THE WANKEL ROTARY ENGINE-竖排.docx

THE WANKELROTARY ENGINE1 A Different Approach to the Spark-Ignition Engine 一种新的内燃机形式The reciprocating internal combustion engine has served mankind for over a century, and will continue to do so for the foreseeable future. The Wankel rotary engine, a much more recent development, is said to have been conceived in its present form in 1954 (ref. 2). An implementation of the rotary engine used in the 1990 Mazda RX-7 automobile and its turbocharger are shown in Figures 7.1(a) and 7.1(b). As of 1987, over 1.5 million Wankel engines had been used in Mazda automobiles (ref. 6).往复式内燃机已经为人类服务了超过一个世纪，在可预见的将来还将继续服务。Wankel转子发动机这项新的发动机技术，诞生于1954年。转子发动机于1990年应用于马自达的RX-7汽车，其发动机与涡轮增压器见图7.1（a）和7.1（b）。到1987年，超过150万转子发动机应用在Mazda汽车中（参考文献6）。The rotary engine has a host of advantages that make it a formidable contender for some of the tasks currently performed by reciprocating engines. The piston in a fourstroke-cycle reciprocating engine must momentarily come to rest four times per cycle as its direction of motion changes. In contrast, the moving parts in a rotary engine are in continuous unidirectional motion. Higher operating speeds, ease of balancing, and absence of vibration are a few of the benefits. The high operating speeds allow the engine to produce twice as much power as a reciprocating engine of the same weight. It has significantly fewer parts and occupies less volume than a reciprocating engine of comparable power.转子发动机拥有很多同用途往复式发动机所不具备的优点。四冲程发动机中的活塞在一个工作循环中往复运动四次。相反，转子发动机中的运动件处于连续的单向运动，具有运转速度高、易平衡、振动小等优点。高转速允许发动机产生两倍于同重量往复式发动机的功率。相同功率下，转子发动机比往复式发动机运动件数量显著减少、体积也更小。With all these advantages, why are there so few Wankel engines in service? Part of the answer lies in the reciprocating engine.s remarkable success in so many applications and its continuing improvement with research. Why change a good thing? Manufacturing techniques for reciprocating engines are well known and established, whereas production of rotary engines requires significantly different tooling.拥有如此多优势的转子发动机为什么应用的这么少？一部分原因是往复式发动机在许多领域已经取得成功应用而且其自身也在不断的改进。已经很好了为什么还要改变呢？往复式发动机的制造技术已经很成熟也很容易建设，而制造转子发动机的却需要不同的工具。It must be admitted, however, that the rotary engine has some drawbacks. A major problem of the Wankel automobile engine is that it does not quite measure up to the fuel economy of some automotive reciprocating SI engines. It is the judgment of some authorities that it does not offer as great a potential for improvement in fuel economy and emissions reduction as reciprocating and gas turbine engines. However, although the rotary engine may never dominate the automotive industry, it is likely to find applications where low weight and volume are critical, such as in sports cars, general aviation, and motorcycles.不容否认，转子发动机也有其缺点。Wankel汽车发动机的一个主要缺点就是其燃油经济性不如往复式汽油发动机。某些权威人士判定其燃油经济性没有潜在的巨大改善，排放减少也比不上往复式和燃气轮机。然而，虽然转子发动机可能永远不能主导汽车行业，它任然可以在其他重量和体积要求严格的领域得到应用，例如运动汽车、通用航空和摩托车。图7.1a RX-7涡轮增压型转子发动机（照片来自美国MAZDA Motors）图7.1b RX-7转子发动机涡轮增压器（照片来自美国MAZDA Motors）While the rotary engine may not enjoy the great success of reciprocating engines, it is worthy of study as an unusual and analytically interesting implementation of the familiar Otto cycle. Even the present success of this latter-day Otto engine should serve as an inspiration to those who search for novel ways of doing things. This chapter is a tribute to Felix Wankel and those who are helping to develop this remarkable engine.虽然转子发动机并没有获得像往复式发动机一样的成功，但作为非常规发动机和颚图循环的有意思的形式还是值得学习研究。近代颚图循环发动机的成功应当被视为思维创新的范例。