关于通过悬架改进设计优化汽车转向特性的研究

对某SUV车建立了刚柔耦合整车系统虚拟样机模型,进行了稳态转向特性仿真分析,发现该车具有先不足转向后过多转向的问题,并且中性转向点的侧向加速度值an偏小.通过对悬架刚度、稳定杆刚度的优化设计,解决了该车的过多转向问题,使之具有了适度的不足转向特性,并且使an达到了设计要求.最后对改进前后的方案进行了对比分析及试验验证,说明优化的效果是非常明显的.     

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.     

Nonlinear PI front and rear steering control in four wheel steering vehicles

Vehicle steering dynamics show resonances, which depend on the longitudinal speed, unstable equilibrium points and limited stability regions depending on the constant steering wheel angle, longitudinal speed and car parameters.

The main contribution of this paper is to show that a combined decentralized proportional active front steering control and proportional-integral active rear steering control from the yaw rate tracking error can assign the eigenvalues of the linearised single track steering dynamics, without lateral speed measurements, using a standard single track car model with nonlinear tire characteristics and a non-linear first-order reference model for the yaw rate dynamics driven by the driver steering wheel input. By choosing a suitable nonlinear reference model it is shown that the responses to driver step inputs tend to zero (or reduced) lateral speed for any value of longitudinal speed: in this case the resulting controlled vehicle static gain from driver input to yaw rate differs from the uncontrolled one at higher speed. The closed loop system shows the advantages of both active front and rear steering control: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres, enlarged stability regions, reduced lateral speed and improved manoeuvrability; in addition comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced.

For the designed control law a robustness analysis is presented with respect to system failures, driver step inputs and critical car parameters such as mass, moment of inertia and front and rear cornering stiffness coefficients. Several simulations are carried out on a higher order experimentally validated nonlinear dynamical model to confirm the analysis and to explore the robustness with respect to unmodelled dynamics.     

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.     

Nonlinear PI front and rear steering control in four wheel steering vehicles

Vehicle steering dynamics show resonances, which depend on the longitudinal speed, unstable equilibrium points and limited stability regions depending on the constant steering wheel angle, longitudinal speed and car parameters.

The main contribution of this paper is to show that a combined decentralized proportional active front steering control and proportional-integral active rear steering control from the yaw rate tracking error can assign the eigenvalues of the linearised single track steering dynamics, without lateral speed measurements, using a standard single track car model with nonlinear tire characteristics and a non-linear first-order reference model for the yaw rate dynamics driven by the driver steering wheel input. By choosing a suitable nonlinear reference model it is shown that the responses to driver step inputs tend to zero (or reduced) lateral speed for any value of longitudinal speed: in this case the resulting controlled vehicle static gain from driver input to yaw rate differs from the uncontrolled one at higher speed. The closed loop system shows the advantages of both active front and rear steering control: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres, enlarged stability regions, reduced lateral speed and improved manoeuvrability; in addition comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced.

For the designed control law a robustness analysis is presented with respect to system failures, driver step inputs and critical car parameters such as mass, moment of inertia and front and rear cornering stiffness coefficients. Several simulations are carried out on a higher order experimentally validated nonlinear dynamical model to confirm the analysis and to explore the robustness with respect to unmodelled dynamics.     

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.     

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.     

Optimal Control of Four Wheel Steering Vehicle

SUMMARY

This paper derives a method of controlling four wheel steering using optimal control theory. The purpose of control is to minimize the sideslip angle at the center of gravity. The control method feeds forward the steering wheel angle and feeds back the yaw velocity and the sideslip angle to the front and rear wheel angles. Theoretical studies show that the sideslip angle is reduced to zero even in the transient state, and that the understeer characteristic and frequency response can be changed regardless of the vehicle static margin. This Paper also examines various characteristics of the influence of the side force nonlinearities of tires and crosswinds.     

Bifurcation analysis of an automobile model negotiating a curve

The paper deals with the bifurcation analysis of a rather simple model describing an automobile negotiating a curve. The mechanical model has two degrees of freedom and the related equations of motion contain the nonlinear tyre characteristics. Bifurcation analysis is adopted as the proper procedure for analysing steady-state cornering. Two independent parameters referring to running conditions, namely steering angle and speed, are varied. Ten different combinations of front and rear tyre characteristics (featuring understeer or oversteer automobiles) are considered for the bifurcation analysis. Many different dynamical behaviours of the model are obtained by slightly varying the parameters describing the tyre characteristics. Both simple and extremely complex bifurcations may occur. Homoclinic bifurcations, stable and unstable limit cycles (of considerable amplitude) are found, giving a sound and ultimate interpretation to some actual (rare but very dangerous) dynamic behaviours of automobiles, as reported by professional drivers. The presented results are cross-validated by exploiting handling diagram theory. The knowledge of the derived set of bifurcations is dramatically important to fully understand the actual vehicle yaw motions occurring while running on an even surface. Such a knowledge is a pre-requisite for robustly designing the chassis and for enhancing the active safety of vehicles.     

