Investigation into untripped rollover of light vehicles in the modified fishhook and the sine maneuvers. Part I: Vehicle modelling, roll and yaw instability

Vehicle rollovers may occur under steering-only maneuvers because of roll or yaw instability. In this paper, the modified fishhook and the sine maneuvers are used to investigate a vehicle's rollover resistance capability through simulation. A 9-degrees of freedom (DOF) vehicle model is first developed for the investigation. The vehicle model includes the roll, yaw, pitch, and bounce modes and passive independent suspensions. It is verified with the existing 3-DOF roll-yaw model. A rollover critical factor (RCF) quantifying a vehicle's rollover resistance capability is then constructed based on the static stability factor (SSF) and taking into account the influence of other key dynamic factors.

Simulation results show that the vehicle with certain parameters will rollover during the fishhook maneuver because of roll instability; however, the vehicle with increased suspension stiffness, which does not rollover during the fishhook maneuver, may exceed its rollover resistance limit because of yaw instability during the sine maneuver. Typically, rollover in the sine maneuver happens after several cycles.

It has been found that the proposed RCF well quantifies the rollover resistance capability of a vehicle for the two specified maneuvers. In general, the larger the RCF, the more kinetically stable is a vehicle. A vehicle becomes unstable when its RCF is less than zero. Detailed discussion on the effects of key vehicle system parameters and drive conditions on the RCF in the fishhook and the sine maneuver is presented in Part II of this study.     

Stability and optimised H∞ control of tripped and untripped vehicle rollover

Vehicle rollover is a serious traffic accident. In order to accurately evaluate the possibility of untripped and some special tripped vehicle rollovers, and to prevent vehicle rollover under unpredictable variations of parameters and harsh driving conditions, a new rollover index and an anti-roll control strategy are proposed in this paper. Taking deflections of steering and suspension induced by the roll at the axles into consideration, a six degrees of freedom dynamic model is established, including lateral, yaw, roll, and vertical motions of sprung and unsprung masses. From the vehicle dynamics theory, a new rollover index is developed to predict vehicle rollover risk under both untripped and special tripped situations. This new rollover index is validated by Carsim simulations. In addition, an H-infinity controller with electro hydraulic brake system is optimised by genetic algorithm to improve the anti-rollover performance of the vehicle. The stability and robustness of the active rollover prevention control system are analysed by some numerical simulations. The results show that the control system can improve the critical speed of vehicle rollover obviously, and has a good robustness for variations in the number of passengers and longitude position of the centre of gravity.     

A method for estimation of vehicle inertial parameters

In this paper, a new method is presented for estimating the current sprung mass inertial parameters of a vehicle, such as the mass, pitch and roll mass moments of inertia, and lateral and longitudinal centre of gravity locations. The method measures the sprung mass response when the vehicle is driven over an unknown and unmeasured random road profile. From these measurements, the equivalent free-decay responses are extracted and modal analysis techniques used to estimate the sprung mass natural frequencies, damping ratios and mode shapes. This information is combined with a simplified vehicle estimation model, least squares analysis and known equivalent stiffness parameters to estimate the vehicles’ inertial parameters. The results obtained from several simulation examples show that estimates of the inertial parameters generally have small relative errors.     

An improvement in rollover detection of articulated vehicles using the grey system theory

A Rollover Index combined with the grey system theory, called a Grey Rollover Index (GRI), is proposed to assess the rollover threat for articulated vehicles with a tractor–semitrailer combination. This index can predict future trends of vehicle dynamics based on current vehicle motion; thus, it is suitable for vehicle-rollover detection. Two difficulties are encountered when applying the GRI for rollover detection. The first difficulty is effectively predicting the rollover threat of the vehicles, and the second difficulty is achieving a definite definition of the real rollover timing of a vehicle. The following methods are used to resolve these problems. First, a nonlinear mathematical model is constructed to accurately describe the vehicle dynamics of articulated vehicles. This model is combined with the GRI to predict rollover propensity. Finally, TruckSim^? software is used to determine the real rollover timing and facilitate the accurate supply of information to the rollover detection system through the GRI. This index is used to verify the simulation based on the common manoeuvres that cause rollover accidents to reduce the occurrence of false signals and effectively increase the efficiency of the rollover detection system.     

