CN100419216C - 透平叶片的翼面形状 - Google Patents

透平叶片的翼面形状 Download PDF

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CN100419216C
CN100419216C CNB2004100899767A CN200410089976A CN100419216C CN 100419216 C CN100419216 C CN 100419216C CN B2004100899767 A CNB2004100899767 A CN B2004100899767A CN 200410089976 A CN200410089976 A CN 200410089976A CN 100419216 C CN100419216 C CN 100419216C
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airfoil
blade
aerofoil
value
inch
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CN1661199A (zh
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T·B·贝达
D·S·佩塞特斯基
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General Electric Co
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
    • F01D5/00—Blades; Blade-carrying members; Heating, heat-insulating, cooling or antivibration means on the blades or the members
    • F01D5/12—Blades
    • F01D5/14—Form or construction
    • F01D5/141—Shape, i.e. outer, aerodynamic form
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2240/00—Components
    • F05D2240/20—Rotors
    • F05D2240/30—Characteristics of rotor blades, i.e. of any element transforming dynamic fluid energy to or from rotational energy and being attached to a rotor
    • F05D2240/301—Cross-sectional characteristics
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2250/00—Geometry
    • F05D2250/50—Inlet or outlet
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10S416/00—Fluid reaction surfaces, i.e. impellers
    • Y10S416/02—Formulas of curves
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10S416/00—Fluid reaction surfaces, i.e. impellers
    • Y10S416/05—Variable camber or chord length

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Abstract

第二级透平叶片(20)具有与表I中列出的X、Y和Z笛卡儿坐标值基本上一致的翼面轮廓(36)，其中X和Y值以英寸为单位，Z值是从0.05到0.95的无量纲值，通将Z值乘以以英寸为单位的翼面高度可以将Z值换算成以英寸为单位的Z长度。X和Y值是长度，当将其用平滑连续的弧连结时，在每个长度Z处形成翼面轮廓截面(38)。将在每个长度Z处的轮廓截面彼此平滑地连结，则形成整个翼面形状。X和Y长度可以作为相同常数或数值的函数按比例变化，从而提供用于叶片的按比例扩大或缩小的翼面截面。由X、Y和Z长度给出的标称翼面处于一个在垂直于翼面表面的方向上±0.160英寸的包络中。

Description

透平叶片的翼面形状
技术领域
本发明涉及燃气透平一个级的叶片的翼面，尤其涉及第二级透平叶片翼面轮廓。
背景技术
为了达到包括总体提高的效率和翼面负荷在内的设计目标，对于燃气透平的热燃气通道部分的每一级来说，必须满足许多系统要求。详细地说，第二级透平叶片部件必须满足该特定级的热的和机械的运转要求。
发明内容
根据本发明的优选实施方式，提供一种用于燃气透平叶片的特殊翼面形状，特别是第二级叶片的翼面形状，该翼面形状提高了燃气透平的性能。此处的翼面形状还提高了透平的各个级之间的交互作用，并在降低第二级翼面热应力和机械应力的同时，提供提高的空气动力学效率。
叶片翼面轮廓由多个点的一种特殊分布确定，以达到必要的效率和负载要求，借此提高透平性能。点的这种特殊分布形成了标称翼面轮廓，并由下面表I中的X、Y和Z笛卡儿坐标确定。在表I中示出的笛卡儿坐标值的1100个点与透平中心线有关，且是在低温(即室温)下在沿着叶片翼面的长度方向的各横截面处取得的。正的X、Y和Z的方向分别为轴向朝向透平排气端的方向、发动机旋转方向的切线方向和径向向外朝向叶片顶端的方向。X和Y的坐标以长度单位给出，例如以英寸为单位，并在每个Z值处将其平滑地连接起来，从而形成一个平滑、连续的翼面横截面。Z坐标以无量纲形式在5％到95％范围内给出，从而将平台和顶罩上的倒角区域排除在外。通过使翼面高度尺寸(例如以英寸为单位)乘以表I中的无量纲Z值，就可以获得叶片翼面的翼面形状，即轮廓。将在每个X和Y平面中形成的翼面截面与Z方向上相邻的翼面截面连结起来，则形成整个翼面形状。
应该理解，当每个叶片翼面在应用中升温时，由于机械负载和温度的原因轮廓会发生变形。因此，由X、Y和Z坐标给出的低温或室温轮廓是用于制造的目的。由于制造的叶片翼面轮廓可能与下面表中给出的标称翼面轮廓不同，所以在垂直于沿着标称轮廓任何表面位置的方向上，将标称轮廓加上或减去0.406cm(0.160英寸)的长度，则确定用于这种叶片翼面的轮廓包络，其中加上或减去0.406cm(0.160英寸)的长度包括任何涂层工艺。该翼面的形状对于这个变化足以承受，不会损害叶片的机械性能和空气动力学性能。
还应该理解，该翼面可以按几何比例扩大或缩小，从而用于引入相似的透平设计中。因此，下面给出的标称翼面轮廓的以英寸为单位的X和Y坐标可以是相同常数或数值的一个函数。也就是说，以英寸为单位的X和Y坐标值可以乘以或除以相同的常数或数值，以在保持翼面截面形状不变的同时，提供该叶片翼面轮廓按比例扩大或缩小的轮廓。
根据本发明的一种优选实施方式，提供一种透平叶片，该叶片包括具有一种翼面形状的叶片翼面，该翼面具有与表I中列出的X、Y和Z笛卡儿坐标值基本上一致的标称轮廓，其中Z值是从0.05到0.95的无量纲值，通过使Z值乘以以英寸为单位的翼面高度，Z值可以换算成以英寸为单位的Z长度，其中X和Y是以英寸为单位的长度，当由平滑连续的弧将X和Y值连结时，在每个长度Z处形成翼面轮廓截面，将在各Z长度处的轮廓截面彼此平滑地连结，则形成整个翼面形状。
在根据本发明的另一种优选实施方式中，提供一种透平叶片，该叶片包括一种叶片翼面，该翼面具有与表I中列出的X、Y和Z笛卡儿坐标值基本上一致的未涂层标称轮廓，其中Z值是从0.05到0.95的无量纲值，通过使Z值乘以以英寸为单位的翼面高度，Z值可以换算成以英寸为单位的Z长度，其中X和Y是以英寸为单位的长度，当由平滑连续的弧将X和Y值连结时，在每个长度Z处形成翼面轮廓截面，将在各Z长度处的轮廓截面彼此平滑地连结，则形成整个翼面形状，X和Y长度作为相同常数或数值的函数可以按比例变化，从而提供按比例扩大或缩小的翼面。
在根据本发明的另一种优选实施方式中，提供一种透平，该透平包括具有多个叶片的透平叶轮，每个叶片包括具有一种翼面形状的翼面，该翼面具有与表I中列出的X、Y和Z笛卡儿坐标值基本上一致的标称轮廓，其中Z值是从0.05到0.95的无量纲值，通过使Z值乘以以英寸为单位的翼面高度，Z值可以换算成以英寸为单位的Z长度，其中X和Y是以英寸为单位的长度，当由平滑连续的弧将X和Y值连结时，在每个长度Z处形成翼面轮廓截面，将在各Z长度处的轮廓截面彼此平滑地连结，则形成整个翼面形状。
在根据本发明的另一种优选实施方式中，提供一种透平，该透平包括具有多个叶片的透平叶轮，每个叶片包括一种叶片翼面，该翼面具有与表I中列出的X、Y和Z笛卡儿坐标值基本上一致的未涂层标称轮廓，其中Z值是从0.05到0.95的无量纲值，通过使Z值乘以以英寸为单位的翼面高度，Z值可以换算成以英寸为单位的Z长度，其中X和Y是以英寸为单位的长度，当由平滑连续的弧将X和Y值连结时，在每个长度Z处形成翼面轮廓截面，将在各Z长度处的轮廓截面彼此平滑地连结，则形成整个翼面形状，X和Y长度作为相同常数或数值的函数可以按比例变化，从而提供按比例扩大或缩小的叶片翼面。
附图说明
