道路几何设计对车辆行驶特性的影响机理研究
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摘要
虽然在过去几十年里手工计算、纸上画图的设计手段已经被CAD技术所取代,但平、纵、横分开考虑的设计习惯依旧没有改变,融于自然环境带来的唯一性,又使设计者不能像对待工业产品那样,用“设计-样品-试验-修改设计”手段实物测试出公路路线的使用性能,而是全凭以往的先验经验来把握线形质量,因此很难有针对性的修改设计方案。大量的设计缺陷和疏漏被带到运营中后,导致公路几何特性与车辆行驶特性、驾驶人特性三者之间的不匹配,最终形成众多的事故多发路段(多发位置)。所以,时至今日,在很多情况下保证行驶安全和驾乘舒适这两个基本性质仍得不到满足。
但如果能够进行类似于机械产品那样的虚拟行驶试验,让车辆动力学模型在建好的三维路面模型上行驶,记录车辆各种响应随行驶里程或者时间的变化,进而评估道路几何设计的质量,显然是一种比较理想的路线质量检验和测试手段,这也正是我们的目的。为此,本文建立了“公路-驾驶人-车辆-环境”仿真系统(RDVES),根据输入的线形要素RDVES能快速得到路面的3维模型,导入整车动力学模型,再设置驾驶行为参数和环境影响后,即可实现三维空间路面上的车辆自动行驶,并且行驶过程可见。通过虚拟行驶试验,设计者能够依据车辆在未来道路的运动状态和驾驶操纵输入直接得到行驶不稳定位置和操纵困难路段,能够有针对性的修改设计参数,并观察改进效果,直至得到让人满意的设计。还可以像对待机械产品那样来对公路路线进行变参数试验研究,找出公路几何特性、车辆特性、驾驶人行为特性三者之间相互作用规律,比如公路线形参数变化对车辆运动学行为和驾驶行为的影响规律,车辆性能和尺寸参数改变、驾驶行为改变时公路线形参数应该如何作出调整,等等,最终使公路设计能够适应不断发展变化的现代车辆设计和驾驶人行为。
论文首先研究了“公路-驾驶人-车辆-环境”仿真系统(RDVES)的子系统建模、耦合技术,然后以验证后的RDVES为虚拟试验手段结合道路实测,进行了线形的设计质量分析和设计控制、不利环境行车模拟、单车事故的力学机理分析、平曲线上的车辆运动规律和驾驶行为分析等研究工作,主要的创新性成果如下：
1.空间3维路面的快速建模算法
论文第二章设计了型元解析算法和型值点插值重构算法,分别用于生成设计阶段和老旧道路的3维路面模型。在型元法中,路线被看作是逐个型元的首尾顺次衔接,由“直线+回旋线1+圆曲线+回旋线2”4个线元构成平面型元,由“直坡+竖曲线”构成纵面型元。通过线元的缺省和型元间的组合,可以构造出任意复杂的线形组合。在设计重构算法时,本文用Multi-Quadric径向基函数作为基本计算单元,提出了“局部、交叠”、“对调值域与自变量域”的插值重构算法,避免了大规模、带状分布、非单射的道路型值点数据引起的系数矩阵病态,试验结果表明该算法能够得到平滑柔顺的空间路面形状。
2.整车动力学建模、轮胎-路面作用模型、以及环境影响设置
论文第3章给出了作为多体动力学建模基础的悬架、转向、横向稳定杆、制动、驱动、车架等子系统多种结构形式的拓扑构型,结合基于MF公式的Pacejke'89和Pacejke'94轮胎模型,完成了ADAMS环境下的小客车、面包车和卡车的整车动力学模型创建。本文设计了左、右半幅路面和不同区段路面分别设定附着系数的算法,以此来模拟积水、湿滑、结冰的作用(比如将位于试验区段的路面附着系数调低)。在车身上侧向施力,能得到侧风作用下的行驶过程,比如模拟车辆行驶在桥面上。
3.车辆行驶方向和速度控制模型
我们在此方面的工作(论文第3章)是建立了能够反映公路线形变化、车辆动力性能、和驾驶人特性三者影响的期望速度计算模型。其计算策略是,由容许侧向加速度ay,tol确定曲线范围内的速度幅值,由减速度ab和加速度ax控制曲线间的速度变化,由环境速度Vx,max控制路段的最大速度。根据公路实测数据,获得了以道路参数为自变量的Vx,max、ay,tol、ax、ab函数模型,使得线形变化能够反映在驾驶人的期望速度选择上。同时,提出了针对不同设计速度分别标定模型参量的方法,解决了现有模型不管如何修改参数,都无法适应不同设计车速的公路的问题。
4.基于速度特性的路线质量分析
论文第5章分析了行驶速度波动特性与道路几何设计之间关系,我们发现：车辆以指定速度行驶时,驾驶人的车速调整频度与小半径曲线的使用次数正相关,所以可通过设计手段来控制路线的驾驶负荷；车辆即将失控时,侧向速度曲线会发生突变,并导致纵向速度不连续,因此可用速度连续性来辨识出对行车构成威胁的位置,进而修改设计
自由可变速行驶(运行车速)时,车辆的进弯减速度要明显大于出弯加速度,减速起点和加速终点通常在回旋线之外,所以先前在缓和段上调整速度的假设是不符合实际的,对于高速公路,目前假定的0.5m／s2的加速度也明显过大；有效控制速度波动的最好办法是使相邻的曲线半径和直线长度相互接近、并且直线不宜过长；除线形因素之外,汽车自身旋转动能和平动动能之间的转化也是导致速度在琐碎山区路线上频繁波动的重要原因,在一致性评价时应加以考虑；四级公路绝大部分路段的行驶速度远高于设计速度,因此目前的速差标准可能需要重新考虑。
5.基于行驶稳定性和操纵负荷特性的路线质量分析
在第6章中,以轮胎垂向力为介质分析了路线的侧翻可能性,以轮胎侧偏角、操舵力、方向盘转角为指标分析了超高／反超高对车辆方向控制的影响,以方向盘转角、转速为参量分析了路线的操纵负荷特性,我们发现：同样是在设计速度附近行驶,道路等级越低,曲线上行驶车辆的侧翻可能性越大；坡向改变了载质量在各轴间的分配,增加了下坡的侧翻可能性。超高会显著减小曲线行驶时的轮胎侧偏角,从而改善行驶稳定性(高速时尤为明显),超高还会减小方向盘角输入和操舵力,让驾驶变得容易,反超高的作用则正好相反；设置超高的不利影响是增加曲线行驶时的车身侧倾摆动,特别是低速车辆。
