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1、 譯文題目： 針對(duì)行車控制應(yīng)用的麥弗遜式懸架系統(tǒng)的 新非線性模型 New Nonlinear Model of Macpherson Suspension System for Ride Control Applications Abstract:In this paper, a new nonlinear model of Macpherson suspension system for ride Control applications is proposed. The model includes the vertical acceleration of the sprung

2、 mass and the motions of the unsprung mass subjected to control arm rotation. In addition, it considers physical characteristics of the spindle such as mass and inertia moment. This two degree-of-freedom (DOF) model not only provides a more accurate representation of the Macpherson suspension system

3、 for ride control applications but also facilitates evaluation of the kinematic parameters such as camber, caster and king-pin angles as well as track alterations on the ride vibrations. The performances of the nonlinear and linear models are investigated and compared. I. INTRODUCTION The Macpher

4、son suspension was created by Earl Macpherson in 1949 for the ford company. Due to its light weight and size compatibility this kind of suspension is widely used in different vehicles. Moreover this kind of vehicle is more popular to be found in the front of the car even though it was also used as a

5、 rear suspension. Performance requirements for a suspension system are to adequately support the vehicle weight, to provide effective ride quality which means isolation of the chassis against excitations due to road roughness, to maintain the wheels in the appropriate position so as to have a better

6、 handling and to keep tire contact with the ground. However it is well known that these requirements are conflicting, for instance to achieve better isolation of the vehicle chassis from road Irregularities, a larger suspension deflection is required with soft damping, while a large damping yields b

7、etter stability at the expense of comfort. Thus, the idea of incorporating of active or semi-active suspensions can be considered so as to reach these specifications more than those passive one. Based on a simplified two DOF quarter car model, many semi-active and active control algorithms have been

8、 developed to handle these conflicting performance requirements. The simplified two DOF quarter car model , so-called conventional model in this paper, represents two lumped masses of a quarter car system. though the conventional model of the suspension has been widely used in suspension control des

9、igns, it is not convenient for the evaluation of the suspension kinematic parameters which significantly affect handling performance of the vehicle. Hence, most of the current control algorithms focus on the enhancement of ride quality without considering structural effects. Note that, without consi

10、dering the effect of the suspension kinematics , the simple model may not be considered effective. Thus the study about the impacts of the suspension kinematics on the dynamical behavior of the system is necessary. Therefore, the need for an accurate model for the Macpherson suspension system become

11、s increasingly important for ride control design applications. Based on three nonlinear models of the Macpherson suspension, analyzed the dynamical behavior of this system. A spatial model of the Macpherson suspension to study its kinematic and dynamic performances was formulated by Fallah and Suh.

12、 Using a three- dimensional model of a Macpherson suspension, Chen and Beale estimated the dynamic parameters of the mechanism. Although these models are useful in analyzing the structure, they are not suitable for ride control design. Moreover, a three-dimensional model of the Macpherson suspension

13、 was employed by Ro and Kim for parameter identification and also for ride control, however, this model, as the previous models, was not applicable for observation of the kinematic parameters. Sohn, et al proposed a new model of the Macpherson suspension for ride control purposes. Nevertheless, in t

14、hat model the structure and properties of the spindle have not been taken into consideration. In this paper, a comprehensive model of the Macpherson strut wheel suspension system with spindle properties is proposed for ride control applications. The model considers the kinematic properties, the ver

15、tical acceleration of the sprung mass and the motions of the unsprung mass subjected to control arm rotation. In addition, it includes physical characteristics of the spindle such as mass and inertia moment. With this model, it is convenient to observe the suspension kinematic parameters subjected t

16、o control actuation force, designed to improve the ride quality. II. NEW MODEL OF MACPHERSON SUSPENSION FOR ACTIVE CONTROL APPLICATIONS To model a Macpherson suspension system for control application, one should take into account both the kinematics and dynamics of the system subjected to the actu

17、ation force and road disturbances. Consider a Macpherson suspension system excited by road disturbance. It comprises a quarter-car body, a spindle and a tire, a helical spring, control arm, load disturbance and an actuation force. The structure has two degrees of freedom including vertical displace

18、ment of the sprung mass and rotational motion of the control arm when the mass of the strut is ignored. In this research, we focus on building a two DOF model of a Macpherson suspension system. The detailed assumptions in this modeling are made as follows: The sprung mass has only vertical displace

19、ment while movements in other directions are ignored. The unsprung mass is connected to the car body through the damper and spring as well as the control arm. Vertical displacement of the sprung mass, rotational displacement of the control arm, are measured from the static equilibrium position and a