图1是穿过一种燃气透平的多个级的热气通道示意图，示出了根据本发明一种优选实施方式的第二级叶片翼面；
图2是根据本发明一种优选实施方式的叶片透视图，其中叶片翼面与它的平台和轴向入口楔形榫连接件一起示出；
图3和图4分别是从负压侧和压力侧在基本上圆周方向上看图2中叶片和与之相连的平台和楔形榫连接件的侧视图；和
图5是基本上从翼面的负压侧看叶片的透视图。
附图中的零件和标号对照表
热气通道      10
燃气透平      12
喷嘴          14，18，22
叶片          16，20，24
透平转子      17
叶轮          19，21，23
箭头          26
平台          30
翼面根部      31
叶根          32
叶片顶部      33
楔形榫    34
叶片翼面  36
轮廓截面  38
具体实施方式
参照附图，尤其是图1，示出了包括多个透平级的燃气透平12的热气通道，该通道总体上用10表示。图中示出了三个级。例如，第一级包括多个周向间隔开的喷嘴14和叶片16。喷嘴彼此沿周向间隔开并围绕转子轴线固定。当然，第一级叶片16通过一个叶轮19安装到透平转子17上。图中也示出了燃气透平12的第二级，包括多个周向间隔开的喷嘴18和多个安装到转子17上并周向间隔开的叶片20。图中也示出了第三级，包括多个周向间隔开的喷嘴22和通过叶轮23安装到转子17上的叶片24。应该理解，喷嘴和叶片位于透平的热气通道10中，穿过热气通道10的热气流的方向由箭头26指示。
应该理解，叶片，例如第二级的叶片20安装到叶轮21上形成转子17的一部分。每个叶片20配有一个平台30、一个叶根32和一个基本上轴向的入口楔形榫34，该楔形榫34用于和叶轮21上的形状互补搭配的楔形榫(未示出)相连接。还应该理解，每个叶片20都有一个如图2-5所示的叶片翼面36。因此，在从平台30中点处的翼面根部31到叶片顶部33间的任一横截面处，每个叶片20都有一个翼面轮廓截面38，该截面形状如图3中的翼面所示。
为了确定第二级叶片翼面36的翼面形状，空间中有一组独特的点的分布能够满足该级需求并且能够制造。这些点的这种独特分布满足了级效率、相对减少热应力和机械应力的需求。通过在能够使透平以高效、安全和平稳的方式运转的空气动力学负载和机械负载之间应用迭代法，可以获得这组点。确定叶片翼面轮廓的点的这种分布包括与透平转动轴线相关的1100个点。在下面表I中给出的X、Y和Z值的笛卡儿坐标系确定了叶片翼面沿着其长度方向在不同位置处的轮廓。虽然当数值作适当变换时也可以应用其它的长度单位，但是在表I中以英寸为单位列出X和Y坐标的坐标值，所述坐标值可按1英寸＝2.54厘米换算为公制单位的数值。在表I中从5％～95％范围内的Z值以无量纲形式列出。这些数值将平台和顶罩的倒角区域排除在外。要将Z值转换成Z的坐标值，例如以英寸为单位，那么需要将表中给出的无量纲Z值乘以以英寸为单位的叶片高度。笛卡儿坐标系具有正交关系的X、Y和Z坐标轴，并且X轴与透平转子中心线平行，即旋转轴线和正的X坐标值是轴向朝向尾部，也就是透平的排气端。正的Y坐标值在转子的旋转方向上切向向后延伸，正的Z坐标值径向向外朝向叶片顶部。
在垂直于X和Y平面的Z方向上，通过确定给定位置处的X和Y的坐标值，沿着翼面的长度方向在每个Z值处就可以确定叶片翼面的轮廓截面，例如，如图3所示的轮廓截面38。通过用光滑连续的弧将X和Y值连结，就可以固定每个长度Z处的每个轮廓截面38。通过光滑地连结彼此相邻的轮廓截面38以形成翼面轮廓，就可以确定介于长度Z之间的各表面位置的翼面轮廓。这些值描绘出在周围的非运行或非热条件下的翼面轮廓，并且用于未涂层的翼面。
表I的数值被产生并示出至小数点后四位，用于确定翼面轮廓。但是小数点后第四位并不重要且可以上下浮动。在实际的翼面轮廓中，必须考虑典型的制造公差以及涂层。因此，表I中给出的用于轮廓的值是用于标称的翼面。因此应当理解，±典型制造公差，即±包括任何涂层厚度在内的值被添加到下面表I给出的X和Y值中。因此，沿着翼面轮廓在垂直于任意一个表面位置的方向上，0.406cm(±0.160英寸)的长度确定了一个用于这种特殊的叶片翼面设计和透平的翼面轮廓包络，即确定了在标称低温或室温下在实际的翼面表面所测量的点和下面表中给出的相同温度下那些点的理想位置之间的波动范围。该叶片翼面的设计对于这个波动范围是足以承受的，不会损害它的机械性能和空气动力学性能。
下面表I中给出的坐标值提供了优选的标称轮廓包络。
表I
  X(5％)   Y(5％)   Z(5％)
  -2.1522   -0.5661   0.05
  -2.0268   -0.5826   0.05
  X(5％)   Y(5％)   Z(5％)
  -1.9086   -0.5264   0.05
  -1.7978   -0.4561   0.05
  -1.6874   -0.3851   0.05
  -1.5738   -0.3195   0.05
  -1.4570   -0.2598   0.05
  -1.3371   -0.2065   0.05
  -1.2141   -0.1608   0.05
  -1.0882   -0.1238   0.05
  -0.9600   -0.0959   0.05
  -0.8302   -0.0772   0.05
  -0.6993   -0.0677   0.05
  -0.5681   -0.0679   0.05
  -0.4373   -0.0779   0.05
  -0.3076   -0.0976   0.05
  -0.1796   -0.1264   0.05
  -0.0537   -0.1636   0.05
  0.0695   -0.2085   0.05
  0.1900   -0.2605   0.05
  X(5％)   Y(5％)   Z(5％)
  0.3076   -0.3188   0.05
  0.4221   -0.3828   0.05
  0.5336   -0.4520   0.05
  0.6422   -0.5257   0.05
  0.7478   -0.6035   0.05
  0.8508   -0.6849   0.05
  0.9511   -0.7695   0.05
  1.0491   -0.8567   0.05
  1.1450   -0.9463   0.05
  1.2389   -1.0380   0.05
  1.3309   -1.1316   0.05
  1.4214   -1.2266   0.05
  1.5104   -1.3230   0.05
  1.5983   -1.4205   0.05
  1.6849   -1.5191   0.05
  1.7700   -1.6189   0.05
  1.8535   -1.7202   0.05
  1.9350   -1.8231   0.05
  X(5％)   Y(5％)   Z(5％)
  2.0139   -1.9279   0.05
  2.0907   -2.0343   0.05
  2.1662   -2.1417   0.05
  2.2398   -2.2503   0.05
  2.3245   -2.3492   0.05
  2.4476   -2.3383   0.05
  2.4836   -2.2203   0.05
  2.4197   -2.1058   0.05
  2.3501   -1.9946   0.05
  2.2820   -1.8824   0.05
  2.2149   -1.7696   0.05
  2.1496   -1.6558   0.05
  2.0859   -1.5411   0.05
  2.0234   -1.4257   0.05
  1.9614   -1.3100   0.05
  1.8994   -1.1943   0.05
  1.8371   -1.0789   0.05
  1.7739   -0.9638   0.05
  X(5％)   Y(5％)   Z(5％)
  1.7100   -0.8493   0.05
  1.6450   -0.7352   0.05
  1.5790   -0.6218   0.05
  1.5118   -0.5091   0.05
  1.4431   -0.3973   0.05
  1.3727   -0.2865   0.05
  1.3005   -0.1770   0.05
  1.2261   -0.0689   0.05
  1.1494   0.0376   0.05
  1.0702   0.1422   0.05
  0.9880   0.2446   0.05
  0.9027   0.3442   0.05
  0.8138   0.4407   0.05
  0.7211   0.5336   0.05
  0.6243   0.6223   0.05
  0.5234   0.7061   0.05
  0.4181   0.7844   0.05
  0.3084   0.8564   0.05
  X(5％)   Y(5％)   Z(5％)
  0.1944   0.9214   0.05
  0.0762   0.9783   0.05
  -0.0458   1.0264   0.05