本章节也是对菲力斯汪克尔等为这种有重要意义的发的做出卓越贡献的人的致敬。2 Rotary Engine Operation 转子发动机运转Figure 7.2 shows a cross-section of a rotary engine. The stationary housing encloses a moving triangular rotor that rotates with its apexes in constant contact with the housing inner surface. Air and combustion gases are transported in the spaces between the rotor and the housing. The rotor rides on an eccentric that is an integral part of a shaft, as shown in the dual rotor crank shaft of Figure 7.3(a). The housing and rotor of a rotary engine designed for aircraft application are shown in Figure 7.3(b).图7.2为转子发动机的剖面图。在静子室内运动的三角转子旋转时转子顶点与腔室的内壁保持接触。空气和燃气在转子和腔室之间的空间内流转。转子在曲轴上的偏心轴上转动，如图7.3（a）所示为双转子发动机曲轴。应用于航空领域的转子发动机壳体及转子如图7.3（b）所示。The operation of the Wankel engine as an Otto-cycle engine may be understood by following in Figure 7.4 the events associated with the counterclockwise movement of a gas volume isolated between the housing and one of the rotor flanks. The air-fuel mixture may be supplied, by a conventional carburetor, through the intake port labeled I in Figure 7.4(a). As the shaft and rotor turn, the intake port is covered, trapping a fixed mass of air and fuel (assuming no leakage). This is analogous to the gas mass captured within the cylinder-piston volume by closure of a reciprocating engine intake valve. As the rotor continues to turn, the captured (crosshatched) volume contained between the rotor and housing decreases, compressing the air-fuel mixture part (b). When it reaches the minor diameter, the active mixture volume is a minimum corresponding to the volume at top center in the reciprocating engine. One or more spark plugs, as indicated at the top of each housing, initiate combustion, causing rapid rises in pressure and temperature part (c). The hot, high-pressure combustion gas part (d) transmits a force to the eccentric through the rotor. Note that, during the acting about the shaft axis. As the rotation proceeds, the expanding gases drive the rotor until the exhaust port is exposed, releasing them part (e). The exhaust process continues as the intake port opens to begin a new cycle. This port overlap is apparent in the lower volume shown in part (b). In summary, each flank of the rotor is seen to undergo the same intake, compression, ignition, power, and exhaust processes as in a four-stroke-cycle reciprocating Otto engine.Wankel发动机的奥图循环示意图见图7.4，发生在由壳体和转子的一个边所围成的随转子逆时针转动变化的腔内。化油器产生的油气混合液通过图7.4（a）中的入口I喷入。随着轴和转子的旋转入口被封闭，油气混合气体被封闭起来（假设无泄漏）。这类似于往复式发动机的进气阀关闭与活塞形成密闭空间。随着转子继续旋转，转子与壳体之间的空间（阴影部分）减小，混合气体被压缩（b部分）。当达到直径最小值时，混合气体体积达到类似于往复式发动机压缩冲程后的最小值。如图示位于外壳顶部的一个或多个火花塞点火燃烧，腔体内的温度和压力迅速升高（c部分）。炽热的高压燃气（d部分）通过转子推动偏心轴转动。需要注意这个过程中主轴的转动。随着转子的继续转动，膨胀的气体推动转子转动并到达排气口并排气（e部分）。排气的同时开始进气并开始一个新的循环。从（b部分）可以明显看出进排气重叠的现象。总的来说，转子的每个边都要经历同样的和四冲程往复式奥图循环发动机类似的吸气、压缩、点火、做功和排气过程。All three flanks of the rotor execute the same processes at equally spaced intervals during one rotor rotation. Hence three power pulses are delivered per rotation of the rotor. Because there are three shaft rotations per rotor rotation, the Wankel engine has one power pulse per shaft rotation. Thus it has twice as many power pulses as a single-cylinder four-stroke-cycle reciprocating engine operating at the same speed, a clear advantage in smoothness of operation. This feature of one power pulse per shaft rotation causes many people to compare the Wankel engine with the two-stroke-cycle reciprocating engine.在转子旋转一周中，转子的三个边在相同的空间间隔中经历同样的步骤。因此转子旋转一圈将有三次做功。因为转子每旋转一周轴旋转三周，Wankel发动机的主轴旋转每一周就做一次功。这是单缸四冲程往复式发动机在同样转速下做功的两倍，而这会显著增加运行的平顺性。