A new formulation of the understeer coefficient to relate yaw torque and vehicle handling

The handling behaviour of vehicles is an important property for its relation to performance and safety. In 1970s, Pacejka did the groundwork for an objective analysis introducing the handling diagram and the understeer coefficient. In more recent years, the understeer concept is still mentioned but the handling is actively managed by direct yaw control (DYC). In this paper an accurate analysis of the vehicle handling is carried out, considering also the effect of drive forces. This analysis brings to a new formulation of the understeer coefficient, which is almost equivalent to the classical one, but it can be obtained by quasi-steady-state manoeuvres. In addition, it relates the vehicle yaw torque to the understeer coefficient, filling up the gap between the classical handling approach and DYC. A multibody model of a Formula SAE car is then used to perform quasi-steady-state simulations in order to verify the effectiveness of the new formulation. Some vehicle set-ups and wheel drive arrangements are simulated and the results are discussed. In particular, the handling behaviours of the rear wheel drive (RWD) and the front wheel drive (FWD) architectures are compared, finding an apparently surprising result: for the analysed vehicle the FWD is less understeering than for RWD. The relation between the yaw torque and the understeer coefficient allows to understand this behaviour and opens-up the possibility for different yaw control strategies.     

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.     

The handling surface: a new perspective in vehicle dynamics

The problem of describing the understeer–oversteer behaviour of a general vehicle, such as one with locked differential or tandem rear axle, is addressed taking a new perspective. The well-known handling diagram and the associated classical understeer gradient may be inadequate, mainly because they are no longer unique. The new concept of handling surface and a new definition of understeer gradient, which is indeed the gradient of the handling surface and hence a vector, are presented. It is also shown how the new concepts relate to and generalize the classical ones. Finally, a procedure for the experimental measure of the new understeer gradient is outlined.     

转矩式限滑差速器对后轮驱动汽车操纵稳定性影响的研究

采用7自由度车辆动力学模型,对装用JA1020LSD型转矩式限滑差速器的后轮驱动汽车进行了操纵稳定性研究。通过仿真分析和道路试验研究表明:装用限滑差速器后增加了后轮驱动车辆的不足转向趋势,即改善了操纵稳定性,但转向力矩略有增加。     

An optimal torque distribution control strategy for four-independent wheel drive electric vehicles

In this paper, an optimal torque distribution approach is proposed for electric vehicle equipped with four independent wheel motors to improve vehicle handling and stability performance. A novel objective function is formulated which works in a multifunctional way by considering the interference among different performance indices: forces and moment errors at the centre of gravity of the vehicle, actuator control efforts and tyre workload usage. To adapt different driving conditions, a weighting factors tuning scheme is designed to adjust the relative weight of each performance in the objective function. The effectiveness of the proposed optimal torque distribution is evaluated by simulations with CarSim and Matlab/Simulink. The simulation results under different driving scenarios indicate that the proposed control strategy can effectively improve the vehicle handling and stability even in slippery road conditions.     

Optimal control of motorsport differentials

Modern motorsport limited slip differentials (LSD) have evolved to become highly adjustable, allowing the torque bias that they generate to be tuned in the corner entry, apex and corner exit phases of typical on-track manoeuvres. The task of finding the optimal torque bias profile under such varied vehicle conditions is complex. This paper presents a nonlinear optimal control method which is used to find the minimum time optimal torque bias profile through a lane change manoeuvre. The results are compared to traditional open and fully locked differential strategies, in addition to considering related vehicle stability and agility metrics. An investigation into how the optimal torque bias profile changes with reduced track-tyre friction is also included in the analysis. The optimal LSD profile was shown to give a performance gain over its locked differential counterpart in key areas of the manoeuvre where a quick direction change is required. The methodology proposed can be used to find both optimal passive LSD characteristics and as the basis of a semi-active LSD control algorithm.     

Lateral handling improvement with dynamic curvature control for an independent rear wheel drive EV

The integrated longitudinal and lateral dynamic motion control is important for four wheel independent drive (4WID) electric vehicles. Under critical driving conditions, direct yaw moment control (DYC) has been proved as effective for vehicle handling stability and maneuverability by implementing optimized torque distribution of each wheel, especially with independent wheel drive electric vehicles. The intended vehicle path upon driver steering input is heavily depending on the instantaneous vehicle speed, body side slip and yaw rate of a vehicle, which can directly affect the steering effort of driver. In this paper, we propose a dynamic curvature controller (DCC) by applying a the dynamic curvature of the path, derived from vehicle dynamic state variables; yaw rate, side slip angle, and speed of a vehicle. The proposed controller, combined with DYC and wheel longitudinal slip control, is to utilize the dynamic curvature as a target control parameter for a feedback, avoiding estimating the vehicle side-slip angle. The effectiveness of the proposed controller, in view of stability and improved handling, has been validated with numerical simulations and a series of experiments during cornering engaging a disturbance torque driven by two rear independent in-wheel motors of a 4WD micro electric vehicle.     

