Vehicle Dynamics Theory and Application
不错的汽车动力学教材，是参与汽车底盘电子开发的动力学基础。Reza n. jazarVehicle DynamicsTheory and ApplicationsSpringerReza n. jazarDept of Mechanical EngineeringManhattan collegeRiverdale. NY 10471ISBN:978-0-387-74243-4e-ISBN:978-0-387-74244-1Library of Congress Control Number: 200794219c 2008 Springer Science+ Business Media, LLCAll rights reserved. This work may not be translated or copied in whole or in part without thewritten permission of the publisher(Springer Science+Business Media, LLC, 233 SpringStreet, New York, NY 10013, USA), except for brief excerpts in connection with reviews orscholarly analysis. Use in connection with any form of information storage and retrievalelectronic adaptation, computer software, or by similar or dissimilar methodology now knownor hereafter developed is forbidden. The use in this publication of trade names, trademarksservice marks and similar terms, even if they are not identified as such, is not to be taken as anexpression of opinion as to whether or not they are subject to proprietary rightsPrinted on acid-free paper987654321springer. comKavoshmy daughter, Vazan,and my wife, MojganHappiness is when you win a race against yourselfPrefaceThis text is for engineering students. It introduces the fundamental knowledge used in vehicle dymamics. This knowledge can be utilized to developcomputer programs for analyzing the ride, handling, and optimization ofroad vehiclesVehicle dynamics has been in the engineering curriculum for more thana hundred years. Books on the subject are available, but most of themare written for specialists and are not suitable for a classroom applicationA new student, engineer, or researcher would not know where and howto start learning vehicle dynamics. So, there is a need for a textbook forbeginners. This textbook presents the fundamentals with a perspective onfuture trendsThe study of classical vehicle dynamics has its roots in the work ofgreat scientists of the past four centuries and creative engineers in thepast century who established the methodology of dynamic systems. Thedevelopment of vehicle dynamics has moved toward modeling, analysisand optimization of multi-body dynamics supported by some compliantmembers. Therefore, merging dynamics with optimization theory was anexpected development. The fast-growing capability of accurate positioninsensing, and calculations, along with intelligent computer programming arethe other important developments in vehicle dynamics. So, a textbook helpthe reader to make a computer model of vehicles, which this book doesLevel of the bookThis book has evolved from nearly a decade of research in nonlineardynamic systems and teaching courses in vehicle dynamics. It is addressedprimarily to the last year of undergraduate study and the first year graduatestudent in engineering. Hence, it is an intermediate textbook. It