CN101169124A - 用于压缩机的翼型形状 - Google Patents

用于压缩机的翼型形状 Download PDF

Info

Publication number
CN101169124A
CN101169124A CNA2007101670994A CN200710167099A CN101169124A CN 101169124 A CN101169124 A CN 101169124A CN A2007101670994 A CNA2007101670994 A CN A2007101670994A CN 200710167099 A CN200710167099 A CN 200710167099A CN 101169124 A CN101169124 A CN 101169124A
Authority
CN
China
Prior art keywords
profile
aerofoil profile
compressor
article
distance
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CNA2007101670994A
Other languages
English (en)
Inventor
J·拉蒂默
M·布洛姆
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
General Electric Co
Original Assignee
General Electric Co
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by General Electric Co filed Critical General Electric Co
Publication of CN101169124A publication Critical patent/CN101169124A/zh
Pending legal-status Critical Current

Links

Images

Classifications

    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00—Details, component parts, or accessories
    • F04D29/26—Rotors specially for elastic fluids
    • F04D29/32—Rotors specially for elastic fluids for axial flow pumps
    • F04D29/321—Rotors specially for elastic fluids for axial flow pumps for axial flow compressors
    • F04D29/324—Blades
    • 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
    • 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
    • Y10S416/02—Formulas of curves

Abstract

本发明公开了一种用于压缩机的翼型形状。带有该翼型形状的制造物品具有主要根据表1中列出的X、Y和Z的笛卡尔坐标值的标称型面。其中，X和Y为当由平滑连续的弧连接时在每个Z英寸距离处限定翼型型面截面的英寸距离。在Z距离处该型面截面彼此平滑地连接，以便形成整个翼型形状(22，23)。

