Quasi steady-state aerodynamic model development for race vehicle simulations

Presented in this paper is a procedure to develop a high fidelity quasi steady-state aerodynamic model for use in race car vehicle dynamic simulations. Developed to fit quasi steady-state wind tunnel data, the aerodynamic model is regressed against three independent variables: front ground clearance, rear ride height, and yaw angle. An initial dual range model is presented and then further refined to reduce the model complexity while maintaining a high level of predictive accuracy. The model complexity reduction decreases the required amount of wind tunnel data thereby reducing wind tunnel testing time and cost. The quasi steady-state aerodynamic model for the pitch moment degree of freedom is systematically developed in this paper. This same procedure can be extended to the other five aerodynamic degrees of freedom to develop a complete six degree of freedom quasi steady-state aerodynamic model for any vehicle.     

Theory and experimental research on six-track steering vehicles

The structural characteristics and steering behaviour of a six-track vehicle are described in this paper. Kinematic analysis for skid steering of a six-track vehicle under steady-state conditions on firm ground is conducted, with the relationship between thrust force and speed instantaneous centre of the track–terrain interface taken into consideration. A mechanical model for steady steering of a six-track vehicle is also presented based on the kinematic analysis. In this model, the steering inaccuracy and efficiency are defined to evaluate steering performance. The steering performance of a six-track vehicle is numerically simulated to analyse the effect of the structural parameters and deflection angles on tracks. A virtual prototype model is established based on the multi-body dynamics software RecurDyn for steering simulation and the findings coincide well with theoretical results. The theory and the virtual prototype simulations presented are verified by a power test of a bucket-wheel excavator. The method for analysing the steering performance of a six-track vehicle proposed in this paper provides a basis for designing a six-track vehicle.     

Influence of unsteady aerodynamics on driving dynamics of passenger cars

Recent approaches towards numerical investigations with computational fluid dynamics methods on unsteady aerodynamic loads of passenger cars identified major differences compared with steady-state aerodynamic excitations. Furthermore, innovative vehicle concepts such as electric-vehicles or hybrid drives further challenge the basic layout of passenger cars. Therefore, the relevance of unsteady aerodynamic loads on cross-wind stability of changing basic vehicle architectures should be analysed. In order to assure and improve handling and ride characteristics at high velocity of the actual range of vehicle layouts, the influence of unsteady excitations on the vehicle response was investigated. For this purpose, a simulation of the vehicle dynamics through multi-body simulation was used. The impact of certain unsteady aerodynamic load characteristics on the vehicle response was quantified and key factors were identified. Through a series of driving simulator tests, the identified differences in the vehicle response were evaluated regarding their significance on the subjective driver perception of cross-wind stability. Relevant criteria for the subjective driver assessment of the vehicle response were identified. As a consequence, a design method for the basic layout of passenger cars and chassis towards unsteady aerodynamic excitations was defined.     

Fundamentals of vehicle–track coupled dynamics

This paper presents a framework to investigate the dynamics of overall vehicle–track systems with emphasis on theoretical modelling, numerical simulation and experimental validation. A three-dimensional vehicle–track coupled dynamics model is developed in which a typical railway passenger vehicle is modelled as a 35-degree-of-freedom multi-body system. A traditional ballasted track is modelled as two parallel continuous beams supported by a discrete-elastic foundation of three layers with sleepers and ballasts included. The non-ballasted slab track is modelled as two parallel continuous beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The vehicle subsystem and the track subsystem are coupled through a wheel–rail spatial coupling model that considers rail vibrations in vertical, lateral and torsional directions. Random track irregularities expressed by track spectra are considered as system excitations by means of a time–frequency transformation technique. A fast explicit integration method is applied to solve the large nonlinear equations of motion of the system in the time domain. A computer program named TTISIM is developed to predict the vertical and lateral dynamic responses of the vehicle–track coupled system. The theoretical model is validated by full-scale field experiments, including the speed-up test on the Beijing–Qinhuangdao line and the high-speed running test on the Qinhuangdao–Shenyang line. Differences in the dynamic responses analysed by the vehicle–track coupled dynamics and by the classical vehicle dynamics are ascertained in the case of vehicles passing through curved tracks.     