providesboth fundamental and advanced topics. The whole book can be coveredin two successive courses, however, it is possible to jump over some sections and cover the book in one course. Students are required to know thefundamentals of kinematics and dynamics, as well as a basic knowledge ofnumerical methodsThe contents of the book have been kept at a fairly theoretical-practicallevel. Many concepts are deeply explained and their application empha-sized, and most of the related theories and formal proofs have been explained. The book places a strong emphasis on the physical meaning andapplications of the concepts. Topics that have been selected are of highinterest in the field. An attempt has been made to expose students to aPrefacebroad range of topics and approachese There are four special chapters that are indirectly related to vehicle dy-amics: Applied Kinematics, Applied Mechanisms, Applied dynamics, andApplied vibrations. These chapters provide the related background to understand vehicle dynamics and its subsystemsOrganization of the bookThe text is organized so it can be used for teaching or for self-studyChapter 1"Fundamentals, "contains general preliminaries about tire andrim with a brief review of road vehicle classificationsPart I"One Dimensional Vehicle Dynamics, " presents forward vehicledynamics, tire dynamics, and driveline dynamics. Forward dynamics refersto weight transfer, accelerating braking, engine performance, and gear ratiodesignPart II"Vehicle Kinematics, presents a detailed discussion of vehiclemechanical subsystems such as steering and suspensionsPart IIT"Vehicle Dynamics, employs Newton and Lagrange methodsto develop the maneuvering dynamics of vehiclesPart Iv "Vehicle Vibrations, presents a detailed discussion of vehi-cle vibrations. An attempt is made to review the basic approaches anddemonstrate how a vehicle can be modeled as a vibrating multiple degreeof-freedom system. The concepts of the Newton-Euler dynamics and La-grangian method are used equally for derivation of equations of motionThe RMS optimization technique for suspension design of vehicles is intro-duced and applied to vehicle suspensions. The outcome of the optimizationtechnique is the optimal stiffness and damping for a car or suspended equipmentMethod of presentationThis book uses a fact-reason-application"structure. The "fact"is themain subject we introduce in each section. Then the reason is given as a" proof. The application of the fact is examined in some examples. Theexamplesare a very important part of the book because they show howto implement the facts. They also cover some other facts that are neededto expand the subjectPrerequisitesSince the book is written for senior undergraduate and first-year graduatelevel students of engineering, the assumption is that users are familiar withmatrix algebra as well as basic dynamics. Prerequisites