  -0.1713   1.0648   0.05
  -0.2995   1.0927   0.05
  -0.4296   1.1094   0.05
  -0.5607   1.1143   0.05
  -0.6917   1.1078   0.05
  -0.8217   1.0898   0.05
  -0.9496   1.0606   0.05
  -1.0746   1.0209   0.05
  -1.1961   0.9715   0.05
  -1.3136   0.9130   0.05
  -1.4264   0.8461   0.05
  -1.5342   0.7713   0.05
  -1.6364   0.6890   0.05
  -1.7326   0.5997   0.05
  -1.8222   0.5039   0.05
  X(5％)   Y(5％)   Z(5％)
  -1.9047   0.4019   0.05
  -1.9795   0.2941   0.05
  -2.0460   0.1810   0.05
  -2.1031   0.0629   0.05
  -2.1497   -0.0597   0.05
  -2.1844   -0.1862   0.05
  -2.2030   -0.3160   0.05
  -2.2002   -0.4470   0.05
Figure C20041008997600131
Figure C20041008997600141
Figure C20041008997600151
Figure C20041008997600161
Figure C20041008997600171
Figure C20041008997600191
  X(20％)   Y(20％)  Z(20％)
  -2.0064   -0.1864   0.20
  -1.8894   -0.2084   0.20
  -1.7752   -0.1647   0.20
  -1.6689   -0.1035   0.20
  -1.5645   -0.0391   0.20
  -1.4586   0.0228   0.20
  -1.3500   0.0797   0.20
  -1.2380   0.1298   0.20
  -1.1226   0.1712   0.20
  -1.0040   0.2024   0.20
  -0.8830   0.2226   0.20
  -0.7607   0.2317   0.20
  -0.6381   0.2296   0.20
  -0.5162   0.2170   0.20
  X(20％)   Y(20％)  Z(20％)
  -0.3957   0.1942   0.20
  -0.2773   0.1622   0.20
  -0.1614   0.1219   0.20
  -0.0485   0.0742   0.20
  0.0615   0.0200   0.20
  0.0615   0.0200   0.20
  0.1685   -0.0401   0.20
  0.2724   -0.1052   0.20
  0.3734   -0.1748   0.20
  0.4715   -0.2484   0.20
  0.5669   -0.3256   0.20
  0.6597   -0.4058   0.20
  0.7499   -0.4889   0.20
  0.8380   -0.5743   0.20
  0.9239   -0.6618   0.20
  1.0080   -0.7512   0.20
  1.0903   -0.8421   0.20
  1.1711   -0.9344   0.20
 X(20％)   Y(20％)  Z(20％)
  1.2505   -1.0279   0.20
  1.3286   -1.1225   0.20
  1.4056   -1.2179   0.20
  1.4818   -1.3141   0.20
  1.5571   -1.4109   0.20
  1.6317   -1.5083   0.20
  1.7057   -1.6061   0.20
  1.7791   -1.7044   0.20
  1.8520   -1.8031   0.20
  1.9240   -1.9024   0.20
  1.9951   -2.0023   0.20
  2.0671   -2.1016   0.20
  2.1394   -2.2006   0.20
  2.2507   -2.2104   0.20
  2.2692   -2.0992   0.20
  2.2100   -1.9918   0.20
  2.1528   -1.8833   0.20
  2.0944   -1.7755   0.20
  X(20％)   Y(20％)  Z(20％)
  2.0363   -1.6674   0.20
  1.9788   -1.5591   0.20
  1.9214   -1.4506   0.20
  1.8060   -1.2341   0.20
  1.7477   -1.1262   0.20
  1.6888   -1.0186   0.20
  1.6293   -0.9113   0.20
  1.5691   -0.8045   0.20
  1.5081   -0.6981   0.20
  1.4462   -0.5921   0.20
  1.3834   -0.4868   0.20
  1.3195   -0.3821   0.20
  1.2544   -0.2781   0.20
  1.1879   -0.1750   0.20
  1.1199   -0.0730   0.20
  1.0499   0.0278   0.20
  0.9779   0.1271   0.20
  0.9035   0.2246   0.20
  X(20％)   Y(20％)  Z(20％)
  0.8266   0.3202   0.20
  0.7470   0.4135   0.20
  0.6643   0.5041   0.20
  0.5784   0.5917   0.20
  0.4890   0.6757   0.20
  0.3959   0.7555   0.20
  0.2988   0.8305   0.20
  0.1978   0.9000   0.20
  0.0927   0.9632   0.20
  -0.0163   1.0194   0.20
  -0.1291   1.0676   0.20
  -0.2453   1.1067   0.20
  -0.3644   1.1360   0.20
  -0.4856   1.1548   0.20
  -0.6079   1.1627   0.20
  -0.7305   1.1594   0.20
  -0.8523   1.1448   0.20
  -0.9722   1.1194   0.20
  X(20％)   Y(20％)  Z(20％)
  -1.0895   1.0835   0.20
  -1.2032   1.0376   0.20
  -1.3126   0.9822   0.20
  -1.4171   0.9181   0.20
  -1.5163   0.8459   0.20
  -1.6095   0.7662   0.20
  -1.6966   0.6798   0.20
  -1.7771   0.5873   0.20
  -1.8504   0.4890   0.20
  -1.9157   0.3852   0.20
  -1.9717   0.2761   0.20
  -2.0169   0.1621   0.20
  -2.0476   0.0435   0.20
  -2.0558   -0.0786   0.20
  X(30％)  Y(30％)  Z(30％)
  -1.9401   0.1020   0.30
  -1.8407   0.0458   0.30
  X(30％)   Y(30％)  Z(30％)
  -1.7259   0.0673   0.30
  -1.6198   0.1183   0.30
  -1.5174   0.1763   0.30
  -1.4150   0.2346   0.30
  -1.3107   0.2892   0.30
  -1.2032   0.3373   0.30
  -1.0924   0.3771   0.30
  -0.9784   0.4063   0.30
  -0.8620   0.4239   0.30
  -0.7444   0.4295   0.30
  -0.6269   0.4231   0.30
  -0.5105   0.4052   0.30
  -0.3962   0.3770   0.30
  -0.2846   0.3395   0.30
  -0.1761   0.2938   0.30
  -0.0707   0.2412   0.30
  0.0314   0.1826   0.30
  0.1304   0.1189   0.30
