外文翻譯--基于GPS速度計算縱向車輪和輪胎滑移參數

附 錄 A 外文文獻 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 錄 B 外文文獻的中文譯文 基于 GPS 速度計算縱向車輪和輪胎滑移參數 一、摘要 雖然輪胎都很 重要參數 ,提出了當前車輛控制系統的系統 ,這些參數的未來有相當大的變化 ,是很難估計的駕駛時由于不能絕對車輛的速度。本文詳細闡述了縱向輪胎的生成方法 force-slip 曲線使用絕對速度信息從全球定位系統(GPS)。結合 GPS 測量結果與實測輪速、有效的輪胎半徑和剛度的輪胎可以確認使用一個簡單的最小二乘回歸方法。初步結果驗證了方法的可行性 ,表明該技術可有效范圍相當可觀的精度和顯示確認縱向剛度變化的敏感性展品明顯通貨膨脹的壓力。 二、介紹 縱向力產生加速和剎車在地面車輛和充氣輪胎產生變形 ,由于滑動輪胎接觸補丁。而正確 的姿勢 ,發(fā)生在接觸補丁是有點復雜 ,一般可產生了足夠的準確性的輪子滑動測量的差異 wheel.轉速和轉化速度輪子的中心。這個標準的定義是輪子滑動節(jié)約 ()eV R wSV (1) 在縱向速度的五輪中心 ,W 是角的速度的輪胎和 R 是有效的輪胎半徑。定義的有效范圍半徑的輪胎時沒有外部扭矩應用滾動的旋轉軸。自從輪胎接觸平坦的補丁 ,這個值之間的地方 在于輪胎的未變形的半徑和靜態(tài)負載半徑。 一個不同的輪胎模型在預測方面的車輪打滑輪胎縱向力產生了一些經驗數據， 這種模式一般涉及的 在正常的力量為給定值車輪打滑輪胎的縱向力，路面狀況，輪胎的特點，以及其他因素，如拱角（ 如傾角 ）。 圖 1 演示了這種從常用的 “ 魔術公式 ” 輪胎模型生成的曲線基本形成。雖然模式不同，在圖 1 所示的幾個特點是常見的各種數學模型和實證檢驗數據。 第一，力與滑移關系，大約是在底下的有相當低滑動滑點值的線性發(fā)證接觸碰撞。 在這一地區(qū)，力可近似為成正比使用有效的防滑輪胎，縱向剛度 。 該剛度對輪胎的基礎剛度和輪胎之間的聯系和道路修補的長度取決于。因此，這個值取決于輪胎強烈呼吁建設和通貨膨脹的壓力。 該剛度對輪胎的基礎剛度和輪胎之間的聯系和道路修補的長度取決于。因此，這個值取決于輪胎強烈呼吁建設和通貨膨脹的壓力。除了這個線性區(qū)域，每單位產生的附加力開始下滑，最終達到減少高峰，之后的輪胎。力減小，制動性能變得不穩(wěn)定。其中，峰力在這種情況取決于強烈呼吁路面，并經常受到摩擦的高峰值，磷比例接近，如圖 1 所示。一些 實驗研究表明，縱向剛度也可能取決于路面條件和摩擦這個高峰值。雖然有許多數學交涉武力與滑移曲線，這種依賴一貫違反了傳統的毛筆模型的輪胎部隊組建物理描述。 由于輪胎力發(fā)電可以在條款中描述的車輪滑移，滑移是在汽車控制系統的控制算法的關鍵參數，如防抱死制動系統（ ABS）和電子穩(wěn)定控制（ ESP）的。 雖然許多 AB