符合规范要求的山岭区各等级公路的ay能够满足可耐受的要求,但还达不到舒适性要求；操纵负荷与路线的设计速度负相关,即高速公路负荷最小而四级路最大,并且,四级公路如省略回旋线,还会使车辆在进弯和出弯时的day/dt会超过1.0m／s3,导致行车不舒适；当半径增大到一定程度时,曲线行驶和直线行驶已经不存在差别,但都需要一定的方向干预；卵形线是比较有利于车辆操纵的,方向盘转角可以在中插回旋线上平滑过渡,而凸型线则要求一直调整方向盘角输入,平曲线的YZ和ZH共点时,YZ/ZH点处的曲率跳跃会导致操纵困难,建议处理成卵形线形式。
6.不利条件下的行驶稳定性分析
论文第7章分析了侧风、直道积水、和隧道洞口等3种典型环境力对行驶稳定性的力学影响,结果表明：侧风行驶时,驾驶者最好把乘客和货物安排在车辆后端,使车辆重心位于风压中心之后,以增强车辆的路线保持能力；车辆重心升高会降低侧风条件下的抗干扰能力,所以应控制装载后的重心高度；降低车速能够减少侧风作用下的车辆侧向位移和偏转。
直道积水事故的发生机理为：装载、路拱、左右弹簧刚度不一致→重心偏离纵轴线→偏载→轮载较大的一侧轮胎摩擦力大→轮周接地线速度大→轮心位移大→偏驶或者侧滑；两侧轮胎都和积水接触时,车辆会向轮载较轻的一侧滑转；如仅有一侧轮胎驶过积水,汽车将向积水一侧偏转,驾驶者应朝着无水侧转动方向盘。
速度越高,车辆在路面过渡位置的横向摆动越大,因此可以把进洞端的过渡布置在大多数车辆制动结束之后,出洞端把过渡安排在加速起点之前；曲线隧道过渡位置的附着系数突变会引起进洞车辆的额外偏转,附着系数差异越大偏转越明显,随后的低附着路面还会造成制动不稳定；为了减小附着系数波动,洞内路面的附着系数应维持在0.35之上。
7.平曲线事故的力学机理分析
论文第8章分析S型曲线缓和段事故和弯道避让事故的力学机理,主要的结论有：车辆以某个速度行驶在S型曲线时,迟滞效应将导致轮胎侧弯变形在回旋线上无法充分释放,残余变形将被带到拐点后的另一反向回旋线上,在反向侧向力作用下残余变形的突然释放会导致胎面与路面之间的相对滑动,从而使车辆失去侧向稳定性,所以S型曲线缓和段上的车辆事故并不一定是侧向力超过路面附着极限所致；由于小圆上的侧弯变形较大并且不易释放,事故更容易发生在S型曲线的小圆→大圆行驶方向上；降低缓和段事故的办法是使轮胎侧弯变形得到释放,拉长小圆回旋线、在拐点处插入短直线都可以起到这个作用。
弯道避让过程中轨迹曲率的额外增加改变了对向行驶车辆安全性,为了减小驶回阶段的附加曲率,曲线外侧车辆在交会之后应尽量延长驶回轨迹；曲线内侧车辆避让轨迹的附加曲率主要出现在开始阶段和驶回阶段,提早避让、平缓驶回是增加车辆稳定性的有效措施。
8.弯道几何特性对车辆运动学行为和驾驶行为的影响规律。
论文第9章分析弯道几何特性与切弯效用——弯道速度增量△VC和轨迹半径增量△R之间的关系,从而解释了什么样的弯道容易发生切弯(切内线)行驶这一问题。现行的公路设计方法假定车辆轨迹与道路中线一致,但实际上切弯时的车辆轨迹半径远大于弯道设计半径,这时,该如何实现我们的设计控制理念?在本章的研究结论能够帮助设计者知道在什么样的参数组合情况下,弯道才会对轨迹起控制作用,又是在什么样的参数组合下,驾驶入会选择切弯行驶,切弯后的轨迹半径是多大,过弯速度又是多少等一系列关键问题。
同时,分析了车辆在单曲线上的转向行为,得到了切弯和跟随两种行使方式下车辆驶进／驶离曲线时的转向长度、转向时间、和转向特征点,从而实现了对驾驶人转向行为的清晰刻画。转向长度.半径关系曲线可以为回旋线长度设计提供依据,因为目前国际上认为理想的回旋线长度应该等于车辆的转向长度。转向时间.半径关系曲线还可以提供另外一种回旋线控制,因为一些国家的设计政策中规定回旋线长度应等于转向时间乘以设计车速。转向提前距离.半径关系曲线可以提高弯道诱导标设置合理性,因为我们能够知道驾驶人是在什么位置开始转向的。
Despite traditional alignment design method such as determination of horizontal or vertical location and drawing on papers using a pen manually has been replaced by CAD technique, dimensions of horizontal, vertical and cross section are still determined separately. Due to the unique of each alignment fitting the topography, the procedure of "design-prototype-test-redesign" commonly used to manufacturing is not suitable for highways designers. Therefore, highway designers are hard to make target modification, and quality of alignment is determined by the early experience of designer's. Numbers of design drawbacks preserved into operation phase always result in the mismatch of highway alignment, modern vehicle and driver behavior, and accident clusters everywhere. So, to this day, driving safety and riding comfort can not be reached for highway design.