20、re considered as generalized coordinates. It is assumed that, in the equilibrium condition, the camber angle is zero. Compared to the other links, the mass and stiffness of the strut are neglected. The spring and tire deflections and the damping force are assumed to be in the linear regions of their

21、 operation ranges. III. SIMULATION AND VERIFICATION OF MODEL A. Comparison of the conventional, linear and nonlinear models The output variables of the conventional model are the vertical displacements of the sprung mass and the unsprung mass whereas in the new model the output vector consists of

22、 the displacement of the sprung mass and the angular displacement of the control arm. Thus, the displacement of the sprung mass, is considered as the output variable in order to compare the two models . As suspension on the ride comfort, specially, in the high frequency ranges. Compares the accelera

23、tion transmissibility of three models for frequencies between 0- 20 Hz. The linear model represents a good performance of the nonlinear model for the frequencies between 0-5 Hz. However, the conventional model shows the performance of the Macpherson suspension systems with some discrepancies. B. Ev

24、aluation of the kinematic parameters Some of the main kinematical parameters which are important in chassis design and affect handling and stability of the vehicle are 1) camber angle; 2) kingpin angle 3) caster angle 4) track. Camber angle alterations are due to rubbing of tires and produce latera

25、l forces acting on the wheel and cause the vehicle to steer to one side. Alterations of kingpin and caster angles affect the self aligning torques and consequently affect the stability and handling of the vehicle when wheels bounce or rebound. When the wheels travel on a bump and rebound, the track

26、changes cause the rolling tire to slip and, also produce lateral forces. In the following simulations, we set the step input for road disturbance equal to 100 mm and time step equal to 0.0001 (s). The camber angle, is the angle between the wheel center plane and a vertical line to the road. In defin

27、ition, the steering axis is the line passing through the point D and A in the three-dimensional case and the kingpin angle is the angle between the projection of the steering axis on y-z plane and the vertical line to the road. The angle between the projection of the steering axis on the x-z plane a

28、nd the vertical line to the road is defined as caster angle. The performance of this parameter is illustrated. Track is the lateral distance between the centers of the front wheels. It is obvious that, unlike the previous parameters, the linearization has a large impact on the track. As a result, l

29、inear model is not sufficiently accurate for studying the track behavior. IV. CONLUSION A new nonlinear model of Macpherson suspension is proposed and equations of motion are derived. The new model is more general than conventional model where the structural kinematics and spindle properties are t

30、aken into account. In addition, the new model allows investigation of the suspension kinematic parameters affecting on handling and stability of the vehicle while it is impossible or difficult using the other models proposed for the Macpherson suspension in the case of ride control implementation. T

31、he nonlinear and linear responses of the model are investigated and shown that the linear model is a good approximation of the nonlinear model for ride quality assessment. However, for evaluation of the kinematic parameter performances nonlinear kinematic relations are used which provide a more accu

32、rate study of handling performance and stability condition of the vehicle. 針對(duì)行車控制應(yīng)用的麥弗遜式懸架系統(tǒng)的新非線性模型 摘要: 在本文中，提出了一種對(duì)于駕駛控制應(yīng)用的麥弗遜式懸架系統(tǒng)新的非線性模型。這種模型包括了懸掛質(zhì)量的垂直加速度，并且進(jìn)行控制臂轉(zhuǎn)動(dòng)的非懸掛質(zhì)量的運(yùn)動(dòng)。除此之外，它還考慮了主軸的物理特性，例如質(zhì)量和慣性力矩。這種雙自由度的模型不僅為駕駛控制應(yīng)用提

33、供了麥弗遜式懸架系統(tǒng)更準(zhǔn)確的表示，同時(shí)也方便評(píng)估運(yùn)動(dòng)學(xué)參數(shù)如外傾角，腳輪和主銷角度以及振動(dòng)軌道的改變。對(duì)非線性和線性模型的性能進(jìn)行了研究和比較。 一 引言 麥弗遜式懸架是1949年麥弗遜式伯爵在福特公司創(chuàng)造的。由于它的輕重量和尺寸兼容性，這種懸架被廣泛用于不同的車輛。此外，這種懸架更加流行的是裝在汽車的前部，盡管它也被用作一個(gè)后懸架。懸架系統(tǒng)的性能是要求充分支撐車輛的重量，以提供有效的乘坐品質(zhì)，這意味著針對(duì)由于路面不平導(dǎo)致機(jī)架與底盤隔離，維持輪子在適當(dāng)?shù)奈恢蒙?，以便具有一個(gè)更好的操控，并保持與地面的輪胎接觸。然而，眾所周知的是，這些要求是相互矛盾的。例如，在不平順的道路中，汽車底盤能獲得更

