CN1607318A - 用于涡轮叶片翼面的内部核心轮廓 - Google Patents
用于涡轮叶片翼面的内部核心轮廓 Download PDFInfo
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Abstract
第一级涡轮叶片(16)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内部标称核心轮廓,其中X和Y值以英寸为单位,Z值是无量纲值,可通过将Z值乘以以英寸为单位的翼面高度来将Z转换成以英寸为单位的Z长度。X和Y值是长度,当用平滑连续的弧将所述X和Y相连结时,就会在各Z值处形成内部核心轮廓截面。将各Z值处的轮廓截面彼此互相平滑地连结,则形成整体的内部核心轮廓。X、Y和Z值作为相同常数或数值的函数可按比例变化,从而提供按比例扩大或缩小的内部核心轮廓。由X、Y和Z值给定的标称内部核心轮廓位于一个包络中,该包络是在垂直于任何内部核心表面位置的方向上±0.050英寸的范围内。
Description
技术领域
本发明涉及一种燃气涡轮的一个级的叶片,尤其涉及第一级涡轮叶片翼面的内部核心轮廓。
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,对于燃气涡轮的热气通道部分的每一级来说,都必须满足许多系统需求。特别是,涡轮部的第一级的叶片必须满足该特殊级的运行需求,并满足叶片冷却气流、重量和叶片寿命的要求。内部冷却需求必须达到最优化,即必须使一个特殊的内部核心轮廓满足该级性能需求,从而使涡轮在安全、高效和平稳的状态下运行。
发明内容
根据本发明的一种优选实施方式,提供一种用于燃气涡轮的叶片翼面(优选第一级翼面)的特殊内部核心轮廓,以提高燃气涡轮的性能。应该理解,叶片翼面的外部翼面形状加强了涡轮的不同级之间的相互作用,并能承受提高了的空气动力学效率和更大的第一级叶片翼面空气动力学负荷和机械负荷。用于优选叶片的外部翼面轮廓在一个共同专利申请中提出,该共同专利申请号为No.10/446688,于2003年5月29日提交,名称为“涡轮叶片的翼面形状”(“AirfoilShape for a Turbine Bucket”),其公开的内容在此引入作为参考。同样的,翼面的内部核心形状也是重要的,这不仅由于结构的原因,而且由于要以合适的壁厚达到内部冷却的最优化。翼面内部核心轮廓通过多个点的一种特殊分布确定,所述点的分布满足必要的结构和冷却需求,借以提高涡轮性能。这些点的这种特殊分布形成了内部标称核心轮廓,该分布由下面表I中X、Y和Z的笛卡儿坐标确定。对应于表I中示出的坐标值的1100个点,是用于低温即室温下的叶片翼面,在沿着翼面的长度方向不同的横截面处截取的。正的X、Y和Z的方向分别为轴向朝向涡轮排气端、从发动机旋转方向的切向看向后的方向和径向向外朝向叶片顶部。X和Y的坐标以长度单位给出,例如以英寸为单位,并且在各Z值处平滑地连结,从而形成一个光滑、连续的内部核心轮廓横截面。Z坐标以无量纲形式从Z=0.043到Z=0.997给出。通过将例如以英寸为单位的翼面高度尺寸,乘以表I中的无量纲Z值,就可以获得翼面的内部核心轮廓。将在X和Y平面内形成的每个内部核心轮廓截面与Z方向上相邻的轮廓截面平滑地连结,则形成完整的内部翼面核心轮廓。
优选的第一级涡轮叶片翼面包括外部凸的和凹的侧壁表面,若干肋在所述侧壁表面内部间延伸,并与确定外部侧壁表面的所述侧壁一体成形。这些肋在翼面的前缘和后缘之间彼此间隔开,并与翼面侧壁的内壁表面一起形成内部冷却通道,优选的是,沿着翼面长度方向成螺旋构形。光滑连续的弧在X和Y坐标之间延伸以形成在各Z值处的每个轮廓截面,该弧沿着冷却通道的内壁表面,并介于沿着各侧壁的相邻通道之间延伸,从而与相邻的外壁表面基本上一致。因此,每个内部核心轮廓截面具有包络部分,所述包络部分穿过介于肋和每个侧壁之间的结合部分或交界面,并与介于肋之间的冷却通道的侧壁同向。这些内部核心轮廓截面总体上形成翼面,并与叶片翼面的外部翼面形状减去每个Z值处的壁厚基本上一致。
应该理解,因为在应用中每个翼面升温,所以作为机械负荷和温度变化的结果,内部核心轮廓会发生变形。因此,由X、Y和Z的坐标给定的在低温或室温下的轮廓是用于制造的目的。由于制造的叶片内部核心轮廓可能与下面表中给出的标称轮廓不同,所以,在垂直于沿着标称轮廓任何表面位置的方向上,从标称轮廓加上或减去0.050英寸的长度,则确定用于这种翼面内部核心轮廓的一个轮廓包络。所述轮廓对于这个变化是足以承受的,不会损害叶片的机械性能、冷却性能和空气动力学性能。
还应该理解,翼面可以按几何比例扩大或缩小,从而用于引入相似的涡轮设计中。因此,下面给出的内部标称核心轮廓的以英寸为单位的X和Y坐标以及无量纲Z坐标,当Z坐标转换成以英寸为单位时,可以是相同常数或数值的函数。也就是说,以英寸为单位的X、Y和Z坐标可以乘以或除以同一个常数或数值,从而提供内部翼面核心轮廓按比例扩大或缩小的形式,同时保持核心轮廓的截面形状不变。
在根据本发明的一种优选实施方式中,提供一种涡轮叶片,该叶片包括翼面、平台、叶根和楔形榫,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内部标称核心轮廓,其中Z值是无量纲值,可通过将Z值乘以以英寸为单位的翼面高度来将Z转换成以英寸为单位的Z长度,并且其中X和Y是以英寸为单位的长度,当用平滑连续的弧将所述X和Y相连接时,则形成沿着翼面在各Z值处的内部核心轮廓截面,在各Z值处的轮廓截面彼此互相平滑地连结,则形成翼面内部核心轮廓。
在根据本发明的另一种优选实施方式中,提供一种涡轮叶片,该叶片包括翼面、平台、叶根和楔形榫,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内部标称核心轮廓,其中Z值是无量纲值,可通过将Z值乘以以英寸为单位的翼面高度来将Z转换成以英寸为单位的Z长度,并且其中X和Y是以英寸为单位的长度,当用平滑连续的弧线将所述X和Y连接起来时,则形成沿着翼面在每个Z值处的内部核心轮廓截面,在各Z值处的轮廓截面彼此互相平滑地连结,则形成叶片内部核心轮廓,其中X、Y和Z值作为相同常数或数值的函数可按比例变化,从而提供按比例扩大或缩小的内部核心轮廓。
在根据本发明的另一种优选实施方式中,提供一种涡轮,该涡轮包括具有多个叶片的涡轮叶轮,每个叶片包括翼面、平台、叶根和楔形榫,每个翼面具有与表I中列出的X、Y和Z笛卡儿坐标值基本上一致的内部标称核心轮廓,其中Z值是无量纲值,可通过将Z值乘以以英寸为单位的叶片高度来将Z转换成以英寸为单位的Z长度,并且其中X和Y是以英寸为单位的长度,当用平滑连续的弧将所述X和Y相连接时,则形成沿着翼面在各Z值处形成内部核心轮廓截面,在各Z值处的轮廓载面彼此互相平滑地连结,则形成叶片内部核心轮廓。
附图说明
图1是穿过燃气涡轮的多个级的热气通道示意图,示出了根据本发明的一种优选实施方式的第一级叶片翼面;
图2是根据本发明一种优选实施方式的叶片透视图,其中叶片与它的翼面、平台和基本上轴向或近轴向的入口楔形榫连接件一起示出;
图3是基本上从周向看,图2中的叶片和与其相连的翼面、平台和楔形榫连接件的立面侧视图;
图4是叶片的顶视图;
图5是从逆流方向上看叶片的端视图;
图6是沿着穿过叶片翼面的切口截取的普通放大横截面图,以示出叶片翼面的内部核心轮廓。
具体实施方式
现在参照附图,尤其是图1,该图示出了包括多个涡轮级的燃气涡轮12的一个热气通道,该通道总体在图中以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。喷嘴沿周向彼此间隔开,并围绕转子的轴固定。当然,第一级叶片16安装在涡轮转子17上。图中还示出了燃气涡轮12的第二级,包括多个周向间隔开的喷嘴18和安装在转子17上周向间隔开的叶片20。图中也示出了第三级,包括多个周向间隔开的喷嘴22和安装在转子17上的叶片24。应该理解,喷嘴和叶片位于涡轮的热气通道10中,通过热气通道10的热气流的方向由箭头26指示。
参照图2,应该理解,这些叶片,例如第一级的叶片16安装在转子叶轮上(未示出)形成转子17的一部分,并且所述叶片16包括平台30,叶根32和楔形榫34。每个叶片16都具有一个基本上轴向或近轴向的入口楔形榫34,例如离轴大约15度,用于和叶轮上的形状互补搭配的楔形榫(未示出)相连接。但是可以安装一个轴向入口楔形榫。还应该理解,每个叶片16都有一个外部叶片翼面38,如图2和6所示。因此,在从翼面平台30到叶片顶部33之间的任一横截面处,每个叶片16都有一个叶片翼面轮廓,该轮廓以翼面38的形状为特征。在第一级涡轮叶片的这个优选实施方式中,有92个叶片翼面。虽然不够成本发明的一个部分,但是每个第一级叶片16都包括多个基本上为螺旋形状的内部冷却通道35(图6),从而形成若干个从平台向叶片翼面顶部延伸的空气冷却回路。这些空气冷却回路从翼面38向在出口位置的热气通道中排入冷却空气,其中出口位置邻近翼面的前缘和后缘。
更具体而言,每个叶片翼面38都包括凸的和凹的外壁表面,即分别为压力面42和负压面44(图6),它们和一个内部核心轮廓40共同确定一个翼面壁厚“t”。每个叶片16还包括多个肋46,这些肋在叶片相对的侧壁48之间延伸或凸出。肋46分别在叶片翼面的前缘52和后缘54之间彼此间隔,并从平台30向叶片翼面顶部33延伸,从而与叶片侧壁48的内壁表面部分49一起,确定多个基本上为螺旋形状的内部冷却通道35。一定量的肋46在未达到翼面顶部的地方终止。