If virtual roadway test like used to machinery production can be apllied in alignment design, let vehicle dynamics model run on 3D road models and log the dynamics/kinematics response, can also a good testing instrument, and it is the main objective of this paper. In this context, the virtual driving system of "roadway-driver-vehicle-enviroment" is develpoed in the paper. According to input date of alignment parameters,3D roadway models can be obtained rapidly, if a full vehicle model inducted, parameters of driving behavior and enviroment impact defined togeter, vehicle model driving on 3 D roadway model can be relized and the driving process is visible. Through conducting virtual driving test, designers can identify the location of driving instability or difficulty in vehicle control and modify its design value based on vehicle response and steering input, can see the effects of improment. By means of virtual roadway test, we can parameterize the design value of hignway alignment and obtain the relationship among highway geometry features, vehicle kinematics and driver behavior, such as the effect of change in alignment parameter on vehicle kinematics and driver behavior, the effect of change in vehicle parameter and driver behavior on highway alignment values, etc. which all can result in highway design compatible with modern vehicle design and driver behavior.
In the paper, creation and coupling of subsystems of "roadway-driver-vehicle-enviroment" are firstly completed, then the simulation system is applied in evaluation of alignment design, driving simulation under under adverse conditions, mechanism analysis of single vehicle run-off-road, and vehicle motion performance and driving behavior on curved segment, which can be described as follows:
1. Creation of 3D roadway models.
The roadway module in the second section of the paper can generate 3D road-surface used to contact with tires, and can deal with arbitrary complex alignment in current design. For different conditions of use, we design two formats of input date and their corresponding algorithm. One input is the design values of horizontal/vertical alignment and cross-section, conception of "typology element" is put forward in the paper, which takes a highway alignment as the sequence of "typology element". A horizontal "typology element" is composed of four elements of "tangent+spiral 1+ circular+spiral 2". A vertical "typology element" is composed of a straight grade and its adjacent vertical curve. The other input is spatial coordinate of sampling point in analyzed roadway, which suitable for alignment date absent. We select multi-quadric radial basis function as the interpolation function, and put forward reconstruction algorithm of "local, overlapping" and "exchange of range and independent variable". These algorithm can prevent ill-conditioning of coefficient matrix caused by huge scale, belt distribution, and non-injection of date, and can obtain smooth and continued 3D road-surface.
2. Creation of full vehicle dynamics models, tire-road contact models, and environment impact.
In the third section of the paper, the topology of suspension, steering gear, anti-roll bar, brake, drive axle, driving-line and frame with different configuration are analyzed, and a database of vehicle models is developed. Which include a microbus, two passenger cars, and a truck built in ADAMS. Tire models come from an edition of magic formula Pacejke’94 or Pacejke’89. To let tire contact with road-surface, we design an algorithm of defining friction coefficient that can define a half roadway or several segments a different coefficient with others. Environment impact IS simulated through tire-road contact model and vehicle models, such as define a small friction coefficient for a given segment to simulate the effect of ice or water gathered, and act a lateral force on vehicle body to simulate the process of driving in lateral wind.
3. Steering and speed models.
Our innovative work in this aspect is developing a prediction model of desired speed on a given highway, which can take in account highway geometry features, vehicle dynamics, and driving behavior. Principle of determination of desired speed is that, the desired speed on curve areas should meet the condition:the lateral acceleration of vehicle bodies no more than the tolerated value aytoal; speed change between two adjacent curves is subject to the acceleration rate ax and deceleration rate ab, and the desired speed is always no more than the environment speed Vxmax. According to speed measurement date on real road, we developed the models of aytoal, ab, ax, and Vxmax·Vxmax is a function of average change rate of curvature and total roadway width, aytoal, ab and axare all functions of curve radii and lane width, so they change along roadway. Currently, models developed by foreign researchers are often aiming at several rural roads in level or level-hilly areas, despite how modify model parameters, the model can not suitable for highways of different design speed in China. Therefore, we put forward a method of calibrate model parameters for design speed separately, by this way, we can use a unitive model to deal with highways of different design speed.
4. Evaluation of highway alignment based on speed.
In the fifth section of the paper, we analysis the speed along given roads. Our conclusions are as follows:When driving at a constant speed, the frequency of driver change pedals is equal to the use of sharp curves, therefore, we can control highway's driving workload by alignment design. When driving vehicle reaches such a situation of lose control, the profile of lateral speed will has a catastrophe in magnitude and cause discontinuity in longitudinal speed, so we can use the continuity of speed to evaluate the vehicle stability when driving at a constant speed, and further do a judgement whether exists threaten to driving vehicle in difficult segment and whether to refine design.
For free driving, our observation indicates that, deceleration rate while entering curve is always more than acceleration rate while exiting curve; beginning point of slow down and ending point of speed up are always beside the spirals, so the suppose of speed change in spirals is wrong. In addition, for freeway, acceleration rate of 0.5m/s2 is too high. The best method to control speed fluctuation is let the curve radii and tangent length of adjacent element similar, and tangent should be short. Besides alignment, the reason cause speed fluctuant frequently on complex and trivial roads in mountainous area is the exchange between kinetic energy of rotation and translational energy, so, we should take in account the factor. Criteria of deference between operation speed and design speed less than 20km/h may not suitable for lower standard rural roads, while for freeway design in high standard, operation speed method also not suitable.