Description

用于压缩机的翼型形状
技术领域
本发明涉及用于燃气涡轮机的转子叶片的翼型件(airfoil)。本发明尤其涉及用于压缩机的各种级的压缩机翼型型面(airfoil profile)。本发明尤其涉及用于在压缩机的各种级的入口导片(inlet guidevane)、转子或定子的压缩机翼型型面。
背景技术
在燃气涡轮机中，对于燃气涡轮机的流动路径部分的每一级应当满足许多系统要求，以便满足设计目的。这些设计目的包括但不限于提高的总效率和翼型件负荷能力。例如，压缩机定子的叶片应当实现对于特定级的热和机械操作要求，但本发明不限于此。另外，例如压缩机转子的叶片应当实现对于特定级的热和机械操作要求，但本发明不限于此。
发明内容
根据本发明的一个示范性方面，提供了一种制造物品，该物品具有主要根据在表1中列出的X、Y和Z的笛卡尔坐标值的标称型面(nominal profile)。其中，X和Y是当由平滑连续的弧连接时在每个Z英寸距离处限定翼型型面截面的英寸距离。在Z距离处该型面截面彼此平滑地连接，以便形成整个翼型形状(airfoil shape)。
根据本发明的另一个示范性方面，压缩机包括压缩机叶轮。该压缩机叶轮具有多个制造物品。其中每个制造物品包括具有翼型形状的翼型件。该翼型件包括主要根据表1中列出的X、Y和Z的笛卡尔坐标值的标称型面，其中X和Y为当由平滑连续弧连接时在每个Z英寸距离处限定翼型型面截面的英寸距离。在Z距离处的型面截面彼此平滑地连接，以便形成整个翼型形状。
根据本发明的再一个示范性方面，压缩机包括具有多个制造物品的压缩机叶轮。其中每个制造物品包括翼型件，该翼型件具有主要根据表1中列出的X、Y和Z的笛卡尔坐标值的未涂敷的标称翼型型面，其中X和Y是当由平滑连续弧连接时在每个Z英寸距离处限定翼型型面截面的英寸距离。在Z距离处的型面截面彼此平滑地连接，以便形成整个翼型形状。
附图说明
图1是经过燃气涡轮机的多个级的压缩机流动路径的示范性示意图，且其说明了根据本发明实施例的示范性翼型件；
图2和图3分别是根据本发明实施例的转子叶片的示范性透视图，该转子叶片具有结合其平台部及其大致轴向进入榫接部或其附近而进行说明的转子叶片翼型件；
图4和图5分别是从翼型件的正压侧和负压侧沿大致周向观测的图2所示的转子叶片以及关联平台部和榫接部的侧视图；
图6是大致沿图5中的线6-6截取的转子叶片翼型件的截面图；
图7是根据本发明示范性实施例的转子叶片的透视图，同时在其上叠加了坐标系统；以及
图8是根据本发明示范性实施例的定子叶片的透视图，同时在其上叠加了坐标系统。
元件符号对照表：
轴向压缩机流动路径      1
燃气涡轮压缩机          2
周向间隔开的转子叶片    22
转子叶轮                51
周向间隔开的定子叶片    23
定子压缩机壳体    59
后面的驱动轴      58
气流箭头方向      60
平台部            61
轴向进入榫接部    62
转子叶片翼型件    63
转子叶片翼型型面  66
翼型翼根          64
转子叶片末端      65
型面截面          66
具体实施方式
现在参照附图，图1说明了包括多个压缩机级的燃气涡轮压缩机2的轴向压缩机流动路径1。在图中，压缩机级按顺序编号。压缩机流动路径包括任何数量的转子级和定子级，例如18个。然而，转子级和定子级的精确数量是工程设计上的选择。任何数量的转子级和定子级都可设置在如本发明所实施的燃烧器中。17个转子级仅仅是一个涡轮机设计的示例。18个转子级决非用于限制本发明。
压缩机转子叶片将动能施加给气流，并且由此在压缩机内产生了所需的压力升高。紧接该转子翼型件下来的是定子翼型件的一个级。转子翼型件和定子翼型件都转动气流、减缓气流速度(分别参照翼型件框)并使得气流静压升高。在本发明其它期望的方面中，包括其外表面的翼型件的构造(连同其与周围翼型件的交互作用)提供了级气流效率、增强的空气力学、级与级之间的平滑层流、降低的热应力、增强的级间相互关系以便在级与级之间有效传送气流，以及降低的机械应力。典型地，多排转子级/定子级叠置在轴向流动的压缩机中，以便获得所需的排出口与入口之间的压力比。转子翼型件和定子翼型件可通过适当的装接构造固定到转子叶轮或定子壳体上，该装接构造通常称为“翼根”、“基部”或“榫接部(dovetail)”(参见图2至图5)。
图1示范性地说明了压缩机2的级。压缩机2的级包括安装在转子叶轮51上的多个周向间隔开的转子叶片22以及装接到定子压缩机壳体59上的多个周向间隔开的定子叶片23。其中每个转子叶轮装接到后面的驱动轴58上，该驱动轴连接到发动机的涡轮机部分上。转子叶片和定子叶片位于压缩机的流动路径1中。箭头60(图1)示出了流经依本发明实施的压缩机流动路径1的气流方向。压缩机2的该级仅仅是本发明范围内压缩机2的级的示范。所说明和描述的压缩机2的级并非试图以任何方式限制本发明。
转子叶片22安装在转子叶轮51上，转子叶轮形成了在后面的驱动轴58的部分。如图2至图6所示，每个转子叶片22设置有平台部61，以及大致轴向或接近轴向进入榫接部62以便在转子叶轮51上与未示出的具有互补形状的相配合的榫接部连接。然而，根据本发明，轴向进入榫接部可以设置有翼型型面。如图2至图6所示，每个转子叶片22包括转子叶片翼型件63。因此，每个转子叶片22从平台部61中点处的翼型翼根64到转子叶片末端65的任何截面中具有大致为翼型形状的转子叶片翼型型面66(图6)。
为了限定转子叶片翼型件的翼型形状，提出了在空间中多个点的独特的设定或轨迹。这种独特的点的设定或轨迹满足了级要求，以致于可以制造出该级。点的这种独特轨迹还满足了级效率以及降低热应力和机械应力的所需要求。通过空气动力负荷和机械负荷之间的迭代(iteration)可获得点的该种轨迹，以便使压缩机能够以高效、安全且平稳的方式运行。
根据本发明的轨迹限定了转子叶片翼型型面，并且可以包括相对于发动机旋转轴的一组点。例如，可提供一组点以便限定转子叶片翼型型面。
以下表中给定的笛卡尔坐标系统的X、Y和Z数值限定了沿其长度在不同位置的转子叶片翼型件的型面。根据本发明实施的翼型件可以找到作为第十八级翼型转子叶片的应用。作为X、Y和Z坐标的坐标值以英寸单位列出，但是通过适当换算还可使用其它的尺寸单位。这些数值不包括平台部的圆角区域。笛卡尔坐标系统具有相对垂直的X、Y和Z轴线。X轴线平行于压缩机叶片的榫接轴线，其与发动机中心线成一角度，如转子的图7和定子的图8所示。正的X坐标值表示轴向朝向后面，例如朝向压缩机的排气端。正的Y坐标值表示垂直于榫接轴线。正的Z坐标值表示径向向外朝向翼型件的末端，其朝向用于转子叶片的压缩机静止壳体)，并且其径向向内朝向用于定子叶片的压缩机的发动机中心线。
仅为参考目的，建立了沿叠置轴线穿过翼型件和平台部的相交处的点-0，如图5所示。在翼型件的示范性实施例中，点-0限定为以上表的Z坐标处于0.000英寸的基准部分，其为距离发动机或转子中心线预先设定的距离。
通过沿垂直于X、Y平面的Z方向在选定位置限定X和Y坐标值，沿翼型件长度在每个Z距离处，可以确定转子叶片翼型件的型面截面，例如但不限于图6中的型面截面66。通过用平滑连续的弧连接X和Y数值，在每个Z距离处可固定每个型面截面66。在距离Z之间的各个表面位置的翼型型面通过平滑地连接彼此相邻的型面截面66从而被确定，进而形成了翼型型面。这些数值表示在周围条件、不运行条件或不热条件下的翼型型面，并且是用于未涂敷的翼型件的。
为了确定翼型件的型面，产生并示出了三个小数位的表中数值。典型的制造公差以及涂层应当计入在翼型件的实际型面中。因此，用于给定型面的数值是用于标称翼型件的。因此应当理解，+/-典型的制造公差例如包括任何涂层厚度的+/-数值加入到X和Y数值中。所以，在垂直于沿翼型型面的任何表面位置的方向上的大约+/-0.160英寸的距离限定了用于转子叶片翼型件设计和压缩机的翼型型面包络(envelope)。换言之，根据本发明，在垂直于沿翼型型面的任何表面位置的方向上的大约+/-0.160英寸的距离，限定了在标称低温或室温时实际型面表面上的被测量点与在相同温度下的那些点的理想位置之间的变化范围。根据本发明，转子叶片翼型件设计对于该变化范围具有足够强度，并且不影响机械和空气动力性能。
以下表1中给定的坐标值提供了用于示范性第十八级翼型转子叶片(airfoil rotor blade)的标称型面包络。
表1
    X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置
    1.592     -0.104     0.007     -0.744     -0.043     0.007     -0.488     0.191     0.007
    1.592     -0.109     0.007     -0.81 1     -0.009     0.007     -0.41     0.174     0.007
    1.59     -0.115     0.007     -0.875     0.026     0.007     -0.328     0.157     0.007
    1.587     -0.121     0.007     -0.934     0.062     0.007     -0.244     0.14     0.007
    1.58     -0.127     0.007     -0.989     0.099     0.007     -0.16     0.123     0.007
    1.568     -0.131     0.007     -1.037     0.135     0.007     -0.075     0.106     0.007
    1.553     -0.133     0.007     -1.08     0.169     0.007     0.009     0.09     0.007
    1.533     -0.136     0.007     -1.116     0.202     0.007     0.094     0.074     0.007
    1.51     -0.139     0.007     -1.15     0.233     0.007     0.178     0.058     0.007
    1.481     -0.143     0.007     -1.177     0.263     0.007     0.263     0.043     0.007
    1.448     -0.148     0.007     -1.196     0.286     0.007     0.348     0.028     0.007
    1.41     -0.153     0.007     -1.21     0.306     0.007     0.432     0.013     0.007
    1.365     -0.16     0.007     -1.218     0.323     0.007     0.517     -0.001     0.007
    1.314     -0.168     0.007     -1.22     0.337     0.007     0.602     -0.014     0.007
    1.257     -0.176     0.007     -1.22     0.344     0.007     0.687     -0.026     0.007
    1.194     -0.185     0.007     -1.218     0.349     0.007     0.77     -0.038     0.007
    1.125     -0.195     0.007     -1.217     0.351     0.007     0.85     -0.048     0.007
    1.053     -0.204     0.007     -1.217     0.352     0.007     0.926     -0.057     0.007
    0.978     -0.213     0.007     -1.216     0.353     0.007     1.001     -0.065     0.007
    0.9     -0.221     0.007     -1.216     0.353     0.007     1.072     -0.071     0.007
    0.819     -0.229     0.007     -1.215     0.354     0.007     1.141     -0.077     0.007
    0.734     -0.237     0.007     -1.214     0.356     0.007     1.206     -0.081     0.007
    0.647     -0.243     0.007     -1.21     0.359     0.007     1.267     -0.084     0.007
    0.557     -0.248     0.007     -1.204     0.363     0.007     1.321     -0.086     0.007
    0.467     -0.251     0.007     -1.192     0.366     0.007     1.37     -0.088     0.007
    0.376     -0.253     0.007     -1.174     0.367     0.007     1.413     -0.088     0.007
    0.286     -0.253     0.007     -1.151     0.364     0.007     1.45     -0.088     0.007
    0.196     -0.251     0.007     -1.124     0.358     0.007     1.482     -0.087     0.007
    0.106     -0.247     0.007     -1.087     0.348     0.007     1.509     -0.086     0.007
    0.016     -0.24     0.007     -1.046     0.336     0.007     1.531     -0.085     0.007
    -0.074     -0.23     0.007     -1.002     0.323     0.007     1.55     -0.084     0.007
    -0.164     -0.218     0.007     -0.953     0.309     0.007     1.565     -0.083     0.007
    -0.254     -0.202     0.007     -0.897     0.293     0.007     1.576     -0.084     0.007
    -0.343     -0.183     0.007     -0.837     0.276     0.007     1.584     -0.089     0.007
    -0432     -0.16     0.007     -0.773     0.259     0.007     1.588     -0.094     0.007
    -0.516     -0.134     0.007     -0.706     0.242     0.007     1.591     -0.1     0.007
    -0.596     -0.106     0.007     -0.636     0.225     0.007
    -0.673     -0.075     0.007     -0.564     0.208     0.007
    X-位置     Y-位置   Z-位置     X-位置     Y-位置     Z-位置     X-位置     Y-位置   Z-位置
    1.542     -0.226   0.362     -0.72     0.031     0.362     -0.493     0.205   0.362
    1.542     -0.23   0.362     -0.787     0.065     0.362     -0.417     0.181   0.362
    1.54     -0.236   0.362     -0.849     0.1     0.362     -0.338     0.158   0.362
    1.536     -0.242   0.362     -0.908     0.134     0.362     -0.256     0.134   0.362
    1.529     -0.247   0.362     -0.964     0.169     0.362     -0.174     0.11   0.362
    1.517     -0.249   0.362     -1.013     0.203     0.362     -0.092     0.086   0.362
    1.502     -0.25   0.362     -1.056     0.234     0.362     -0.01     0.064   0.362
    1.483     -0.251   0.362     -1.094     0.264     0.362     0.072     0.042   0.362
    1.459     -0.252   0.362     -1.128     0.292     0.362     0.155     0.02   0.362
    1.432     -0.253   0.362     -1.157     0.318     0.362     0.237     -0.001   0.362
    1.399     -0.255   0.362     -1.178     0.339     0.362     0.32     -0.021   0.362
    1.361     -0.257   0.362     -1.194     0.357     0.362     0.403     -0.041   0.362
    1.317     -0.26   0.362     -1.203     0.372     0.362     0.486     -0.06   0.362
    1.267     -0.263   0.362     -1.207     0.385     0.362     0.569     -0.078   0.362