34、好的隔離，一個(gè)更大的懸架偏轉(zhuǎn)需要具有柔和減震，而較大的減震實(shí)在犧牲舒適性的前提下產(chǎn)生更好的穩(wěn)定性。因此，可以考慮納入主動(dòng)或半主動(dòng)懸架的想法達(dá)成這些規(guī)格?；诤?jiǎn)化的雙自由度汽車模型，許多半主動(dòng)和主動(dòng)控制算法已經(jīng)被開(kāi)發(fā)來(lái)處理這些相互矛盾的性能要求。簡(jiǎn)化雙自由度汽車模型，在這篇文章中就是所謂的常規(guī)模型，表示兩個(gè)集中質(zhì)量的汽車系統(tǒng)。雖然懸架的傳統(tǒng)模型中懸架控制設(shè)計(jì)已被廣泛使用，這不便于懸架運(yùn)動(dòng)學(xué)參數(shù)有對(duì)明顯影響車輛處理性能的評(píng)價(jià)。因此，大多數(shù)的電流控制算法注重乘車質(zhì)量的提高，而不考慮結(jié)構(gòu)性影響。需要注意的是，在不考慮懸架運(yùn)動(dòng)學(xué)的影響，簡(jiǎn)單的模型可能被認(rèn)為是無(wú)效的。因此對(duì)懸架運(yùn)動(dòng)學(xué)上系統(tǒng)的動(dòng)力學(xué)行為的影

35、響研究是必要的。因此，需要對(duì)行駛平順性控制設(shè)計(jì)應(yīng)用了麥弗遜懸架系統(tǒng)的精確模型變得越來(lái)越重要。 基于對(duì)麥弗遜懸架的三種非線性模型，分析了該系統(tǒng)的動(dòng)力學(xué)行為。研究麥弗遜式懸架運(yùn)動(dòng)學(xué)和動(dòng)力學(xué)性能的空間模型是法拉赫和徐制定的。利用麥弗遜式懸架的三維模型，陳和比爾估算該機(jī)構(gòu)的動(dòng)態(tài)參數(shù)。雖然這些模型對(duì)分析構(gòu)造是有用的，但是它們不適合于駕駛控制設(shè)計(jì)。此外，麥弗遜式前懸架的三維模型被榮和金用來(lái)識(shí)別參數(shù)，也用來(lái)識(shí)別行駛平順性。然而，因?yàn)橐郧暗男吞?hào)，這種模式并不適用于運(yùn)動(dòng)學(xué)參數(shù)研究的觀察。孫某等人提出了一種麥弗遜式懸架行車控制目的的新模式。然而，在該模型中的構(gòu)造和主軸的性質(zhì)沒(méi)有考慮進(jìn)去。 在本文中，麥弗遜式懸

36、架支柱車輪懸架系統(tǒng)與主軸性能的綜合模型運(yùn)用在行車控制運(yùn)用中。該模型考慮了運(yùn)動(dòng)學(xué)特性，懸掛質(zhì)量的垂直加速度，并進(jìn)行控制臂轉(zhuǎn)動(dòng)的非懸掛質(zhì)量的運(yùn)動(dòng)。除此之外，它還包括了主軸物理特性，例如質(zhì)量和慣性力矩。使用此模型，它可以很方便地觀察懸架運(yùn)動(dòng)學(xué)參數(shù)受到的驅(qū)動(dòng)力，旨在提高行車的的品質(zhì)。 二 新麥弗遜式懸架主動(dòng)控制應(yīng)用程序模型 為了模擬控制應(yīng)用中的麥弗遜式懸架系統(tǒng)，其中應(yīng)考慮到遭受的驅(qū)動(dòng)力和道路干擾的運(yùn)動(dòng)學(xué)和動(dòng)力學(xué)系統(tǒng)。 考慮路面干擾勵(lì)磁的麥弗遜式懸架系統(tǒng)，它包括了四分之一個(gè)車身，一個(gè)主軸和一個(gè)輪胎，一個(gè)螺旋彈簧，控制臂，負(fù)荷干擾和致動(dòng)力。該結(jié)構(gòu)具有包括彈簧支撐體的垂直位移和控制臂的旋轉(zhuǎn)運(yùn)動(dòng)時(shí)在支柱