5. Evaluation of highway alignment based on vehicle driving stability and steering workload.
In the sixth section of the paper, rollover probability of alignment is evaluated by indicator of vertical force of tires; effect of superelevation/reverse superelevation on steering control is analyzed by measurement of tire slip angle, steering force and steering input; and steering workload of alignment is measured by medium of steering input and its angular speed. Our main conclusions are as follows:within curve areas, rollover probability increases as design speed of the road decreases when driving speed around design speed. Exposure can change load sharing effect among front/middle/rear axle, and further change the rollover probability of upgrade and downgrade, the results indicate downgrade is favorable to rollover. Superelevation can reduce tire slip angle when driving on curve, therefore, stability of driving vehicle is improved. In addition, superelevation also can reduce steering input and the force acting steering wheel and make handing easy. But its disadvantage is increasing vehicle's lateral inclination when traveling on curves. Reverse superelevation make against stability of running vehicle on curves, it can increase tire slip angle, steering force, and steering input.
Lateral acceleration of running vehicle will no more than tolerated limit, but it exceeds the comfort limit, if the highway alignment meet the design standard recommended in Chinese policy. If spiral no exists in the fourth-class roads, change rate of lateral acceleration when entering/exiting curve will larger than 1.0 m/s3. There does not exist difference between steering on curve and steering on tangent if curve radii exceeds a certain value, but they all need steering corrections. Even in mountain terrain, steering workload of freeway alignment is very small; although riding comfort of secondary roads is not as good as freeways, alignment of secondary roads can not lead to drivers stress; third-class roads may cause drivers who like high speed stress. Egg-shape curves are in favor of steering control, because steering wheel angle can change in the middle spirals, whereas, convex curves call for continuous steering input. When point of circular to tangent overlap point of tangent to spiral, the skip of horizontal curvature will result in difficulty in steering, so, this overlapping should be eliminated and change this alignment combination to an egg-shape curve.
6. Vehicle driving stability under adverse conditions.
In the seventh section of the paper, the effect of crosswind, water gathered on tangent, and tunnel entrance/exit on driving vehicle are analyzed, our main findings as follows:To assure the straight line performance of driving vehicle, drivers should let passengers and goods close to rear end of their vehicles, by this mean, vehicle'cg can locate behind wind pressure center. Vehicle's straight line performance increases as its cg reduces, vice versa, so drivers should control the height of center of gravity of laden vehicle. Drivers decrease their speed before entering crosswind areas can reduce the lateral displacement and deflection angle.
Mechanism of crash on tangent segment gathered water is that, unbalanced loading, road crown, difference in spring stiffness of both side→cg of vehicle departures its longitudinal axis→unbalanced wheel load between right to left→the tire with larger load has larger friction forcee→it has larger linear rolling speed→it has larger displacement in wheel center→side skidding occurs. If tires of two sides simultaneously contact with water, vehicle will deflect toward the side of lighter tire load. If one side tires contact with water, vehicle will deflect toward the water areas.
The abrupt change in adherence at location of pavement transition of curved tunnel entrance can cause additional deflection of driving car, and cement pavement lower adherence in sequence can lead to instability of braking vehicle. Yaw motion of driving vehicle at location of pavement transition increases as speed increases, so we can layout the transition location of entrance behind the end of brake and the transition location of exit before the beginning of acceleration. The abrupt change in adherence at location of pavement transition is the factors that mostly contribute to the occurrence of accidents near tunnel opening, to reduce the yaw motion caused by adherence change, and assure adherence of inside tunnel more than 0.35.
7. Mechanism of several typical run-off-road crashes on horizontal curves.
In the eighth section of the paper, we simulate the process of avoiding on curved segment and recur the process of vehicle running off roadway on spiral of S-shape curve, our findings are as follows:When vehicle travels at a special speed, lateral deformation of tire generated on circular will not release adequately on the adjacent spiral, residual deformation of tire will be maintained to the spiral jointed another circular and will release suddenly under increasing lateral force cause by spiral, which will result in lateral slip between tire and pavement and cause vehicle instability. The crashes caused by hysteresis effect of tire more often occur on the detection of sharp curve to flatter curve, because sharp circular curves often joint to shorter spirals, which results in residual deformation. The best method to reduce these crashes is releasing tire's lateral deformation adequately, so, increase the spiral length or insert a tangent at point of reversing curvature can reach this effect.
When Avoiding on curved segment, increase/decrease in curvature of track results in change in driving safety of two running vehicle in opposite. To reduce the additional increment in track curvature while recovering, the driver in outside curve should prolong the recover track of vehicle. The driver inside curve should begin his lane change earlier and recover smoothly, because the additional curvature always occurs on the phase of avoiding beginning and recovering.
8. Effect of change in bend geometry on vehicle kinematics and driving behavior.
In the ninth section of the paper, we analyzed the effect of change in bend features on two benefits resulting from corner cutting driving pattern, speed increment and radii flatting on curves, consequently, answer the question of where drivers cut the curve. Current alignment design assume track the same as road centerline, but when driver choose corner cutting pattern, radii of track will exceeds design value of curve radii a lot, at this time, how can we achieve our design control? According to our findings, designers can know in which kind of parameters combination the curve can really influence driver's speed choice and track radii equal to curve design radii; and in which kind of parameters combination drivers will cut the curve, how much the track radii and traveling speed when corner is cut.