    1.211     -0.266   0.362     -1.207     0.393     0.362     0.653     -0.095   0.362
    1.149     -0.269   0.362     -1.206     0.397     0.362     0.734     -0.11   0.362
    1.081     -0.273   0.362     -1.205     0.4     0.362     0.812     -0.124   0.362
    1.01     -0.275   0.362     -1.204     0.401     0.362     0.888     -0.137   0.362
    0.937     -0.278   0.362     -1.204     0.401     0.362     0.961     -0.148   0.362
    0.86     -0.28   0.362     -1.204     0.402     0.362     1.031     -0.159   0.362
    0.78     -0.28   0.362     -1.203     0.403     0.362     1.099     -0.168   0.362
    0.698     -0.28   0.362     -1.202     0.404     0.362     1.164     -0.176   0.362
    0.613     -0.278   0.362     -1.198     0.408     0.362     1.223     -0.183   0.362
    0.526     -0.274   0.362     -1.192     0.411     0.362     1.277     -0.188   0.362
    0.438     -0.268   0.362     -1.18     0.414     0.362     1.325     -0.193   0.362
    0.351     -0.261   0.362     -1.163     0.414     0.362     1.368     -0.196   0.362
    0.264     -0.251   0.362     -1.14     0.41     0.362     1.405     -0.199   0.362
    0.178     -0.24   0.362     -1.113     0.404     0.362     1.436     -0.2   0.362
    0.091     -0.227   0.362     -1.077     0.394     0.362     1.462     -0.201   0.362
    0.005     -0.211   0.362     -1.036     0.381     0.362     1.485     -0.202   0.362
    -0.08     -0.193   0.362     -0.993     0.367     0.362     1.503     -0.203   0.362
    -0.166     -0.173   0.362     -0.944     0.351     0.362     1.518     -0.203   0.362
    -0.25     -0.15   0.362     -0.89     0.333     0.362     1.529     -0.205   0.362
    -0.335     -0.124   0.362     -0.831     0.3 13     0.362     1.536     -0.21   0.362
    -0.419     -0.096   0.362     -0.769     0.293     0.362     1.54     -0.216   0.362
    -0.5     -0.066   0.362     -0.704     0.272     0.362     1.542     -0.222   0.362
    -0.577     -0.035   0.362     -0.637     0.25     0.362
    -0.651     -0.002   0.362     -0.566     0.228     0.362
    X-位置   Y-位置     Z-位置     X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置
    1.53   -0.352     0.717     -0.702     0.061     0.717     -0.483     0.199     0.717
    1.529   -01356     0.717     -0.767     0.095     0.717     -0.407     0.173     0.717
    1.526   -0.362     0.717     -0.829     0.129     0.717     -0.329     0.146     0.717
    1.521   -0.367     0.717     -0.888     0.163     0.717     -0.248     0.119     0.717
    1.514   -0.371     0.717     -0.943     0.197     0.717     -0.167     0.092     0.717
    1.502   -0.372     0.717     -0.992     0.229     0.717     -0.086     0.065     0.717
    1.487   -0.371     0.717     -1.035     0.259     0.717     -0.005     0.039     0.717
    1.468   -0.369     0.717     -1.073     0.287     0.717     0.077     0.013     0.717
    1.445   -0.368     0.717     -1.108     0.314     0.717     0.158     -0.012     0.717
    1.418   -0.366     0.717     -1.138     0.339     0.717     0.24     -0.037     0.717
    1.385   -0.365     0.717     -1.159     0.359     0.717     0.322     -0.062     0.717
    1.348   -0.363     0.717     -1.176     0.375     0.717     0.404     -0.085     0.717
    1.304   -0.36     0.717     -1.186     0.39     0.717     0.486     -0.109     0.717
    1.254   -0.358     0.717     -1.191     0.402     0.717     0.568     -0.132     0.717
    1.199   -0.355     0.717     -1.192     0.409     0.717     0.651     -0.154     0.717
    1.138    -0.352     0.717     -1.191     0.414     0.717     0.731     -0.174     0.717
    1.071   -0.349     0.717     -1.19     0.416     0.717     0.808     -0.194     0.717
    1.001   -0.344     0.717     -1.19     0.417     0.717     0.883     -0.211     0.717
    0.928   -0.339     0.717     -1.189     0.418     0.717     0.955     -0.228     0.717
    0.852   -0.333     0.717     -1.189     0.41 8     0.717     1.025     -0.243     0.717
    0.774   -0.327     0.717     -1.188     0.419     0.717     1.092     -0.257     0.717
    0.693   -0.318     0.717     -1.187     0.421     0.717     1.156     -0.271     0.717
    0.609   -0.309     0.717     -1.183     0.424     0.717     1.215     -0.282     0.717
    0.523   -0.298     0.717     -1.177     0.427     0.717     1.268     -0.292     0.717
    0.437   -0.285     0.717     -1.164     0.429     0.717     1.316     -0.3     0.717
    0.351   -0.272     0.717     -1.147     0.428     0.717     1.358     -0.307     0.717
    0.266   -0.256     0.717     -1.125     0.423     0.717     1.394     -0.313     0.717
    0.1 8   -0.239     0.717     -1.098     0.416     0.717     1.425     -0.317     0.717
    0.095   -0.221     0.717     -1.062     0.405     0.717     1.452     -0.321     0.717
    0.011   -0.2     0.717     -1.022     0.391     0.717     1.474     -0.324     0.717
    -0.073   -0.178     0.717     -0.979     0.376     0.717     1.492     -0.326     0.717
    -0.157   -0.154     0.717     -0.93     0.359     0.717     1.507     -0.328     0.717
    -0.241   -0.128     0.717     -0.877     0.34     0.717     1.518     -0.331     0.717
    -0.324   -0.1     0.717     -0.818     0.318     0.717     1.525     -0.336     0.717
    -0.406   -0.069     0.717     -0.756     0.296     0.717     1.528     -0.342     0.717
    -0.485   -0.038     0.717     -0.692     0.273     0.717     1.529     -0.348     0.717
    -0.561   -0.005     0.717     -0.625     0.249     0.717
    -0.633   0.028     0.717     -0.555     0.224     0.717
    X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置
    1.547     -0.457     1.072     -0.682     0.065     1.072     -0.461     0.186     1.072
    1.546     -0.461     1.072     -0.747     0.099     1.072     -0.386     0.158     1.072
    1.543     -0.466     1.072     -0.809     0.134     1.072     -0.308     0.129     1.072
    1.538     -0.471     1.072     -0.867     0.168     1.072     -0.227     0.099     1.072
    1.529     -0.474     1.072     -0.922     0.203     1.072     -0.145     0.069     1.072
    1.518     -0.474     1.072     -0.971     0.235     1.072     -0.064     0.04     1.072
    1.503     -0.472     1.072     -1.015     0.266     1.072     0.017     0.011     1.072
    1.484     -0.469     1.072     -1.053     0.293     1.072     0.098     -0.017     1.072
    1.461     -0.466     1.072     -1.088     0.32     1.072     0.18     -0.046     1.072
    1.433     -0.462     1.072     -1.117     0.345     1.072     0.261     -0.074     1.072
    1.401     -0.458     1.072     -1.139     0.365     1.072     0.343     -0.102     1.072
    1.363     -0.453     1.072     -1.156     0.381     1.072     0.425     -0.129     1.072
    1.32     -0.448     1.072     -1.166     0.395     1.072     0.507     -0.156     1.072
    1.27     -0.442     1.072     -1.172     0.408     1.072     0.589     -0.182     1.072
    1.215     -0.436     1.072     -1.172     0.415     1.072     0.672     -0.208     1.072
    1.154     -0.428     1.072     -1.172     0.42     1.072     0.751     -0.232     1.072
    1.087     -0.42     1.072     -1.171     0.422     1.072     0.829     -0.255     1.072
    1.017     -0.411     1.072     -1.17     0.423     1.072     0.903     -0.277     1.072
    0.944     -0.401     1.072     -1.17     0.423     1.072     0.975     -0.297     1.072
    0.869     -0.391     1.072     -1.17     0.424     1.072     1.044     -0.317     1.072
    0.791     -0.379     1.072     -1.169     0.425     1.072     1.111     -0.335     1.072
    0.71     -0.366     1.072     -1.168     0.427     1.072     1.175     -0.352     1.072
    0.626     -0.352     1.072     -1.164     0.43     1.072     1.234     -0.367     1.072
    0.54     -0.337     1.072     -1.157     0.432     1.072     1.287     -0.38     1.072
    0.454     -0.32     1.072     -1.144     0.434     1.072     1.334     -0.391     1.072
    0.368     -0.302     1.072     -1.127     0.432     1.072     1.376     -0.401     1.072
    0.283     -0.283     1.072     -1.105     0.426     1.072     1.413     -0.409     1.072
    0.198     -0.262     1.072     -1.078     0.418     1.072     1.444     -0.416     1.072
    0.113     -0.24     1.072     -1.042     0.406     1.072     1.47     -0.421     1.072
    0.028     -0.216     1.072     -1.002     0.392     1.072     1.492     -0.426     1.072
    -0.056     -0.191     1.072     -0.958     0.376     1.072     1.511     -0.429     1.072