Black-box modelling of nonlinear railway vehicle dynamics for track geometry assessment using neural networks

ABSTRACT

The use of vehicle dynamics simulation for the track geometry assessment gives rise to new demands. In order to analyse the responses of the vehicles to the measured track geometry defects, the integration of the simulation process in the measurement chain of the track geometry recording car is envisaged. Fast and reliable simulation results are required. This work studies the use of black-box modelling approaches as an alternative to multi-body simulation. The performances of different linear and nonlinear black-box models for the simulation of the vertical and lateral bogie accelerations are compared. While linear transfer function models give good results for the simulation of the vertical responses, their use is not suitable for the highly nonlinear lateral vehicle dynamics. The lateral accelerations are best represented by recurrent neural networks. For the training and validation on high-speed lines using measured vehicle responses, the performance of the black-box simulation outperforms the multi-body simulation. Due to the larger variability of track design and track quality conditions on conventional lines, the model performance degrades and depends significantly on the analysed vehicle type and the track characteristics.     

High downforce race car vertical dynamics: aerodynamic index

Race car performance is strongly affected by aerodynamics. Due to downforce generated by the vehicle floor (i.e. diffuser), vehicle ride heights are key parameters to improve performance, and the coupling of aerodynamics and suspension is one of the key points of race car setting. This work focuses on the suspension and aerodynamic coupling from the vertical dynamics point of view. Besides road holding performance, for race cars, aerodynamic performance and stability are major factors. Downforce decreases laptime (the main performance target) but pitch instability is a non-desired effect that can happen in high downforce race cars. A new vertical dynamic performance index is proposed through the use of simulation to improve aerodynamic performance and understand the pitch instability phenomenon. This new index uses all relevant vehicle nonlinearities related to vertical dynamics and can handle a specific track profile and vehicle speed range, allowing the analysis be conducted according to a circuit specification. A previously validated Formula 3 car model was used as an example.     

Vehicle response-based track geometry assessment using multi-body simulation

The assessment of the geometry of railway tracks is an indispensable requirement for safe rail traffic. Defects which represent a risk for the safety of the train have to be identified and the necessary measures taken. According to current standards, amplitude thresholds are applied to the track geometry parameters measured by recording cars. This geometry-based assessment has proved its value but suffers from the low correlation between the geometry parameters and the vehicle reactions. Experience shows that some defects leading to critical vehicle reactions are underestimated by this approach. The use of vehicle responses in the track geometry assessment process allows identifying critical defects and improving the maintenance operations. This work presents a vehicle response-based assessment method using multi-body simulation. The choice of the relevant operation conditions and the estimation of the simulation uncertainty are outlined. The defects are identified from exceedances of track geometry and vehicle response parameters. They are then classified using clustering methods and the correlation with vehicle response is analysed. The use of vehicle responses allows the detection of critical defects which are not identified from geometry parameters.     

Optimisation of driver actions in RWD race car including tyre thermodynamics

ABSTRACT

The paper presents an innovative method for a lap time minimisation by using genetic algorithms for a multi objective optimisation of a race driver–vehicle model. The decision variables consist of 16 parameters responsible for actions of a professional driver (e.g. time traces for brake, accelerator and steering wheel) on a race track part with RH corner. Purpose-built, high fidelity, multibody vehicle model (called ‘miMa’) is described by 30 generalised coordinates and 440 parameters, crucial in motorsport. Focus is put on modelling of the tyre tread thermodynamics and its influence on race vehicle dynamics. Numerical example considers a Rear Wheel Drive BMW E36 prepared for track day events. In order to improve the section lap time (by 5%) and corner exit velocity (by 4%) a few different driving strategies are found depending on thermal conditions of semi-slick tyres. The process of the race driver adaptation to initially cold or hot tyres is explained.     

An approach for the validation of railway vehicle models based on on-track measurements

This paper proposes an approach for the validation of railway vehicle models based on on-track measurements. The validation of simulation models has gained importance with the introduction of new applications of multi-body simulation in railway vehicle dynamics as the assessment of track geometry defects, the investigation of derailments and the analysis of gauging. These applications are not only interested in qualitative predictions of the vehicle behaviour but also in precise quantitative results of the safety and comfort relevant vehicle responses. The validation process aims at guaranteeing that the simulation model represents the dynamic behaviour of the real vehicle with a sufficient good precision. A misfit function is defined which quantifies the distance between the simulated and the measured vehicle response allowing to evaluate different models at different running conditions. The obtained modelling errors are compared to the measurement uncertainty estimated for one vehicle using repeatability analysis.     