In this section, we also analyzed the steering behavior while vehicle driving on simple curves. Steering time, steering distance and steering characteristic point are obtained, therefore, steering behavior on simple curves can be depicted clearly. Profile of steering length versus curve radii in this section can provide design control for spiral length, because a typical viewpoint currently believes desired spiral length equal to the distance traveled during the steering time. Profile of steering time depending curve radii in this section can provide another control for spiral design, because spiral length recommended in design policies of several countries no less than steering time multiply design speed. In addition, profile of advanced steering length versus curve radii can help designers install curve alignment markers rightly, because we can know where drivers begin their steering.
但如果能够进行类似于机械产品那样的虚拟行驶试验,让车辆动力学模型在建好的三维路面模型上行驶,记录车辆各种响应随行驶里程或者时间的变化,进而评估道路几何设计的质量,显然是一种比较理想的路线质量检验和测试手段,这也正是我们的目的。为此,本文建立了“公路-驾驶人-车辆-环境”仿真系统(RDVES),根据输入的线形要素RDVES能快速得到路面的3维模型,导入整车动力学模型,再设置驾驶行为参数和环境影响后,即可实现三维空间路面上的车辆自动行驶,并且行驶过程可见。通过虚拟行驶试验,设计者能够依据车辆在未来道路的运动状态和驾驶操纵输入直接得到行驶不稳定位置和操纵困难路段,能够有针对性的修改设计参数,并观察改进效果,直至得到让人满意的设计。还可以像对待机械产品那样来对公路路线进行变参数试验研究,找出公路几何特性、车辆特性、驾驶人行为特性三者之间相互作用规律,比如公路线形参数变化对车辆运动学行为和驾驶行为的影响规律,车辆性能和尺寸参数改变、驾驶行为改变时公路线形参数应该如何作出调整,等等,最终使公路设计能够适应不断发展变化的现代车辆设计和驾驶人行为。
论文首先研究了“公路-驾驶人-车辆-环境”仿真系统(RDVES)的子系统建模、耦合技术,然后以验证后的RDVES为虚拟试验手段结合道路实测,进行了线形的设计质量分析和设计控制、不利环境行车模拟、单车事故的力学机理分析、平曲线上的车辆运动规律和驾驶行为分析等研究工作,主要的创新性成果如下：
1.空间3维路面的快速建模算法
论文第二章设计了型元解析算法和型值点插值重构算法,分别用于生成设计阶段和老旧道路的3维路面模型。在型元法中,路线被看作是逐个型元的首尾顺次衔接,由“直线+回旋线1+圆曲线+回旋线2”4个线元构成平面型元,由“直坡+竖曲线”构成纵面型元。通过线元的缺省和型元间的组合,可以构造出任意复杂的线形组合。在设计重构算法时,本文用Multi-Quadric径向基函数作为基本计算单元,提出了“局部、交叠”、“对调值域与自变量域”的插值重构算法,避免了大规模、带状分布、非单射的道路型值点数据引起的系数矩阵病态,试验结果表明该算法能够得到平滑柔顺的空间路面形状。
2.整车动力学建模、轮胎-路面作用模型、以及环境影响设置
论文第3章给出了作为多体动力学建模基础的悬架、转向、横向稳定杆、制动、驱动、车架等子系统多种结构形式的拓扑构型,结合基于MF公式的Pacejke'89和Pacejke'94轮胎模型,完成了ADAMS环境下的小客车、面包车和卡车的整车动力学模型创建。本文设计了左、右半幅路面和不同区段路面分别设定附着系数的算法,以此来模拟积水、湿滑、结冰的作用(比如将位于试验区段的路面附着系数调低)。在车身上侧向施力,能得到侧风作用下的行驶过程,比如模拟车辆行驶在桥面上。
3.车辆行驶方向和速度控制模型
我们在此方面的工作(论文第3章)是建立了能够反映公路线形变化、车辆动力性能、和驾驶人特性三者影响的期望速度计算模型。其计算策略是,由容许侧向加速度ay,tol确定曲线范围内的速度幅值,由减速度ab和加速度ax控制曲线间的速度变化,由环境速度Vx,max控制路段的最大速度。根据公路实测数据,获得了以道路参数为自变量的Vx,max、ay,tol、ax、ab函数模型,使得线形变化能够反映在驾驶人的期望速度选择上。同时,提出了针对不同设计速度分别标定模型参量的方法,解决了现有模型不管如何修改参数,都无法适应不同设计车速的公路的问题。
4.基于速度特性的路线质量分析
论文第5章分析了行驶速度波动特性与道路几何设计之间关系,我们发现：车辆以指定速度行驶时,驾驶人的车速调整频度与小半径曲线的使用次数正相关,所以可通过设计手段来控制路线的驾驶负荷；车辆即将失控时,侧向速度曲线会发生突变,并导致纵向速度不连续,因此可用速度连续性来辨识出对行车构成威胁的位置,进而修改设计
自由可变速行驶(运行车速)时,车辆的进弯减速度要明显大于出弯加速度,减速起点和加速终点通常在回旋线之外,所以先前在缓和段上调整速度的假设是不符合实际的,对于高速公路,目前假定的0.5m／s2的加速度也明显过大；有效控制速度波动的最好办法是使相邻的曲线半径和直线长度相互接近、并且直线不宜过长；除线形因素之外,汽车自身旋转动能和平动动能之间的转化也是导致速度在琐碎山区路线上频繁波动的重要原因,在一致性评价时应加以考虑；四级公路绝大部分路段的行驶速度远高于设计速度,因此目前的速差标准可能需要重新考虑。
5.基于行驶稳定性和操纵负荷特性的路线质量分析
