measures to improve the centre feel and steering response were a stiffer torsion bar, a higher cornering stiffness or a lower overall steering ratio. The steering response, however, suffers when the centre feel is improved by a higher trail. The steering rack friction reduces mainly the steering response while the steering column friction decreases the centre feel whereas a stiffer torsion bar lessens the understeer tendency.     

Comparing rear wheel steering and rear active differential approaches to vehicle yaw control

A comparison between two different approaches to vehicle stability control is carried out, employing a robust non-parametric technique in the controller design. In particular, an enhanced internal model control strategy, together with a feedforward action and a suitably generated reference map, is employed for the control of a vehicle equipped either with a rear wheel steering (RWS) system or with a rear active differential (RAD) device. The uncertainty arising from the wide range of operating conditions is described by an additive model set employed in the controller design. Extensive steady state and transient tests simulated with an accurate 14 degrees of freedom nonlinear model of the considered vehicle show that both systems are able to improve handling and safety in normal driving conditions. RAD devices can make the vehicle reach higher lateral acceleration values but they achieve only slight stability improvements against oversteer. On the other hand, 4WS systems can greatly improve both vehicle safety and manoeuvrability in all driving situations, making this device an interesting and powerful stability system.     

Fuzzy-logic applied to yaw moment control for vehicle stability

In this paper, we propose a new yaw moment control based on fuzzy logic to improve vehicle handling and stability. The advantages of fuzzy methods are their simplicity and their good performance in controlling non-linear systems. The developed controller generates the suitable yaw moment which is obtained from the difference of the brake forces between the front wheels so that the vehicle follows the target values of the yaw rate and the sideslip angle. The simulation results show the effectiveness of the proposed control method when the vehicle is subjected to different cornering steering manoeuvres such as change line and J-turn under different driving conditions (dry road and snow-covered).     

Fuzzy-logic applied to yaw moment control for vehicle stability

In this paper, we propose a new yaw moment control based on fuzzy logic to improve vehicle handling and stability. The advantages of fuzzy methods are their simplicity and their good performance in controlling non-linear systems. The developed controller generates the suitable yaw moment which is obtained from the difference of the brake forces between the front wheels so that the vehicle follows the target values of the yaw rate and the sideslip angle. The simulation results show the effectiveness of the proposed control method when the vehicle is subjected to different cornering steering manoeuvres such as change line and J-turn under different driving conditions (dry road and snow-covered).     

Handling performance control for hybrid 8-wheel-drive vehicle and simulation verification

In order to improve handling performance of a hybrid 8-Wheel-Drive vehicle, the handling performance control strategy was proposed. For armoured vehicle, besides handling stability in high speed, the minimum steer radius in low speed is also a key tactical and technical index. Based on that, the proposed handling performance control strategy includes ‘Handling Stability’ and ‘Radius Minimization’ control modes. In ‘Handling Stability’ control mode, ‘Neutralsteer Radio’ is defined to adjust the steering characteristics to satisfy different demand in different speed range. In ‘Radius Minimization’ control mode, the independent motors are controlled to provide an additional yaw moment to decrease the minimum steer radius. In order to verify the strategy, a simulation platform was built including engine and continuously variable transmission systems, generator and battery systems, independent motors and controllers systems, vehicle dynamic and tyre mechanical systems. The simulation results show that the handling performance of the vehicle can be enhanced significantly, and the minimum steer radius can be decreased by 20% which is significant improvement compared to the common level of main battle armoured vehicle around the world.     

多功能车操纵稳定性的虚拟样机实验研究

采用面向整车系统的数字化虚拟样机技术,利用ADAMS软件,建立了某多功能车(MPV)的整车虚拟样机模型,在ADAMS虚拟环境模式中对其操纵稳定性进行了大量的仿真计算和实验研究,研究结果表明,该车初始参数匹配状态下整车操纵稳定性能较好。实验结果数据为评估、改进、优化同型车辆提供了重要的理论参考。     

Effect of handling characteristics on minimum time cornering with torque vectoring