Wankel发动机主轴每旋转一周做一次功的特点使许多人将它和两冲程往复式发动机相比。3 Rotary Engine Geometry 转子发动机几何The major elements of the rotary engine-the housing and the rotor- are shown in cross-section in Figure 7.2. The housing inner surface has a mathematical form known as a trochoid or epitrochoid. A single-rotor engine housing may be thought of as two parallel planes separated by a cylinder of epitrochoidal cross-section. Following the notation of Figure 7.5, the parametric form of the epitrochoid is given by转子发动机的主要部件，即转子及壳体，如图7.2中阴影部分所示。机壳的内表面轮廓数学上称为摆线，或长短辐圆外旋轮线。单转子发动机壳体可以被视为有两个平行平面截一个横截面为摆线的柱体所得。如图7.5所示，摆线的参数方程如下：x = e cos 3 + R cos ft | m(7.1a)y = e sin 3 + R sin ft | m(7.1b)where e is the eccentricity and R is the rotor center-to-tip distance. For given values of e and R, Equations (7.1) give the x and y coordinates defining the housing shape when is varied from 0 to 360 degrees.式中e为偏心率，R为转子中心到顶点的距离。通过方程7.1，给定e和R的值后，当从0变到360，可以得到x和y的坐标值。The rotor shape may be thought of as an equilateral triangle, as shown in Figures 7.2 and 7.4 (flank rounding and other refinements are discussed later in the chapter). Because the rotor moves inside the housing in such a way that its three apexes are in constant contact with the housing periphery, the positions of the tips are also given by equations of the form of Equations (7.1):转子形状可视为一个等边三角形，如图7.2和7.4所示（圆弧边及其他细节将在后面章节中讨论）。因为转子在壳体内转动时，顶点总是和内壁保持接触，所以顶点的方程表示如下：x = e cos 3 + R cos( + 2n/3)ft | m(7.2a)y = e sin 3 + R sin( + 2n)ft | m(7.2b)where n = 0, 1, or 2, the three values identifying the positions of the three rotor tips, each separated by 120. Because R represents the rotor center-to-tip distance, the motion of the center of the rotor can be obtained from Equations (7.2) by setting R = 0. The equations and Figure 7.5 indicate that the path of the rotor center is a circle of radius e.当n = 0,1,或2时，三个方程分别对应转子的三个顶点，三顶点之间相差120。因为R表示转子中心到顶点的距离，所以当R=0时方程表示转子中心的轨迹方程。方程和图7.5中可以看出，转子中心的运动轨迹为一个半径为e的圆。Note that Equations (7.1) and (7.2) can be nondimensionalized by dividing through by R. This yields a single geometric parameter governing the equations, e/R, known as the eccentricity ratio. It will be seen that this parameter is critical to successful performance of the rotary engine.需要注意的是方程7.1和7.2都是无量纲的，并与由R划分。这就是方程由一个参数e/R控制，即偏心率。这个参数的选取对转子发动机的性能有重要影响。The power from the engine is delivered to an external load by a cylindrical shaft. The shaft axis coincides with the axis of the housing, as seen in Figure 7.2. A second circular cylinder, the eccentric, is rigidly attached to the shaft and is offset from the shaft axis by a distance, e, the eccentricity. The rotor slides on the eccentric. Note that the axes of the rotor and the eccentric coincide. Gas forces exerted on the rotor are transmitted to the eccentric to provide the driving torque to the engine shaft and to the external load.供给外部负载发动机动力由主轴输出。轴的轴心正好与壳体轴心一致，如图7.2所示。第二个轴，及偏心轮，与主轴刚性连接，其轴心和主轴轴心距离为e，及偏心距为e。转子在偏心轮上滑动。转子的轴心与偏心轮轴心重合。燃气产生的力作用于转子上并通过偏心轮对主轴产生扭矩并输出到外部负载。The motion of the rotor may now be understood in terms of the notation of Figure 7.5. The line labeled e rotates with the shaft and eccentric through an angle 3, while the line labeled R is fixed to the rotor and turns with it through an angle about the moving eccentric center. Thus the entire engine motion is related to the motion of these two lines. Clearly, the rotor (and thus line R) rotates at one-third of the speed of the shaft, and there are three shaft rotations for each rotor revolution.转子的运动如图7.5所示。标为e的线段和偏心轮绕主轴旋转角度3，同时转子上标为R的线段将绕偏心轮中心旋转角度。