    -0.14     -0.164     1.072     -0.91     0.357     1.072     1.526     -0.432     1.072
    -0.223     -0.135     1.072     -0.856     0.337     1.072     1.536     -0.435     1.072
    -0.306     -0.104     1.072     -0.797     0.314     1.072     1.543     -0.441     1.072
    -0.388     -0.072     1.072     -0.735     0.29     1.072     1.546     -0.447     1.072
    -0.467     -0.038     1.072     -0.671     0.265     1.072     1.547     -0.453     1.072
    -0.542     -0.004     1.072     -0.604     0.24     1.072
    -0.614     0.03     1.072     -0.534     0.213     1.072
    X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置
    1.579     -0.54     1.427     -0.662     0.051     1.427     -0.433     0.176     1.427
    1.578     -0.545     1.427     -0.727     0.087     1.427     -0.357     0.146     1.427
    1.575     -0.55     1.427     -0.789     0.124     1.427     -0.278     0.115     1.427
    1.569     -0.554     1.427     -0.847     0.16     1.427     -0.197     0.083     1.427
    1.561     -0.557     1.427     -0.902     0.196     1.427     -0.116     0.051     1.427
    1.549     -0.556     1.427     -0.951     0.23     1.427     -0.034     0.019     1.427
    1.534     -0.553     1.427     -0.994     0.262     1.427     0.047     -0.012     1.427
    1.515     -0.55     1.427     -1.032     0.291     1.427     0.129     -0.043     1.427
    1.492     -0.546     1.427     -1.067     0.32     1.427     0.21     -0.074     1.427
    1.464     -0.541     1.427     -1.096     0.345     1.427     0.292     -0.105     1.427
    1.432     -0.536     1.427     -1.117     0.366     1.427     0.374     -0.136     1.427
    1.394     -0.53     1.427     -1.134     0.383     1.427     0.456     -0.166     1.427
    1.35     -0.523     1.427     -1.144     0.398     1.427     0.538     -0.196     1.427
    1.3     -0.516     1.427     -1.149     0.41     1.427     0.62     -0.226     1.427
    1.244     -0.507     1.427     -1.15     0.418     1.427     0.703     -0.255     1.427
    1.182     -0.498     1.427     -1.149     0.423     1.427     0.783     -0.282     1.427
    1.115     -0.487     1.427     -1.148     0.425     1.427     0.86     -0.309     1.427
    1.044     -0.476     1.427     -1.147     0.426     1.427     0.934     -0.333     1.427
    0.971     -0.464     1.427     -1.147     0.426     1.427     1.006     -0.357     1.427
    0.895     -0.451     1.427     -1.147     0.427     1.427     1.076     -0.379     1.427
    0.816     -0.437     1.427     -1.146     0.428     1.427     1.143     -0.4     1.427
    0.735     -0.422     1.427     -1.145     0.43     1.427     1.207     -0.42     1.427
    0.651     -0.405     1.427     -1.141     0.433     1.427     1.265     -0.437     1.427
    0.564     -0.387     1.427     -1.134     0.435     1.427     1.318     -0.453     1.427
    0.477     -0.367     1.427     -1.121     0.437     1.427     1.366     -0.466     1.427
    0.391     -0.347     1.427     -1.104     0.435     1.427     1.408     -0.478     1.427
    0.305     -0.325     1.427     -1.081     0.429     1.427     1.445     -0.487     1.427
    0.219     -0.301     1.427     -1.053     0.421     1.427     1.476     -0.495     1.427
    0.134     -0.277     1.427     -1.018     0.408     1.427     1.503     -0.502     1.427
    0.049     -0.251     1.427     -0.977     0.393     1.427     1.525     -0.507     1.427
    -0.035     -0.223     1.427     -0.933     0.376     1.427     1.543     -0.511     1.427
    -0.119     -0.193     1.427     -0.884     0.357     1.427     1.558     -0.514     1.427
    -0.203     -0.162     1.427     -0.83     0.336     1.427     1.569     -0.518     1.427
    -0.286     -0.129     1.427     -0.771     0.312     1.427     1.576     -0.524     1.427
    -0.368     -0.094     1.427     -0.709     0.287     1.427     1.579     -0.53     1.427
    -0.447     -0.058     1.427     -0.644     0.26     1.427     1.58     -0.536     1.427
    -0.522     -0.022     1.427     -0.576     0.233     1.427
    -0.594     0.014     1.427     -0.506     0.205     1.427
    X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置
    1.619     -0.613     1.781     -0.646     0.027     1.781     -0.401     0.17     1.781
    1.618     -0.617     1.781     -0.711     0.067     1.781     -0.324     0.138     1.781
    1.615     -0.622     1.781     -0.772     0.106     1.781     -0.245     0.106     1.781
    1.609     -0.627     1.781     -0.83     0.145     1.781     -0.163     0.072     1.781
    1.6     -0.63     1.781     -0.885     0.183     1.781     -0.082     0.038     1.781
    1.588     -0.628     1.781     -0.934     0.219     1.781     0     0.003     1.781
    1.573     -0.625     1.781     -0.976     0.253     1.781     0.082     -0.03     1.781
    1.553     -0.622     1.781     -1.014     0.285     1.781     0.164     -0.064     1.781
    1.53     -0.617     1.781     -1.048     0.315     1.781     0.246     -0.098     1.781
    1.502     -0.612     1.781     -1.076     0.342     1.781     0.328     -0.132     1.781
    1.469     -0.606     1.781     -1.097     0.364     1.781     0.41     -0.165     1.781
    1.431     -0.6     1.781     -1.113     0.383     1.781     0.492     -0.198     1.781
    1.386     -0.592     1.781     -1.122     0.398     1.781     0.575     -0.231     1.781
    1.335     -0.584     1.781     -1.126     0.411     1.781     0.657     -0.264     1.781
    1.279     -0.575     1.781     -1.126     0.419     1.781     0.74     -0.296     1.781
    1.216     -0.564     1.781     -1.125     0.424     1.781     0.82     -0.327     1.781
    1.148     -0.553     1.781     -1.124     0.426     1.781     0.897     -0.356     1.781
    1.077     -0.54     1.781     -1.124     0.427     1.781     0.972     -0.384     1.781
    1.002     -0.527     1.781     -1.123     0.428     1.781     1.044     -0.41     1.781
    0.925     -0.513     1.781     -1.123     0.428     1.781     1.114     -0.435     1.781
    0.845     -0.497     1.781     -1.122     0.429     1.781     1.181     -0.458     1.781
    0.763     -0.481     1.781     -1.121     0.431     1.781     1.245     -0.48     1.781
    0.678     -0.462     1.781     -1.117     0.434     1.781     1.304     -0.499     1.781
    0.59     -0.442     1.781     -1.11     0.437     1.781     1.357     -0.517     1.781
    0.502     -0.421     1.781     -1.097     0.439     1.781     1.405     -0.532     1.781
    0.415     -0.399     1.781     -1.079     0.438     1.781     1.447     -0.545     1.781
    0.328     -0.375     1.781     -1.056     0.432     1.781     1.484     -0.556     1.781
    0.242     -0.35     1.781     -1.028     0.423     1.781     1.516     -0.565     1.781
    0.155     -0.324     1.781     -0.992     0.411     1.781     1.542     -0.572     1.781
    0.07     -0.296     1.781     -0.95     0.396     1.781     1.565     -0.578     1.781
    -0.015     -0.266     1.781     -0.906     0.379     1.781     1.584     -0.583     1.781
    -0.1     -0.234     1.781     -0.857     0.359     1.781     1.598     -0.586     1.781
    -0.184     -0.201     1.781     -0.802     0.337     1.781     1.61     -0.59     1.781
    -0.267     -0.165     1.781     -0.742     0.312     1.781     1.616     -0.596     1.781
    -0.35     -0.128     1.781     -0.679     0.286     1.781     1.619     -0.603     1.781
    -0.43     -0.09     1.781     -0.614     0.259     1.781     1.62     -0.609     1.781
    -0.505     -0.051     1.781     -0.545     0.23     1.781
    -0.577     -0.012     1.781     -0.475     0.201     1.781
    X-位置   Y-位置     Z-位置     X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置
    1.661   -0.688     2.136     -0.63     0.002     2.136     -0.368     0.165     2.136
    1.66   -0.692     2.136     -0.696     0.044     2.136     -0.291     0.132     2.136
    1.657   -0.697     2.136     -0.757     0.086     2.136     -0.211     0.097     2.136
    1.651   -0.702     2.136     -0.815     0.127     2.136     -0.129     0.061     2.136
    1.642   -0.704     2.136     -0.869     0.168     2.136     -0.046     0.024     2.136
    1.63   -0.703     2.136     -0.918     0.207     2.136     0.036     -0.012     2.136
    1.614   -0.7     2.136     -0.96     0.243     2.136     0.11 8     -0.049     2.136
    1.594   -0.696     2.136     -0.997     0.277     2.136     0.201     -0.085     2.136