Effect of curved track support failure on vehicle derailment

In order to investigate the effect of curved track support failure on railway vehicle derailment, a coupled vehicle–track dynamic model is put forward. In the model, the vehicle and the structure under rails are, respectively, modelled as a multi-body system, and the rail is modelled with a Timoshenko beam rested on the discrete sleepers. The lateral, vertical, and torsional deformations of the beam are taken into account. The model also considers the effect of the discrete support by sleepers on the coupling dynamics of the vehicle and track. The sleepers are assumed to move backward at a constant speed to simulate the vehicle running along the track at the same speed. In the calculation of the coupled vehicle and track dynamics, the normal forces of the wheels/rails are calculated using the Hertzian contact theory and their creep forces are determined with the nonlinear creep theory by Shen et al [Z.Y. Shen, J.K. Hedrick, and J.A. Elkins, A comparison of alternative creep-force models for rail vehicle dynamic analysis, Proceedings of the 8th IAVSD Symposium, Cambridge, MA, 1984, pp. 591–605]. The motion equations of the vehicle/track are solved by means of an explicit integration method. The failure of the components of the curved track is simulated by changing the track stiffness and damping along the track. The cases where zero to six supports of the curved rails fail are considered. The transient derailment coefficients are calculated. They are, respectively, the ratio of the wheel/rail lateral force to the vertical force and the wheel load reduction. The contact points of the wheels/rails are in detail analysed and used to evaluate the risk of the vehicle derailment. Also, the present work investigates the effect of friction coefficient, axle load and vehicle speed on the derailments under the condition of track failure. The numerical results obtained indicate that the failure of track supports has a great influence on the whole vehicle running safety.     

Handling and safety enhancement of race cars using active aerodynamic systems

A methodology is presented in this work that employs the active inverted wings to enhance the road holding by increasing the downward force on the tyres. In the proposed active system, the angles of attack of the vehicle's wings are adjusted by using a real-time controller to increase the road holding and hence improve the vehicle handling. The handling of the race car and safety of the driver are two important concerns in the design of race cars. The handling of a vehicle depends on the dynamic capabilities of the vehicle and also the pneumatic tyres’ limitations. The vehicle side-slip angle, as a measure of the vehicle dynamic safety, should be narrowed into an acceptable range. This paper demonstrates that active inverted wings can provide noteworthy dynamic capabilities and enhance the safety features of race cars. Detailed analytical study and formulations of the race car nonlinear model with the airfoils are presented. Computer simulations are carried out to evaluate the performance of the proposed active aerodynamic system.     

转向横拉杆弹性对车辆操纵稳定性的影响研究

为了研究转向横拉杆的弹性对车辆操纵稳定性的影响,利用ADAMS软件建立了某轿车的多体动力学模型并进行了操纵稳定性的仿真分析。对于操纵稳定性的稳态特性,采用了ISO4138标准,在车辆行驶100 km/h下的固定圆周转向规程来进行评价;对于瞬态操纵稳定性特性,则采用ISO7401标准中方向盘扫频输入的响应特性来进行评价。仿真结果表明,转向横拉杆的弹性与轿车操纵稳定性的不足有很大关系,如果弹性横拉杆刚性过大,则需要1个较大的转向传动比以弥补其不足转向特性。因此,在汽车设计开发中,必须将转向横拉杆的弹性特性和转向传动比综合平衡考虑,两需要很好的匹配才能保证其具有良好的操纵稳定性。     

