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THE WANKEL ROTARY ENGINE

1 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 contin

ue 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). 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. 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. 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.

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） 。 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。

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。 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。

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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. 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). 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

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。

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。 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

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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. 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.

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。 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。

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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 x = e cos 3α + R cos α y = e sin 3α + R sin α

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：

[ft | m] [ft | m]

(7.1a) (7.1b)

where e is the eccentricity and R is the rotor center-to-tip distance. 式中 e 为偏心率，R 为转子中心到顶 For given values of e and R, Equations (7.1) give the x and y 点的距离。通过方程 7.1，给定 e 和 R 的 coordinates defining the housing shape when α is varied from 0 to 值后，当 α 从 0°变到 360°，可以得到 360 degrees. 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): x = e cos 3α + R cos(α + 2nπ/3) y = e sin 3α + R sin(α + 2nπ) 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.

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：

[ft | m] [ft | m]

(7.2a) (7.2b)

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 需要注意的是方程 7.1 和 7.2 都是无 by dividing through by R. This yields a single geometric parameter 量纲的，并与由 R 划分。这就是方程由一 governing the equations, e/R, known as the eccentricity ratio. It will 个参数 e/R 控制，即偏心率。这个参数的

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be seen that this parameter is critical to successful performance of 选取对转子发动机的性能有重要影响。 the rotary engine. 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. 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 3α, while the line labeled R is fixed to the rotor and turns with it through an angle α 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.

EXAMPLE 7.1

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。 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 3α，同时 转子上标为 R 的线段将绕偏心轮中心旋 转角度 α。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。 例 7.1

Derive expressions for the major (largest) and minor (smallest) 用图 7.5 中符号列出最大和最小直径的摆 diameters of an epitrochoid in terms the notation of Figure 7.5. 线表达式。

Solution

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， α = 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。

The 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 α = 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 当 x=0 时，摆线有最小半径，此时 e and R lines oppositely directed. The two cases correspond to α = 和 R 共线但方向相反。 这两点处 α 取值为 90°and 270° . For α = 90° , the e line is directed downward and the 90°and 270° 。 当 α=90° 时， e 的方向向下， R line upward in Figure 7.5. This yields y = R - e and, by R 方向向上， 如图 7.5 所示。 此时， y=R-e。 symmetry, the minor diameter is 2(R - e). Hence

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)

Major diameter = 2(R + e) Minor diameter = 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: d = (R - e) - (e + R/2) = R/2 - 2e

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):

[ft | m]

(7.3)

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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. Now let’s 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: dAmax = 2y dx= 2(e sin3α + R sinα) d(e cos3α + R cosα)

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。 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：

[ft2 | m2]

(7.4)

Dividing by R2 and differentiating on the right-hand side, we 两边除以 R2 并对等式右侧积分，我 obtain an equation for the dimensionless area in terms of the 们得到关于偏心率和角度 α 的积分面积： eccentricity ratio and the angle α: 2 = ?2

60 0

3 + 3 3 +

[dl]

(7.5)

In order for the differential area to sweep over the maximum 要得到最大面积积分， 角度 α 的积分 trapped volume in Figure 7.7, the limits on the angle α must vary 范围为 0° 到 60° ，此时等式 7.5 的积分

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from 0°to 60° . Thus integration of Equation (7.5) with these limits 结果为： and using standard integrals yields Amax/R2 =π [(e/R)2 + 1/3] - 31/2/4[1 - 6(e/R)] [dl] (7.6)

Similarly, using Figure 7.6 and the differential volume shown there, 同理，图 7.6 中所示无量纲化的最小面积 the nondimension-alized minimum area can be written as: 为： Amin/R2 =π [(e/R)2 + 1/3] - 31/2/4 [1 + 6(e/R)] 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 disp = 3·31/2 wR2(e/R) and forming their ratio yields the compression ratio as

CR =

max 2 min 2

[dl]

(7.7)

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：

[ft3 | m3]

(7.8)

转子发动机的压缩比如下：

=

2 +1/3 ?3 1/2 4 1 ?6 2 +1/3 ?3 1/2 4 1+6

[dl]

(7.9)

Thus the displacement increases with increases in rotor width, 可以看出，发动机排量与转子宽度、 the square of the rotor radius, and with the eccentricity ratio, 转子半径的平方和偏心率成正比， 而压比 whereas the compression ratio is independent of size but increases 与转子尺寸无关仅和偏心率有关。 with increase in eccentricity ratio.