    1.571   -0.691     2.136     -1.03     0.309     2.136     0.283     -0.122     2.136
    1.542   -0.685     2.136     -1.058     0.338     2.136     0.365     -0.158     2.136
    1.509   -0.679     2.136     -1.078     0.362     2.136     0.448     -0.195     2.136
    1.47   -0.671     2.136     -1.093     0.382     2.136     0.53     -0.231     2.136
    1.424   -0.663     2.136     -1.101     0.398     2.136     0.612     -0.267     2.136
    1.373   -0.654     2.136     -1.104     0.412     2.136     0.695     -0.303     2.136
    1.316   -0.644     2.136     -1.104     0.42     2.136     0.778     -0.338     2.136
    1.252   -0.633     2.136     -1.103     0.424     2.136     0.858     -0.372     2.136
    1.182   -0.62     2.136     -1.102     0.427     2.136     0.936     -0.404     2.136
    1.11   -0.607     2.136     -1.101     0.428     2.136     1.011     -0.435     2.136
    1.034   -0.592     2.136     -1.101     0.428     2.136     1.083     -0.464     2.136
    0.956   -0.577     2.136     -1.1     0.429     2.136     1.153     -0.491     2.136
    0.875   -0.56     2.136     -1.1     0.43     2.136     1.22     -0.517     2.136
    0.791   -0.542     2.136     -1.098     0.432     2.136     1.285     -0.541     2.136
    0.705   -0.523     2.136     -1.094     0.435     2.136     1.344     -0.563     2.136
    0.616   -0.501     2.136     -1.087     0.438     2.136     1.398     -0.582     2.136
    0.527   -0.479     2.136     -1.074     0.441     2.136     1.446     -0.599     2.136
    0.438   -0.455     2.136     -1.056     0.44     2.136     1.489     -0.614     2.136
    0.35   -0.429     2.136     -1.032     0.434     2.136     1.526     -0.626     2.136
    0.263   -0.403     2.136     -1.004     0.426     2.136     1.557     -0.636     2.136
    0.176   -0.374     2.136     -0.967     0.414     2.136     1.584     -0.644     2.136
    0.09   -0.344     2.136     -0.924     0.398     2.136     1.607     -0.65     2.136
    0.004   -0.312     2.136     -0.879     0.381     2.136     1.626     -0.656     2.136
    -0.081   -0.278     2.136     -0.829     0.361     2.136     1.641     -0.66     2.136
    -0.166   -0.242     2.136     -0.774     0.338     2.136     1.652     -0.664     2.136
    -0.25   -0.205     2.136     -0.713     0.313     2.136     1.658     -0.67     2.136
    -0.333   -0.164     2.136     -0.649     0.286     2.136     1.661     -0.677     2.136
    -0.413   -0.123     2.136     -0.583     0.258     2.136     1.662     -0.683     2.136
    -0.489   -0.082     2.136     -0.514     0.228     2.136
    -0.562   -0.04     2.136     -0.442     0.197     2.136
    X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置
    1.708     -0.758     2.491     -0.615     -0.02     2.491     -0.337     0.153     2.491
    1.706     -0.763     2.491     -0.68     0.024     2.491     -0.259     0.117     2.491
    1.703     -0.768     2.491     -0.741     0.068     2.491     -0.178     0.081     2.491
    1.696     -0.772     2.491     -0.799     0.112     2.491     -0.095     0.042     2.491
    1.687     -0.774     2.491     -0.853     0.155     2.491     -0.012     0.004     2.491
    1.675     -0.772     2.491     -0.901     0.196     2.491     0.071     -0.035     2.491
    1.659     -0.768     2.491     -0.943     0.235     2.491     0.154     -0.074     2.491
    1.639     -0.764     2.491     -0.979     0.27     2.491     0.236     -0.113     2.491
    1.615     -0.759     2.491     -1.012     0.304     2.491     0.319     -0.152     2.491
    1.586     -0.753     2.491     -1.039     0.334     2.491     0.402     -0.191     2.491
    1.552     -0.746     2.491     -1.058     0.359     2.491     0.485     -0.23     2.491
    1.512     -0.738     2.491     -1.073     0.38     2.491     0.568     -0.269     2.491
    1.466     -0.729     2.491     -1.081     0.397     2.491     0.651     -0.307     2.491
    1.414     -0.719     2.491     -1.083     0.411     2.491     0.734     -0.345     2.491
    1.356     -0.708     2.491     -1.082     0.419     2.491     0.817     -0.383     2.491
    1.291     -0.696     2.491     -1.081     0.423     2.491     0.898     -0.42     2.491
    1.221     -0.683     2.491     -1.08     0.426     2.491     0.976     -0.454     2.491
    1.147     -0.669     2.491     -1.079     0.427     2.491     1.051     -0.487     2.491
    1.07     -0.653     2.491     -1.079     0.427     2.491     1.124     -0.519     2.491
    0.991     -0.637     2.491     -1.078     0.428     2.491     1.195     -0.548     2.491
    0.909     -0.619     2.491     -1.078     0.429     2.491     1.262     -0.576     2.491
    0.823     -0.6     2.491     -1.076     0.431     2.491     1.327     -0.603     2.491
    0.736     -0.579     2.491     -1.072     0.434     2.491     1.387     -0.626     2.491
    0.645     -0.556     2.491     -1.065     0.437     2.491     1.441     -0.647     2.491
    0.555     -0.532     2.491     -1.052     0.44     2.491     1.49     -0.665     2.491
    0.465     -0.506     2.491     -1.033     0.439     2.491     1.533     -0.681     2.491
    0.376     -0.479     2.491     -1.009     0.433     2.491     1.57     -0.694     2.491
    0.287     -0.45     2.491     -0.98     0.425     2.491     1.602     -0.705     2.491
    0.199     -0.42     2.491     -0.942     0.412     2.491     1.629     -0.713     2.491
    0.111     -0.388     2.491     -0.899     0.396     2.491     1.652     -0.721     2.491
    0.024     -0.354     2.491     -0.854     0.379     2.491     1.671     -0.726     2.491
    -0.062     -0.318     2.491     -0.803     0.358     2.491     1.686     -0.731     2.491
    -0.148     -0.28     2.491     -0.747     0.334     2.491     1.698     -0.735     2.491
    -0.233     -0.239     2.491     -0.685     0.308     2.491     1.705     -0.741     2.491
    -0.317     -0.196     2.491     -0.621     0.279     2.491     1.708     -0.748     2.491
    -0.397     -0.153     2.491     -0.554     0.25     2.491     1.709     -0.754     2.491
    -0.474     -0.109     2.491     -0.484     0.219     2.491
    -0.546     -0.065     2.491     -0.412     0.186     2.491
    X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置
    1.751     -0.818     2.846     -0.591     -0.038     2.846     -0.313     0.128     2.846
    1.749     -0.822     2.846     -0.657     0.009     2.846     -0.234     0.091     2.846
    1.745     -0.827     2.846     -0.719     0.055     2.846     -0.154     0.052     2.846
    1.738     -0.831     2.846     -0.776     0.1     2.846     -0.07     0.012     2.846
    1.728     -0.83     2.846     -0.831     0.146     2.846     0.013     -0.028     2.846
    1.716     -0.827     2.846     -0.879     0.188     2.846     0.097     -0.069     2.846
    1.7     -0.824     2.846     -0.921     0.228     2.846     0.18     -0.11     2.846
    1.679     -0.82     2.846     -0.957     0.264     2.846     0.264     -0.15     2.846
    1.655     -0.814     2.846     -0.99     0.299     2.846     0.347     -0.191     2.846
    1.626     -0.808     2.846     -1.017     0.331     2.846     0.431     -0.231     2.846
    1.591     -0.801     2.846     -1.036     0.356     2.846     0.514     -0.272     2.846
    1.551     -0.793     2.846     -1.051     0.377     2.846     0.598     -0.312     2.846
    1.504     -0.784     2.846     -1.06     0.394     2.846     0.681     -01352     2.846
    1.451     -0.774     2.846     -1.063     0.409     2.846     0.765     -0.392     2.846
    1.392     -0.762     2.846     -1.062     0.417     2.846     0.849     -0.432     2.846
    1.326     -0.749     2.846     -1.06     0.421     2.846     0.93     -0.47     2.846
    1.255     -0.735     2.846     -1.059     0.424     2.846     1.009     -0.506     2.846
    1.18     -0.72     2.846     -1.058     0.425     2.846     1.085     -0.54     2.846
    1.102     -0.704     2.846     -1.058     0.425     2.846     1.159     -0.573     2.846
    1.022     -0.686     2.846     -1.058     0.426     2.846     1.229     -0.603     2.846
    0.938     -0.667     2.846     -1.057     0.427     2.846     1.298     -0.633     2.846
    0.851     -0.646     2.846     -1.055     0.429     2.846     1.363     -0.66     2.846
    0.762     -0.623     2.846     -1.051     0.432     2.846     1.424     -0.684     2.846
    0.67     -0.599     2.846     -1.044     0.435     2.846     1.478     -0.706     2.846