State estimation in roll dynamics for commercial vehicles

Accurate lateral load transfer estimation plays an important role in improving the performance of the active rollover prevention system equipped in commercial vehicles. This estimation depends on the accurate prediction of roll angles for both the sprung and the unsprung subsystems. This paper proposes a novel computational method for roll-angle estimation in commercial vehicles employing sensors which are already used in a vehicle dynamic control system without additional expensive measurement units. The estimation strategy integrates two blocks. The first block contains a sliding-mode observer which is responsible for calculating the lateral tyre forces, while in the second block, the Kalman filter estimates the roll angles of the sprung mass and those of axles in the truck. The validation is conducted through MATLAB/TruckSim co-simulation. Based on the comparison between the estimated results and the simulation results from TruckSim, it can be concluded that the proposed estimation method has a promising tracking performance with low computational cost and high convergence speed. This approach enables a low-cost solution for the rollover prevention in commercial vehicles.     

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.     

Optimal Performance of Variable Component Suspensions

SUMMARY

Most vehicle suspension systems use fixed passive components that offer a compromise in performance between sprung mass isolation, suspension travel, and tireroad contact force. Recently, systems with discretely adjustable dampers and air springs been added to production vehicles. Active and semi-active damping concepts for vehicle suspensions have also been studied theoretically and with physical prototypes. This paper examines the optimal performance comparisons of variable component suspensions, including active damping and full-state feedback, for “quartercar” heave models. Two and three dimensional optimizations are computed using performance indicators to find the component parameters (control gains) that provide “optimal” performance for statistically described roadway inputs. The effects of performance weighting and feedback configuration are examined. Active damping is shown to be mainly important for vehicle isolation. A passive vehicle suspension can control suspension travel and tire contact force nearly as well as a full state feedback control strategy.     

Coordinated control strategies for active steering,differential braking and active suspension for vehicle stability,handling and safety improvement

ABSTRACT

In this paper, a coordinated control strategy is proposed to provide an effective improvement in handling stability of the vehicle, safety, and comfortable ride for passengers. This control strategy is based on the coordination among active steering, differential braking, and active suspension systems. Two families of controllers are used for this purpose, which are the high order sliding mode and the backstepping controllers. The control strategy was tested on a full nonlinear vehicle model in the environment of MATLAB/Simulink. Rollover avoidance and yaw stability control constraints have been considered. The control system mainly focuses on yaw stability control. When rollover risk is detected, the proposed strategy controls the roll dynamics to decrease rollover propensity. Simulation results for two different critical driving scenarios, the first one is a double lane change and the other one is a J-turn manoeuvre, show the effectiveness of the coordination strategy in stabilising the vehicle, enhancing handling and reducing rollover propensity.     

Optimal roll control of an articulated vehicle: theory and model validation

This paper investigates optimal roll control of an experimental articulated vehicle. The test vehicle and the mathematical model used to design the control strategies are presented. The vehicle model is validated against experimental data from the test vehicle in passive configuration. The initial controller design, performed by Sampson (Sampson, D.J.M. and Cebon, D., 2003a, Achievable roll stability of heavy road vehicles. Proc. Instn. Mech. Engrs, Part D, J. Automobile Engineering, 217(4), 269–287), is reviewed and adapted for the experimental vehicle. The effect of not controlling all the axles on the vehicle is investigated and a variable vehicle speed controller is designed by interpolating between constant speed controllers. Substantial reduction in normalized load transfer is achieved for a range of manoeuvres, both in steady-state and transient conditions.     