为了在从平台30到叶片翼面38的顶部33之间形成每个第一级叶片的内部核心轮廓,在空间中设置有一组独特的点的分布,其能够满足该级需求,即能满足叶片冷却面积和壁厚且能够制造。确定叶片内部核心轮廓40的点的这种特殊分布包括与涡轮转动轴线相关的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翼面38沿着其长度方向在不同位置处的该内部核心轮廓40。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。在表I中Z值以无量纲形式从Z=0.043到Z=0.997列出。要将Z值转换成Z的坐标值,例如以英寸为单位,那么将表中给出的无量纲Z值乘以以英寸为单位的翼面38的高度就可以。对于这个优选的第一级叶片来说,从平台30到翼面顶部的翼面高度是6.3英寸。对于这个优选的翼面来说,Z=0的无量纲坐标值是离转子中心线(发动机轴线)28.0英寸位置处。对于这个优选的翼面来说,Z=1的无量纲坐标值是离转子中心线(发动机轴线)Z=32.3英寸处。笛卡儿坐标系具有正交关系的X、Y和Z坐标轴,并且X轴与涡轮转子中心线平行,即旋转轴线和正的X坐标值是轴向朝向尾部,也就是涡轮的排气端。正的Y坐标值在转子的旋转方向的切向看向后的方向,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,在沿着翼面的长度方向上每个Z值处就可以确定叶片的内部核心轮廓40,例如,在图6中由虚线和实线示意性地表示出来的内部核心轮廓。通过用光滑连续的弧将X和Y值连结,就可以固定在每个Z值处形成的的每个内部核心轮廓。通过光滑地连结彼此相邻的轮廓截面以形成核心轮廓,就可以确定介于长度Z之间的各内部位置的内部核心轮廓。这些值描绘出在周围的非运行或非热条件下的内部核心轮廓。
光滑连续的弧在X和Y坐标之间延伸以形成各Z值处截面轮廓,该弧沿着内壁表面部分49,并介于沿着从平台朝向叶片翼面顶部的各侧壁48的相邻通道35之间延伸。因此,每个内部核心轮廓40都有包络部分,该包络部分穿过介于肋46和侧壁48之间的结合部分(在图6中用虚线表示),并与冷却通道的侧壁同向(在图6中用实线表示)。
表I的数值产生并示出至小数点后三位,用于确定叶片的内部核心轮廓。在翼面的实际内部轮廓中,必须考虑常规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内部核心轮廓。因此应当理解,±常规制造公差,即±包括涂层厚度在内的值,被附加到下面表I中给出的X和Y值中。因此,在垂直于沿着内部核心轮廓的任何表面位置的方向上,±0.050英寸的长度为这种特殊的叶片设计和涡轮确定了一个内部核心轮廓包络,即在标称低温或室温下,在实际的内部核心轮廓上测量的点和同温下如下面表中给出的那些点的理想分布之间变化的范围。该内部核心轮廓相对于这个变化范围是足以承受的,不会损害机械性能和冷却性能。
下面表I中给出的坐标值提供了优选的标称内部核心轮廓包络。
表I
X | Y | Z | X | Y | Z | X | Y | Z |
-1.335 | -0.336 | 0.043 | -0.157 | 0.180 | 0.043 | -1.374 | -0.107 | 0.139 |
-1.278 | -0.312 | 0.043 | -0.095 | 0.173 | 0.043 | 0.157 | 0.530 | 0.139 |
-1.224 | -0.281 | 0.043 | -0.033 | 0.163 | 0.043 | -1.014 | -0.053 | 0.139 |
-1.170 | -0.247 | 0.043 | 0.029 | 0.148 | 0.043 | -1.059 | -0.095 | 0.139 |
-1.118 | -0.212 | 0.043 | 0.088 | 0.128 | 0.043 | 0.108 | 0.567 | 0.139 |
-1.067 | -0.175 | 0.043 | 0.147 | 0.105 | 0.043 | 0.202 | 0.488 | 0.139 |
-1.019 | -0.134 | 0.043 | 0.204 | 0.079 | 0.043 | -1.378 | -0.226 | 0.139 |
-0.970 | -0.096 | 0.043 | 0.260 | 0.049 | 0.043 | -0.964 | -0.018 | 0.139 |
-0.919 | -0.059 | 0.043 | 0.313 | 0.017 | 0.043 | -0.912 | 0.016 | 0.139 |
-0.867 | -0.023 | 0.043 | 0.366 | -0.019 | 0.043 | -1.108 | -0.132 | 0.139 |
-0.814 | 0.012 | 0.043 | 0.416 | -0.057 | 0.043 | -1.323 | -0.247 | 0.139 |
-0.759 | 0.042 | 0.043 | 0.464 | -0.097 | 0.043 | -1.389 | -0.166 | 0.139 |
-0.703 | 0.070 | 0.043 | 0.511 | -0.139 | 0.043 | -1.195 | 0.142 | 0.139 |
-0.646 | 0.098 | 0.043 | 0.556 | -0.183 | 0.043 | -1.158 | 0.191 | 0.139 |
-0.589 | 0.124 | 0.043 | 0.599 | -0.229 | 0.043 | -0.861 | 0.050 | 0.139 |
-0.530 | 0.147 | 0.043 | 0.639 | -0.277 | 0.043 | -1.160 | -0.166 | 0.139 |
X | Y | Z | X | Y | Z | X | Y | Z |
-0.470 | 0.165 | 0.043 | 0.679 | -0.326 | 0.043 | 0.055 | 0.598 | 0.139 |
-0.408 | 0.177 | 0.043 | 0.717 | -0.376 | 0.043 | 0.245 | 0.443 | 0.139 |
-0.346 | 0.184 | 0.043 | 0.754 | -0.427 | 0.043 | -1.265 | -0.229 | 0.139 |
-0.283 | 0.187 | 0.043 | 0.791 | -0.479 | 0.043 | -1.120 | 0.239 | 0.139 |
-0.154 | 0.669 | 0.043 | 0.825 | -0.532 | 0.043 | -1.081 | 0.287 | 0.139 |
-0.216 | 0.681 | 0.043 | 0.855 | -0.587 | 0.043 | -1.040 | 0.333 | 0.139 |
-0.279 | 0.686 | 0.043 | 0.910 | -0.602 | 0.043 | -0.999 | 0.379 | 0.139 |
-0.342 | 0.682 | 0.043 | 0.949 | -0.559 | 0.043 | -0.958 | 0.425 | 0.139 |
-0.404 | 0.672 | 0.043 | 0.924 | -0.502 | 0.043 | -0.915 | 0.469 | 0.139 |
-0.465 | 0.659 | 0.043 | 0.894 | -0.446 | 0.043 | -0.866 | 0.506 | 0.139 |
-0.526 | 0.642 | 0.043 | 0.865 | -0.390 | 0.043 | -0.813 | 0.537 | 0.139 |
-0.586 | 0.622 | 0.043 | 0.835 | -0.335 | 0.043 | -0.760 | 0.568 | 0.139 |
-0.644 | 0.599 | 0.043 | 0.803 | -0.281 | 0.043 | -0.706 | 0.598 | 0.139 |
-0.702 | 0.573 | 0.043 | 0.770 | -0.227 | 0.043 | -0.652 | 0.627 | 0.139 |
-0.757 | 0.543 | 0.043 | 0.736 | -0.174 | 0.043 | -0.595 | 0.652 | 0.139 |
-0.811 | 0.510 | 0.043 | 0.703 | -0.121 | 0.043 | -0.537 | 0.671 | 0.139 |
-0.863 | 0.475 | 0.043 | 0.670 | -0.067 | 0.043 | -0.477 | 0.687 | 0.139 |
-0.913 | 0.437 | 0.043 | 0.636 | -0.014 | 0.043 | -0.417 | 0.698 | 0.139 |
X | Y | Z | X | Y | Z | X | Y | Z |
-0.961 | 0.397 | 0.043 | 0.598 | 0.036 | 0.043 | -0.356 | 0.706 | 0.139 |
-1.007 | 0.353 | 0.043 | 0.557 | 0.084 | 0.043 | -0.294 | 0.707 | 0.139 |
-1.049 | 0.306 | 0.043 | 0.516 | 0.132 | 0.043 | -0.233 | 0.703 | 0.139 |
-1.088 | 0.257 | 0.043 | 0.476 | 0.180 | 0.043 | -0.173 | 0.691 | 0.139 |
-1.126 | 0.207 | 0.043 | 0.435 | 0.229 | 0.043 | -0.282 | 0.230 | 0.139 |
-1.163 | 0.156 | 0.043 | 0.395 | 0.277 | 0.043 | -0.344 | 0.230 | 0.139 |