    0.579     -0.573     2.846     -1.03     0.437     2.846     1.527     -0.725     2.846
    0.489     -0.546     2.846     -1.012     0.434     2.846     1.571     -0.741     2.846
    0.399     -0.517     2.846     -0.988     0.428     2.846     1.609     -0.755     2.846
    0.309     -0.487     2.846     -0.958     0.419     2.846     1.641     -0.766     2.846
    0.221     -0.454     2.846     -0.92     0.405     2.846     1.668     -0.775     2.846
    0.133     -0.42     2.846     -0.877     0.387     2.846     1.692     -0.782     2.846
    0.046     -0.385     2.846     -0.832     0.368     2.846     1.711     -0.788     2.846
    -0.04     -0.347     2.846     -0.781     0.346     2.846     1.726     -0.793     2.846
    -0.126     -0.307     2.846     -0.724     0.321     2.846     1.738     -0.796     2.846
    -0.21     -0.265     2.846     -0.663     0.292     2.846     1.746     -0.801     2.846
    -0.294     -0.221     2.846     -0.598     0.262     2.846     1.75     -0.807     2.846
    -0.374     -0.176     2.846     -0.531     0.231     2.846     1.751     -0.813     2.846
    -0.45     -0.13     2.846     -0.461     0.198     2.846
    -0.522     -0.084     2.846     -0.388     0.164     2.846
    X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置
    1.749     -0.884     3.201     -0.569     -0.034     3.201     -0.304     0.094     3.201
    1.747     -0.889     3.201     -0.634     0.013     3.201     -0.227     0.055     3.201
    1.743     -0.893     3.201     -0.695     0.06     3.201     -0.147     0.014     3.201
    1.735     -0.896     3.201     -0.752     0.106     3.201     -0.064     -0.028     3.201
    1.726     -0.895     3.201     -0.805     0.151     3.201     0.019     -0.07     3.201
    1.714     -0.892     3.201     -0.853     0.194     3.201     0.101     -0.113     3.201
    1.698     -0.889     3.201     -0.895     0.234     3.201     0.184     -0.155     3.201
    1.677     -0.884     3.201     -0.931     0.269     3.201     0.267     -0.197     3.201
    1.653     -0.879     3.201     -0.964     0.304     3.201     0.35     -0.239     3.201
    1.624     -0.872     3.201     -0.991     0.335     3.201     0.433     -0.281     3.201
    1.59     -0.865     3.201     -1.012     0.36     3.201     0.516     -0.323     3.201
    1.549     -0.856     3.201     -1.027     0.381     3.201     0.599     -0.365     3.201
    1.503     -0.847     3.201     -1.036     0.398     3.201     0.682     -0.407     3.201
    1.45     -0.835     3.201     -1.041     0.411     3.201     0.765     -0.448     3.201
    1.391     -0.823     3.201     -1.042     0.419     3.201     0.848     -0.489     3.201
    1.326     -0.808     3.201     -1.041     0.424     3.201     0.929     -0.529     3.201
    1.255     -0.792     3.201     -1.04     0.426     3.201     1.007     -0.566     3.201
    1.181     -0.774     3.201     -1.039     0.427     3.201     1.083     -0.602     3.201
    1.104     -0.756     3.201     -1.038     0.428     3.201     1.156     -0.636     3.201
    1.024     -0.735     3.201     -1.038     0.428     3.201     1.226     -0.667     3.201
    0.942     -0.713     3.201     -1.037     0.429     3.201     1.295     -0.697     3.201
    0.857     -0.689     3.201     -1.035     0.431     3.201     1.36     -0.726     3.201
    0.769     -0.663     3.201     -1.031     0.433     3.201     1.42     -0.751     3.201
    0.679     -0.636     3.201     -1.023     0.435     3.201     1.475     -0.773     3.201
    0.589     -0.606     3.201     -1.009     0.434     3.201     1.524     -0.792     3.201
    0.5     -0.576     3.201     -0.991     0.43     3.201     1.567     -0.808     3.201
    0.411     -0.544     3.201     -0.968     0.423     3.201     1.605     -0.822     3.201
    0.323     -0.51     3.201     -0.939     0.411     3.201     1.637     -0.833     3.201
    0.235     -0.475     3.201     -0.902     0.395     3.201     1.665     -0.842     3.201
    0.149     -0.438     3.201     -0.86     0.375     3.201     1.688     -0.85     3.201
    0.062     -0.399     3.201     -0.815     0.354     3.201     1.707     -0.856     3.201
    -0.023     -0.358     3.201     -0.765     0.329     3.201     1.723     -0.86     3.201
    -0.108     -0.316     3.201     -0.71     0.301     3.201     1.735     -0.864     3.201
    -0.191     -0.271     3.201     -0.649     0.27     3.201     1.743     -0.868     3.201
    -0.275     -0.224     3.201     -0.586     0.238     3.201     1.748     -0.874     3.201
    -0.354     -0.177     3.201     -0.52     0.204     3.201     1.75     -0.88     3.201
    -0.43     -0.129     3.201     -0.451     0.169     3.201
    -0.501     -0.082     3.201     -0.379     0.132     3.201
    X-位置   Y-位置     Z-位置     X-位置     Y-位置     Z-位置     X-位置     Y-位置     Z-位置
    1.693   -0.934     3.556     -0.533     0     3.556     -0.3     0.07     3.556
    1.691   -0.938     3.556     -0.595     0.047     3.556     -0.226     0.028     3.556
    1.687   -0.943     3.556     -0.654     0.092     3.556     -0.149     -0.015     3.556
    1.68   -0.947     3.556     -0.71     0.137     3.556     -0.069     -0.06     3.556
    1.671   -0.946     3.556     -0.762     0.182     3.556     0.011     -0.104     3.556
    1.658   -0.944     3.556     -0.809     0.223     3.556     0.09     -0.148     3.556
    1.643   -0.941     3.556     -0.85     0.261     3.556     0.17     -0.192     3.556
    1.623   -0.937     3.556     -0.886     0.295     3.556     0.25     -0.236     3.556
    1.599   -0.933     3.556     -0.919     0.329     3.556     0.33     -0.28     3.556
    1.57   -0.927     3.556     -0.947     0.358     3.556     0.41     -0.325     3.556
    1.536   -0.92     3.556     -0.968     0.381     3.556     0.49     -0.369     3.556
    1.497   -0.912     3.556     -0.983     0.401     3.556     0.57     -0.413     3.556
    1.451   -0.902     3.556     -0.994     0.416     3.556     0.65     -0.457     3.556
    1.4   -0.89     3.556     -1     0.429     3.556     0.73     -0.5     3.556
    1.342   -0.876     3.556     -1.003     0.436     3.556     0.81     -0.544     3.556
    1.279   -0.86     3.556     -1.003     0.441     3.556     0.888     -0.585     3.556
    1.21   -0.841     3.556     -1.003     0.443     3.556     0.964     -0.625     3.556
    1.138   -0.82     3.556     -1.002     0.445     3.556     1.037     -0.662     3.556
    1.064   -0.797     3.556     -1.002     0.445     3.556     1.108     -0.697     3.556
    0.988   -0.772     3.556     -1.002     0.446     3.556     1.176     -0.73     3.556
    0.909   -0.744     3.556     -1.001     0.446     3.556     1.243     -0.76     3.556
    0.827   -0.715     3.556     -0.998     0.447     3.556     1.307     -0.788     3.556
    0.743   -0.683     3.556     -0.993     0.448     3.556     1.366     -0.812     3.556
    0.657   -0.649     3.556     -0.986     0.447     3.556     1.42     -0.834     3.556
    0.572   -0.614     3.556     -0.973     0.444     3.556     1.468     -0.852     3.556
    0.487   -0.577     3.556     -0.955     0.438     3.556     1.511     -0.867     3.556
    0.402   -0.54     3.556     -0.933     0.428     3.556     1.549     -0.879     3.556
    0.319   -0.501     3.556     -0.906     0.414     3.556     1.581     -0.889     3.556
    0.235   -0.461     3.556     -0.871     0.395     3.556     1.609     -0.897     3.556
    0.153   -0.42     3.556     -0.831     0.373     3.556     1.632     -0.903     3.556
    0.071   -0.377     3.556     -0.789     0.349     3.556     1.651     -0.908     3.556
    -0.01   -0.333     3.556     -0.741     0.322     3.556     1.666     -0.912     3.556
    -0.091   -0.287     3.556     -0.689     0.291     3.556     1.678     -0.915     3.556
    -0.17   -0.24     3.556     -0.631     0.258     3.556     1.687     -0.918     3.556
    -0.249   -0.192     3.556     -0.57     0.223     3.556     1.691     -0.924     3.556
    -0.325   -0.143     3.556     -0.507     0.187     3.556     1.693     -0.929     3.556
    -0.398   -0.095     3.556     -0.441     0.149     3.556
    -0.467   -0.047     3.556     -0.372     0.11     3.556
也应当理解，在以上表1中公开的示范性翼型件可几何地放大或缩小，以便用于其它相似的压缩机设计中。因此，在表1中提出的坐标值可放大或缩小，以使翼型件型面形状保持不变。表1中坐标的缩放方案将以表1中的X、Y和Z坐标值乘或除以一常数来表示。
尽管本文中描述了各种实施例，但是应当从说明书中理解：本领域技术人员可以作出本发明中各种部件的组合、变更或改进，且其属于本发明的范围内。