  X(30％)   Y(30％)  Z(30％)
  0.2264   0.0506   0.30
  0.3194   -0.0215   0.30
  0.4098   -0.0970   0.30
  0.4975   -0.1756   0.30
  0.5829   -0.2567   0.30
  0.6659   -0.3402   0.30
  0.7469   -0.4257   0.30
  0.8260   -0.5130   0.30
  0.9034   -0.6018   0.30
  0.9792   -0.6919   0.30
  1.0536   -0.7831   0.30
  1.1268   -0.8754   0.30
  1.1989   -0.9685   0.30
  1.2700   -1.0624   0.30
  1.3404   -1.1568   0.30
  1.4101   -1.2517   0.30
  1.4792   -1.3471   0.30
  1.5479   -1.4428   0.30
 X(30％)   Y(30％)  Z(30％)
  1.6161   -1.5387   0.30
  1.6840   -1.6349   0.30
  1.7517   -1.7313   0.30
  1.8192   -1.8278   0.30
  1.8870   -1.9241   0.30
  1.9560   -2.0196   0.30
  2.0238   -2.1158   0.30
  2.1291   -2.1308   0.30
  2.1470   -2.0246   0.30
  2.0922   -1.9204   0.30
  2.0390   -1.8153   0.30
  1.9853   -1.7105   0.30
  1.9312   -1.6059   0.30
  1.8767   -1.5015   0.30
  1.8219   -1.3973   0.30
  1.7666   -1.2933   0.30
  1.7110   -1.1895   0.30
  1.6549   -1.0859   0.30
  X(30％)   Y(30％)  Z(30％)
  1.5983   -0.9827   0.30
  1.5412   -0.8797   0.30
  1.4835   -0.7770   0.30
  1.4251   -0.6748   0.30
  1.3659   -0.5729   0.30
  1.3060   -0.4716   0.30
  1.2451   -0.3708   0.30
  1.1831   -0.2706   0.30
  1.1200   -0.1712   0.30
  1.0556   -0.0726   0.30
  0.9896   0.0250   0.30
  0.9221   0.1214   0.30
  0.8526   0.2165   0.30
  0.7812   0.3101   0.30
  0.7075   0.4020   0.30
  0.6313   0.4918   0.30
  0.5523   0.5791   0.30
  0.4703   0.6637   0.30
  X(30％)   Y(30％)  Z(30％)
  0.3851   0.7449   0.30
  0.2964   0.8224   0.30
  0.2040   0.8954   0.30
  0.1079   0.9634   0.30
  0.0078   1.0255   0.30
  -0.0961   1.0808   0.30
  -0.2039   1.1281   0.30
  -0.3152   1.1667   0.30
  -0.4293   1.1957   0.30
  -0.5455   1.2141   0.30
  -0.6630   1.2213   0.30
  -0.7807   1.2173   0.30
  -0.8974   1.2021   0.30
  -1.0121   1.1756   0.30
  -1.1238   1.1383   0.30
  -1.2316   1.0911   0.30
  -1.3349   1.0346   0.30
  -1.4331   0.9696   0.30
  X(30％)  Y(30％)  Z(30％)
  -1.5258   0.8970   0.30
  -1.6126   0.8175   0.30
  -1.6934   0.7319   0.30
  -1.7673   0.6402   0.30
  -1.8331   0.5426   0.30
  -1.8897   0.4394   0.30
  -1.9342   0.3304   0.30
  -1.9600   0.2158   0.30
  X(40％)   Y(40％)  Z(40％)
  -1.8010   0.3250   0.40
  -1.6903   0.3146   0.40
  -1.5830   0.3502   0.40
  -1.4810   0.3993   0.40
  -1.3802   0.4509   0.40
  -1.2783   0.5003   0.40
  -1.1738   0.5440   0.40
  -1.0664   0.5797   0.40
  X(40％)   Y(40％)  Z(40％)
  -0.9560   0.6051   0.40
  -0.8436   0.6184   0.40
  -0.7304   0.6193   0.40
  -0.6178   0.6079   0.40
  -0.5070   0.5847   0.40
  -0.3989   0.5510   0.40
  -0.2941   0.5081   0.40
  -0.1928   0.4575   0.40
  -0.0951   0.4003   0.40
  -0.0008   0.3376   0.40
  0.0904   0.2704   0.40
  0.1786   0.1994   0.40
  0.2640   0.1250   0.40
  0.3468   0.0478   0.40
  0.4273   -0.0319   0.40
  0.5055   -0.1138   0.40
  0.5818   -0.1975   0.40
  0.6562   -0.2829   0.40
 X(40％)   Y(40％)  Z(40％)
  0.7289   -0.3697   0.40
  0.8001   -0.4578   0.40
  0.8701   -0.5469   0.40
  0.9388   -0.6369   0.40
  1.0065   -0.7277   0.40
  1.0732   -0.8192   0.40
  1.1391   -0.9113   0.40
  1.2044   -1.0039   0.40
  1.2690   -1.0969   0.40
  1.3332   -1.1902   0.40
  1.3970   -1.2838   0.40
  1.4605   -1.3776   0.40
  1.5237   -1.4715   0.40
  1.5868   -1.5656   0.40
  1.6498   -1.6597   0.40
  1.7129   -1.7537   0.40
  1.7762   -1.8476   0.40
  1.8397   -1.9414   0.40
 X(40％)   Y(40％)  Z(40％)
  1.9044   -2.0343   0.40
  2.0069   -2.0468   0.40
  2.0312   -1.9459   0.40
  1.9800   -1.8449   0.40
  1.9288   -1.7439   0.40
  1.8775   -1.6429   0.40
  1.8256   -1.5422   0.40
  1.7734   -1.4418   0.40
  1.7207   -1.3415   0.40
  1.6678   -1.2413   0.40
  1.6145   -1.1414   0.40
  1.5608   -1.0417   0.40
  1.5066   -0.9423   0.40
  1.4519   -0.8431   0.40
  1.3967   -0.7442   0.40
  1.3409   -0.6457   0.40
  1.2844   -0.5475   0.40
  1.2273   -0.4497   0.40
  X(40％)   Y(40％)  Z(40％)
  1.1693   -0.3524   0.40
  1.1105   -0.2556   0.40
  1.0507   -0.1594   0.40
  0.9898   -0.0639   0.40
  0.9279   0.0309   0.40
  0.8647   0.1249   0.40