大型车辆横向稳定性对公路设计极限平曲线半径取值的影响分析

针对目前公路设计研究采用的汽车横向稳定性计算模型仍然是刚性车辆的简化结构,未考虑汽车悬架及轮胎的弹性变形影响的问题,通过分析悬挂系统对车辆行驶的横向稳定性的影响以及大型车横向倾覆特点,推导出考虑车辆悬挂结构后的公路平面设计指标计算方法及公式;参考Bonneson等的研究成果,给出了为保证车辆横向行驶安全舒适条件下的横向力系数推荐取值及不同设计速度时的圆曲线极限最小半径值。结果表明:提出的设计指标的计算方法及取值为现有标准规范的修订提供了一定的参考。     

Comparison of the properties of active and semiactive suspension

In this article, the properties of active and semi-active suspension for heavy goods vehicles are compared. The criteria for the comparison are the RMS sprung mass vertical acceleration, RMS dynamic tyre force, and suspension power consumption. The active system is based on an air-spring with controlled in-flow and out-flow of the air. In the semi-active system, a controlled hydraulic damper is employed. The results concerning the semi-active suspension system were taken from the article by Besinger et al. [Besinger, F.H., Cebon, D. and Cole, D.J., 1995, Force control of a semi-active damper. Vehicle System Dynamics, 24(9), 695–723.].     

多用途乘用车侧翻稳定性能动态测试方法研究

对比分析了国内外车辆侧翻稳定性相关的标准法规的基本情况。研究了车辆发生侧翻的类型和机理,基于侧向加速度判断车辆侧翻状态的方法,通过整车道路试验对比了正弦停滞试验和鱼钩试验诱导车辆发生侧翻的效果,初步探讨了多用途乘用车侧翻稳定性动态测试方法和评价指标,为国内车辆侧翻稳定系统的开发和测评标准的制定提供了参考。     

Estimating the ride quality characteristics of vehicles with random decrement analysis of on-the-road vibration response data

This paper describes the application of a practical analytical technique based on the random decrement method to estimate the rigid sprung mass dynamic characteristics (frequency response function) of road vehicles using only vibration response data during constant-speed operation. A brief history and development of the random decrement technique is presented, along with a summary of work undertaken on optimal parameter selection to establish the random decrement signature. Two approaches to estimate the dynamic characteristics from the random decrement signature are described and evaluated. A custom, single-wheeled vehicle (physical quarter car) was commissioned to undertake a series of on-the-road experiments at various nominally constant operating speeds. The vehicle, also instrumented as an inertial profilometer, simultaneously measured the longitudinal pavement profile to establish the vehicle's actual dynamic characteristics during operation. The main outcome of the paper is that the random decrement technique can be used to provide accurate estimates of the sprung mass mode of the vehicle's dynamic characteristics for both linear and nonlinear suspension systems of an idealised vehicle.     

Root mean square optimization criterion for vibration behaviour of linear quarter car using analytical methods

In this paper, a linear two-degree-of-freedom quarter car model is used to derive a number of analytical formulae describing the dynamic behaviour of passively suspended vehicles running on a harmonically bumped road. The linearity of the system allows us to analytically investigate the steady-state response characteristics. We derive analytical expressions for the root mean square (RMS) of the sprung mass absolute acceleration and relative displacement. This paper demonstrates the shortcomings of existing classical optimization methods. Hence we introduce a new optimization method based on minimizing the absolute acceleration RMS with respect to the relative displacement RMS. The RMS optimization method is applied for the symbolic derivation of analytical formulae featuring the best compromise among conflicting performance indices pertaining to the vehicle suspension system, i.e., sprung mass acceleration and working space. The proposed optimization technique is utilized to find the optimal damping and stiffness curves for the main suspension. The RMS optimal values are used to create design charts for suspension parameters, which are very useful particularly in the presence of physical constraints such as a limit on relative displacement. We introduce a numerical example to illustrate the optimality of the obtained solutions.     

基于柔性模型的多轴汽车平顺性的仿真研究

基于弹性梁弯曲振动理论和模态分析法建立了多轴汽车平顺性分析的柔性模型。按照汽车行驶平顺性评价方法，运用建立的柔性模型，分析了车速、路面等级、悬挂质量的分布、车架刚度以及悬架系统的刚度和阻尼对多轴汽车平顺性的影响。分析结果表明：悬挂质量的弯曲振动是影响多轴汽车行驶平顺性的一个不可忽略的重要因素；常用的刚体模型不能准确地描述多轴汽车的平顺性，不适合用于多轴汽车平顺性的分析。     