In this paper, the effect of both passive and actively-modified vehicle handling characteristics on minimum time manoeuvring for vehicles with 4-wheel torque vectoring (TV) capability is studied. First, a baseline optimal TV strategy is sought, independent of any causal control law. An optimal control problem (OCP) is initially formulated considering 4 independent wheel torque inputs, together with the steering angle rate, as the control variables. Using this formulation, the performance benefit using TV against an electric drive train with a fixed torque distribution, is demonstrated. The sensitivity of TV-controlled manoeuvre time to the passive understeer gradient of the vehicle is then studied. A second formulation of the OCP is introduced where a closed-loop TV controller is incorporated into the system dynamics of the OCP. This formulation allows the effect of actively modifying a vehicle's handling characteristic via TV on its minimum time cornering performance of the vehicle to be assessed. In particular, the effect of the target understeer gradient as the key tuning parameter of the literature-standard steady-state linear single-track model yaw rate reference is analysed.     

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.     

A combined use of phase plane and handling diagram method to study the influence of tyre and vehicle characteristics on stability

This paper deals with in-curve vehicle lateral behaviour and is aimed to find out which vehicle physical characteristics affect significantly its stability. Two different analytical methods, one numerical (phase plane) and the other graphical (handling diagram) are discussed. The numerical model refers to the complete quadricycle, while the graphical one refers to a bicycle model. Both models take into account lateral load transfers and nonlinear Pacejka tyre–road interactions. The influence of centre of mass longitudinal position, tyre cornering stiffness and front/rear roll stiffness ratio on vehicle stability are analysed. The presented results are in good agreement with theoretical expectations about the above parameters influence, and show how some physical characteristics behave as saddle-node bifurcation parameters.     

Active yaw damper for the improvement of railway vehicle stability and curving performances: simulations and experimental results

To further increase passenger train comfort and handling performances, a mechatronic approach to the design of railway vehicles is necessary. In fact, active systems on board a railway vehicle allow to push design barriers beyond those encountered with just passive systems. The article deals with the development of an electro-mechanical actuator to improve the running behaviour of a railway vehicle, both in straight track and curve. The main components of the active system are a brushless motor and a mechanical transmission, used to apply a longitudinal force between the carbody and the bogie of the vehicle. The actuator is operated in force control. Different control strategies were developed for straight track running, where the aim is to increase the vehicle critical speed, and for curve negotiation, where the goal is to reduce the maximum values of track shift forces. A mathematical model of the railway vehicle incorporating the active control device has been developed and used to optimise control strategies and hardware set-up of the active device and to estimate the increase in operating performances with respect to a conventional passive vehicle. The active control device has then been mounted on an ETR470 railway vehicle, and its performances have been evaluated during in-line tests in both straight and curved tracks.     

Active yaw damper for the improvement of railway vehicle stability and curving performances: simulations and experimental results

To further increase passenger train comfort and handling performances, a mechatronic approach to the design of railway vehicles is necessary. In fact, active systems on board a railway vehicle allow to push design barriers beyond those encountered with just passive systems. The article deals with the development of an electro-mechanical actuator to improve the running behaviour of a railway vehicle, both in straight track and curve. The main components of the active system are a brushless motor and a mechanical transmission, used to apply a longitudinal force between the carbody and the bogie of the vehicle. The actuator is operated in force control. Different control strategies were developed for straight track running, where the aim is to increase the vehicle critical speed, and for curve negotiation, where the goal is to reduce the maximum values of track shift forces. A mathematical model of the railway vehicle incorporating the active control device has been developed and used to optimise control strategies and hardware set-up of the active device and to estimate the increase in operating performances with respect to a conventional passive vehicle. The active control device has then been mounted on an ETR470 railway vehicle, and its performances have been evaluated during in-line tests in both straight and curved tracks.     

A method to find correlations between steering feel and vehicle handling properties using a moving base driving simulator

There have been several investigations to find out how drivers experience a change in vehicle-handling behaviour. However, the hypothesis that there is a correlation between what the driver perceives and vehicle- handling properties remains to be verified. To define what people feel, the human feeling of steering systems was divided into dimensions of perception. Then 28 test drivers rated different steering system characteristics of a semi-trailer tractor combination in a moving base-driving simulator. Characteristics of the steering system differed in friction, damping, inertia and stiffness. The same steering system characteristics were also tested in accordance with international standards of vehicle-handling tests resulting in characteristic quantities. The instrumental measurements and the non-instrumental ratings were analysed with respect to correlation between each other with the help of regression analysis and neural networks. Results show that there are correlations between measurements and ratings. Moreover, it is shown that which one of the handling variables influence the different dimensions of the steering feel.     