EXAMPLE 7.2

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：

What 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?

Solution

For 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.3 Equation (7.9) can be written as CR = (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. Then CR = (0.6849 + 0.3897)/(0.6849 - 0.3897) = 3.64 The very low compression ratio of Example 7.2 would yield a 例 7.2 中的低压缩比将导致低的奥图 poor Otto-cycle thermal efficiency. The compression ratio could be 循环热效率。通过增大 e/R 可以增加压缩 increased by increasing e/R, but it would still be low for most 比，但这仍低于常见的压比。因此，转子 applications. It is therefore important to consider the favorable 圆边对于转子发动机的性能非常重要。 influence of flank rounding on rotary engine performance.

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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, θ, subtended by the flank arc by r sin(θ/2) = R sin(π /3) = 31/2R/2 or r/R = 31/2/[2sin(θ/2)] Thus either the included angle, θ, or the radius of curvature, r, may be used to define the degree of flank rounding for a given rotor radius R.

或 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θ 相关，

[ft | m]

[dl]

(7.10)

式中既含有角度θ ， 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 Rounding

圆边转子间隙

The additional area obtained by capping a side of a triangle with a 由三角形一边和通过这个边两端点 circular arc is called a segment. The segment height, h, shown in 的圆弧所围成的部分成为弦。 如图 7.8 示， Figure 7.8, is the difference between r and the projection of r on the 弦的高度 h 是 r 和 r 在对称轴上投影的差： axis of symmetry: h/R = (r/R)[1 - cos(θ /2)] Substitution of Equation (7.10) in Equation (7.11) yields h/R = 31/2 [1 - cos(θ /2)] / [2sin(θ /2)] [dl] (7.11)

将式 7.10 带入式 7.11 得：

[dl]

(7.12)

10 / 17

It is evident from the figure that the clearance for the rotor with 很明显， 圆弧边转子的间隙为平边转 circular arc flanks is the difference between the clearance of the 子间隙和 h 的差。因此，利用时 7.3，可 flat-flanked rotor and h. Thus, using Equation (7.3), the clearance is 得到： given by d/R = 1/2 - 2(e/R) - 31/2 [1 - cos(θ /2)] / [2sin(θ /2)] In a real engine, of course, the clearance must be non-negative.

值。

[dl]

(7.13)

在实际发动机中，此间隙不能为负 圆边转子相对直边转子增加的体积 弦的面积等于 θ 角范围内所包含的 扇形的面积减去其中包含的三角形面积。 扇形部分面积， 或者说每个转子单元的宽 度，是一个半径为 r 的圆的一部分，对应 圆心角为θ ，也就是：πr2 (θ/2π ) = r2θ/2。 如此利用式 7.10 ，无量纲的弦部分体积 为：

Added Volume per Flank Due to Rounding The segment area is the difference between the pie-shaped area of the sector subtended by its included angle, θ, and the enclosed triangular area. The sector area, or volume per unit rotor width, is the fraction of the area of a circle of radius, r, subtended by the angle θ; i.e., π r2 (θ/2π ) = r2θ/2. Thus using Equation (7.10), the dimensionless segment volume is

As /R2 = (Asec - Atri ) /R2 = (r/R)2(θ -sinθ) /2= (3/8)( θ-sinθ) /sin2θ/2 Displacement and Compression Ratio It was pointed out earlier that the displacement of the flat-flanked engine is the difference between the maximum and minimum capture volumes, and is given by Equation (7.8). This is true also for the engine with rounded flanks. The additional volume added to the rotor by flank rounding subtracts from both of the flat-flanked maximum and minimum capture volumes, leaving the difference unchanged. Thus the displacement of one flank of a rounded-flank engine is disp = 3·31/2 wR2 (e/R)