-1.198 | 0.104 | 0.043 | 0.355 | 0.325 | 0.043 | -0.405 | 0.223 | 0.139 |
-1.233 | 0.051 | 0.043 | 0.314 | 0.373 | 0.043 | -0.466 | 0.214 | 0.139 |
-1.266 | -0.002 | 0.043 | 0.272 | 0.421 | 0.043 | -0.527 | 0.205 | 0.139 |
-1.300 | -0.055 | 0.043 | 0.230 | 0.467 | 0.043 | -0.582 | 0.179 | 0.139 |
-1.335 | -0.108 | 0.043 | 0.184 | 0.511 | 0.043 | -0.639 | 0.156 | 0.139 |
-1.374 | -0.157 | 0.043 | 0.135 | 0.550 | 0.043 | -0.696 | 0.133 | 0.139 |
-1.402 | -0.212 | 0.043 | 0.081 | 0.582 | 0.043 | -0.754 | 0.110 | 0.139 |
-1.412 | -0.274 | 0.043 | 0.025 | 0.609 | 0.043 | -0.809 | 0.083 | 0.139 |
-1.383 | -0.327 | 0.043 | -0.034 | 0.633 | 0.043 | -1.212 | -0.198 | 0.139 |
-0.220 | 0.186 | 0.043 | -0.094 | 0.653 | 0.043 | -1.265 | -0.229 | 0.139 |
X | Y | Z | X | Y | Z | X | Y | Z |
X | Y | Z | X | Y | Z | X | Y | Z |
0.286 | 0.397 | 0.139 | -1.328 | -0.162 | 0.234 | -0.190 | 0.258 | 0.234 |
0.521 | 0.113 | 0.139 | -1.269 | -0.158 | 0.234 | -0.131 | 0.246 | 0.234 |
0.560 | 0.065 | 0.139 | -1.216 | -0.131 | 0.234 | -0.073 | 0.232 | 0.234 |
0.598 | 0.016 | 0.139 | -1.166 | -0.098 | 0.234 | -0.016 | 0.215 | 0.234 |
0.633 | -0.034 | 0.139 | -1.117 | -0.064 | 0.234 | 0.040 | 0.194 | 0.234 |
0.666 | -0.086 | 0.139 | -1.069 | -0.029 | 0.234 | 0.094 | 0.168 | 0.234 |
0.700 | -0.138 | 0.139 | -1.023 | 0.011 | 0.234 | 0.146 | 0.138 | 0.234 |
0.733 | -0.190 | 0.139 | -0.977 | 0.049 | 0.234 | 0.196 | 0.105 | 0.234 |
0.765 | -0.242 | 0.139 | -0.928 | 0.082 | 0.234 | 0.246 | 0.072 | 0.234 |
0.795 | -0.296 | 0.139 | -0.876 | 0.112 | 0.234 | 0.295 | 0.038 | 0.234 |
0.825 | -0.349 | 0.139 | -0.823 | 0.141 | 0.234 | 0.344 | 0.004 | 0.234 |
0.854 | -0.404 | 0.139 | -0.770 | 0.168 | 0.234 | 0.393 | -0.032 | 0.234 |
0.883 | -0.458 | 0.139 | -0.716 | 0.193 | 0.234 | 0.440 | -0.069 | 0.234 |
0.910 | -0.513 | 0.139 | -0.660 | 0.216 | 0.234 | 0.485 | -0.108 | 0.234 |
0.881 | -0.560 | 0.139 | -0.604 | 0.236 | 0.234 | 0.526 | -0.151 | 0.234 |
0.827 | -0.553 | 0.139 | -0.547 | 0.253 | 0.234 | 0.565 | -0.197 | 0.234 |
0.795 | -0.500 | 0.139 | -0.488 | 0.262 | 0.234 | 0.604 | -0.242 | 0.234 |
0.761 | -0.449 | 0.139 | -0.428 | 0.268 | 0.234 | 0.642 | -0.289 | 0.234 |
X | Y | Z | X | Y | Z | X | Y | Z |
0.726 | -0.398 | 0.139 | -0.368 | 0.272 | 0.234 | 0.678 | -0.337 | 0.234 |
0.689 | -0.348 | 0.139 | -0.308 | 0.273 | 0.234 | 0.712 | -0.385 | 0.234 |
0.652 | -0.300 | 0.139 | -0.249 | 0.268 | 0.234 | 0.746 | -0.435 | 0.234 |
0.613 | -0.252 | 0.139 | -0.141 | 0.699 | 0.234 | 0.779 | -0.485 | 0.234 |
0.573 | -0.205 | 0.139 | -0.198 | 0.715 | 0.234 | 0.818 | -0.527 | 0.234 |
0.532 | -0.160 | 0.139 | -0.257 | 0.727 | 0.234 | 0.870 | -0.502 | 0.234 |
0.488 | -0.116 | 0.139 | -0.317 | 0.733 | 0.234 | 0.863 | -0.448 | 0.234 |
0.441 | -0.076 | 0.139 | -0.376 | 0.732 | 0.234 | 0.835 | -0.395 | 0.234 |
0.392 | -0.039 | 0.139 | -0.436 | 0.726 | 0.234 | 0.806 | -0.342 | 0.234 |
0.342 | -0.004 | 0.139 | -0.495 | 0.716 | 0.234 | 0.778 | -0.290 | 0.234 |
0.291 | 0.031 | 0.139 | -0.553 | 0.701 | 0.234 | 0.748 | -0.238 | 0.234 |
0.239 | 0.064 | 0.139 | -0.609 | 0.680 | 0.234 | 0.718 | -0.186 | 0.234 |
0.187 | 0.097 | 0.139 | -0.663 | 0.655 | 0.234 | 0.686 | -0.135 | 0.234 |
0.134 | 0.128 | 0.139 | -0.716 | 0.628 | 0.234 | 0.654 | -0.085 | 0.234 |
0.078 | 0.154 | 0.139 | -0.769 | 0.600 | 0.234 | 0.622 | -0.035 | 0.234 |
0.020 | 0.174 | 0.139 | -0.821 | 0.570 | 0.234 | 0.589 | 0.015 | 0.234 |
-0.040 | 0.190 | 0.139 | -0.871 | 0.537 | 0.234 | 0.554 | 0.064 | 0.234 |
-0.100 | 0.204 | 0.139 | -0.919 | 0.502 | 0.234 | 0.519 | 0.112 | 0.234 |
X | Y | Z | X | Y | Z | X | Y | Z |
-0.160 | 0.216 | 0.139 | -0.964 | 0.462 | 0.234 | 0.482 | 0.160 | 0.234 |
-0.221 | 0.225 | 0.139 | -1.007 | 0.420 | 0.234 | 0.445 | 0.207 | 0.234 |
-1.347 | -0.052 | 0.139 | -1.047 | 0.376 | 0.234 | 0.408 | 0.254 | 0.234 |
-1.235 | 0.095 | 0.139 | -1.086 | 0.330 | 0.234 | 0.370 | 0.300 | 0.234 |
-0.114 | 0.673 | 0.139 | -1.124 | 0.284 | 0.234 | 0.331 | 0.346 | 0.234 |
-0.056 | 0.650 | 0.139 | -1.162 | 0.238 | 0.234 | 0.292 | 0.391 | 0.234 |
0.000 | 0.625 | 0.139 | -1.199 | 0.191 | 0.234 | 0.252 | 0.435 | 0.234 |
0.326 | 0.351 | 0.139 | -1.236 | 0.144 | 0.234 | 0.210 | 0.478 | 0.234 |
0.365 | 0.303 | 0.139 | -1.272 | 0.096 | 0.234 | 0.167 | 0.519 | 0.234 |