A nonlinear model for top fuel dragster dynamic performance assessment

The top fuel dragster is the fastest and quickest vehicle in drag racing. This vehicle is capable of travelling a quarter mile in less than 4.5 s, reaching a final speed in excess of 330 miles per hour. The average power delivered by its engine exceeds 7000 Hp. To analyse and eventually increase the performance of a top fuel dragster, a dynamic model of the vehicle is developed. Longitudinal, vertical, and pitching chassis motions are considered, as well as drive-train dynamics. The aerodynamics of the vehicle, the engine characteristics, and the force due to the combustion gases are incorporated into the model. Further, a simplified model of the traction characteristics of the rear tyres is developed where the traction is calculated as a function of the slip ratio and the velocity. The resulting nonlinear, coupled differential equations of motion are solved using a fourth-order Runge–Kutta numerical integration scheme. Several simulation runs are made to investigate the effects of the aerodynamics and of the engine's initial torque in the performance of the vehicle. The results of the computational simulations are scrutinised by comparisons with data from actual dragster races. Ultimately, the proposed dynamic model of the dragster can be used to improve the aerodynamics, the engine and clutch set-ups of the vehicle, and possibly facilitate the redesign of the dragster.     

A study on model fidelity for model predictive control-based obstacle avoidance in high-speed autonomous ground vehicles

This paper investigates the level of model fidelity needed in order for a model predictive control (MPC)-based obstacle avoidance algorithm to be able to safely and quickly avoid obstacles even when the vehicle is close to its dynamic limits. The context of this work is large autonomous ground vehicles that manoeuvre at high speed within unknown, unstructured, flat environments and have significant vehicle dynamics-related constraints. Five different representations of vehicle dynamics models are considered: four variations of the two degrees-of-freedom (DoF) representation as lower fidelity models and a fourteen DoF representation with combined-slip Magic Formula tyre model as a higher fidelity model. It is concluded that the two DoF representation that accounts for tyre nonlinearities and longitudinal load transfer is necessary for the MPC-based obstacle avoidance algorithm in order to operate the vehicle at its limits within an environment that includes large obstacles. For less challenging environments, however, the two DoF representation with linear tyre model and constant axle loads is sufficient.     

Vertical random vibration analysis of vehicle–track coupled system using Green's function method

A vertical vehicle–track coupled dynamic model, consisting of a high-speed train on a continuously supported rail, is established in the frequency-domain. The solution is obtained efficiently by use of the Green's function method, which can determine the vibration response over a wide range of frequency without any limitations due to modal truncation. Moreover, real track irregularity spectra can be used conveniently as input. The effect of the flexibility of both track and car body on the entire vehicle–track coupled dynamic response is investigated. A multi-body model of a vehicle with either rigid or flexible car body is defined running on three kinds of track: a rigid rail, a track stiffness model and a Timoshenko beam model. The results show that neglecting the track flexibility leads to an overestimation of both the contact force and the whole vehicle vibration response. The car body flexibility affects the ride quality of the vehicle and the coupling through the track and can be significant in certain frequency ranges. Finally, the effect of railpad and ballast stiffness on the vehicle–track coupled vibration is analysed, indicating that the stiffness of the railpad has an influence on the system in a higher frequency range than the ballast.     

面向低速清扫车的信息融合车辆跟踪方法

交通参与者运动的准确跟踪与预测对智能车行为决策的有效性至关重要。传统运动目标的跟踪系统多采用单一传感器，难以保证数据的精度与可信度。为提高系统的鲁棒性与可靠性，设计一种融合毫米波雷达和相机的目标跟踪方案，该方案针对多目标的特征级信息进行融合。首先，考虑低速行驶的自动驾驶清扫车所处环境杂波较多，方案选择基于IMM/JPDA的多目标跟踪方法估计局部航迹。为降低JPDA数据关联的计算复杂度，结合基于马氏距离构造的椭圆关联门和基于车辆非完整性约束构造的扇形关联门，实现关联门的自适应调整，减少关联杂波的干扰。其次，结合传感器的配置与特性，对目标的航迹状态进行空间对准和时间对准，按照航迹点间的欧氏距离和互协方差选择融合模式，进行局部航迹融合。最后，为验证多目标跟踪和航迹融合方法的有效性与实用性，分别设计基于MATLAB/PreScan环境的仿真试验和基于智能清扫车平台的实车试验。研究结果表明：在横、纵方向上，融合后的系统状态都比单一传感器的估计状态更为准确，融合结果对单一传感器的估计误差有35%以上的提升；实车试验证明，该方案能有效融合ESR毫米波雷达和Mobileye单目前视相机的状态估计信息，能基本正确地跟踪目标和估计航迹；融合状态的横、纵向误差都在可接受范围以内，且融合状态比单一传感器的估计波动更小。     

