外文翻译--基于GPS速度计算纵向车轮和轮胎滑移参数

附 录 A 外文文献 Calculating Longitudinal Wheel Slip and Tire Parameters Using GPS Velocity ABSTRACT While tire parameters are quite important to both current vehicle control systems and proposed future systems, these parameters are subject to considerable variability and are difficult to estimate while driving due to the unavailability of absolute vehicle velocity. This paper details a method of generating longitudinal tire force-slip curves using absolute velocity information from the Global Positioning System (GPS). By combining GPS measurements with measured wheel speeds, the effective tire radius and longitudinal stiffness of the tires can be identified using a simple least-squares regression technique. Preliminary results demonstrate the feasibility of the technique, show that the effective radius can be identified with considerable precision and suggest that the identified longitudinal stiffness exhibits noticeable sensitivity to changes in inflation pressure. INTRODUCTION The longitudinal forces that produce acceleration and braking on ground vehicles with pneumatic tires arise due to deformation and sliding in the tire contact patch. While the actual motions that take place in the contact patch are somewhat complex, the force generation can generally be described with sufficient accuracy in terms of wheel slip a measure of the difference between the rotational speed of the wheel. and the translational velocity of the wheel center. The standard SAE definition of wheel slip is ()eV R wSV (1) where V is the longitudinal speed of the wheel center, w is the angular speed of the tire and R, is the effective tire radius. The effective radius is defined to be the radius of the tire when rolling with no external torque applied about the spin axis. Since the tire flattens in the contact patch, this value lies somewhere between the tires undeformed radius and static loadearadius. A number of different tire models for predicting tire longitudinal force in terms of wheel slip have been derived from empirical data. Such models generally relate the longitudinal force on a tire to the wheel slip for given values of normal force, road surface conditions, tire characteristics, and other factors (such as camber angle). Figure 1 demonstrates the general shape of such a curve generated from the commonly-used “Magic Formula” tire model . While models vary, several of the traits shown in Figure 1 are common to various mathematical models and empirical test data. First, the relation between force and slip is roughly linear at low values of slip below the point at which significant sliding occurs in the contact patch. In this region, force can be approximated as proportional to slip using an effective longitudinal stiffness of the tire. The stiffness depends on the foundation stiffness of the tire and the length of the contact patch between the tire and the road . As a result, this value depends strongly upon tire construction and inflation pressure. Beyond this linear region, the additional force generated per unit slip begins to decrease and ultimately reaches a peak, after which tire. force decreases and braking behavior becomes unstable. The peak force at which this occurs depends strongly upon the road surface and is often approximated by scaling by a peak friction value,p , as shown in Figure 1. Some experimental research has suggested that the longitudinal stiffness may also depend on road surface condition and this peak friction value . While consistent with many mathematical representations of force versus slip curves, such dependence violates the traditional brush models physical description of tire force generation . Since tire force generation can be described in terms of wheel slip, slip is a critical parameter in control algorithms for vehicle control systems such as anti-lock brake systems (ABS) and electronic stability control (ESP) . While many ABS algorithms rely primarily on the deceleration of the wheel , some estimate of slip is necessary to avoid lock-up on low friction surfaces. Although the definition of wheel slip in Equation 1 is quite simple, calculating slip on a vehicle is complicated by the lack of accurate measurements of either the radius or the absolute vehicle velocity. While an average