在第6章中,以轮胎垂向力为介质分析了路线的侧翻可能性,以轮胎侧偏角、操舵力、方向盘转角为指标分析了超高／反超高对车辆方向控制的影响,以方向盘转角、转速为参量分析了路线的操纵负荷特性,我们发现：同样是在设计速度附近行驶,道路等级越低,曲线上行驶车辆的侧翻可能性越大；坡向改变了载质量在各轴间的分配,增加了下坡的侧翻可能性。超高会显著减小曲线行驶时的轮胎侧偏角,从而改善行驶稳定性(高速时尤为明显),超高还会减小方向盘角输入和操舵力,让驾驶变得容易,反超高的作用则正好相反；设置超高的不利影响是增加曲线行驶时的车身侧倾摆动,特别是低速车辆。
符合规范要求的山岭区各等级公路的ay能够满足可耐受的要求,但还达不到舒适性要求；操纵负荷与路线的设计速度负相关,即高速公路负荷最小而四级路最大,并且,四级公路如省略回旋线,还会使车辆在进弯和出弯时的day/dt会超过1.0m／s3,导致行车不舒适；当半径增大到一定程度时,曲线行驶和直线行驶已经不存在差别,但都需要一定的方向干预；卵形线是比较有利于车辆操纵的,方向盘转角可以在中插回旋线上平滑过渡,而凸型线则要求一直调整方向盘角输入,平曲线的YZ和ZH共点时,YZ/ZH点处的曲率跳跃会导致操纵困难,建议处理成卵形线形式。
6.不利条件下的行驶稳定性分析
论文第7章分析了侧风、直道积水、和隧道洞口等3种典型环境力对行驶稳定性的力学影响,结果表明：侧风行驶时,驾驶者最好把乘客和货物安排在车辆后端,使车辆重心位于风压中心之后,以增强车辆的路线保持能力；车辆重心升高会降低侧风条件下的抗干扰能力,所以应控制装载后的重心高度；降低车速能够减少侧风作用下的车辆侧向位移和偏转。
直道积水事故的发生机理为：装载、路拱、左右弹簧刚度不一致→重心偏离纵轴线→偏载→轮载较大的一侧轮胎摩擦力大→轮周接地线速度大→轮心位移大→偏驶或者侧滑；两侧轮胎都和积水接触时,车辆会向轮载较轻的一侧滑转；如仅有一侧轮胎驶过积水,汽车将向积水一侧偏转,驾驶者应朝着无水侧转动方向盘。
速度越高,车辆在路面过渡位置的横向摆动越大,因此可以把进洞端的过渡布置在大多数车辆制动结束之后,出洞端把过渡安排在加速起点之前；曲线隧道过渡位置的附着系数突变会引起进洞车辆的额外偏转,附着系数差异越大偏转越明显,随后的低附着路面还会造成制动不稳定；为了减小附着系数波动,洞内路面的附着系数应维持在0.35之上。
7.平曲线事故的力学机理分析
论文第8章分析S型曲线缓和段事故和弯道避让事故的力学机理,主要的结论有：车辆以某个速度行驶在S型曲线时,迟滞效应将导致轮胎侧弯变形在回旋线上无法充分释放,残余变形将被带到拐点后的另一反向回旋线上,在反向侧向力作用下残余变形的突然释放会导致胎面与路面之间的相对滑动,从而使车辆失去侧向稳定性,所以S型曲线缓和段上的车辆事故并不一定是侧向力超过路面附着极限所致；由于小圆上的侧弯变形较大并且不易释放,事故更容易发生在S型曲线的小圆→大圆行驶方向上；降低缓和段事故的办法是使轮胎侧弯变形得到释放,拉长小圆回旋线、在拐点处插入短直线都可以起到这个作用。
弯道避让过程中轨迹曲率的额外增加改变了对向行驶车辆安全性,为了减小驶回阶段的附加曲率,曲线外侧车辆在交会之后应尽量延长驶回轨迹；曲线内侧车辆避让轨迹的附加曲率主要出现在开始阶段和驶回阶段,提早避让、平缓驶回是增加车辆稳定性的有效措施。
8.弯道几何特性对车辆运动学行为和驾驶行为的影响规律。
论文第9章分析弯道几何特性与切弯效用——弯道速度增量△VC和轨迹半径增量△R之间的关系,从而解释了什么样的弯道容易发生切弯(切内线)行驶这一问题。现行的公路设计方法假定车辆轨迹与道路中线一致,但实际上切弯时的车辆轨迹半径远大于弯道设计半径,这时,该如何实现我们的设计控制理念?在本章的研究结论能够帮助设计者知道在什么样的参数组合情况下,弯道才会对轨迹起控制作用,又是在什么样的参数组合下,驾驶入会选择切弯行驶,切弯后的轨迹半径是多大,过弯速度又是多少等一系列关键问题。
同时,分析了车辆在单曲线上的转向行为,得到了切弯和跟随两种行使方式下车辆驶进／驶离曲线时的转向长度、转向时间、和转向特征点,从而实现了对驾驶人转向行为的清晰刻画。转向长度.半径关系曲线可以为回旋线长度设计提供依据,因为目前国际上认为理想的回旋线长度应该等于车辆的转向长度。转向时间.半径关系曲线还可以提供另外一种回旋线控制,因为一些国家的设计政策中规定回旋线长度应等于转向时间乘以设计车速。转向提前距离.半径关系曲线可以提高弯道诱导标设置合理性,因为我们能够知道驾驶人是在什么位置开始转向的。
Despite traditional alignment design method such as determination of horizontal or vertical location and drawing on papers using a pen manually has been replaced by CAD technique, dimensions of horizontal, vertical and cross section are still determined separately. Due to the unique of each alignment fitting the topography, the procedure of "design-prototype-test-redesign" commonly used to manufacturing is not suitable for highways designers. Therefore, highway designers are hard to make target modification, and quality of alignment is determined by the early experience of designer's. Numbers of design drawbacks preserved into operation phase always result in the mismatch of highway alignment, modern vehicle and driver behavior, and accident clusters everywhere. So, to this day, driving safety and riding comfort can not be reached for highway design.