0.405 | 0.256 | 0.139 | -1.306 | 0.047 | 0.234 | 0.121 | 0.558 | 0.234 |
0.444 | 0.208 | 0.139 | -1.338 | -0.004 | 0.234 | 0.074 | 0.595 | 0.234 |
0.482 | 0.161 | 0.139 | -1.362 | -0.059 | 0.234 | 0.023 | 0.627 | 0.234 |
-1.313 | 0.000 | 0.139 | -1.367 | -0.118 | 0.234 | -0.030 | 0.655 | 0.234 |
-1.275 | 0.048 | 0.139 | -1.330 | -0.161 | 0.234 | -0.084 | 0.679 | 0.234 |
X | Y | Z | X | Y | Z | X | Y | Z |
-1.281 | -0.082 | 0.330 | 0.019 | 0.225 | 0.330 | -1.257 | 0.009 | 0.425 |
-1.222 | -0.063 | 0.330 | 0.075 | 0.200 | 0.330 | -1.203 | 0.024 | 0.425 |
X | Y | Z | X | Y | Z | X | Y | Z |
-1.170 | -0.030 | 0.330 | 0.129 | 0.170 | 0.330 | -1.154 | 0.054 | 0.425 |
-1.120 | 0.006 | 0.330 | 0.178 | 0.133 | 0.330 | -1.108 | 0.086 | 0.425 |
-1.070 | 0.043 | 0.330 | 0.227 | 0.094 | 0.330 | -1.061 | 0.119 | 0.425 |
-1.022 | 0.081 | 0.330 | 0.276 | 0.057 | 0.330 | -1.016 | 0.153 | 0.425 |
-0.972 | 0.117 | 0.330 | 0.325 | 0.020 | 0.330 | -0.968 | 0.184 | 0.425 |
-0.920 | 0.150 | 0.330 | 0.375 | -0.016 | 0.330 | -0.920 | 0.213 | 0.425 |
-0.867 | 0.182 | 0.330 | 0.424 | -0.054 | 0.330 | -0.871 | 0.242 | 0.425 |
-0.814 | 0.213 | 0.330 | 0.472 | -0.093 | 0.330 | -0.822 | 0.271 | 0.425 |
-0.758 | 0.239 | 0.330 | 0.515 | -0.137 | 0.330 | -0.773 | 0.299 | 0.425 |
-0.700 | 0.260 | 0.330 | 0.555 | -0.184 | 0.330 | -0.691 | 0.713 | 0.425 |
-0.643 | 0.283 | 0.330 | 0.594 | -0.232 | 0.330 | -0.743 | 0.689 | 0.425 |
-0.584 | 0.302 | 0.330 | 0.632 | -0.280 | 0.330 | -0.794 | 0.665 | 0.425 |
-0.523 | 0.312 | 0.330 | 0.669 | -0.330 | 0.330 | -0.844 | 0.638 | 0.425 |
-0.461 | 0.316 | 0.330 | 0.705 | -0.380 | 0.330 | -0.888 | 0.603 | 0.425 |
-0.400 | 0.317 | 0.330 | 0.739 | -0.431 | 0.330 | -0.932 | 0.567 | 0.425 |
-0.338 | 0.316 | 0.330 | 0.772 | -0.484 | 0.330 | -0.977 | 0.531 | 0.425 |
-0.276 | 0.312 | 0.330 | 0.802 | -0.538 | 0.330 | -1.021 | 0.496 | 0.425 |
-0.150 | 0.720 | 0.330 | 0.832 | -0.592 | 0.330 | -1.065 | 0.460 | 0.425 |
X | Y | Z | X | Y | Z | X | Y | Z |
-0.209 | 0.739 | 0.330 | 0.862 | -0.645 | 0.330 | -1.107 | 0.422 | 0.425 |
-0.269 | 0.753 | 0.330 | 0.914 | -0.648 | 0.330 | -1.145 | 0.380 | 0.425 |
-0.330 | 0.761 | 0.330 | 0.917 | -0.595 | 0.330 | -1.179 | 0.334 | 0.425 |
-0.392 | 0.763 | 0.330 | 0.890 | -0.539 | 0.330 | -1.212 | 0.288 | 0.425 |
-0.453 | 0.758 | 0.330 | 0.864 | -0.484 | 0.330 | -1.244 | 0.242 | 0.425 |
-0.514 | 0.746 | 0.330 | 0.837 | -0.428 | 0.330 | -1.275 | 0.194 | 0.425 |
-0.573 | 0.729 | 0.330 | 0.809 | -0.373 | 0.330 | -1.301 | 0.144 | 0.425 |
-0.630 | 0.706 | 0.330 | 0.780 | -0.319 | 0.330 | -1.318 | 0.090 | 0.425 |
-0.686 | 0.680 | 0.330 | 0.750 | -0.265 | 0.330 | -1.308 | 0.035 | 0.425 |
-0.741 | 0.652 | 0.330 | 0.719 | -0.212 | 0.330 | -1.260 | 0.009 | 0.425 |
-0.796 | 0.623 | 0.330 | 0.687 | -0.158 | 0.330 | -0.719 | 0.317 | 0.425 |
-0.849 | 0.592 | 0.330 | 0.656 | -0.105 | 0.330 | -0.664 | 0.331 | 0.425 |
-0.898 | 0.555 | 0.330 | 0.624 | -0.052 | 0.330 | -0.609 | 0.346 | 0.425 |
-0.944 | 0.514 | 0.330 | 0.589 | -0.001 | 0.330 | -0.554 | 0.359 | 0.425 |
-0.989 | 0.472 | 0.330 | 0.553 | 0.048 | 0.330 | -0.498 | 0.370 | 0.425 |
-1.034 | 0.430 | 0.330 | 0.515 | 0.097 | 0.330 | -0.442 | 0.365 | 0.425 |
-1.079 | 0.387 | 0.330 | 0.477 | 0.146 | 0.330 | -0.385 | 0.361 | 0.425 |
-1.123 | 0.344 | 0.330 | 0.439 | 0.194 | 0.330 | -0.329 | 0.357 | 0.425 |
X | Y | Z | X | Y | Z | X | Y | Z |
-1.164 | 0.298 | 0.330 | 0.401 | 0.243 | 0.330 | -0.272 | 0.353 | 0.425 |
-1.202 | 0.249 | 0.330 | 0.362 | 0.291 | 0.330 | -0.216 | 0.344 | 0.425 |
-1.238 | 0.199 | 0.330 | 0.324 | 0.339 | 0.330 | -0.145 | 0.737 | 0.425 |
-1.273 | 0.148 | 0.330 | 0.285 | 0.388 | 0.330 | -0.198 | 0.759 | 0.425 |
-1.305 | 0.095 | 0.330 | 0.247 | 0.436 | 0.330 | -0.252 | 0.775 | 0.425 |
-1.333 | 0.040 | 0.330 | 0.207 | 0.483 | 0.330 | -0.308 | 0.786 | 0.425 |
-1.347 | -0.020 | 0.330 | 0.162 | 0.525 | 0.330 | -0.364 | 0.790 | 0.425 |
-1.317 | -0.071 | 0.330 | 0.115 | 0.566 | 0.330 | -0.421 | 0.789 | 0.425 |
-0.215 | 0.302 | 0.330 | 0.067 | 0.604 | 0.330 | -0.477 | 0.785 | 0.425 |
-0.155 | 0.288 | 0.330 | 0.016 | 0.639 | 0.330 | -0.533 | 0.776 | 0.425 |
-0.097 | 0.269 | 0.330 | -0.037 | 0.670 | 0.330 | -0.588 | 0.759 | 0.425 |
-0.039 | 0.248 | 29.417 | -0.093 | 0.697 | 0.330 | -0.640 | 0.737 | 0.425 |