车辆气动力展向相关性传递函数及其对桥上运动车辆响应的影响

为研究运动车辆气动力的展向相关性对桥上运动车辆响应的影响,在分析运动车辆顺风向和竖向脉动风速谱的基础上,发展出一种新型的运动车辆脉动风速相干函数形式,推导出与顺风向和竖向脉动风速对应的运动车辆气动力的展向相关性传递函数,并根据“余弦规则”得到作用在运动车辆上的抖振力谱。通过建立列车-轨道-桥梁多体系统耦合振动仿真模型,以单节列车在典型的高速铁路桥梁上行驶为例,对比不同车速、不同风速与不同地表类型时,运动车辆气动力的传递函数对桥上运动车辆响应的影响。研究结果表明：当考虑上述传递函数时,车辆响应的均方根均有不同程度的降低,其中对车体横向和竖向加速度均方根的影响最为显著;当车速为40 m·s^-1时,在考虑与不考虑传递函数情况下,车体横向加速度均方根的相对误差高达40.6%,车体竖向加速度均方根的相对误差也高达36.6%;随着车速的提高,各车辆响应均方根的相对误差均逐渐变小;随着风速的提高,轮重减载率和轮轨垂向力均方根的相对误差均逐渐变大,而车体竖向Sperling指标和轮轨横向力均方根的相对误差却先增加后减小;从A类地表类型到D类地表类型,车体加速度均方根以及车体Sperling指标的相对误差均逐渐增大,而轮轨力均方根、脱轨系数均方根、轮重减载率均方根的相对误差均先增大后减小。     

货车-两轮车前碰撞事故中骑行者运动学响应及损伤分析

为探究货车-两轮车前部碰撞事故中参与双方速度对骑行者运动学响应与损伤的影响,基于MADYMO软件开展事故重建并进行了分析。建立了货车和两轮车的多体碰撞模型,对一起货车前部碰撞两轮车事故进行了事故重建;使用验证后的模型进行了25组不同速度下的全因子仿真试验;分析了不同碰撞速度和骑行速度对骑行者运动学响应和损伤的影响。研究结果表明,骑行者身体旋转幅度会随着两轮车及货车车速的升高而增加;当货车速度超过 20 km/h时,骑行者头部损伤指标 （Head Injury Criterion,HIC） 与胸部3 ms加速度将超过阈值;而当货车速度超过25 km/h时,骑行者下肢接触力也超过阈值;货车速度处于 30～40 km/h时,相同货车速度下,骑行者头部 HIC值出现随着两轮车速度的增加而升高的趋势,而胸部加速度出现相反的趋势。     

Experimental and numerical investigation of the effect of rail corrugation on the behaviour of rail fastenings

This paper presents the results of a detailed investigation of the effects of rail corrugation on the dynamic behaviour of metro rail fastenings, obtained from extensive experiments conducted on site and from simulations of train–track dynamics. The results of tests conducted with a metro train operating on corrugated tracks are presented and discussed first. A three-dimensional (3D) model of the metro train and a slab track was developed using multi-body dynamics modelling and the finite element method to simulate the effect of rail corrugation on the dynamic behaviour of rail fastenings. In the model, the metro train is modelled as a multi-rigid body system, and the slab track is modelled as a discrete elastic support system consisting of two Timoshenko beams for the rails, a 3D solid finite element (FE) model for the slabs, periodic discrete viscoelastic elements for the rail fastenings that connect the rails to the slabs, and uniformly viscoelastic elements for the subgrade beneath the slabs. The proposed train–track model was used to investigate the effects of rail corrugation on the dynamic behaviour of the metro track system and fastenings. An FE model for the rail fastenings was also developed and was used to calculate the stresses in the clips, some of which rupture under the excitation of rail corrugation. The results of the field experiments and dynamics simulations provide an insight into the root causes of the fracture of the clips, and several remedies are suggested for mitigating strong vibrations and failure of metro rail fastening systems.