整个发动机的运动与这两条线的运动密切相关。很明显，转子（即线段R）转速为主轴转速的三分之一，转子旋转一周主轴将旋转三周。EXAMPLE 7.1Derive expressions for the major (largest) and minor (smallest) diameters of an epitrochoid in terms the notation of Figure 7.5.SolutionThe major diameter is defined by adding the lengths of the lines representing the eccentricity and the rotor radius when they are horizontal and colinear or by using Equation 7.1(a). Thus the major diameter at y = 0 corresponds to = 0 and 180, for which x = e + R and x = e R, respectively. The distance between these x coordinates is the length of the major diameter 2(e + R).The minor diameter is similarly defined along x = 0, but with e and R lines oppositely directed. The two cases correspond to = 90 and 270. For = 90, the e line is directed downward and the R line upward in Figure 7.5. This yields y = R - e and, by symmetry, the minor diameter is 2(R - e). HenceMajor diameter = 2(R + e)Minor diameter = 2(R - e)例7.1用图7.5中符号列出最大和最小直径的摆线表达式。解：最大直径定义为当偏心距与转子半径水平共线时偏心距与转子半径之和的2倍。也可通过方程7.1（a）推导出来。即，当y = 0， = 0或180时，x = e + R或x = e R。这两个x值之间的距离2(e + R)就是摆线的最大半径。当x=0时，摆线有最小半径，此时e和R共线但方向相反。这两点处取值为90 and 270。当=90时，e的方向向下，R方向向上，如图7.5所示。此时，y=R-e。最小半径等于2（R-e）。因此：最大半径= 2(R + e)最小半径= 2(R - e)4 A Simple Model for a Rotary Engine 转子发动机简单模型Additional important features of the rotary engine can be easily studied by considering an engine with an equilateral triangular rotor. Figure 7.6 shows the rotor in the position where a rotor flank defines the minimum volume. We will call this position top center, TC, by analogy to the reciprocating engine. The rotor housing clearance parameter, d, is the difference between the housing minor radius, R - e, and the distance from the housing axis to mid-flank, e + R cos 60 = e + R/2:转子发动机的其他性能可以按等边三角形转子来考虑。图7.6中转子位于最小容积点。类比往复式发动机，我们称此点位TC点（top center）。转子室间隙参数d为壳体内壁最小半径（R-e）与主轴中心到转子边中之间的距离(e + R cos 60 = e + R/2):d = (R - e) - (e + R/2) = R/2 - 2eft | m (7.3)Setting the clearance to zero establishes an upper limiting value for the eccentricity ratio: (e/R)crit = 1/4. Study of Equations (7.1), at the other extreme, shows that, for e/R = 0, the epitrochoid degenerates to a circle. In this case the rotor would spin with no eccentricity and thus produce no compression and no torque. Thus, for the flat-flanked rotor, it is clear that usable values of e/R lie between 0 and 0.25.当设间隙d为0时可得到偏心率的上限值，即(e/R)crit = 1/4。根据式7.1，在另一种极端情况下，及e/R = 0时，摆线退化为圆。这种情况下，转子将在无偏心的状态下旋转而不产生扭矩。因此，对于直边转子，偏心率e/R的范围为0到0.25。Now lets examine some other fundamental parameters of the flat-flanked engine model. Consider the maximum mixture volume shown in Figure 7.7. For a given rotor width w, the maximum volume can be determined by calculating the area between the housing and the flank of the rotor. Using Equations (7.1), the differential area 2y dx can be written as:我们再来研究直边转子发动机的其他基本参数。对于图7.7中所示的最大混合气体体积，对于给定的转子宽度w，最大混合气体积由壳体和转子边所围成的面积决定。由等式7.1，其微分面积2y dx可写为：dAmax = 2y dx= 2(e sin3 + R sin) d(e cos3 + R cos) ft2 | m2 (7.4)Dividing by R2 and differentiating on the right-hand side, we obtain an equation for the dimensionless area in terms of the eccentricity ratio and the angle :两边除以R2并对等式右侧积分，我们得到关于偏心率和角度的积分面积：AmaxR2=-2060eRsin3+sin3eRsin3+sind dl (7.5)In order for the differential area to sweep over the maximum trapped volume in Figure 7.7, the limits on the angle must vary from 0 to 60. Thus integration of Equation (7.5) with these limits and using standard integrals yields要得到最大面积积分，角度的积分范围为0 到 60，此时等式7.5的积分结果为：Amax/R2 = (e/R)2 + 1/3 - 31/2/41 - 6(e/R) dl (7.6)Similarly, using