X | Y | Z | X | Y | Z | X | Y | Z |
-0.162 | 0.327 | 0.425 | 0.755 | -0.326 | 0.520 | 0.635 | -0.293 | 0.520 |
-0.108 | 0.310 | 0.425 | 0.729 | -0.278 | 0.520 | 0.667 | -0.338 | 0.520 |
-0.055 | 0.290 | 0.425 | -1.226 | 0.110 | 0.520 | 0.696 | -0.384 | 0.520 |
-0.004 | 0.266 | 0.425 | -1.173 | 0.123 | 0.520 | 0.738 | -0.411 | 0.520 |
X | Y | Z | X | Y | Z | X | Y | Z |
0.046 | 0.239 | 0.425 | -1.125 | 0.149 | 0.520 | 0.777 | -0.376 | 0.520 |
0.095 | 0.210 | 0.425 | -1.079 | 0.179 | 0.520 | 0.676 | -0.182 | 0.520 |
0.142 | 0.178 | 0.425 | -1.034 | 0.210 | 0.520 | 0.648 | -0.135 | 0.520 |
0.187 | 0.143 | 0.425 | -0.988 | 0.241 | 0.520 | 0.619 | -0.088 | 0.520 |
0.230 | 0.107 | 0.425 | -0.941 | 0.268 | 0.520 | 0.591 | -0.041 | 0.520 |
0.275 | 0.072 | 0.425 | -0.893 | 0.295 | 0.520 | 0.563 | 0.006 | 0.520 |
0.320 | 0.037 | 0.425 | -0.846 | 0.323 | 0.520 | 0.532 | 0.052 | 0.520 |
0.365 | 0.002 | 0.425 | -0.798 | 0.349 | 0.520 | 0.500 | 0.096 | 0.520 |
0.409 | -0.033 | 0.425 | -0.748 | 0.373 | 0.520 | 0.467 | 0.140 | 0.520 |
0.452 | -0.070 | 0.425 | -0.957 | 0.604 | 0.520 | 0.434 | 0.184 | 0.520 |
0.492 | -0.110 | 0.425 | -1.002 | 0.572 | 0.520 | 0.401 | 0.228 | 0.520 |
0.529 | -0.154 | 0.425 | -1.045 | 0.538 | 0.520 | 0.368 | 0.272 | 0.520 |
0.565 | -0.198 | 0.425 | -1.253 | 0.285 | 0.520 | 0.335 | 0.316 | 0.520 |
0.600 | -0.242 | 0.425 | -1.275 | 0.235 | 0.520 | -0.673 | 0.769 | 0.520 |
0.634 | -0.287 | 0.425 | -1.289 | 0.182 | 0.520 | -0.724 | 0.747 | 0.520 |
0.667 | -0.333 | 0.425 | -1.278 | 0.129 | 0.520 | -0.773 | 0.723 | 0.520 |
0.699 | -0.380 | 0.425 | -1.229 | 0.110 | 0.520 | -0.821 | 0.696 | 0.520 |
0.730 | -0.428 | 0.425 | -0.696 | 0.388 | 0.520 | -0.867 | 0.667 | 0.520 |
X | Y | Z | X | Y | Z | X | Y | Z |
0.772 | -0.459 | 0.425 | -0.642 | 0.400 | 0.520 | -0.912 | 0.636 | 0.520 |
0.813 | -0.424 | 0.425 | -0.588 | 0.412 | 0.520 | -0.144 | 0.758 | 0.520 |
0.792 | -0.372 | 0.425 | -0.534 | 0.421 | 0.520 | -0.193 | 0.782 | 0.520 |
0.767 | -0.321 | 0.425 | -0.480 | 0.424 | 0.520 | -0.244 | 0.801 | 0.520 |
0.740 | -0.271 | 0.425 | -0.425 | 0.420 | 0.520 | -0.298 | 0.813 | 0.520 |
0.712 | -0.222 | 0.425 | -0.370 | 0.414 | 0.520 | -0.352 | 0.821 | 0.520 |
0.684 | -0.173 | 0.425 | -0.316 | 0.407 | 0.520 | -0.407 | 0.825 | 0.520 |
0.654 | -0.124 | 0.425 | -0.262 | 0.396 | 0.520 | -0.462 | 0.823 | 0.520 |
0.625 | -0.076 | 0.425 | -0.209 | 0.381 | 0.520 | -0.516 | 0.817 | 0.520 |
0.594 | -0.028 | 0.425 | -0.158 | 0.363 | 0.520 | -0.570 | 0.805 | 0.520 |
0.564 | 0.020 | 0.425 | -0.107 | 0.343 | 0.520 | -0.622 | 0.788 | 0.520 |
0.532 | 0.067 | 0.425 | -0.057 | 0.320 | 0.520 | 0.302 | 0.360 | 0.520 |
0.500 | 0.114 | 0.425 | -0.007 | 0.296 | 0.520 | 0.270 | 0.404 | 0.520 |
0.466 | 0.160 | 0.425 | 0.040 | 0.269 | 0.520 | 0.236 | 0.447 | 0.520 |
0.432 | 0.205 | 0.425 | 0.086 | 0.239 | 0.520 | 0.202 | 0.490 | 0.520 |
0.397 | 0.250 | 0.425 | 0.130 | 0.206 | 0.520 | 0.164 | 0.530 | 0.520 |
0.362 | 0.294 | 0.425 | 0.173 | 0.171 | 0.520 | 0.124 | 0.567 | 0.520 |
0.327 | 0.339 | 0.425 | 0.215 | 0.136 | 0.520 | 0.082 | 0.602 | 0.520 |
X | Y | Z | X | Y | Z | X | Y | Z |
0.290 | 0.382 | 0.425 | 0.257 | 0.101 | 0.520 | 0.038 | 0.636 | 0.520 |
0.254 | 0.426 | 0.425 | 0.299 | 0.066 | 0.520 | -0.006 | 0.668 | 0.520 |
0.216 | 0.468 | 0.425 | 0.341 | 0.031 | 0.520 | -0.051 | 0.699 | 0.520 |
0.178 | 0.510 | 0.425 | 0.383 | -0.004 | 0.520 | -0.097 | 0.730 | 0.520 |
0.137 | 0.550 | 0.425 | 0.425 | -0.041 | 0.520 | -1.085 | 0.501 | 0.520 |
0.095 | 0.588 | 0.425 | 0.464 | -0.079 | 0.520 | -1.122 | 0.461 | 0.520 |
0.051 | 0.623 | 0.425 | 0.501 | -0.120 | 0.520 | -1.157 | 0.418 | 0.520 |
0.004 | 0.655 | 0.425 | 0.535 | -0.162 | 0.520 | -1.192 | 0.375 | 0.520 |
-0.044 | 0.685 | 0.425 | 0.569 | -0.205 | 0.520 | -1.224 | 0.331 | 0.520 |
-0.094 | 0.712 | 0.425 | 0.603 | -0.249 | 0.520 | 0.702 | -0.230 | 0.520 |
X | Y | Z | X | Y | Z | X | Y | Z |
-1.247 | 0.334 | 0.616 | 0.168 | 0.194 | 0.616 | -0.706 | 0.514 | 0.711 |
0.831 | -0.522 | 0.616 | 0.211 | 0.156 | 0.616 | -0.632 | 0.877 | 0.711 |
-1.184 | 0.217 | 0.616 | 0.253 | 0.118 | 0.616 | -0.681 | 0.861 | 0.711 |
-1.129 | 0.231 | 0.616 | 0.296 | 0.081 | 0.616 | -0.730 | 0.842 | 0.711 |
-1.079 | 0.257 | 0.616 | 0.339 | 0.043 | 0.616 | -0.777 | 0.822 | 0.711 |