Claims (9)

1.一种制造物品，所述物品具有主要根据在表1中列出的X、Y和Z的笛卡尔坐标值的标称型面，且其中X和Y为当由平滑连续的弧连接时在每个Z英寸距离处限定翼型型面截面的英寸距离，在Z距离处的所述型面截面彼此平滑地连接，以便形成整个翼型形状(22，23)。
2.根据权利要求1所述的制造物品，其特征在于，所述物品包括翼型件(22，23)。
3.根据权利要求2所述的制造物品，其特征在于，所述物品形状处于沿垂直于所述物品任何表面位置的方向在±0.160英寸内的包络中。
4.根据权利要求1所述的制造物品，其特征在于，所述物品包括转子(22)。
5.一种包括压缩机叶轮的压缩机，所述压缩机叶轮具有多个制造物品，所述制造物品中的每个都包括具有翼型形状的翼型件，所述翼型件具有主要根据表1中列出的X、Y和Z的笛卡尔坐标值的标称型面，其中X和Y为当由平滑连续的弧连接时在每个Z英寸距离处限定翼型型面截面的英寸距离，在Z距离处所述型面截面彼此平滑地连接，以便形成整个翼型形状(22，23)。
6.根据权利要求5所述的压缩机，其特征在于，所述制造物品包括转子(22)。
7.一种包括压缩机叶轮(51)的压缩机(2)，所述压缩机叶轮具有多个制造物品，所述制造物品中的每个都包括具有主要根据表1中列出的X、Y和Z的笛卡尔坐标值的未涂敷标称翼型型面的翼型件，其中X和Y为当由平滑连续的弧连接时在每个Z英寸距离处限定翼型型面截面的英寸距离，在Z距离处所述型面截面彼此平滑地连接，以便形成整个翼型形状(22，23)，所述X和所述Y可作为相同常数或数字的函数而缩放，以便提供放大或缩小的转子叶片翼型件(22，23)。
8.根据权利要求7所述的压缩机(2)，其特征在于，所述制造物品包括转子(22)。
9.根据权利要求7所述的压缩机(2)，其特征在于，所述翼型形状处于沿垂直于任何翼型表面位置的方向在±0.160英寸内的包络中。
CNA2007101670994A 2006-10-25 2007-10-25 用于压缩机的翼型形状 Pending CN101169124A (zh)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US11/586055 2006-10-25
US11/586,055 US7494321B2 (en) 2006-10-25 2006-10-25 Airfoil shape for a compressor