[dl]

(7.14)

排量及压比 前面已经指出， 平边转子发动机的排 量是最大容积和最小容积只差， 见式 7.8。 圆边转子发动机也是如此。 圆边转子所增 加的体积同时减小了平边转子发放机中 的最大和最小容积，见减小的量相同。因 此圆边转子发动机的排量如下：

[ft3 | m3]

(7.15)

Likewise, the ratio of the maximum and minimum capture 类似的，由式 7.6 和 7.7 中最大容积 volumes given by Equations (7.6) and (7.7), corrected for the 与最小容积分别减去弦部分体积修正后 segment volume from Equation (7.14) provides a relation for the 得到后的比率为圆边转子发动及的压缩 rounded-flank engine compression ratio: 比：

CR =

2 +1/3 ?3 1 2 4 1 ?6 ? 2 2 +1/3 ?3 1 2 4 1+6 ? 2

[dl]

(7.16)

The added rotor volume due to rounding subtracts from the flat-flanked capture volumes and therefore reduces the denominator of Equation (7.16) more than the numerator. As a result, the compression ratio is greater for rounded-flank than for flatflanked engines. Rotary engines usually have the maximum rounding possible consistent with adequate engineering clearances.

Effect of the Recess Volume

圆边转子中增加的体积导致其容积 相对直边转子减小，其导致式 7.16 中分 母的减小程度大于分子减小程度。因此， 圆边转子发动机的压缩比大于直边转子 发动机。 转子发动机通常在间隙允许的条 件下选用最大的圆边。 凹面效应 式 7.16 中并没有计算在转子发动机 中常见的凹陷部分容积。如图 7.9 所示， 凹陷部分会增加容积。 其对发动机排量和 压缩比的影响类似于转子弦体积的影响。 凹面同时同量地增大了最大和最小容积。 因此对发动机排量无影响， 但会减小发动

Equation (7.16) accounts for flank rounding but not for the recess usually found in rotor flanks. The additional capture volume associated with the recess is seen in Figure 7.9. Its influence on the displacement and compression ratio may be reasoned in the same way as with the segment volume. The recess increases both minimum and maximum mixture volumes by the same amount. It therefore has no effect on displacement and it decreases the

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compression ratio.

机的压缩比。

Figure 7.10 shows the influence of flank rounding and recession on clearance and compression ratio. While flank recession reduces the compression ratio for given values of θ and e/R, it improves the shape of the long, narrow combustion pocket forming the minimum capture volume. Rotary engines usually have more than one spark plug, to help overcome the combustion problems associated with this elongated shape.

EXAMPLE 7.3

图 7.10 所示为转子圆边和凹面对发 动机间隙率和压缩比的影响图。 虽然转子 边的凹面见笑了发动机的压缩比， 但是它 可以改善狭长的燃烧室形状构成最小容 积的一部分。 转子发动机通常有不止一个 火花塞， 从来帮助克服狭长燃烧室的燃烧 问题。

Rework Example 7.2, taking into account a flank-arc included angle of 0.65 radians. What is the flank clearance for this engine?

Solution

Because flank rounding does not influence it, the displacement is still 194.9 cm3. Equation (7.16) rewritten using the notation of Example 7.2 becomes

12 / 17

CR = (a + b . As /R2) / (a . b . As /R2) where As /R2 = (3/8)[0.65 . sin(0.65)]/sin2(0.65/2) = 0.1648. Then the compression ratio is CR = [0.6849 + 0.3897 . 0.1648] / [0.6849 . 0.3897 . 0.1648] = 6.98 This represents a significant improvement over the value of 3.64 for the flat-flanked rotor. The flank clearance is given by Equation (7.13): d = 10{0.5 . 2(0.15) . 31/2[1 . cos(0.65/2)]} / [2sin(0.65/2)] = 0.58 cm. We have already noted that the displacement volume associated with one flank of the rotary engine produces one power stroke during each rotor revolution and during three shaft rotations. Because there are three flanks per rotor, a rotor executes one complete thermodynamic cycle per shaft rotation. Thus the power produced by a single rotor is determined by the displacement volume of a single flank and the rotational speed:

= or =

disp in 3 /Rev 12 in /ft MEP 1b/cm 2 N Rev /min 33,000 ft ?1b/HP ?min disp cm 3 /Rev MEP kN /cm 2 N Rev /min 60 sec /min 100 cm /m

我们已经研究了转子发动机的一个 边在转子旋转一周、周周旋转三周，完成 一个做工循环的过程。 因为转子发动机有 三个边， 主轴没旋转一周就有一个完整的 热力循环。因此，单转子发动机所产生的 功率取决于单个边的排量和发动机转速。

[kW]

或

[HP]

6 Design and Performance of the Wankel Engine

Wankel 发动机的设计与性能

由图 7.4 可以看出， Wankel 发动机中 的进排气的开关是通过转子旋转时顶点 的的运动来实现的， 类似于往复式发动机 的机械阀。Wankel 发动机中的这种简单 方式不再需要往复式发动机中大量的运 动件，例如凸轮、凸轮轴、挺杆、气门及 推杆。事实上，往复式发动机相比转子发 动机拥有更多的零部件。 然而， 顶点密封和转子边密封对于转 子发动机的高效率运行至关重要。 转子发 动机中三个处于不同奥图循环阶段的空 间中具有显著的压力差， 这就要求拥有类 似于往复式发动机活塞环的高效密封， 以 防止相邻空间之间因泄露而造成的压力 及功率损失。据估算，密封摩擦占转子发 动机总摩擦的 25%。弹簧承载、自润滑的 菱封结构见图 7.11， 该结构可以在壳体经 镀铬处理的合金内表面低摩擦滑动。

It is evident from Figure 7.4 that, in the Wankel engine, the opening and closing of the intake and exhaust ports by the motion of the rotor apexes serves a function equivalent to that of mechanical valves in reciprocating engines. This simple operation in the Wankel engine eliminates the need for many of the moving parts required by the reciprocating engine, such as cams, camshafts, tappets, valves, and lifters. There are, in fact, many more parts in a reciprocating engine than in a comparable rotary engine. However, sealing at the apexes and sides of the rotor is critical for efficient operation of the rotary engine. Significant pressure differences between the three active mixture volumes of a rotor in different phases of the Otto cycle require efficient seals analogous to piston rings in the reciprocating engine. These are needed to avoid leakage between adjacent volumes, which causes a loss of compression and power. Seal friction has been estimated to account for about 25% of rotary engine friction. Spring loaded, self-lubricating apex seals, as shown in Figure 7.11, allow for sliding with low friction over the treated-chrome-alloy-plated housing inner surface.

13 / 17

The figure shows improvements in apex seal design (ref. 6). The three-piece seal design, with two leaf springs rather than one, decreases seal mass through reduced thickness, and offers a configuration that promotes area contact rather than line contact between seal and rotor. Side seals are also important to maintain pressure integrity of each flank mixture pocket. Reductions in the thickness of both apex and side seals have decreased friction with the housing by reducing the seal area producing the friction-causing normal force on the housing. Oil seals, also on the rotor sides, are used to control oil consumption. Though the peripheral intake port shown in Figures 7.4 and 7.9 provides better performance under heavy loads than a single side port, its associated intake-exhaust port overlap may allow excessive flow of exhaust gas into the fresh mixture, causing unreliable combustion in low-speed operation. Consequently, one or more side intake ports, in addition to or instead of a peripheral

上图所示为改进后的菱封结构 （参考 文献 6） 。该结构采用三片式密封设计， 采用双簧片取代单簧片， 通过减少厚度减 少密封材料的使用， 通过楔形面结构实现 密封片与转子的面接触， 取代原有结构的 线接触。 边封对保持每个转子边的混合器 压力也很重要。 通过减少菱封和边封的厚 度可以减少摩擦面积从而减少密封和壳 体的摩擦。转子的侧边还有油封，用以控 制润滑油的消耗。 虽然图 7.4 和 7.9 中所示的周边进气 口提供了在重载下优于单进气口的性能， 但这回使进排气的重叠从而使废气混入 新鲜气体中，导致低转速下燃烧不可靠。 因此，通常使用用一个或多个侧面进气 口，增强或替代周边进气口。当然，侧面