  0.8001   0.2179   0.40
  0.7339   0.3098   0.40
  0.6660   0.4004   0.40
  0.5960   0.4895   0.40
  0.5238   0.5767   0.40
  0.4491   0.6618   0.40
  0.3716   0.7444   0.40
  0.2912   0.8241   0.40
  0.2075   0.9005   0.40
  0.1205   0.9729   0.40
  0.0297   1.0406   0.40
  -0.0650   1.1027   0.40
  X(40％)   Y(40％)  Z(40％)
  -0.1637   1.1582   0.40
  -0.2663   1.2061   0.40
  -0.3725   1.2452   0.40
  -0.4819   1.2744   0.40
  -0.5936   1.2928   0.40
  -0.7066   1.3001   0.40
  -0.8197   1.2959   0.40
  -0.9318   1.2798   0.40
  -1.0417   1.2526   0.40
  -1.1484   1.2149   0.40
  -1.2513   1.1675   0.40
  -1.3496   1.1114   0.40
  -1.4431   1.0475   0.40
  -1.5313   0.9766   0.40
  -1.6138   0.8990   0.40
  -1.6895   0.8148   0.40
  -1.7573   0.7241   0.40
  -1.8153   0.6269   0.40
  X(40％)  Y(40％)  Z(40％)
  -1.8583   0.5223   0.40
  -1.8692   0.4107   0.40
  X(50％)   Y(50％)  Z(50％)
  -1.7547   0.6388   0.50
  -1.6616   0.5889   0.50
  -1.5542   0.6014   0.50
  -1.4518   0.6378   0.50
  -1.3515   0.6798   0.50
  -1.2509   0.7210   0.50
  -1.1484   0.7573   0.50
  -1.0435   0.7859   0.50
  -0.9365   0.8048   0.50
  -0.8280   0.8117   0.50
  -0.7195   0.8061   0.50
  -0.6122   0.7885   0.50
  -0.5075   0.7594   0.50
  -0.4061   0.7202   0.50
  X(50％)   Y(50％)  Z(50％)
  -0.3085   0.6723   0.50
  -0.2148   0.6173   0.50
  -0.1248   0.5562   0.50
  -0.0383   0.4904   0.50
  0.0451   0.4206   0.50
  0.1256   0.3475   0.50
  0.2035   0.2717   0.50
  0.2791   0.1935   0.50
  0.3526   0.1134   0.50
  0.4241   0.0315   0.50
  0.4939   -0.0519   0.50
  0.5621   -0.1366   0.50
  0.6289   -0.2224   0.50
  0.6944   -0.3092   0.50
  0.7588   -0.3968   0.50
  0.8223   -0.4851   0.50
  0.8848   -0.5741   0.50
  0.9466   -0.6635   0.50
 X(50％)   Y(50％)  Z(50％)
  1.0078   -0.7535   0.50
  1.0683   -0.8438   0.50
  1.1284   -0.9344   0.50
  1.1881   -1.0253   0.50
  1.2474   -1.1164   0.50
  1.3065   -1.2077   0.50
  1.3655   -1.2990   0.50
  1.4245   -1.3904   0.50
  1.4834   -1.4818   0.50
  1.5425   -1.5731   0.50
  1.6018   -1.6643   0.50
  1.6613   -1.7552   0.50
  1.7209   -1.8462   0.50
  1.7828   -1.9354   0.50
  1.8823   -1.9456   0.50
  1.9100   -1.8492   0.50
  1.8620   -1.7518   0.50
  1.8135   -1.6544   0.50
  X(50％)   Y(50％)  Z(50％)
  1.7646   -1.5573   0.50
  1.7153   -1.4604   0.50
  1.6655   -1.3637   0.50
  1.6153   -1.2672   0.50
  1.5648   -1.1709   0.50
  1.5140   -1.0748   0.50
  1.4627   -0.9790   0.50
  1.4110   -0.8833   0.50
  1.3588   -0.7879   0.50
  1.3062   -0.6927   0.50
  1.2530   -0.5979   0.50
  1.1993   -0.5033   0.50
  1.1451   -0.4091   0.50
  1.0902   -0.3152   0.50
  1.0347   -0.2217   0.50
  0.9784   -0.1287   0.50
  0.9213   -0.0361   0.50
  0.8634   0.0559   0.50
  X(50％)  Y(50％)  Z(50％)
  0.8046   0.1474   0.50
  0.7447   0.2381   0.50
  0.6835   0.3280   0.50
  0.6210   0.4170   0.50
  0.5570   0.5049   0.50
  0.4912   0.5915   0.50
  0.4235   0.6766   0.50
  0.3537   0.7599   0.50
  0.2814   0.8411   0.50
  0.2064   0.9199   0.50
  0.1284   0.9956   0.50
  0.0469   1.0676   0.50
  -0.0383   1.1352   0.50
  -0.1274   1.1975   0.50
  -0.2206   1.2534   0.50
  -0.3180   1.3016   0.50
  -0.4193   1.3411   0.50
  -0.5238   1.3709   0.50
  X(50％)   Y(50％)  Z(50％)
  -0.6308   1.3901   0.50
  -0.7392   1.3977   0.50
  -0.8478   1.3937   0.50
  -0.9555   1.3785   0.50
  -1.0611   1.3527   0.50
  -1.1637   1.3170   0.50
  -1.2628   1.2722   0.50
  -1.3578   1.2193   0.50
  -1.4482   1.1590   0.50
  -1.5332   1.0913   0.50
  -1.6117   1.0161   0.50
  -1.6823   0.9335   0.50
  -1.7413   0.8423   0.50
  -1.7791   0.7408   0.50
  X(60％)  Y(60％)  Z(60％)
  -1.6313   0.9111   0.60
  X(60％)   Y(60％)  Z(60％)
  -1.5310   0.8888   0.60
  -1.4284   0.9072   0.60
  -1.3282   0.9363   0.60
  -1.2281   0.9658   0.60
  -1.1269   0.9912   0.60
  -1.0241   1.0092   0.60
  -0.9201   1.0180   0.60
  -0.8158   1.0159   0.60
  -0.7124   1.0018   0.60
  -0.6113   0.9764   0.60
  -0.5132   0.9408   0.60
  -0.4190   0.8959   0.60
  -0.3289   0.8432   0.60
  -0.2429   0.7842   0.60
  -0.1605   0.7200   0.60
  -0.0816   0.6517   0.60