Publications (1)

Publication Number Publication Date
CN101169124A true CN101169124A (zh) 2008-04-30

Family

ID=38982772

Family Applications (1)

Application Number Title Priority Date Filing Date
CNA2007101670994A Pending CN101169124A (zh) 2006-10-25 2007-10-25 用于压缩机的翼型形状

Country Status (4)

Country Link
US (1) US7494321B2 (zh)
EP (1) EP1921261A3 (zh)
JP (1) JP2008106750A (zh)
CN (1) CN101169124A (zh)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111156195A (zh) * 2020-01-07 2020-05-15 哈尔滨工程大学 一种新型的压气机叶片前缘结构

Families Citing this family (56)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7581930B2 (en) * 2006-08-16 2009-09-01 United Technologies Corporation High lift transonic turbine blade
US7611326B2 (en) * 2006-09-06 2009-11-03 Pratt & Whitney Canada Corp. HP turbine vane airfoil profile
US7534092B2 (en) * 2006-10-25 2009-05-19 General Electric Company Airfoil shape for a compressor
US7572105B2 (en) * 2006-10-25 2009-08-11 General Electric Company Airfoil shape for a compressor
US7566202B2 (en) * 2006-10-25 2009-07-28 General Electric Company Airfoil shape for a compressor
US7520729B2 (en) * 2006-10-25 2009-04-21 General Electric Company Airfoil shape for a compressor
US7510378B2 (en) * 2006-10-25 2009-03-31 General Electric Company Airfoil shape for a compressor
US7530793B2 (en) * 2006-10-25 2009-05-12 General Electric Company Airfoil shape for a compressor
US7572104B2 (en) * 2006-10-25 2009-08-11 General Electric Company Airfoil shape for a compressor
US7517197B2 (en) * 2006-10-25 2009-04-14 General Electric Company Airfoil shape for a compressor
US7513748B2 (en) * 2006-10-25 2009-04-07 General Electric Company Airfoil shape for a compressor
US7497665B2 (en) * 2006-11-02 2009-03-03 General Electric Company Airfoil shape for a compressor
US7537434B2 (en) * 2006-11-02 2009-05-26 General Electric Company Airfoil shape for a compressor
US7568892B2 (en) * 2006-11-02 2009-08-04 General Electric Company Airfoil shape for a compressor
US7559748B2 (en) * 2006-11-28 2009-07-14 Pratt & Whitney Canada Corp. LP turbine blade airfoil profile
US9297259B2 (en) * 2012-06-14 2016-03-29 Alstom Technology Compressor blade
US9732761B2 (en) 2015-09-04 2017-08-15 General Electric Company Airfoil shape for a compressor
US10041370B2 (en) 2015-09-04 2018-08-07 General Electric Company Airfoil shape for a compressor
US9745994B2 (en) 2015-09-04 2017-08-29 General Electric Company Airfoil shape for a compressor
US9951790B2 (en) 2015-09-04 2018-04-24 General Electric Company Airfoil shape for a compressor
US9759227B2 (en) 2015-09-04 2017-09-12 General Electric Company Airfoil shape for a compressor
US9957964B2 (en) 2015-09-04 2018-05-01 General Electric Company Airfoil shape for a compressor
US9777744B2 (en) 2015-09-04 2017-10-03 General Electric Company Airfoil shape for a compressor
US9759076B2 (en) 2015-09-04 2017-09-12 General Electric Company Airfoil shape for a compressor
US9771948B2 (en) 2015-09-04 2017-09-26 General Electric Company Airfoil shape for a compressor
US9938985B2 (en) 2015-09-04 2018-04-10 General Electric Company Airfoil shape for a compressor
US9746000B2 (en) 2015-09-04 2017-08-29 General Electric Company Airfoil shape for a compressor
US10415594B2 (en) 2016-09-21 2019-09-17 General Electric Company Airfoil shape for second stage compressor stator vane
US10393144B2 (en) 2016-09-21 2019-08-27 General Electric Company Airfoil shape for tenth stage compressor rotor blade
US10415593B2 (en) 2016-09-21 2019-09-17 General Electric Company Airfoil shape for inlet guide vane of a compressor
US10415463B2 (en) 2016-09-21 2019-09-17 General Electric Company Airfoil shape for third stage compressor rotor blade
US10422342B2 (en) 2016-09-21 2019-09-24 General Electric Company Airfoil shape for second stage compressor rotor blade
US10415585B2 (en) 2016-09-21 2019-09-17 General Electric Company Airfoil shape for fourth stage compressor rotor blade
US10415464B2 (en) 2016-09-21 2019-09-17 General Electric Company Airfoil shape for thirteenth stage compressor rotor blade
US10443610B2 (en) 2016-09-22 2019-10-15 General Electric Company Airfoil shape for eleventh stage compressor rotor blade
US10415595B2 (en) 2016-09-22 2019-09-17 General Electric Company Airfoil shape for fifth stage compressor stator vane
US10443618B2 (en) 2016-09-22 2019-10-15 General Electric Company Airfoil shape for ninth stage compressor stator vane
US10287886B2 (en) 2016-09-22 2019-05-14 General Electric Company Airfoil shape for first stage compressor rotor blade
US10233759B2 (en) 2016-09-22 2019-03-19 General Electric Company Airfoil shape for seventh stage compressor stator vane
US10436214B2 (en) 2016-09-22 2019-10-08 General Electric Company Airfoil shape for tenth stage compressor stator vane
US10436215B2 (en) 2016-09-22 2019-10-08 General Electric Company Airfoil shape for fifth stage compressor rotor blade
US10422343B2 (en) 2016-09-22 2019-09-24 General Electric Company Airfoil shape for fourteenth stage compressor rotor blade
US10087952B2 (en) 2016-09-23 2018-10-02 General Electric Company Airfoil shape for first stage compressor stator vane
US10443492B2 (en) 2016-09-27 2019-10-15 General Electric Company Airfoil shape for twelfth stage compressor rotor blade
US10443611B2 (en) 2016-09-27 2019-10-15 General Electric Company Airfoil shape for eighth stage compressor rotor blade
US10465710B2 (en) 2016-09-28 2019-11-05 General Electric Company Airfoil shape for thirteenth stage compressor stator vane
US10465709B2 (en) 2016-09-28 2019-11-05 General Electric Company Airfoil shape for eighth stage compressor stator vane
US10519973B2 (en) 2016-09-29 2019-12-31 General Electric Company Airfoil shape for seventh stage compressor rotor blade
US10519972B2 (en) 2016-09-29 2019-12-31 General Electric Company Airfoil shape for sixth stage compressor rotor blade
US10041503B2 (en) 2016-09-30 2018-08-07 General Electric Company Airfoil shape for ninth stage compressor rotor blade
US10288086B2 (en) 2016-10-04 2019-05-14 General Electric Company Airfoil shape for third stage compressor stator vane
US10132330B2 (en) 2016-10-05 2018-11-20 General Electric Company Airfoil shape for eleventh stage compressor stator vane
US10066641B2 (en) 2016-10-05 2018-09-04 General Electric Company Airfoil shape for fourth stage compressor stator vane
US10012239B2 (en) 2016-10-18 2018-07-03 General Electric Company Airfoil shape for sixth stage compressor stator vane
US10060443B2 (en) 2016-10-18 2018-08-28 General Electric Company Airfoil shape for twelfth stage compressor stator vane
US10648338B2 (en) * 2018-09-28 2020-05-12 General Electric Company Airfoil shape for second stage compressor stator vane

Family Cites Families (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6331100B1 (en) * 1999-12-06 2001-12-18 General Electric Company Doubled bowed compressor airfoil
US6299412B1 (en) * 1999-12-06 2001-10-09 General Electric Company Bowed compressor airfoil
GB0001399D0 (en) * 2000-01-22 2000-03-08 Rolls Royce Plc An aerofoil for an axial flow turbomachine
US6450770B1 (en) * 2001-06-28 2002-09-17 General Electric Company Second-stage turbine bucket airfoil
US6715990B1 (en) * 2002-09-19 2004-04-06 General Electric Company First stage turbine bucket airfoil
US6779977B2 (en) * 2002-12-17 2004-08-24 General Electric Company Airfoil shape for a turbine bucket
US6779980B1 (en) * 2003-03-13 2004-08-24 General Electric Company Airfoil shape for a turbine bucket
US6769878B1 (en) * 2003-05-09 2004-08-03 Power Systems Mfg. Llc Turbine blade airfoil
US6854961B2 (en) * 2003-05-29 2005-02-15 General Electric Company Airfoil shape for a turbine bucket
US6884038B2 (en) * 2003-07-18 2005-04-26 General Electric Company Airfoil shape for a turbine bucket
US6923623B2 (en) * 2003-08-07 2005-08-02 General Electric Company Perimeter-cooled turbine bucket airfoil cooling hole location, style and configuration
US7094034B2 (en) * 2004-07-30 2006-08-22 United Technologies Corporation Airfoil profile with optimized aerodynamic shape
US7186090B2 (en) * 2004-08-05 2007-03-06 General Electric Company Air foil shape for a compressor blade

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111156195A (zh) * 2020-01-07 2020-05-15 哈尔滨工程大学 一种新型的压气机叶片前缘结构
CN111156195B (zh) * 2020-01-07 2023-11-17 哈尔滨工程大学 一种压气机叶片前缘结构

Also Published As

Publication number Publication date
JP2008106750A (ja) 2008-05-08
EP1921261A2 (en) 2008-05-14
EP1921261A3 (en) 2008-12-03
US7494321B2 (en) 2009-02-24
US20080101948A1 (en) 2008-05-01

Similar Documents

Publication Publication Date Title
CN101169124A (zh) 用于压缩机的翼型形状
CN101169123A (zh) 用于压缩机的翼型形状
US7993100B2 (en) Airfoil shape for a compressor
CN101169126A (zh) 用于压缩机的翼片形状
CN101169047B (zh) 转子叶片外形优化
CN101173677A (zh) 用于压缩机的翼面形状
CN101173678A (zh) 用于压缩机的翼面形状
CN101173679A (zh) 用于压缩机的翼面形状
CN1924299B (zh) 定子叶片的型面优化
CN100419216C (zh) 透平叶片的翼面形状
US8591193B2 (en) Airfoil shape for a compressor blade
JP2008115854A (ja) 圧縮機用の翼形状
JP2008115853A (ja) 圧縮機用の翼形状
JP2008115852A (ja) 圧縮機用の翼形状
US20100092298A1 (en) Airfoil shape for a compressor
CN102384103B (zh) 用于压缩机的翼型件形状
JP2008106755A (ja) 圧縮機用の翼形状
JP2008106762A (ja) 圧縮機用の翼形状
CN100339558C (zh) 用于涡轮叶片的内部芯轮廓
US20100092283A1 (en) Airfoil shape for a compressor
JP2008106763A (ja) 圧縮機用の翼形状
JP2008106761A (ja) 圧縮機用の翼形部形状
JP2008106771A (ja) 圧縮機用の翼形部形状
JP2008106759A (ja) 圧縮機用の翼形部形状
JP2008106767A (ja) 圧縮機用の翼形部形状

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C02 Deemed withdrawal of patent application after publication (patent law 2001)
WD01 Invention patent application deemed withdrawn after publication

Open date: 20080430