radius value can usually be assumed without producing much error, some form of observer must be employed to estimate the vehicle speed . Other systems determine the vehicles absolute velocity by comparing the front and rear wheel speeds (assuming the car is two-wheel drive) . Recent work has demonstrated that velocity measurements derived from the Global Positioning System (GPS) can be used to provide an absolute velocity for calculating wheel slip . This avoids the drift problems inherent in observers based upon wheel speed measurement. The use of GPS velocity information has an even greater benefit beyond the generation of an accurate slip measurement. By comparing the wheel slip to estimates of the forces acting on the vehicle, the tire force versus slip characteristics can be obtained. These, in turn, can be used to feed model-based controllers for ABS or ESP systems or more advanced driver assistance systems for lanekeeping or collision avoidance. They could also be used to provide more accurate observers for periods of time when GPS information is not available. Several researchers have also suggested that by fitting the low slip region of the force-slip curve to a parameterized model - ranging in complexity from the form of Equation 2 to dynamic friction models - the peak friction point can be determined. This application represents a further use for the information that can be generated from GPS-based slip measurement, although preliminary results achieved with the system demonstrate some care in interpretation is necessary for friction detection. This paper demonstrates how tire force-slip curves - and in particular the linear region of these curves - can be determined using GPS velocity measurements and wheel speed sensors. The GPS velocity measurement is differenced to obtain absolute vehicle acceleration, which is multiplied by the vehicle mass to calculate the longitudinal force on the tires. The accuracy of the GPS data enables the estimation of the effective tire radius and longitudinal stiffness of the tires, thus completely specifying the linear part of the force-slip curves. Some preliminary tests at different pressures indicate that these values exhibit some strong dependence on tire pressure, raising a cautionary note about inferring peak friction from tire behavior at low levels of slip. CONCLUSIONS The data shows that GPS velocity information can be combined with wheel speed information to measure tire slip and estimate longitudinal stiffness and effective radius. The data gathered are consistent with the assumption of a linear relationship between force and ship at low levels of slip as predicted by classical tire models. Radius estimation using this method exhibited considerable precision and accuracy within the difference between the undeformed and static loaded tire radii. In preliminary testing, increased inflation pressure appeared to systematically lower the longitudinal stiffness. Future work will concentrate on increasing the amount of collected data and refining data processing to establish more definitive statistical information regarding the effectiveness and sensitivity of this measurement system. 附 录 B 外文文献的中文译文 基于 GPS 速度计算纵向车轮和轮胎滑移参数 一、摘要 虽然轮胎都很 重要参数 ,提出了当前车辆控制系统的系统 ,这些参数的未来有相当大的变化 ,是很难估计的驾驶时由于不能绝对车辆的速度。本文详细阐述了纵向轮胎的生成方法 force-slip 曲线使用绝对速度信息从全球定位系统(GPS)。结合 GPS 测量结果与实测轮速、有效的轮胎半径和刚度的轮胎可以确认使用一个简单的最小二乘回归方法。初步结果验证了方法的可行性 ,表明该技术可有效范围相当可观的精度和显示确认纵向刚度变化的敏感性展品明显通货膨胀的压力。 二、介绍 纵向力产生加速和刹车在地面车辆和充气轮胎产生变形 ,由于滑动轮胎接触补丁。而正确 的姿势 ,发生在接触补丁是有点复杂 ,一般可产生了足够的准确性的轮子滑动测量的差异 wheel.转速和转化速度轮子的中心。这个标准的定义是轮子滑动节约 ()eV R wSV (1) 在纵向速度的五轮中心 ,W 是角的速度的轮胎和 R 是有效的轮胎半径。定义的有效范围半径的轮胎时没有外部扭矩应用滚动的旋转轴。自从轮胎接触平坦的补丁 ,这个值之间的地方 在于轮胎的未变形的半径和静态负载半径。 一个不同的轮胎模型在预测方面的车轮打滑轮胎纵向力产生了一些经验数据， 这种模式一般涉及的 在正常的力量为给定值车轮打滑轮胎的纵向力，路面状况，轮胎的特点，以及其他因素，如拱角（ 如倾角 ）。 图 1 演示了这种从常用的 “ 魔术公式 ” 轮胎模型生成的曲线基本形成。虽然模式不同，在图 1 所示的几个特点是常见的各种数学模型和实证检验数据。 第一，力与滑移关系，大约是在底下的有相当低滑动滑点值的线性发证接触碰撞。 在这一地区，力可近似为成正比使用有效的防滑轮胎，纵向刚度 。 该刚度对轮胎的基础刚度和轮胎之间的联系和道路修补的长度取决于。因此，这个值取决于轮胎强烈呼吁建设和通货膨胀的压力。 该刚度对轮胎的基础刚度和轮胎之间的联系和道路修补的长度取决于。因此，这个值取决于轮胎强烈呼吁建设和通货膨胀的压力。除了这个线性区域，每单位产生的附加力开始下滑，最终达到减少高峰，之后的轮胎。力减小，制动性能变得不稳定。其中，峰力在这种情况取决于强烈呼吁路面，并经常受到摩擦的高峰值，磷比例接近，如图 1 所示。一些 实验研究表明，纵向刚度也可能取决于路面条件和摩擦这个高峰值。虽然有许多数学交涉武力与滑移曲线，这种依赖一贯违反了传统的毛笔模型的轮胎部队组建物理描述。 由于轮胎力发电可以在条款中描述的车轮滑移，滑移是在汽车控制系统的控制算法的关键参数，如防抱死制动系统（ ABS）和电子稳定控制（ ESP）的。 虽然许多 AB