  -0.0057   0.5801   0.60
  0.0676   0.5058   0.60
  X(60％)   Y(60％)  Z(60％)
  0.1386   0.4293   0.60
  0.2074   0.3508   0.60
  0.2744   0.2708   0.60
  0.3397   0.1894   0.60
  0.4036   0.1068   0.60
  0.4661   0.0232   0.60
  0.5275   -0.0612   0.60
  0.5879   -0.1463   0.60
  0.6474   -0.2321   0.60
  0.7060   -0.3185   0.60
  0.7640   -0.4053   0.60
  0.8213   -0.4925   0.60
  0.8782   -0.5800   0.60
  0.9346   -0.6678   0.60
  0.9906   -0.7559   0.60
  1.0465   -0.8441   0.60
  1.1021   -0.9324   0.60
  1.1576   -1.0208   0.60
 X(60％)   Y(60％)  Z(60％)
  1.2131   -1.1092   0.60
  1.2684   -1.1977   0.60
  1.3238   -1.2862   0.60
  1.3791   -1.3747   0.60
  1.4345   -1.4632   0.60
  1.4902   -1.5515   0.60
  1.5464   -1.6394   0.60
  1.6030   -1.7271   0.60
  1.6633   -1.8120   0.60
  1.7593   -1.8205   0.60
  1.7900   -1.7288   0.60
  1.7454   -1.6345   0.60
  1.6991   -1.5410   0.60
  1.6528   -1.4474   0.60
  1.6061   -1.3541   0.60
  1.5590   -1.2609   0.60
  1.5115   -1.1680   0.60
  1.4635   -1.0753   0.60
  X(60％)   Y(60％)  Z(60％)
  1.4152   -0.9828   0.60
  1.3664   -0.8905   0.60
  1.3172   -0.7984   0.60
  1.2676   -0.7066   0.60
  1.2176   -0.6150   0.60
  1.1672   -0.5236   0.60
  1.1163   -0.4324   0.60
  1.0650   -0.3415   0.60
  1.0132   -0.2509   0.60
  0.9609   -0.1606   0.60
  0.9080   -0.0706   0.60
  0.8546   0.0191   0.60
  0.8006   0.1084   0.60
  0.7459   0.1973   0.60
  0.6904   0.2857   0.60
  0.6339   0.3735   0.60
  0.5764   0.4606   0.60
  0.5178   0.5469   0.60
  X(60％)   Y(60％)  Z(60％)
  0.4580   0.6325   0.60
  0.3968   0.7170   0.60
  0.3340   0.8004   0.60
  0.2692   0.8822   0.60
  0.2022   0.9622   0.60
  0.1325   1.0400   0.60
  0.0599   1.1149   0.60
  -0.0161   1.1865   0.60
  -0.0957   1.2539   0.60
  -0.1794   1.3163   0.60
  -0.2673   1.3725   0.60
  -0.3594   1.4216   0.60
  -0.4555   1.4623   0.60
  -0.5550   1.4935   0.60
  -0.6573   1.5142   0.60
  -0.7611   1.5243   0.60
  -0.8655   1.5238   0.60
  -0.9692   1.5128   0.60
  X(60％)  Y(60％)  Z(60％)
  -1.0714   1.4918   0.60
  -1.1713   1.4615   0.60
  -1.2682   1.4227   0.60
  -1.3613   1.3757   0.60
  -1.4496   1.3201   0.60
  -1.5317   1.2558   0.60
  -1.6054   1.1820   0.60
  -1.6645   1.0962   0.60
  -1.6873   0.9960   0.60
Figure C20041008997600471
Figure C20041008997600491
Figure C20041008997600501
Figure C20041008997600511
Figure C20041008997600531
  X(80％)  Y(80％)  Z(80％)
  -1.4814   1.5187   0.80
  -1.4034   1.4661   0.80
  -1.3074   1.4561   0.80
  -1.2108   1.4541   0.80
  -1.1142   1.4494   0.80
  -1.0183   1.4380   0.80
  -0.9237   1.4181   0.80
  -0.8313   1.3897   0.80
  -0.7419   1.3531   0.80
  -0.6560   1.3088   0.80
  -0.5739   1.2579   0.80
  -0.4955   1.2013   0.80
  -0.4207   1.1401   0.80
  X(80％)   Y(80％)  Z(80％)
  -0.3492   1.0750   0.80
  -0.2809   1.0067   0.80
  -0.2153   0.9357   0.80
  -0.1521   0.8625   0.80
  -0.0910   0.7876   0.80
  -0.0316   0.7113   0.80
  0.0263   0.6339   0.80
  0.0829   0.5556   0.80
  0.1384   0.4764   0.80
  0.1929   0.3966   0.80
  0.2466   0.3162   0.80
  0.2997   0.2354   0.80
  0.3522   0.1542   0.80
  0.4041   0.0727   0.80
  0.4557   -0.0091   0.80
  0.5068   -0.0911   0.80
  0.5576   -0.1734   0.80
  0.6081   -0.2558   0.80
  X(80％)   Y(80％)  Z(80％)
  0.6584   -0.3384   0.80
  0.7085   -0.4211   0.80
  0.7584   -0.5038   0.80
  0.8083   -0.5867   0.80
  0.8581   -0.6695   0.80
  0.9079   -0.7523   0.80
  0.9578   -0.8351   0.80
  1.0079   -0.9178   0.80
  1.0581   -1.0004   0.80
  1.1085   -1.0829   0.80
  1.1592   -1.1652   0.80
  1.2103   -1.2473   0.80
  1.2616   -1.3292   0.80
  1.3134   -1.4109   0.80
  1.3650   -1.4926   0.80
  1.4215   -1.5706   0.80
  1.5113   -1.5780   0.80
  1.5477   -1.4952   0.80
  X(80％)   Y(80％)  Z(80％)
  1.5095   -1.4066   0.80
  1.4684   -1.3191   0.80
  1.4271   -1.2317   0.80
  1.3852   -1.1446   0.80
  1.3429   -1.0577   0.80
  1.3002   -0.9710   0.80
  1.2572   -0.8844   0.80
  1.2140   -0.7979   0.80
  1.1704   -0.7116   0.80
  1.1265   -0.6255   0.80
  1.0823   -0.5395   0.80
  1.0377   -0.4537   0.80
  0.9928   -0.3681   0.80