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.     

Optimal Control of Four Wheel Steering Vehicle

This paper derives a method of controlling four wheel steering using optimal control theory. The purpose of control is to minimize the sideslip angle at the center of gravity. The control method feeds forward the steering wheel angle and feeds back the yaw velocity and the sideslip angle to the front and rear wheel angles. Theoretical studies show that the sideslip angle is reduced to zero even in the transient state, and that the understeer characteristic and frequency response can be changed regardless of the vehicle static margin. This Paper also examines various characteristics of the influence of the side force nonlinearities of tires and crosswinds.     

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.     

High Performance ACC System Based on Sensor Fusion with Distance Sensor, Image Processing Unit, and Navigation System

Curve sensors used in first generation “Adaptive Cruise Control” systems (ACC) are based on steering angle sensors, lateral accelerometers or yaw rate sensors. The disadvantage of these curve sensors is that they do not have any preview characteristics. This leads in many driving situations to misinterpretations by the ACC system, e.g. wrong path assignments of vehicles ahead because of non-constant curve radii particularly in the beginning and ending of curves. The consequence is that the ACC car brakes due to vehicles in adjacent lanes or it ignores relevant obstacles. In the following a second generation ACC system will be presented whose curve sensor is realized by a real time image processing system with the support of a GPS-based navigation system. This multi-sensor fusion system is now suitable for collision avoidance and stop and go applications.     

Using µ Feedforward for Vehicle Stability Enhancement

A differential braking control strategy using yaw rate feedback, coupled with µ feedforward is introduced for a vehicle cornering on different µ roads. A nonlinear 4-wheel car model is developed. A desired yaw rate is calculated from the reference model based on the driver steering input. It is shown that knowledge of µ offers significant improvement of the vehicle desired trajectory over that of a yaw rate controller alone. Uncertainties and time delay in estimating µ are shown to still yield a system that is superior to using no µ information at all.     

Using µ Feedforward for Vehicle Stability Enhancement

A differential braking control strategy using yaw rate feedback, coupled with µ feedforward is introduced for a vehicle cornering on different µ roads. A nonlinear 4-wheel car model is developed. A desired yaw rate is calculated from the reference model based on the driver steering input. It is shown that knowledge of µ offers significant improvement of the vehicle desired trajectory over that of a yaw rate controller alone. Uncertainties and time delay in estimating µ are shown to still yield a system that is superior to using no µ information at all.     

Directional Dynamics of a Tractor-Loader-Backhoe

SUMMARY

This paper presents a study of the directional dynamics of large industrial tractors. These vehicles have special properties which make their dynamics interesting, including soft rear tires, large yaw moments of inertia and low or negative understeer gradients.

A linear yaw plane model was used for the analysis. The lateral compliance of the tires was included via a simplified version of the stretched-string model. Measurements were performed in support of the modeling effort, including inertial parameters, understeer gradient and transient response. A comparison between calculations and test results indicated that lateral compliance was an important influence on the transient response of these vehicles.     

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.     

Directional Dynamics of a Tractor-Loader-Backhoe

This paper presents a study of the directional dynamics of large industrial tractors. These vehicles have special properties which make their dynamics interesting, including soft rear tires, large yaw moments of inertia and low or negative understeer gradients.

A linear yaw plane model was used for the analysis. The lateral compliance of the tires was included via a simplified version of the stretched-string model. Measurements were performed in support of the modeling effort, including inertial parameters, understeer gradient and transient response. A comparison between calculations and test results indicated that lateral compliance was an important influence on the transient response of these vehicles.     

An Investigation of High-Speed Automobile Steering Response

SUMMARY

The significance of the effects of steering compliance and aerodynamic life on high speed automobile's steering response was investigated on two vehicles, a Ford Falcon XW (1969) station-wagon and a GM-Holden Kingswood HQ (1974) sedan. An aerofoil was mounted above the front bumper bar of the Ford Falcon to enable the simulation of vehicles with very degraded aerodynamic characteristics. Mathematical analysis showed the importance of the inclusion of steering compliance effects in determining stability factor, and hence the vehicle's high speed yaw rate sensitivity. Both experiments and theory showed that the actual high speed yaw rate response is not significantly less than that predicted from a low speed skid pad test, however, slight errors were found which are likely to be due to steering system nonlinearity and the effects of aerodynamic lift.     

The Static Stability of Articulated Commercial Vehicles

This review of the state of the art emphasizes recent results that have been obtained in extending conventionalanalysis techniques to the treatment of “Highway Trains”, that is, to heavy trucks that have multiple articulation points and employ suspensions with multiple axles. Equations of motion applicable to the equilibrium turning performances of articulated vehicles are examined with respect to using analysis techniques involving steering gains, understeer gradients, effective wheel-bases, handling diagrams, and critical speeds. These examinations provide the basis for in sights into simplified approaches for understanding the steady turning mechanics of articulated, multi-axle vehicles riding on pneumatic tires.