are the fundamentals of kinematics, dynamics, vector analysis, and matrix theory. Thesebasics are usually taught in the first three undergraduate yearsPrefaceUnit SystemThe system of units adopted in this book is, unless otherwise stated, theinternational system of units(SI). The units of degree(deg)or radian(rad)are utilized for variables representing angular quantitiesSymbolse Lowercase bold letters indicate a vector. Vectors may be expressed inan n dimensional Euclidian space. ExamplerCUppercase bold letters indicate a dynamic vector or a dynamic matrix, such as force and moment. ExampleFo Lowercase letters with a hat indicate a unit vector. Unit vectors arenot bolded. ExampleLowercase letters with a tilde indicate a 3 x 3 skew symmetric matrixassociated to a vector. Examplea3211An arrow above two uppercase letters indicates the start and endpoints of a position vector. ExampleON = a position vector from point o to point Ne The length of a vector is indicated by a non-bold lowercase letterExampleCapital letter B is utilized to denote a body coordinate frame. ExampleB(ocgB(Oxyz)B1(o1x19121)ⅹ11PrefaceCapital letter G is utilized to denote a global, inertial, or fixed coordinate frame. ExampleG(XYZG(OXYZRight subscript on a transformation matrix indicates the departureframes. ExampleRB= transformation matrix from frame B(oxyz)Left superscript on a transformation matrix indicates the destinationframe. ExampleRBtransformation matrix from frame B(o cgz)to frame G(OxYZ)Capital letter R indicates rotation or a transformation matrix, if itshows the beginning and destination coordinate frames. Example0BSIn a0Whenever there is no sub or superscript, the matrices are shown in abracket. ExampleCOS asin a osIn aCOs O0e Left superscript on a vector denotes the frame in which the vectoris expressed. That superscript indicates the frame that the vectorbelongs to; so the vector is expressed using the unit vectors of thatEr= position vector expressed in frame G(OXYZ)Right subscript on a vector denotes the tip point that the vector isreferred to. ExamplePsition vector ofexpressed in coordinate frame G(OXYZ)Right subscript on an angular velocity vector indicates the frame thatthe angular vector is referred to. ExampleB= angularof the body coordinate frame B(oxyz)
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汽车噪声与振动-理论与应用
汽车NVH领域的经典入门读物，引领进入汽车振动噪声研究的最佳选择。第一章管道声学(1.12)时,声压幅值达到最大,反节点的位子是:(1.13)驻波是由频率相同的向右传播的入射波和向左传播的反射波迭加而成。驻波并不是运动的波,而是静止的,这是“驻”波名称的由来。波表示管道中的声音的模态。对於长度一定的管道来说,由于有许多频率的波,因此也就有很多驻波。这里所提到的驻波是假设管壁刚硬,所冇声波遇到管壁时全部被反射回来。可是实际上,管端壁不是完全刚性,因此反射波的声压不完全等於入射波声压,因此在节点处,入射波和反射波不可能完全抵消。但是这些点处的声压大部分被抵消,声压最低。第二节管道声阻抗阻抗是指当对媒质受到压力或者搾动力时,媒质会对传播产生阻碍。管道中的声学阻抗Z,定义声压与质点体积速度的比值,即(1.14)式中,u,U和S分别是管道中的速度,体积速度和截面积。体积速度与质点速度的关系为:L=SL。声吝在管道內传播,当管道的截面积发生变化的时候,声阻抗也发生变化。图1.3是截面积变化的管道,在变截面的地方,由于阻抗发生变化,一部分入射波就会被发射回原来的管道而另一部分入射波会在新的截面管道中继续传播。抗性消音器的工作原就是基于这种阻抗的变化。