  0.9476   -0.2827   0.80
  0.9020   -0.1975   0.80
  0.8560   -0.1124   0.80
  0.8098   -0.0275   0.80
  0.7631   0.0571   0.80
  X(80％)   Y(80％)  Z(80％)
  0.7161   0.1416   0.80
  0.6687   0.2259   0.80
  0.6209   0.3099   0.80
  0.5726   0.3936   0.80
  0.5238   0.4771   0.80
  0.4744   0.5602   0.80
  0.4244   0.6429   0.80
  0.3738   0.7253   0.80
  0.3223   0.8071   0.80
  0.2698   0.8882   0.80
  0.2159   0.9685   0.80
  0.1605   1.0477   0.80
  0.1034   1.1257   0.80
  0.0443   1.2022   0.80
  -0.0169   1.2770   0.80
  -0.0806   1.3497   0.80
  -0.1473   1.4197   0.80
  -0.2171   1.4866   0.80
  X(80％)  Y(80％)  Z(80％)
  -0.2904   1.5496   0.80
  -0.3674   1.6080   0.80
  -0.4481   1.6612   0.80
  -0.5324   1.7084   0.80
  -0.6202   1.7489   0.80
  -0.7110   1.7819   0.80
  -0.8044   1.8068   0.80
  -0.8996   1.8233   0.80
  -0.9959   1.8311   0.80
  -1.0925   1.8294   0.80
  -1.1883   1.8169   0.80
  -1.2816   1.7920   0.80
  -1.3698   1.7526   0.80
  -1.4465   1.6943   0.80
  -1.4949   1.6118   0.80
  X(90％)  Y(90％)  Z(90％)
  -1.3647   1.7661   0.90
  X(90％)   Y(90％)  Z(90％)
  -1.2844   1.7209   0.90
  -1.1932   1.6997   0.90
  -1.1020   1.6789   0.90
  -1.0124   1.6519   0.90
  -0.9256   1.6170   0.90
  -0.8425   1.5740   0.90
  -0.7632   1.5243   0.90
  -0.6878   1.4689   0.90
  -0.6162   1.4087   0.90
  -0.5479   1.3447   0.90
  -0.4824   1.2779   0.90
  -0.4193   1.2088   0.90
  -0.3583   1.1378   0.90
  -0.2994   1.0651   0.90
  -0.2422   0.9910   0.90
  -0.1865   0.9158   0.90
  -0.1321   0.8396   0.90
  -0.0786   0.7628   0.90
  X(90％)   Y(90％)  Z(90％)
  -0.0261   0.6854   0.90
  0.0256   0.6074   0.90
  0.0767   0.5289   0.90
  0.1271   0.4501   0.90
  0.1771   0.3710   0.90
  0.2267   0.2916   0.90
  0.2760   0.2120   0.90
  0.3250   0.1323   0.90
  0.3737   0.0524   0.90
  0.4222   -0.0276   0.90
  0.4706   -0.1078   0.90
  0.5189   -0.1879   0.90
  0.5671   -0.2681   0.90
  0.6153   -0.3484   0.90
  0.6635   -0.4286   0.90
  0.7118   -0.5088   0.90
  0.7602   -0.5889   0.90
  0.8088   -0.6689   0.90
 X(90％)   Y(90％)  Z(90％)
  0.8575   -0.7488   0.90
  0.9063   -0.8286   0.90
  0.9553   -0.9084   0.90
  1.0043   -0.9881   0.90
  1.0535   -1.0677   0.90
  1.1028   -1.1473   0.90
  1.1526   -1.2265   0.90
  1.2031   -1.3053   0.90
  1.2538   -1.3840   0.90
  1.3092   -1.4590   0.90
  1.3963   -1.4660   0.90
  1.4335   -1.3864   0.90
  1.3983   -1.3000   0.90
  1.3592   -1.2149   0.90
  1.3200   -1.1299   0.90
  1.2804   -1.0451   0.90
  1.2406   -0.9604   0.90
  1.2004   -0.8759   0.90
  X(90％)   Y(90％)  Z(90％)
  1.1599   -0.7915   0.90
  1.1190   -0.7073   0.90
  1.0779   -0.6233   0.90
  1.0365   -0.5393   0.90
  0.9948   -0.4555   0.90
  0.9529   -0.3719   0.90
  0.9107   -0.2883   0.90
  0.8683   -0.2049   0.90
  0.8256   -0.1216   0.90
  0.7825   -0.0385   0.90
  0.7390   0.0443   0.90
  0.6952   0.1270   0.90
  0.6509   0.2095   0.90
  0.6062   0.2917   0.90
  0.5610   0.3736   0.90
  0.5152   0.4553   0.90
  0.4688   0.5366   0.90
  0.4219   0.6175   0.90
  X(90％)   Y(90％)  Z(90％)
  0.3743   0.6981   0.90
  0.3260   0.7783   0.90
  0.2769   0.8580   0.90
  0.2270   0.9371   0.90
  0.1761   1.0157   0.90
  0.1241   1.0935   0.90
  0.0711   1.1706   0.90
  0.0168   1.2468   0.90
  -0.0389   1.3220   0.90
  -0.0963   1.3960   0.90
  -0.1557   1.4683   0.90
  -0.2173   1.5388   0.90
  -0.2812   1.6071   0.90
  -0.3476   1.6731   0.90
  -0.4168   1.7361   0.90
  -0.4891   1.7955   0.90
  -0.5649   1.8503   0.90
  -0.6445   1.8996   0.90
  X(90％)   Y(90％)  Z(90％)
  -0.7276   1.9425   0.90
  -0.8141   1.9782   0.90
  -0.9034   2.0060   0.90
  -0.9952   2.0239   0.90
  -1.0886   2.0294   0.90
  -1.1816   2.0202   0.90
  -1.2705   1.9917   0.90
  -1.3448   1.9360   0.90
  -1.3880   1.8543   0.90
  X(95％)  Y(95％)  Z(95％)
  -1.3374   1.9806   0.95
  -1.3211   1.8911   0.95
  -1.2461   1.8393   0.95
  -1.1572   1.8126   0.95
  -1.0688   1.7844   0.95
  -0.9830   1.7490   0.95
  -0.9010   1.7055   0.95
  X(95％)   Y(95％)  Z(95％)
  -0.8235   1.6545   0.95
  -0.7504   1.5973   0.95
  -0.6814   1.5353   0.95