Road roughness estimation based on discrete Kalman filter with unknown input

ABSTRACT

The road roughness acts as a disturbance input to the vehicle dynamics, and causes undesirable vibrations associated with the ride and handing characteristics. Furthermore, the accurate measurement of road roughness plays a key role in better understanding a vehicle dynamic behaviour and active suspension control systems. However, the direct measurement by laser profilometer or other distance sensors are not trivial due to technical and economic issues. This study proposes a new road roughness estimation method by using the discrete Kalman filter with unknown input (DKF-UI). This algorithm is built on a quarter-car model and uses the measurements of the wheel stroke (suspension deflection), and the acceleration of the sprung mass and unsprung mass. The estimation results are compared to the measurements by laser profilometer in-vehicle test.     

A theoretical justification of the sine with dwell manoeuvre

The sine with dwell (SWD) manoeuvre has received much attention within the context of vehicle stability testing. This manoeuvre is used in a test developed by the NHTSA, designed to certificate electronic stability control systems in light vehicles. The test is used in legislations as well as in consumer tests all over the globe. The SWD manoeuvre was designed using test vehicles on a test track and experimentally validated. The paper at hand uses optimal control theory to theoretically justify the use of the SWD manoeuvre to produce a severe lateral motion and over-steering based on steering input. It is shown that a manoeuvre similar to the SWD manoeuvre can be obtained from an optimal control problem using simple vehicle dynamics models. The optimal control method is further used to analyse the manoeuvre's robustness with respect to vehicle dimensions and tyre properties. It is shown that the manoeuvre is robust in dimensions, which theoretically motivates its application for various sizes of vehicles.     

Analytical solutions for optimal ride comfort and tyre grip for passive vehicle suspensions

The paper derives analytical solutions for the global optimum of the ride comfort and tyre grip performance measures for a quarter-car vehicle model optimised both individually and in combination. The solutions are derived for six simple suspension networks comprising one or two springs, one damper and possibly one inerter. The solutions are functions of four vehicle parameters: the sprung mass, the unsprung mass, the tyre stiffness and the static stiffness, of the suspension.     

Optimal Performance of Variable Component Suspensions

Most vehicle suspension systems use fixed passive components that offer a compromise in performance between sprung mass isolation, suspension travel, and tireroad contact force. Recently, systems with discretely adjustable dampers and air springs been added to production vehicles. Active and semi-active damping concepts for vehicle suspensions have also been studied theoretically and with physical prototypes. This paper examines the optimal performance comparisons of variable component suspensions, including active damping and full-state feedback, for “quartercar” heave models. Two and three dimensional optimizations are computed using performance indicators to find the component parameters (control gains) that provide “optimal” performance for statistically described roadway inputs. The effects of performance weighting and feedback configuration are examined. Active damping is shown to be mainly important for vehicle isolation. A passive vehicle suspension can control suspension travel and tire contact force nearly as well as a full state feedback control strategy.     

Using the lead vehicle as preview sensor in convoy vehicle active suspension control

Both ride quality and roadholding of actively suspended vehicles can be improved by sensing the road ahead of the vehicle and using this information in a preview controller. Previous applications have used look-ahead sensors mounted on the front bumper to measure terrain beneath. Such sensors are vulnerable, potentially confused by water, snow, or other soft obstacles and offer a fixed preview time. For convoy vehicle applications, this paper proposes using the overall response of the preceding vehicle(s) to generate preview controller information for follower vehicles. A robust observer is used to estimate the states of a quarter-car vehicle model, from which road profile is estimated and passed on to the follower vehicle(s) to generate a preview function. The preview-active suspension, implemented in discrete time using a shift register approach to improve simulation time, reduces sprung mass acceleration and dynamic tyre deflection peaks by more than 50% and 40%, respectively. Terrain can change from one vehicle to the next if a loose obstacle is dislodged, or if the vehicle paths are sufficiently different so that one vehicle misses a discrete road event. The resulting spurious preview information can give suspension performance worse than that of a passive or conventional active system. In this paper, each vehicle can effectively estimate the road profile based on its own state trajectory. By comparing its own road estimate with the preview information, preview errors can be detected and suspension control quickly switched from preview to conventional active control to preserve performance improvements compared to passive suspensions.