声波从发动机出来并在进气或者排气系统中传播,当遇到消音元件或者截面积变化时,入射声波被反射回发动机声源,从而抑制声音的传播。进排气系统中声阻抗不匹配的情况主要有截面积变化,主管道中插入了其他管道(如旁支消音器等),管道开口通往大气等等图1.3截面积变化的管道进排气系统中管道的长度都是有限的。图1.4表小一个长度为L的管道。假改管道两端的声阻抗分别已知,即在=处,声阻抗为,在=处,声阻抗为由公式(1.6)和(1.9),可以得到管道中仟一点的声阻抗为管道声学图1.4长度为L的管道将=代入公式(1.15)中,得到该处的声阻抗为:将三代入公式(1.15)中,得到该处的声阻抗:公式(17)可以重新写成下面的形式18将方程(1.16)代入到方程(1.18中,消除和,就得到输入声阻抗和输出声阻抗的关系,如下第一章管道声学(1.20第三节管口封闭与管口敞廾声波从管道入口端发射出来,传播到尾端。管道尾端通常有两种情况,一种是开口的,如进气管口,排气尾管口;另一种是封口的,如四分之一波长管。下面就来分析这两种尾端的声学特征。1.开∏-封闭管道图1.5表示管道尾端封闭状况。声音在管道里问石传播,当声波碰到刚性的封闭端时,声波被全部反弹冋来,再向左传播管口封闭图1.5开凵封闭管道对一个刚性的封闭口来说,其声阻抗为无穷大,即>0,根据公式(1.19),得到:1.21)声阻抗可以写成下面的形式:(1.22)式中R和粉别是阻抗的实部和虚部,R为声阻,称为声抗。声阻取决于结构的材料特性,而声抗则取决」结构的儿何特性。当声抗为零的时候,结构就发生共振。公式(1.21)中的声阻抗也可以写成公式(1.22)那样的形式,为(1.23)上式如果满足下亩的条件:(1.24)即,那么这个开口-封闭管道就发生共振,其固有频率为:(1.25)当n-=1,2,3,.,时,分别对应著管道第·阶、第二阶、第三阶,,.,等阶次频率图1.6是管道声波的第一阶和第阶模态。这个声波在封闭端时,声压达大最大值,然后发射第一章管道声学到入口处,使得入口端的声压为零,即在开口端形成驻波节点。四分之一波长管就是应用这个原理来工作的。图1.6管道声波的第一阶模态(A)和第二阶模态(B)公式(1.25)可以转变为管道长度与波长的关系,表达如下1.26)当n=1时,管道的长度是波长的四分之,即:。所以这种开∏封闭的管道通常叫著四分之一泼长管2.开口开口答道图1.7为一个尾端开口的管」。声波从入口端向右传播进入开口端时,声音与大气产生声耦合。大气的辐射声阻抗会将一部分声波返回管口敞开图1.7开口-开口管道声波在尾端的声阻抗为周围坏境的声阻抗,也就是说这个声阻抗不为零。为了使问题简化起见,我们先假设这个阻抗为零,然后再对所得到的结构进行修正。如果在x=处的声阻抗为零,那么由公式(1.19)可以得到下式(1.27)同样,当这个声阻抗中的声抗为零的吋候,管道就发生共振,这时必须满足:即:这时,开口-开口管道的共振频率为:当n=1,2,3,,时,分别对应著管道第一阶、第二阶、第三阶,.,等阶次频率第一章管道声学图1.8是开口-开口管道声波的第一阶和第二阶模态。图1.8开口-开口管道的第一阶模态(A)和第二阶模态(B)公式(1.30)可以转变为管道长度与波长的关系,衣达如下(1.31)3.开口管道的修正在推导尾端廾口公式时,我们假设了出口周围坯境的声阻抗为零,但是实际上这个阻抗不为零,因此必须对公式(1.27-1.31)的结论做修止。对图1.9这样的开∏终端,被称为自由自由开口。该开口处的声阻抗为:等效管图1.9自山开口-开口修正管道山于管道的直径非常小,因此和都远远小于1。山公式(1.27)和(1.32)得到:(1.33)这样,管道内的频率为34)管道长度与波长的关系为(1.35这样管道的长度比声阻抗为零的时候要短些,也就是说好像有一根等效的延长管与原来的管道相连接。管道的计算长度就是实际管子长度加上等效延长管长度△即第一章管道声学(1.36有时侯,在出口管处还会加类似与法兰的结构,如图1.10所示。这时,有效延长管的长度为△实际管子的长度为:△式中是管子的计算长度发等效管图1.10法兰开口-开口修正管道第四节四端网终分析进气系统或者排气系统都是有很多管道和消音元件组成。分析整个系统往往是非常复杂的,但是如果将系统分解到一些小的段落,那么分析起来就相对容易些。得到了每个段落或者是每个部件的分析结果,然后将之合成起来就得到了整个系统的结果。四端网络分析就是这种分析方法,在管道声学分析中得到了广泛的应用。对於管道中一小段质量(如图1.11)来说,动力方程可以写成如下:(1.39)式中,S是管道的截面积,是这个小质量段的长度,和分别是质量端两边的压力图1.11管道中一小段质量的受力分析公式(1.39)可以表达为(1.40)第一章管道声学对这一小段质量来说,假设两边的速度是相等的,即将这公式(1.40)和(1.41)写成矩阵形式,得到:(1.42)公式(1.42)建立起这段小质量块两边的压力和速度的关系。管道中小段质量块后端的压力和速度可以用它前端的压力和速度来表示。也就是说质量块后端与前端之间建立起来一种传递关系。同样对一个长度为L的管道(如图1.4所示)也可以得到管道两端的传递关系。在=处的压力和速度可以通过公式(1.6)和(1.9)分别求得(1.13)由以上两式可以得到和,如下:45(1.46根据公式(6)和(9),在处的压力和速度分别为将公式(1.45)和(1.46)中和的表达式代入公式(1.47)和(1.48)之中,就得到管道入冂与出∏之间声压和速度之间的关系,为:+49将公式(1.49)和(1.50)写成如下的矩阵形式第一章管道声学这样就得到了管道两边的压力和速度的传递关系。公式(1.51)可以简单地写成如下形式式中,被称为传递矩阵。如果管道的传递矩阵知道,那么只要知道管道端的压力和速度,就可以通过传递矩阵算出另一端的压力和速度。在传递矩阵两边分别是两个输入参数和两个输出参数。这四个参数的关系由传递矩阵来确定,因此这种表达方式称为四端网络法。上面介绍了小段质量和长度为L的管道的传递矩阵表达方法。这种方法可以推广到任何一个声学元件,其输入端和输出端的声压和速度都可以用四端网络米表示。图1.12代表某个声学元件i。图1.12一个管道元件的四端网终图这个元件两边的压力和速度关系为式中是传递矩阵,是传递矩阵系数。汽车的进气系统包括进气管道、空气过滤器、赫耳姆兹消音器、四分之波长管等。排气系统包括排气多支管、催化器、谐振器、消音器和管道等。一个系统如果由N个元件组成。而且每个元件的传递矩阵都知道,那么出声口的声压和速度就可以用声源的声压和速度来表示如下形式:(1.54)式中的L1是系统的传递矩阵,如下形式(1.55)
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