-1.029 | 0.286 | 0.616 | 0.381 | 0.005 | 0.616 | -0.824 | 0.800 | 0.711 |
X | Y | Z | X | Y | Z | X | Y | Z |
-0.981 | 0.315 | 0.616 | 0.423 | -0.035 | 0.616 | -0.871 | 0.779 | 0.711 |
-0.931 | 0.344 | 0.616 | 0.462 | -0.076 | 0.616 | -0.918 | 0.757 | 0.711 |
-0.881 | 0.372 | 0.616 | 0.500 | -0.119 | 0.616 | -0.964 | 0.732 | 0.711 |
-0.831 | 0.398 | 0.616 | 0.535 | -0.164 | 0.616 | -1.006 | 0.703 | 0.711 |
-0.779 | 0.423 | 0.616 | 0.569 | -0.210 | 0.616 | -1.046 | 0.669 | 0.711 |
-0.726 | 0.444 | 0.616 | 0.604 | -0.255 | 0.616 | -1.082 | 0.632 | 0.711 |
-0.801 | 0.756 | 0.616 | 0.637 | -0.302 | 0.616 | -1.116 | 0.593 | 0.711 |
-0.851 | 0.729 | 0.616 | 0.668 | -0.349 | 0.616 | -0.656 | 0.527 | 0.711 |
-0.901 | 0.701 | 0.616 | 0.759 | -0.367 | 0.616 | -0.605 | 0.537 | 0.711 |
-0.950 | 0.672 | 0.616 | 0.734 | -0.316 | 0.616 | -0.553 | 0.540 | 0.711 |
-0.997 | 0.639 | 0.616 | 0.707 | -0.265 | 0.616 | -0.502 | 0.538 | 0.711 |
-1.041 | 0.603 | 0.616 | 0.680 | -0.215 | 0.616 | -0.450 | 0.532 | 0.711 |
-1.083 | 0.564 | 0.616 | 0.652 | -0.165 | 0.616 | -0.399 | 0.522 | 0.711 |
-1.258 | 0.278 | 0.616 | 0.623 | -0.116 | 0.616 | -0.349 | 0.511 | 0.711 |
-1.242 | 0.226 | 0.616 | 0.594 | -0.067 | 0.616 | -0.299 | 0.497 | 0.711 |
-1.188 | 0.216 | 0.616 | 0.564 | -0.018 | 0.616 | -0.250 | 0.481 | 0.711 |
-0.671 | 0.459 | 0.616 | 0.534 | 0.030 | 0.616 | -0.202 | 0.461 | 0.711 |
-0.615 | 0.470 | 0.616 | 0.503 | 0.078 | 0.616 | -0.136 | 0.803 | 0.711 |
X | Y | Z | X | Y | Z | X | Y | Z |
-0.558 | 0.476 | 0.616 | 0.471 | 0.125 | 0.616 | -0.181 | 0.829 | 0.711 |
-0.501 | 0.478 | 0.616 | 0.438 | 0.173 | 0.616 | -0.228 | 0.851 | 0.711 |
-0.444 | 0.476 | 0.616 | 0.406 | 0.219 | 0.616 | -0.276 | 0.871 | 0.711 |
-0.645 | 0.827 | 0.616 | 0.372 | 0.266 | 0.616 | -0.325 | 0.886 | 0.711 |
-0.698 | 0.807 | 0.616 | 0.339 | 0.312 | 0.616 | -0.376 | 0.897 | 0.711 |
-0.750 | 0.783 | 0.616 | 0.305 | 0.358 | 0.616 | -0.427 | 0.902 | 0.711 |
-0.387 | 0.471 | 0.616 | 0.270 | 0.403 | 0.616 | -0.479 | 0.902 | 0.711 |
-0.331 | 0.460 | 0.616 | 0.235 | 0.448 | 0.616 | -0.531 | 0.898 | 0.711 |
-0.276 | 0.446 | 0.616 | 0.198 | 0.492 | 0.616 | -0.582 | 0.889 | 0.711 |
-0.222 | 0.427 | 0.616 | 0.160 | 0.535 | 0.616 | -1.181 | 0.321 | 0.711 |
-0.149 | 0.785 | 0.616 | 0.121 | 0.576 | 0.616 | -1.130 | 0.326 | 0.711 |
-0.200 | 0.810 | 0.616 | 0.081 | 0.617 | 0.616 | -1.080 | 0.340 | 0.711 |
-0.253 | 0.832 | 0.616 | 0.039 | 0.655 | 0.616 | -1.033 | 0.361 | 0.711 |
-0.307 | 0.848 | 0.616 | -0.006 | 0.691 | 0.616 | -0.988 | 0.387 | 0.711 |
-0.364 | 0.858 | 0.616 | -0.052 | 0.725 | 0.616 | -0.943 | 0.413 | 0.711 |
-0.420 | 0.862 | 0.616 | -0.099 | 0.756 | 0.616 | -0.898 | 0.438 | 0.711 |
-0.478 | 0.861 | 0.616 | 0.698 | -0.398 | 0.616 | -0.851 | 0.461 | 0.711 |
-0.534 | 0.854 | 0.616 | 0.726 | -0.448 | 0.616 | -0.804 | 0.481 | 0.711 |
X | Y | Z | X | Y | Z | X | Y | Z |
-0.590 | 0.843 | 0.616 | 0.753 | -0.498 | 0.616 | -0.755 | 0.499 | 0.711 |
-0.169 | 0.406 | 0.616 | 0.785 | -0.418 | 0.616 | -1.148 | 0.553 | 0.711 |
-0.117 | 0.382 | 0.616 | -1.122 | 0.523 | 0.616 | -1.179 | 0.511 | 0.711 |
-0.066 | 0.356 | 0.616 | -1.159 | 0.480 | 0.616 | -1.205 | 0.467 | 0.711 |
-0.016 | 0.329 | 0.616 | -1.194 | 0.434 | 0.616 | -1.224 | 0.418 | 0.711 |
0.032 | 0.299 | 0.616 | -1.224 | 0.386 | 0.616 | -1.230 | 0.367 | 0.711 |
0.079 | 0.266 | 0.616 | 0.810 | -0.469 | 0.616 | -1.205 | 0.326 | 0.711 |
0.124 | 0.231 | 0.616 | 0.783 | -0.546 | 0.616 | -0.155 | 0.438 | 0.711 |
X | Y | Z | X | Y | Z | X | Y | Z |
-0.110 | 0.414 | 0.711 | -1.161 | 0.428 | 0.806 | -0.118 | 0.452 | 0.806 |
-0.065 | 0.388 | 0.711 | -1.111 | 0.429 | 0.806 | -0.076 | 0.424 | 0.806 |
-0.021 | 0.360 | 0.711 | -1.062 | 0.441 | 0.806 | -0.035 | 0.395 | 0.806 |
0.022 | 0.332 | 0.711 | -1.017 | 0.462 | 0.806 | 0.006 | 0.366 | 0.806 |
0.064 | 0.301 | 0.711 | -0.972 | 0.483 | 0.806 | 0.046 | 0.335 | 0.806 |
0.105 | 0.269 | 0.711 | -0.926 | 0.504 | 0.806 | 0.085 | 0.304 | 0.806 |
0.144 | 0.236 | 0.711 | -0.879 | 0.521 | 0.806 | 0.124 | 0.272 | 0.806 |
0.415 | 0.194 | 0.711 | -0.833 | 0.542 | 0.806 | 0.160 | 0.238 | 0.806 |
X | Y | Z | X | Y | Z | X | Y | Z |
0.387 | 0.237 | 0.711 | -0.785 | 0.557 | 0.806 | 0.197 | 0.203 | 0.806 |