If virtual roadway test like used to machinery production can be apllied in alignment design, let vehicle dynamics model run on 3D road models and log the dynamics/kinematics response, can also a good testing instrument, and it is the main objective of this paper. In this context, the virtual driving system of "roadway-driver-vehicle-enviroment" is develpoed in the paper. According to input date of alignment parameters,3D roadway models can be obtained rapidly, if a full vehicle model inducted, parameters of driving behavior and enviroment impact defined togeter, vehicle model driving on 3 D roadway model can be relized and the driving process is visible. Through conducting virtual driving test, designers can identify the location of driving instability or difficulty in vehicle control and modify its design value based on vehicle response and steering input, can see the effects of improment. By means of virtual roadway test, we can parameterize the design value of hignway alignment and obtain the relationship among highway geometry features, vehicle kinematics and driver behavior, such as the effect of change in alignment parameter on vehicle kinematics and driver behavior, the effect of change in vehicle parameter and driver behavior on highway alignment values, etc. which all can result in highway design compatible with modern vehicle design and driver behavior.
In the paper, creation and coupling of subsystems of "roadway-driver-vehicle-enviroment" are firstly completed, then the simulation system is applied in evaluation of alignment design, driving simulation under under adverse conditions, mechanism analysis of single vehicle run-off-road, and vehicle motion performance and driving behavior on curved segment, which can be described as follows:
1. Creation of 3D roadway models.
The roadway module in the second section of the paper can generate 3D road-surface used to contact with tires, and can deal with arbitrary complex alignment in current design. For different conditions of use, we design two formats of input date and their corresponding algorithm. One input is the design values of horizontal/vertical alignment and cross-section, conception of "typology element" is put forward in the paper, which takes a highway alignment as the sequence of "typology element". A horizontal "typology element" is composed of four elements of "tangent+spiral 1+ circular+spiral 2". A vertical "typology element" is composed of a straight grade and its adjacent vertical curve. The other input is spatial coordinate of sampling point in analyzed roadway, which suitable for alignment date absent. We select multi-quadric radial basis function as the interpolation function, and put forward reconstruction algorithm of "local, overlapping" and "exchange of range and independent variable". These algorithm can prevent ill-conditioning of coefficient matrix caused by huge scale, belt distribution, and non-injection of date, and can obtain smooth and continued 3D road-surface.
2. Creation of full vehicle dynamics models, tire-road contact models, and environment impact.
In the third section of the paper, the topology of suspension, steering gear, anti-roll bar, brake, drive axle, driving-line and frame with different configuration are analyzed, and a database of vehicle models is developed. Which include a microbus, two passenger cars, and a truck built in ADAMS. Tire models come from an edition of magic formula Pacejke’94 or Pacejke’89. To let tire contact with road-surface, we design an algorithm of defining friction coefficient that can define a half roadway or several segments a different coefficient with others. Environment impact IS simulated through tire-road contact model and vehicle models, such as define a small friction coefficient for a given segment to simulate the effect of ice or water gathered, and act a lateral force on vehicle body to simulate the process of driving in lateral wind.
3. Steering and speed models.
Our innovative work in this aspect is developing a prediction model of desired speed on a given highway, which can take in account highway geometry features, vehicle dynamics, and driving behavior. Principle of determination of desired speed is that, the desired speed on curve areas should meet the condition:the lateral acceleration of vehicle bodies no more than the tolerated value aytoal; speed change between two adjacent curves is subject to the acceleration rate ax and deceleration rate ab, and the desired speed is always no more than the environment speed Vxmax. According to speed measurement date on real road, we developed the models of aytoal, ab, ax, and Vxmax·Vxmax is a function of average change rate of curvature and total roadway width, aytoal, ab and axare all functions of curve radii and lane width, so they change along roadway. Currently, models developed by foreign researchers are often aiming at several rural roads in level or level-hilly areas, despite how modify model parameters, the model can not suitable for highways of different design speed in China. Therefore, we put forward a method of calibrate model parameters for design speed separately, by this way, we can use a unitive model to deal with highways of different design speed.
4. Evaluation of highway alignment based on speed.
In the fifth section of the paper, we analysis the speed along given roads. Our conclusions are as follows:When driving at a constant speed, the frequency of driver change pedals is equal to the use of sharp curves, therefore, we can control highway's driving workload by alignment design. When driving vehicle reaches such a situation of lose control, the profile of lateral speed will has a catastrophe in magnitude and cause discontinuity in longitudinal speed, so we can use the continuity of speed to evaluate the vehicle stability when driving at a constant speed, and further do a judgement whether exists threaten to driving vehicle in difficult segment and whether to refine design.
For free driving, our observation indicates that, deceleration rate while entering curve is always more than acceleration rate while exiting curve; beginning point of slow down and ending point of speed up are always beside the spirals, so the suppose of speed change in spirals is wrong. In addition, for freeway, acceleration rate of 0.5m/s2 is too high. The best method to control speed fluctuation is let the curve radii and tangent length of adjacent element similar, and tangent should be short. Besides alignment, the reason cause speed fluctuant frequently on complex and trivial roads in mountainous area is the exchange between kinetic energy of rotation and translational energy, so, we should take in account the factor. Criteria of deference between operation speed and design speed less than 20km/h may not suitable for lower standard rural roads, while for freeway design in high standard, operation speed method also not suitable.