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.     

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.     

Independent control of all-wheel-drive torque distribution

The sophistication of all-wheel-drive (AWD) technology is approaching the point where the drive torque to each wheel can be independently controlled. This potentially offers vehicle handling enhancements similar to those provided by dynamic stability control, but without the inevitable reduction in vehicle acceleration. Independent control of AWD torque distribution would therefore be especially beneficial under acceleration close to the limit of stability. A vehicle model of a typical sports sedan was developed in Simulink, with fully independent control of torque distribution. Box–Behnken experimental design was employed to determine which torque distribution parameters have the greatest impact on the vehicle course and acceleration. A proportional-integral control strategy was implemented, applying yaw rate feedback to vary the front–rear torque distribution and lateral acceleration feedback to adjust the left–right distribution. The resulting system shows a significant improvement over conventional driveline configurations under aggressive cornering acceleration on a high-μ surface. The performance approaches the theoretical limit for these conditions. In the medium term, such a system is only likely to be economically viable for premium vehicles. However, a future revolution of powertrain technology towards, for example, wheel-mounted motors, could realize these handling benefits far more widely.     

Independent control of all-wheel-drive torque distribution

The sophistication of all-wheel-drive (AWD) technology is approaching the point where the drive torque to each wheel can be independently controlled. This potentially offers vehicle handling enhancements similar to those provided by dynamic stability control, but without the inevitable reduction in vehicle acceleration. Independent control of AWD torque distribution would therefore be especially beneficial under acceleration close to the limit of stability. A vehicle model of a typical sports sedan was developed in Simulink, with fully independent control of torque distribution. Box-Behnken experimental design was employed to determine which torque distribution parameters have the greatest impact on the vehicle course and acceleration. A proportional-integral control strategy was implemented, applying yaw rate feedback to vary the front-rear torque distribution and lateral acceleration feedback to adjust the left-right distribution. The resulting system shows a significant improvement over conventional driveline configurations under aggressive cornering acceleration on a high-μ surface. The performance approaches the theoretical limit for these conditions. In the medium term, such a system is only likely to be economically viable for premium vehicles. However, a future revolution of powertrain technology towards, for example, wheel-mounted motors, could realize these handling benefits far more widely.     

Effects of Free-Control Variables on Automobile Handling

Compared with the fixed-control case, relatively few studies of the effects on handling quality of the nature of the free-control response of an automobile to steering torque inputs have been reported. Prior to reviewing these studies, an attempt is made in this paper to provide a conceptual framework for assessing the results, by drawing on analytical and experimental work concerned with manual control in closed-loop tracking systems. Application of these ideas to the automobile shows that a fixed-control driver strategy is required where precise path control is necessary. Less demanding situations would allow a free-control driving mode. Steering task performance is found to be relatively insensitive to free-control vehicle responses. However, drivers exhibit clear preferences for certain ranges of steering torque gradient, and for rapid responses of steering wheel angle to torque inputs. Vehicle handling variables interact strongly in their effect on driver opinion. For example, the optimum steering torque gradient (in N m/G) decreases, and the optimum steering “stiffness” (in N m/rad) increases, as the fixed-control response sensitivity increases. Within fairly wide ranges, the damping of the free-control oscillatory mode has little effect on handling quality.     

Haptic steering support for driving near the vehicle’s handling limits; skid-pad case

Current vehicle dynamic control systems from simple yaw control to high-end active steering support systems are designed to primarily actuate on the vehicle itself, rather than stimulate the driver to adapt his/her inputs for better vehicle control. The driver though dictates the vehicle’s motion, and centralizing him/her in the control loop is hypothesized to promote safety and driving pleasure. Exploring the above statement, the goal of this study is to develop and evaluate a haptic steering support when driving near the vehicle’s handling limits (Haptic Support Near the Limits; HSNL). The support aims to promote the driver’s perception of the vehicle’s behaviour and handling capacity (the vehicle’s internal model) by providing haptic (torque) cues on the steering wheel. The HSNL has been evaluated in (a) driving simulator tests and (b) tests with a vehicle (Opel Astra G/B) equipped with a variable steering feedback torque system. Drivers attempted to achieve maximum velocity while trying to retain control in a circular skid-pad. In the simulator (a) 25 subjects drove a vehicle model parameterised as the Astra on a dry skid-pad while in (b) 17 subjects drove the real Astra on a wet skid-pad. Both the driving simulator and the real vehicle tests led to the conclusion that the HSNL assisted subjects to drive closer to the designated path while achieving effectively the same speed. With the HSNL the drivers operated the tires in smaller slip angles and hence avoided saturation of the front wheels’ lateral forces and excessive understeer. Finally, the HSNL reduced their mental and physical demand.     