0.358 | 0.280 | 0.711 | -0.737 | 0.571 | 0.806 | 0.232 | 0.168 | 0.806 |
0.328 | 0.323 | 0.711 | -0.689 | 0.585 | 0.806 | 0.268 | 0.133 | 0.806 |
0.298 | 0.365 | 0.711 | -0.620 | 0.933 | 0.806 | 0.304 | 0.098 | 0.806 |
0.267 | 0.406 | 0.711 | -0.669 | 0.920 | 0.806 | 0.340 | 0.063 | 0.806 |
0.236 | 0.448 | 0.711 | -0.717 | 0.906 | 0.806 | 0.375 | 0.027 | 0.806 |
0.204 | 0.488 | 0.711 | -0.764 | 0.890 | 0.806 | 0.410 | -0.009 | 0.806 |
0.171 | 0.528 | 0.711 | -0.812 | 0.873 | 0.806 | 0.468 | 0.106 | 0.806 |
0.137 | 0.567 | 0.711 | -0.859 | 0.855 | 0.806 | 0.440 | 0.148 | 0.806 |
0.102 | 0.605 | 0.711 | -0.905 | 0.836 | 0.806 | 0.413 | 0.190 | 0.806 |
0.066 | 0.642 | 0.711 | -0.950 | 0.814 | 0.806 | 0.385 | 0.232 | 0.806 |
0.028 | 0.678 | 0.711 | -0.993 | 0.787 | 0.806 | 0.357 | 0.274 | 0.806 |
-0.011 | 0.712 | 0.711 | -1.031 | 0.755 | 0.806 | 0.329 | 0.315 | 0.806 |
-0.051 | 0.745 | 0.711 | -1.066 | 0.719 | 0.806 | 0.301 | 0.357 | 0.806 |
-0.093 | 0.775 | 0.711 | -1.098 | 0.681 | 0.806 | 0.271 | 0.398 | 0.806 |
0.182 | 0.201 | 0.711 | -1.129 | 0.641 | 0.806 | 0.241 | 0.438 | 0.806 |
0.220 | 0.165 | 0.711 | -1.158 | 0.600 | 0.806 | 0.211 | 0.477 | 0.806 |
0.257 | 0.130 | 0.711 | -1.182 | 0.556 | 0.806 | 0.180 | 0.517 | 0.806 |
X | Y | Z | X | Y | Z | X | Y | Z |
0.295 | 0.094 | 0.711 | -1.200 | 0.509 | 0.806 | 0.149 | 0.556 | 0.806 |
0.332 | 0.058 | 0.711 | -1.200 | 0.460 | 0.806 | 0.116 | 0.594 | 0.806 |
0.369 | 0.022 | 0.711 | -1.164 | 0.429 | 0.806 | 0.082 | 0.631 | 0.806 |
0.406 | -0.015 | 0.711 | -0.640 | 0.594 | 0.806 | 0.047 | 0.667 | 0.806 |
0.442 | -0.052 | 0.711 | -0.590 | 0.598 | 0.806 | 0.011 | 0.702 | 0.806 |
0.476 | -0.091 | 0.711 | -0.540 | 0.598 | 0.806 | -0.026 | 0.736 | 0.806 |
0.508 | -0.132 | 0.711 | -0.490 | 0.595 | 0.806 | -0.064 | 0.769 | 0.806 |
0.539 | -0.173 | 0.711 | -0.440 | 0.588 | 0.806 | -0.103 | 0.800 | 0.806 |
0.570 | -0.215 | 0.711 | -0.391 | 0.576 | 0.806 | 0.444 | -0.046 | 0.806 |
0.601 | -0.256 | 0.711 | -0.344 | 0.560 | 0.806 | 0.475 | -0.085 | 0.806 |
0.629 | -0.299 | 0.711 | -0.298 | 0.540 | 0.806 | 0.506 | -0.125 | 0.806 |
0.659 | -0.342 | 0.711 | -0.252 | 0.519 | 0.806 | 0.536 | -0.165 | 0.806 |
0.705 | -0.342 | 0.711 | -0.206 | 0.499 | 0.806 | 0.565 | -0.206 | 0.806 |
0.708 | -0.294 | 0.711 | -0.144 | 0.830 | 0.806 | 0.594 | -0.247 | 0.806 |
0.683 | -0.249 | 0.711 | -0.186 | 0.856 | 0.806 | 0.623 | -0.288 | 0.806 |
0.659 | -0.203 | 0.711 | -0.231 | 0.879 | 0.806 | 0.668 | -0.285 | 0.806 |
0.634 | -0.158 | 0.711 | -0.277 | 0.899 | 0.806 | 0.669 | -0.241 | 0.806 |
0.609 | -0.112 | 0.711 | -0.325 | 0.915 | 0.806 | 0.645 | -0.197 | 0.806 |
X | Y | Z | X | Y | Z | X | Y | Z |
0.583 | -0.068 | 0.711 | -0.373 | 0.929 | 0.806 | 0.621 | -0.153 | 0.806 |
0.555 | -0.024 | 0.711 | -0.422 | 0.940 | 0.806 | 0.597 | -0.109 | 0.806 |
0.528 | 0.020 | 0.711 | -0.471 | 0.947 | 0.806 | 0.572 | -0.065 | 0.806 |
0.500 | 0.064 | 0.711 | -0.521 | 0.948 | 0.806 | 0.546 | -0.022 | 0.806 |
0.472 | 0.107 | 0.711 | -0.571 | 0.943 | 0.806 | 0.520 | 0.021 | 0.806 |
0.443 | 0.151 | 0.711 | -0.161 | 0.477 | 0.806 | 0.494 | 0.064 | 0.806 |
X | Y | Z | X | Y | Z | X | Y | Z |
-1.136 | 0.536 | 0.902 | 0.038 | 0.360 | 0.902 | -0.585 | 1.069 | 0.997 |
-1.083 | 0.533 | 0.902 | 0.078 | 0.326 | 0.902 | -0.631 | 1.070 | 0.997 |
-1.032 | 0.544 | 0.902 | 0.117 | 0.291 | 0.902 | -0.677 | 1.068 | 0.997 |
-0.982 | 0.562 | 0.902 | 0.155 | 0.255 | 0.902 | -0.723 | 1.061 | 0.997 |
-0.933 | 0.580 | 0.902 | 0.192 | 0.218 | 0.902 | -0.768 | 1.051 | 0.997 |
-0.883 | 0.596 | 0.902 | 0.229 | 0.181 | 0.902 | -0.812 | 1.038 | 0.997 |
-0.832 | 0.609 | 0.902 | 0.266 | 0.143 | 0.902 | -0.855 | 1.021 | 0.997 |
-0.781 | 0.621 | 0.902 | 0.302 | 0.105 | 0.902 | -0.896 | 1.001 | 0.997 |
-0.729 | 0.630 | 0.902 | 0.339 | 0.067 | 0.902 | -0.936 | 0.979 | 0.997 |
-0.677 | 0.639 | 0.902 | 0.375 | 0.029 | 0.902 | -0.975 | 0.953 | 0.997 |
X | Y | Z | X | Y | Z | X | Y | Z |
-0.632 | 0.993 | 0.902 | 0.410 | -0.010 | 0.902 | -1.011 | 0.925 | 0.997 |
-0.684 | 0.983 | 0.902 | 0.444 | -0.050 | 0.902 | -1.046 | 0.895 | 0.997 |
-0.735 | 0.969 | 0.902 | 0.476 | -0.092 | 0.902 | -1.079 | 0.863 | 0.997 |
-0.784 | 0.953 | 0.902 | 0.507 | -0.134 | 0.902 | -1.109 | 0.828 | 0.997 |
-0.834 | 0.935 | 0.902 | 0.539 | -0.176 | 0.902 | -1.136 | 0.791 | 0.997 |