Integration of vehicle yaw stabilisation and rollover prevention through nonlinear hierarchical control allocation

This work presents an approach to rollover prevention that takes advantage of the modular structure and optimisation properties of the control allocation paradigm. It eliminates the need for a stabilising roll controller by introducing rollover prevention as a constraint on the control allocation problem. The major advantage of this approach is the control authority margin that remains with a high-level controller even during interventions for rollover prevention. In this work, the high-level control is assigned to a yaw stabilising controller. It could be replaced by any other controller. The constraint for rollover prevention could be replaced by or extended to different control objectives. This work uses differential braking for actuation. The use of additional or different actuators is possible. The developed control algorithm is computationally efficient and suitable for low-cost automotive electronic control units. The predictive design of the rollover prevention constraint does not require any sensor equipment in addition to the yaw controller. The method is validated using an industrial multi-body vehicle simulation environment.     

A review on bicycle and motorcycle rider control with a perspective on handling qualities

This paper is a review study on handling and control of bicycles and motorcycles, the so-called single-track vehicles. The first part gives a brief overview on the modelling of the dynamics of single-track vehicles and the experimental validation. The second part focusses on a review of modelling and measuring human rider control. The third part deals with the concepts of handling and manoeuvrability and their experimental validation. Parallels are drawn with the literature on aircraft handling and pilot models. The paper concludes with the open ends and promising directions for future work in the field of handling and control of single-track vehicles.     

Estimation of land vehicle roll and pitch angles

In this article, two kinematics-based observers are proposed to estimate the vehicle roll and pitch angles by using an inertial measurement unit. The observers are mathematically proven to be stable if the vehicle yaw rate is not zero. With a design variation of the observer gains, the estimated roll or pitch angle is shown to further asymptotically converge to the true value, eliminating possible errors caused by the biases of the acceleration signals. Simulation results show that accurate estimation of both pitch and roll angles can be achieved without the help of external sensors such as global positioning systems, either by using the accelerometer-based reference pitch or roll angle as the maneuver varies, or by using an observer with zero steady-state error property.     

Optimisation of handling and traction in a rear wheel drive vehicle by means of magneto-rheological semi-active differential

This paper presents a semi-active differential, magneto-rheological fluid limited slip differential, which allows us to bias the torque between the driving wheels. It is based on the magneto-rheological fluid employment, by which it is possible to change, in a controlled manner, the internal friction torque and, consequently, the torque bias ratio. This device is an adaptive one and allows us to obtain an asymmetric torque distribution in order to improve vehicle handling. The device modelling and the control algorithm, realised for this activity, are described. The illustrated results highlight the advantages that are attainable regarding directional behaviour, stability, and traction.     

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.     

Predictive control of a vehicle trajectory using a coupled vector with vehicle velocity and sideslip angle

In this paper, a predictive algorithm for vehicle trajectory control using the vehicle velocity and sideslip angle is proposed. Since the driving state of a vehicle generates nonholonomic constraint equations, it is difficult to control the trajectory with a conventional control algorithm. Furthermore, control vectors such as vehicle velocity and sideslip angle are coupled together; hence, a separate control for each variable is not suitable. In this study, a coupled control vector that combines the velocity and sideslip angle is proposed for the predictive control of vehicle trajectory. Since the coupled control vector is derived from the status of the vehicle’s motion, it is easy to generate a feedback control vector for the predictive controller. The coupled vector cannot be directly used as input to the vehicle systems; therefore, the vehicle input vector should be calculated from the control vector using a nonlinear function. Since nonlinear functions are not inserted in the control loop, they are calculated by the controller. Therefore, this method does not require a linearization process in the control logic, which enhances the stability and accuracy of the predictive controller.