基于横向稳定杆的汽车操纵稳定性影响分析

文章基于横向稳定杆在整车的功能,分析车辆安装横向稳定杆和不安装横向稳定杆两个状态,研究了横向稳定杆对车辆操稳性能的影响,进一步在Trucksim软件中建立虚拟整车和驾驶员模型,模拟稳态回转和蛇形试验工况,并结合试验评价标准进行评分,对比分析结果表明,安装横向稳定杆的车辆对不足转向和车辆侧倾度性能影响较大,对转向性能影响较小。     

Effects of Free-Control Variables on Automobile Handling

SUMMARY

Compared with the fixed-control case, relatively few studies of the effects on handling quality of the nature of the free-control response of an automobile to steering torque inputs have been reported. Prior to reviewing these studies, an attempt is made in this paper to provide a conceptual framework for assessing the results, by drawing on analytical and experimental work concerned with manual control in closed-loop tracking systems. Application of these ideas to the automobile shows that a fixed-control driver strategy is required where precise path control is necessary. Less demanding situations would allow a free-control driving mode. Steering task performance is found to be relatively insensitive to free-control vehicle responses. However, drivers exhibit clear preferences for certain ranges of steering torque gradient, and for rapid responses of steering wheel angle to torque inputs. Vehicle handling variables interact strongly in their effect on driver opinion. For example, the optimum steering torque gradient (in N m/G) decreases, and the optimum steering “stiffness” (in N m/rad) increases, as the fixed-control response sensitivity increases. Within fairly wide ranges, the damping of the free-control oscillatory mode has little effect on handling quality.     

A Variable Free Control Characteristic Vehicle

A variable characteristic car (VCC) has been developed at Melbourne University for driverlvehicle handling research. The vehicle is unusual in that it has facilities for varying both its fixed control and free control dynamic characteristics over wide ranges. In this paper the servo systems used to effect these changes are described. The calibration methods used to relate the vehicle response characteristics to the variable servo settings are detailed. Sample calibration results are given for the fixed control parameters steering ratio, yaw response time and stability factor. Calibration of the free control parameters is also described and results are given for the steering torque gradient, and the time-to-peak and percentage overshoot of the steering wheel motion in response to a step input of torque.     

摩擦片式防滑差速器转矩特性对汽车操纵稳定性的影响研究

进行了摩擦片式防滑差速器防滑转矩输出特性测定试验,并分别对装有摩擦片式防滑差速器和普通差速器的汽车,通过试验测定的车厢侧倾角、转弯半径比、前后轴侧偏角差值、横摆角速度及侧向加速度作为对比参数,研究了摩擦片式防滑差速器转矩特性对汽车操纵稳定性的影响。结果表明,摩擦片式防滑差速器能够显著提高汽车的动力性、通过性,改善汽车的操纵稳定性。     

Nonlinear optimal integrated vehicle control using individual braking torque and steering angle with on-line control allocation by using state-dependent Riccati equation technique

This paper proposes the solution of state-dependent Riccati equation as a nonlinear optimal regulator to stabilise the motion dynamics of the vehicle model subjected to sudden disturbance inputs in the lateral direction. The proposed nonlinear regulator coordinates individually actuated wheel braking torque and steering wheel angle simultaneously in an optimal manner. Performance criteria are satisfied by solving the Riccati equation based on the given cost function subjected to the nonlinear vehicle dynamics. On-line control allocation in terms of optimal brake torque distribution enhanced by optimal wheel steering angle input is achieved. Furthermore, the proposed optimal nonlinear regulator is an active fault-tolerant control system against partial by-wire actuator failures while guaranteeing stability with good performance due to its capability to allocate the individual control inputs in an optimal way. The main aim is to stabilise the motion dynamics of the vehicle model during short-term emergency situations along the desired straight trajectory manageable by average drivers and to provide vehicle stability and handling predictability through the interaction of individual wheel braking and steering actuators. Simulation results are used to illustrate the effectiveness of the proposed methodology.     

Desired yaw rate and steering control method during cornering for a six-wheeled vehicle

This paper proposes a steering control method based on optimal control theory to improve the maneuverability of a six-wheeled vehicle during cornering. The six-wheeled vehicle is believed to have better performance than a four-wheeled vehicle in terms of its capability for crossing obstacles, off-road maneuvering and fail-safe handling when one or two of the tires are punctured. Although many methods to improve the four-wheeled vehicle’s lateral stability have been studied and developed, there have only been a few studies on the six-wheeled vehicle’s lateral stability. Some studies of the six-wheeled vehicle have been reported recently, but they are related to the desired yaw rate of a four-wheeled vehicle to control the six-wheeled vehicle’s maneuvering during corning. In this paper, the sideslip angle and yaw rate are controlled to improve the maneuverability during cornering by independent control of the steering angles of the six wheels. The desired yaw rate that is suitable for a six-wheeled vehicle is proposed as a control target. In addition, a scaled-down vehicle with six drive motors and six steering motors that can be controlled independently is designed. The performance of the proposed control methods is verified using a full model vehicle simulation and scaled-down vehicle experiment.