37、的質(zhì)量?jī)蓚€(gè)自由度。在這項(xiàng)研究中，我們著力構(gòu)建麥弗遜式懸架系統(tǒng)的雙自由度模型。 這個(gè)建模的詳細(xì)假設(shè)如下：彈簧加載的質(zhì)量?jī)H具有垂直位移，而忽略了它在其他方向上的運(yùn)動(dòng)。非懸掛質(zhì)量是通過(guò)阻尼器和彈簧以及控制臂連接到車身的。彈簧支撐體的垂直位移以及該控制臂的旋轉(zhuǎn)位移，都是從靜態(tài)平衡位置附近所測(cè)得的并且被認(rèn)為是廣義坐標(biāo)。假設(shè)在平衡狀態(tài)下外傾角為零。相比于其他鏈接，支柱的質(zhì)量和剛度都被忽略了。彈簧和輪胎偏轉(zhuǎn)以及阻尼力都被假定為在其操作范圍內(nèi)的在線性區(qū)域內(nèi)。 三 仿真和模型驗(yàn)證 A．常規(guī)的線性和非線性模型的比較 輸出變量的常規(guī)模型，彈簧的豎向位移質(zhì)量和非簧載的質(zhì)量而在新的模型輸出向量包括位移的彈簧質(zhì)量

38、和角位移的控制臂。因此，位移的簧載質(zhì)量，被考慮作為輸出變量來(lái)比較這兩個(gè)模型。而作為懸架的乘坐舒適性，特別是在高頻率范圍內(nèi)。比較加速度傳遞率的三種模式為 0-20 赫茲之間的頻率。線性模型表示的 0-5 之間頻率的非線性模型的良好性能。然而，傳統(tǒng)的模型顯示的麥弗遜式懸架系統(tǒng)存在著某些差距。 B．運(yùn)動(dòng)參數(shù)的評(píng)估 一些主要的運(yùn)動(dòng)參數(shù)，底盤的設(shè)計(jì)和處理車輛穩(wěn)定性的影響是很重要的，例如 1) 外傾角2) 主銷內(nèi)傾角 3) 主銷后傾角 4) 軌道。外傾角的改變是由于輪胎的摩擦而產(chǎn)生作用在車輪上的側(cè)向力，并導(dǎo)致車輛轉(zhuǎn)向一側(cè)。主銷和主銷后傾角的改變影響它們的自回正力矩，當(dāng)車輪反彈或被反彈時(shí)，會(huì)影響到整車的

39、穩(wěn)定性和操控性。當(dāng)車輪行駛在顛簸路段并且被反彈時(shí)，軌道的變化會(huì)導(dǎo)致滾動(dòng)輪胎打滑，并且會(huì)產(chǎn)生側(cè)向力。在以下的模擬，我們?cè)O(shè)置了道路干擾為100毫米，時(shí)間步長(zhǎng)等于0.0001（S）的步驟的輸入。外傾角，是車輪中心平面和垂直線上的角度。在定義中，轉(zhuǎn)向軸是通過(guò)點(diǎn)D和A傳遞三維情況下的線與主銷角度是轉(zhuǎn)向軸的上y-z平面的投影和垂直線的道路之間的角度。在x-z平面和豎直線的道路的轉(zhuǎn)向軸的投影之間的角被定義為傾角。說(shuō)明了此參數(shù)的性能。磁道是在前輪的中心之間的橫向距離。顯而易見(jiàn)的是，不象以前的參數(shù)，線性化已經(jīng)在軌道上有了很大的影響。?其結(jié)果是，利用線性模型來(lái)研究軌道特性是不夠精確的。 四.結(jié)論 一個(gè)新的、 非線性的麥弗遜式懸架模型和運(yùn)動(dòng)方程的推導(dǎo)。新模型比傳統(tǒng)模型結(jié)構(gòu)的運(yùn)動(dòng)學(xué)和主軸性能考慮到的更一般。除此之外，新的模型允許在操控以及車輛穩(wěn)定性的影響，而這是不可能或難以利用提出了的麥弗遜式懸架的行車控制實(shí)施的情況下，其他型號(hào)的懸架運(yùn)動(dòng)學(xué)參數(shù)研究的調(diào)查。在該模型的非線性和線性調(diào)查中顯示，該線性模型非常近似于為評(píng)估行車質(zhì)量的非線性模型。然而，對(duì)于運(yùn)動(dòng)參數(shù)性能的評(píng)估，非線性運(yùn)動(dòng)學(xué)方程均采用了為其提供操控車輛的性能及穩(wěn)定性的更準(zhǔn)確的研究。