14 / 17

intake port, are sometimes used. Side ports, of course, are also opened and closed by rotor motion. In addition to reducing intake-exhaust overlap at light loads, side intake ports also induce combustion-enhancing swirl in the air-fuel mixture. It is evident that the moving combustion volume at the time of ignition has a long and narrow flame propagation path. Rounded rotor flanks are usually recessed to provide a wider flame front path between the two lobes of the active volume. In highspeed operation, the brief time for combustion may dictate additional design features. Multiple spark plugs, swirl induced by side intake ports and multiple ports, the "squish" produced by the the relative motion of the walls of the active volume, fuel injection, and stratified-charge design all can contribute to improvement of the combustion process. It may be noted in Figures 7.3 and 7.9 that an internal ring gear is attached to the rotor. This gear meshes with a stationary gear attached to the engine housing. The function of this gearset is to position the rotor as the shaft turns--not to transmit torque. Engine torque, as indicated earlier, is transmitted by direct contact of surface forces between the rotor and the eccentric. Stratified-Charge Rotary Engine Reference 7 discusses the design and performance of stratified-charge rotary engines developed for commercial aviation propulsion and APU (auxiliary power unit) application as well as for marine, industrial, and military requirements. Figure 7.12 shows a direct fuel injection configuration that has performed well under a wide range of speed, load, and environmental conditions and with a variety of liquid fuels. The reference reports a lack of octane and cetane sensitivities, so that diesel, gasoline, and jet fuel can all be used with this configuration. As air in the rotor recess passes below, the spark plug ignites a locally rich pilot stream that in turn ignites the fuel from the main injector. The net fuel-air ratio is lean, resulting in improved fuel economy over normal carburetion. Figure 7.13 presents data for full-load brake horsepower and specific fuel consumption obtained with Jet-A fuel for the twin-rotor 2034R engine. The maximum takeoff power at 5800 rpm was 430 horsepower, with a brake specific fuel consumption (BSFC) of 0.44 lbm/BHP-hr. Throughout a range of loads and altitude conditions the engine operates with a fuel-air ratio between 0.035 and 0.037, well below the stoichiometric value. The reference reports a best thermal efficiency of 35.8% (BSFC = 0.387 lbm/BHP-hr) at 3500 rpm and 225-horsepower output.

进气口也是由转子的转动来实现开闭。 这 样可以减少轻载下进排气的混合， 侧面进 气同时可以在油气混合中产生有利于燃 烧的涡流。 很明显， 点火时运动中的燃烧室的火 焰传播路径狭长。 圆边转子通常通过凹坑 来提供一个更宽的沟通两侧空间的火焰 通道。在高速运转时，短时间燃烧可能要 求额外的设计特点。多火花塞、侧面进气 口诱导涡流及多进气口、 活动空间与壁的 相对运动产生的挤压效应、燃油喷射、分 层进气设计等都可以改善燃烧进程。

通过图 7.3 和 7.9 你可能注意到，转 子上有一个环齿， 这个齿轮与安装在发动 机机壳上的固定齿轮相啮合。 这对齿轮用 于在主轴旋转时定位转子， 而不是传递扭 矩。正如之前所说，发动机扭矩，有转子 和偏心轮之间传递。 分层进气转子发动机 参考文献 7 中讨论了用于商用航空 推进、APU 及海运、工业应用及军用领 域的分层进气转子发动机。图 7.12 所示 为燃油直喷式转子发动机， 该发动机转速 和功率范围大， 对环境友好并适用于多种 燃料。该报告提出对辛烷和十六烷不敏 感，所以柴油、汽油及航空煤油都可以用 于此结构形式的发动机。 通过转子上凹槽里的气体， 火花塞点 燃预点火喷嘴燃油再有先导燃油点燃主 喷油嘴喷出的燃油。 其油气混合比是贫油 的，从而得到由于常规燃烧的燃油经济 性。图 7.13 所示为 2034R 双转子发动机 在燃用 Jet-A 汗孔没有下的全功率燃油消 耗。其最大起飞功率为 5800 转 430hp， 制 动 燃 油 消 耗 （ 比 油 耗 ） 为 0.44 lbm/BHP-hr。 在功率和海拔变化范围内其 油气比介于 0.035 和 0.037 之间，低于化 学当量值。 该文献值指出在 3500 转 225hp 输出下的热效率高 达 35.8% （ BSFC = 0.387 lbm/BHP-hr） 。