5. Evaluation of highway alignment based on vehicle driving stability and steering workload.
In the sixth section of the paper, rollover probability of alignment is evaluated by indicator of vertical force of tires; effect of superelevation/reverse superelevation on steering control is analyzed by measurement of tire slip angle, steering force and steering input; and steering workload of alignment is measured by medium of steering input and its angular speed. Our main conclusions are as follows:within curve areas, rollover probability increases as design speed of the road decreases when driving speed around design speed. Exposure can change load sharing effect among front/middle/rear axle, and further change the rollover probability of upgrade and downgrade, the results indicate downgrade is favorable to rollover. Superelevation can reduce tire slip angle when driving on curve, therefore, stability of driving vehicle is improved. In addition, superelevation also can reduce steering input and the force acting steering wheel and make handing easy. But its disadvantage is increasing vehicle's lateral inclination when traveling on curves. Reverse superelevation make against stability of running vehicle on curves, it can increase tire slip angle, steering force, and steering input.
Lateral acceleration of running vehicle will no more than tolerated limit, but it exceeds the comfort limit, if the highway alignment meet the design standard recommended in Chinese policy. If spiral no exists in the fourth-class roads, change rate of lateral acceleration when entering/exiting curve will larger than 1.0 m/s3. There does not exist difference between steering on curve and steering on tangent if curve radii exceeds a certain value, but they all need steering corrections. Even in mountain terrain, steering workload of freeway alignment is very small; although riding comfort of secondary roads is not as good as freeways, alignment of secondary roads can not lead to drivers stress; third-class roads may cause drivers who like high speed stress. Egg-shape curves are in favor of steering control, because steering wheel angle can change in the middle spirals, whereas, convex curves call for continuous steering input. When point of circular to tangent overlap point of tangent to spiral, the skip of horizontal curvature will result in difficulty in steering, so, this overlapping should be eliminated and change this alignment combination to an egg-shape curve.
6. Vehicle driving stability under adverse conditions.
In the seventh section of the paper, the effect of crosswind, water gathered on tangent, and tunnel entrance/exit on driving vehicle are analyzed, our main findings as follows:To assure the straight line performance of driving vehicle, drivers should let passengers and goods close to rear end of their vehicles, by this mean, vehicle'cg can locate behind wind pressure center. Vehicle's straight line performance increases as its cg reduces, vice versa, so drivers should control the height of center of gravity of laden vehicle. Drivers decrease their speed before entering crosswind areas can reduce the lateral displacement and deflection angle.
Mechanism of crash on tangent segment gathered water is that, unbalanced loading, road crown, difference in spring stiffness of both side→cg of vehicle departures its longitudinal axis→unbalanced wheel load between right to left→the tire with larger load has larger friction forcee→it has larger linear rolling speed→it has larger displacement in wheel center→side skidding occurs. If tires of two sides simultaneously contact with water, vehicle will deflect toward the side of lighter tire load. If one side tires contact with water, vehicle will deflect toward the water areas.
The abrupt change in adherence at location of pavement transition of curved tunnel entrance can cause additional deflection of driving car, and cement pavement lower adherence in sequence can lead to instability of braking vehicle. Yaw motion of driving vehicle at location of pavement transition increases as speed increases, so we can layout the transition location of entrance behind the end of brake and the transition location of exit before the beginning of acceleration. The abrupt change in adherence at location of pavement transition is the factors that mostly contribute to the occurrence of accidents near tunnel opening, to reduce the yaw motion caused by adherence change, and assure adherence of inside tunnel more than 0.35.
7. Mechanism of several typical run-off-road crashes on horizontal curves.
In the eighth section of the paper, we simulate the process of avoiding on curved segment and recur the process of vehicle running off roadway on spiral of S-shape curve, our findings are as follows:When vehicle travels at a special speed, lateral deformation of tire generated on circular will not release adequately on the adjacent spiral, residual deformation of tire will be maintained to the spiral jointed another circular and will release suddenly under increasing lateral force cause by spiral, which will result in lateral slip between tire and pavement and cause vehicle instability. The crashes caused by hysteresis effect of tire more often occur on the detection of sharp curve to flatter curve, because sharp circular curves often joint to shorter spirals, which results in residual deformation. The best method to reduce these crashes is releasing tire's lateral deformation adequately, so, increase the spiral length or insert a tangent at point of reversing curvature can reach this effect.
When Avoiding on curved segment, increase/decrease in curvature of track results in change in driving safety of two running vehicle in opposite. To reduce the additional increment in track curvature while recovering, the driver in outside curve should prolong the recover track of vehicle. The driver inside curve should begin his lane change earlier and recover smoothly, because the additional curvature always occurs on the phase of avoiding beginning and recovering.
8. Effect of change in bend geometry on vehicle kinematics and driving behavior.
In the ninth section of the paper, we analyzed the effect of change in bend features on two benefits resulting from corner cutting driving pattern, speed increment and radii flatting on curves, consequently, answer the question of where drivers cut the curve. Current alignment design assume track the same as road centerline, but when driver choose corner cutting pattern, radii of track will exceeds design value of curve radii a lot, at this time, how can we achieve our design control? According to our findings, designers can know in which kind of parameters combination the curve can really influence driver's speed choice and track radii equal to curve design radii; and in which kind of parameters combination drivers will cut the curve, how much the track radii and traveling speed when corner is cut.
In this section, we also analyzed the steering behavior while vehicle driving on simple curves. Steering time, steering distance and steering characteristic point are obtained, therefore, steering behavior on simple curves can be depicted clearly. Profile of steering length versus curve radii in this section can provide design control for spiral length, because a typical viewpoint currently believes desired spiral length equal to the distance traveled during the steering time. Profile of steering time depending curve radii in this section can provide another control for spiral design, because spiral length recommended in design policies of several countries no less than steering time multiply design speed. In addition, profile of advanced steering length versus curve radii can help designers install curve alignment markers rightly, because we can know where drivers begin their steering.
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