Figure 7.6 and the differential volume shown there, the nondimension-alized minimum area can be written as:同理，图7.6中所示无量纲化的最小面积为：Amin/R2 = (e/R)2 + 1/3 - 31/2/4 1 + 6(e/R)dl(7.7)These maximum and minimum volumes (area-rotor width products) are analogous to the volumes trapped between the piston and cylinder at BC and TC in the four-stroke reciprocating engine. In that engine the difference between the volumes at BC and TC is the displacement volume, and their ratio is the compression ratio. A little thought should convince the reader that the analogy holds quantitatively for the displacement and compression ratio of the rotary engine. Therefore, subtracting Equation (7.7) from Equation (7.6) gives the displacement for a rotor width w for one flank of the flat-flanked engine as这些最大和最下容积（与转子宽度产生）类似于往复式四冲程发动机的活塞与汽缸之间的容积BC及TC点。在活塞式发动机中BC与TC的差值就是发动机排量，他们之间的比及压缩比。读者应当考虑用类似的方法度量转子发动机的排量和压缩比。将式7.6减去式7.7就得到了转子宽度为w的直边转子发动机排量计算式：disp = 331/2 wR2(e/R) ft3 | m3 (7.8)and forming their ratio yields the compression ratio as转子发动机的压缩比如下：CR=AmaxR2AminR2=eR2+1/3-31/241-6eReR2+1/3-31/241+6eRdl(7.9)Thus the displacement increases with increases in rotor width, the square of the rotor radius, and with the eccentricity ratio, whereas the compression ratio is independent of size but increases with increase in eccentricity ratio.可以看出，发动机排量与转子宽度、转子半径的平方和偏心率成正比，而压比与转子尺寸无关仅和偏心率有关。EXAMPLE 7.2What are the displacement and the compression ratio for a flat-flanked rotary engine with a rotor radius of 10 cm, an eccentricity of 1.5 cm, and a rotor width of 2.5 cm?SolutionFor this engine, e/R = 1.5/10 = 0.15. Equation (7.8) then yields the displacement:3(3)0.5(0.15)(10)2(2.5) = 194.9 cm3 or (194.9)(0.0610) = 11.89 in.3Equation (7.9) can be written asCR = (a + b)/(a . b)where a = (3.14159)(0.15)2 + 1/3 . 31/2/4 = 0.6849, and b = 3_ 31/2(0.15)/2 = 0.3897.ThenCR = (0.6849 + 0.3897)/(0.6849 - 0.3897) = 3.64例 7.2求转子半径10cm，偏心距1.5cm，转子宽度2.5cm的转子发动机的排量和压缩比。解：The very low compression ratio of Example 7.2 would yield a poor Otto-cycle thermal efficiency. The compression ratio could be increased by increasing e/R, but it would still be low for most applications. It is therefore important to consider the favorable influence of flank rounding on rotary engine performance.例7.2中的低压缩比将导致低的奥图循环热效率。通过增大e/R可以增加压缩比，但这仍低于常见的压比。因此，转子圆边对于转子发动机的性能非常重要。5 The Circular-Arc-Flank Model 圆边转子模型While the triangular rotor model represents a possible engine and is useful as a learning tool, such an engine would perform poorly compared with one having a rotor with rounded flanks. A more realistic model is one in which the triangular rotor is augmented with circular-arc flanks, as shown in Figure 7.8. The radius of curvature, r, of a flank could vary from infinity, corresponding to a flat flank, to a value for which the arc touches the minor axis of the epitrochoid. Note that the center of curvature of an arc terminated by two flank apexes depends on the value of r. It can also be seen from Figure 7.8 that r is related to the angle, , subtended by the flank arc by虽然等边三角形转子发动机是一个很好的学习模型，但相比圆边转子发动机，其性能极低。拥有圆弧边的发动机转子是一种更具使用价值的发动机模型，如图7.8所示。转子边的圆弧半径r，可以从无穷大（对应直边转子）到一个特定的值使圆弧达到摆线最小直径点。需要注意，当圆弧的两个顶点已经确定时，圆弧的中点由半径r确定。由图7.8可以看出r的值又于圆弧所对圆心角相关，r sin(/2) = R sin( /3) = 31/2R/2ft | mor或r/R = 31/2/2sin(/2) dl (7.10)Thus either the included angle, , or the radius of curvature, r, may be used to define the degree of flank rounding for a given rotor radius R.式中既含有角度，也好有圆弧半径r，可以用此式来定义给定转子半径R多对应的转子边所对角度。Clearance with Flank RoundingThe additiona