15 / 17

Closure Continued engineering research on the rotary engine has resulted in performance improvements through improved seals, lean-burn combustion, fuel injection, integral electronic control, improved intake design, weight reduction, and turbocharging. Despite vehicle weight increases, the Mazda RX-7 with a two-rotor 80-in3 –displacement engine improved 9.4% in fuel consumption and 8%

结语 持续不断的转子发动机研究不断地 提升其性能，这些研究包括改善密封、贫 油燃烧、燃油喷射、整体电控、进气设计 改进、 减重及涡轮增压。 在 1984 年到 1987 年之间，尽管汽车的重量增加了，Mazda RX-7 中所使用的 80 in3 排量的双转子发

16 / 17

in power output between 1984 and 1987 (ref. 6). During this time 动机燃油消耗减少 9.4%，同时功率输出 period, the addition to the engine of a turbocharger with 增加 8%（参考文献 6） 。这段时间内，中 intercooling increased its power output by 35%. 冷涡轮增压器的使用使其功率输出增大

35%。

Reference 8 reports that the Mazda RX-Evolv, a year-2000 concept car, has a naturally-aspirated rotary engine called .RENESIS.. The two-rotor, side intake and exhaust engine is reported to have reduced emissions and improved fuel economy and to have attained 280 horsepower at 9000 rpm and 226 N-m torque at 8000 rpm.

EXAMPLE 7.4

参考文献 8 提出，Mazda 在 2000 年 发布的概念车 RX-Evolv 搭载一台自然吸 气式转子发动机 RENESIS。据报道，这 款双转子发动机采用侧面进排气， 在降低 排放的同时改善了燃油经济性，达到 9000rpm 下 280hp 输 出 ， 8000rpm 下 226N·m 的扭矩。

If the BMEP of the 11.89-in3-diplacement engine in Example 7.2 is 150 psi at 4000 rpm, what is the brake horsepower?

Solution The brake horsepower is BHP = (150)(4000)(11.89)/(12)(33000) = 18 horsepower or BHP = (18)(0.746) =13.44kW

Bibliography and References 参考文献 1. Cole, David E. "The Wankel Engine," Scientific American, Vol. 227, No. 2, (August 1972): 14.23. 2. Ansdale, R. F., The Wankel R C Engine. South Brunswick, N.J.: A. S. Barnes, 1969. 3. Yamamoto, Kenichi, Rotary Engine, Tokyo: Sankaido Co., 1981. 4. Weston, Kenneth C. "Computer Simulation of a Wankel Rotary Engine.Analysis and Graphics." Proceedings of the Conference of the Society for Computer Simulation, July 1986, pp. 213-216. 5. Weston, Kenneth C., "Computerized Instruction in the Design of the Wankel Rotary Engine." ASEE Annual Conference Proceedings, June 1988. 279 6. Fujimoto, Y. et al., "Present and Prospective Technologies of Rotary Engine." Society of Automotive Engineers Paper 870446, 1987. 7. Mount, Robert E., and LaBouff, Gary A., .Advanced Stratified-Charge Rotary Engine Design.. Society of Automotive Engineers Paper 890324 (also in SAE SP-768, Rotary Engine Design; Analysis and Developments), 1989. 8. Jost, Kevin, (ed.), .Global Concepts.Mazda RX.Evolv,. Automotive Engineering International, Vol 8, No.8, (August 2000), p 59.

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