  -0.6160   1.4694   0.95
  -0.5536   1.4007   0.95
  -0.4938   1.3297   0.95
  -0.4360   1.2571   0.95
  -0.3797   1.1833   0.95
  -0.3246   1.1086   0.95
  -0.2707   1.0330   0.95
  -0.2178   0.9567   0.95
  -0.1658   0.8799   0.95
  -0.1145   0.8025   0.95
  -0.0639   0.7247   0.95
  -0.0137   0.6466   0.95
  0.0360   0.5681   0.95
  0.0852   0.4895   0.95
  0.1342   0.4106   0.95
  X(95％)   Y(95％)  Z(95％)
  0.1828   0.3315   0.95
  0.2311   0.2523   0.95
  0.2792   0.1729   0.95
  0.3272   0.0934   0.95
  0.3749   0.0138   0.95
  0.4226   -0.0658   0.95
  0.4703   -0.1454   0.95
  0.5181   -0.2251   0.95
  0.5659   -0.3046   0.95
  0.6139   -0.3841   0.95
  0.6621   -0.4634   0.95
  0.7105   -0.5426   0.95
  0.7590   -0.6218   0.95
  0.8076   -0.7008   0.95
  0.8562   -0.7799   0.95
  0.9049   -0.8590   0.95
  0.9535   -0.9381   0.95
  1.0020   -1.0172   0.95
  X(95％)   Y(95％)  Z(95％)
  1.0509   -1.0961   0.95
  1.1006   -1.1745   0.95
  1.1515   -1.2521   0.95
  1.2019   -1.3301   0.95
  1.2553   -1.4057   0.95
  1.3404   -1.4224   0.95
  1.3859   -1.3479   0.95
  1.3541   -1.2613   0.95
  1.3160   -1.1766   0.95
  1.2777   -1.0921   0.95
  1.2390   -1.0077   0.95
  1.2001   -0.9234   0.95
  1.1607   -0.8394   0.95
  1.1211   -0.7554   0.95
  1.0812   -0.6716   0.95
  1.0411   -0.5879   0.95
  1.0008   -0.5043   0.95
  0.9602   -0.4208   0.95
  X(95％)   Y(95％)  Z(95％)
  0.9194   -0.3374   0.95
  0.8782   -0.2542   0.95
  0.8368   -0.1711   0.95
  0.7951   -0.0882   0.95
  0.7530   -0.0055   0.95
  0.7105   0.0770   0.95
  0.6675   0.1593   0.95
  0.6241   0.2414   0.95
  0.5803   0.3232   0.95
  0.5358   0.4047   0.95
  0.4908   0.4858   0.95
  0.4451   0.5666   0.95
  0.3988   0.6471   0.95
  0.3517   0.7271   0.95
  0.3039   0.8067   0.95
  0.2554   0.8858   0.95
  0.2060   0.9644   0.95
  0.1559   1.0425   0.95
  X(95％)  Y(95％)  Z(95％)
  0.1050   1.1201   0.95
  0.0533   1.1973   0.95
  0.0009   1.2739   0.95
  -0.0523   1.3499   0.95
  -0.1066   1.4252   0.95
  -0.1621   1.4996   0.95
  -0.2190   1.5730   0.95
  -0.2771   1.6452   0.95
  -0.3368   1.7162   0.95
  -0.3989   1.7853   0.95
  -0.4639   1.8515   0.95
  -0.5331   1.9133   0.95
  -0.6077   1.9686   0.95
  -0.6866   2.0174   0.95
  -0.7685   2.0610   0.95
  -0.8538   2.0976   0.95
  -0.9425   2.1247   0.95
  -1.0341   2.1393   0.95
  X(95％)  Y(95％)  Z(95％)
  -1.1267   2.1376   0.95
  -1.2162   2.1141   0.95
  -1.2903   2.0594   0.95
在第二级透平叶片的这个优选实施方式中，有92个叶片翼面是用空气冷却的。在第二级透平叶片的该优选实施方式中，在0％～100％的跨度内，叶片径向高度为36.297cm(14.290英寸)。在从发动机中心线的0％跨度处翼面径向高度是118.94cm(46.828英寸)，而在100％跨度处翼面径向高度是155.24cm(61.118英寸)。表I中的翼面截面从Z＝5％跨度处开始，并在Z＝95％跨度处截止，这样就除去了倒角区域。虽然每个第二级叶片翼面36没有形成本发明的部分，但是每个第二级叶片翼面36包括多个内部空气冷却通道(未示出)，这些内部空气冷却通道将冷却空气排入与顶罩42相邻的热气通道中。
还应该理解，在上面表中公开的翼面可以按几何比例扩大或缩小，从而应用到其它相似的透平设计中。因此，在表I中列出的坐标值可以按比例增加或减小，这样翼面轮廓形状保持不变。通过将表中的X和Y坐标值乘以或除以一个常数，就可以提供一个按比例变化的轮廓。
要在Z方向上按比例变化叶片翼面，也可以将该常数应用到表I中给出的5％～95％径向跨度范围内。
虽然在与目前认为是最实用的和最优选的实施方式相关的描述中说明了本发明，但是应该理解，本发明并不局限于所公开的实施方式，相反的，本发明旨在涵盖包括在所附权利要求书的精神和范围内的各种改进和等效设置。

Claims (8)

1. 一种透平叶片(20)，包括具有一种翼面形状的叶片翼面(36)，该翼面具有与表I中列出的X、Y和Z笛卡儿坐标值一致的标称轮廓，其中Z值是从0.05到0.95的无量纲值，通过使Z值乘以以英寸为单位的翼面高度，Z值可以换算成以英寸为单位的Z长度，其中X和Y是以英寸为单位的长度，当由平滑连续的弧将X和Y值连结时，在每个长度Z处即定翼面轮廓截面(38)，将在各Z长度处的轮廓截面彼此平滑地连结，则形成完整的翼面形状。
2. 如权利要求1所述的透平叶片，其特征在于，形成透平第二级的一部分。
3. 如权利要求1所述的透平叶片，其特征在于，该翼面形状是一个沿垂直于任意翼面表面位置的方向±0.406cm(±0.160英寸)内的包络面。
4. 如权利要求1所述的透平叶片，其特征在于，从Z＝0.0％到Z＝100％跨度的透平翼面高度为36.297cm(14.290英寸)。
5. 一种透平叶片(20)，包括一个叶片翼面(36)，该翼面具有与表I中列出的X、Y和Z笛卡儿坐标值一致的未涂层的标称翼面轮廓，其中Z值是从0.05到0.95的无量纲值，通过使Z值乘以以英寸为单位的翼面高度，Z值可以换算成以英寸为单位的Z长度，其中X和Y是以英寸为单位的长度，当由平滑连续的弧将X和Y值连结时，在每个Z长度处限定翼面轮廓截面(38)，将在各Z长度处的轮廓截面彼此平滑地连结，则形成完整的翼面形状，X和Y值作为相同常数或数值的函数可以按比例变化，从而提供按比例放大或缩小的翼面。
6. 如权利要求5所述的透平叶片，其特征在于，形成透平第二级的一部分。
7. 如权利要求5所述的透平叶片，其特征在于，该翼面形状是一个沿垂直于任意翼面表面位置的方向±0.406cm(±0.160英寸)内的包络面。
8. 如权利要求5所述的透平叶片，其特征在于，从Z＝0.0％到Z＝100％跨度内的叶片翼面高度为36.297cm(14.290英寸)。
CNB2004100899767A 2003-10-09 2004-10-09 透平叶片的翼面形状 Expired - Fee Related CN100419216C (zh)

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CN1661199A (zh) 2005-08-31
US6881038B1 (en) 2005-04-19

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