-0.883 | 0.917 | 0.902 | 0.569 | -0.219 | 0.902 | -1.158 | 0.751 | 0.997 |
-0.932 | 0.896 | 0.902 | 0.634 | -0.207 | 0.902 | -1.173 | 0.707 | 0.997 |
-0.977 | 0.871 | 0.902 | 0.609 | -0.161 | 0.902 | -1.171 | 0.662 | 0.997 |
-1.017 | 0.837 | 0.902 | 0.584 | -0.115 | 0.902 | -1.140 | 0.629 | 0.997 |
-1.053 | 0.798 | 0.902 | 0.558 | -0.069 | 0.902 | -1.096 | 0.616 | 0.997 |
-1.086 | 0.758 | 0.902 | 0.533 | -0.023 | 0.902 | -1.050 | 0.615 | 0.997 |
-1.118 | 0.715 | 0.902 | 0.506 | 0.023 | 0.902 | -1.004 | 0.620 | 0.997 |
-1.147 | 0.672 | 0.902 | 0.479 | 0.068 | 0.902 | -0.959 | 0.630 | 0.997 |
-1.170 | 0.625 | 0.902 | 0.451 | 0.112 | 0.902 | -0.914 | 0.642 | 0.997 |
-1.175 | 0.573 | 0.902 | 0.423 | 0.156 | 0.902 | -0.870 | 0.654 | 0.997 |
-1.140 | 0.537 | 0.902 | 0.394 | 0.200 | 0.902 | -0.825 | 0.664 | 0.997 |
-0.625 | 0.641 | 0.902 | 0.365 | 0.244 | 0.902 | -0.780 | 0.673 | 0.997 |
-0.573 | 0.640 | 0.902 | 0.336 | 0.288 | 0.902 | -0.734 | 0.678 | 0.997 |
X | Y | Z | X | Y | Z | X | Y | Z |
-0.520 | 0.636 | 0.902 | 0.307 | 0.332 | 0.902 | -0.688 | 0.681 | 0.997 |
-0.468 | 0.629 | 0.902 | 0.278 | 0.376 | 0.902 | -0.131 | 0.863 | 0.997 |
-0.417 | 0.617 | 0.902 | 0.249 | 0.419 | 0.902 | -0.167 | 0.891 | 0.997 |
-0.367 | 0.600 | 0.902 | 0.219 | 0.462 | 0.902 | -0.204 | 0.918 | 0.997 |
-0.318 | 0.581 | 0.902 | 0.187 | 0.505 | 0.902 | -0.242 | 0.944 | 0.997 |
-0.270 | 0.560 | 0.902 | 0.154 | 0.545 | 0.902 | -0.282 | 0.968 | 0.997 |
-0.223 | 0.537 | 0.902 | 0.120 | 0.585 | 0.902 | -0.322 | 0.990 | 0.997 |
-0.177 | 0.512 | 0.902 | 0.084 | 0.624 | 0.902 | -0.364 | 1.011 | 0.997 |
-0.142 | 0.843 | 0.902 | 0.049 | 0.662 | 0.902 | -0.406 | 1.028 | 0.997 |
-0.186 | 0.872 | 0.902 | 0.012 | 0.700 | 0.902 | -0.450 | 1.043 | 0.997 |
-0.231 | 0.900 | 0.902 | -0.025 | 0.738 | 0.902 | -0.494 | 1.056 | 0.997 |
-0.277 | 0.925 | 0.902 | -0.062 | 0.774 | 0.902 | -0.539 | 1.064 | 0.997 |
-0.324 | 0.948 | 0.902 | -0.101 | 0.810 | 0.902 | -0.642 | 0.681 | 0.997 |
-0.373 | 0.967 | 0.902 | 0.598 | -0.263 | 0.902 | -0.596 | 0.678 | 0.997 |
-0.423 | 0.981 | 0.902 | 0.624 | -0.308 | 0.902 | -0.550 | 0.672 | 0.997 |
-0.475 | 0.991 | 0.902 | 0.650 | -0.354 | 0.902 | -0.505 | 0.663 | 0.997 |
-0.527 | 0.996 | 0.902 | 0.675 | -0.400 | 0.902 | -0.460 | 0.652 | 0.997 |
-0.580 | 0.997 | 0.902 | 0.710 | -0.433 | 0.902 | -0.416 | 0.639 | 0.997 |
X | Y | Z | X | Y | Z | X | Y | Z |
-0.132 | 0.485 | 0.902 | 0.730 | -0.394 | 0.902 | -0.373 | 0.624 | 0.997 |
-0.088 | 0.456 | 0.902 | 0.706 | -0.347 | 0.902 | -0.330 | 0.606 | 0.997 |
-0.045 | 0.425 | 0.902 | 0.682 | -0.300 | 0.902 | -0.288 | 0.587 | 0.997 |
-0.003 | 0.393 | 0.902 | 0.659 | -0.253 | 0.902 | -0.248 | 0.565 | 32.287 |
X | Y | Z |
-0.208 | 0.542 | 0.997 |
0.213 | 0.186 | 0.997 |
0.243 | 0.152 | 0.997 |
0.274 | 0.117 | 0.997 |
0.304 | 0.082 | 0.997 |
0.333 | 0.046 | 0.997 |
0.362 | 0.010 | 0.997 |
0.390 | -0.026 | 0.997 |
0.418 | -0.062 | 0.997 |
0.446 | -0.099 | 0.997 |
0.477 | -0.133 | 0.997 |
0.522 | -0.135 | 0.997 |
X | Y | Z |
0.553 | -0.103 | 0.997 |
0.550 | -0.059 | 0.997 |
0.527 | -0.018 | 0.997 |
0.504 | 0.021 | 0.997 |
0.482 | 0.062 | 0.997 |
0.459 | 0.102 | 0.997 |
0.436 | 0.142 | 0.997 |
0.412 | 0.181 | 0.997 |
0.388 | 0.220 | 0.997 |
0.364 | 0.260 | 0.997 |
0.339 | 0.298 | 0.997 |
0.314 | 0.337 | 0.997 |
0.289 | 0.376 | 0.997 |
0.263 | 0.414 | 0.997 |
0.236 | 0.452 | 0.997 |
0.210 | 0.489 | 0.997 |
0.182 | 0.526 | 0.997 |
0.154 | 0.563 | 0.997 |
X | Y | Z |
0.126 | 0.599 | 0.997 |
0.096 | 0.634 | 0.997 |
0.066 | 0.669 | 0.997 |
0.036 | 0.704 | 0.997 |
0.004 | 0.737 | 0.997 |
-0.028 | 0.770 | 0.997 |
-0.062 | 0.802 | 0.997 |
-0.096 | 0.833 | 0.997 |
-0.168 | 0.518 | 0.997 |
-0.130 | 0.493 | 0.997 |
-0.093 | 0.466 | 0.997 |
-0.056 | 0.438 | 0.997 |
-0.020 | 0.409 | 0.997 |
0.015 | 0.379 | 0.997 |
0.050 | 0.349 | 0.997 |
0.084 | 0.318 | 0.997 |
0.117 | 0.286 | 0.997 |
0.149 | 0.253 | 0.997 |
X | Y | Z |
0.181 | 0.220 | 0.997 |
0.213 | 0.186 | 0.997 |
也应该理解,上面表中公开的翼面内部核心轮廓可以按几何比例扩大或缩小,从而用于其它类似的涡轮设计。因此,在表I中列出的坐标值可以按比例增加或减小,这样翼面内部轮廓的形状保持不变。表I中坐标值依比例变化的版本可以由表I中的X、Y和Z的坐标值表示,其中无量纲的Z坐标值通过乘以或除以一个常数转换成以英寸为单位。
虽然与目前认为是最实用和最优选的实施方式相结合对本发明进行了描述,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,本发明旨在涵盖各种改进和等效装置,这些包含在附加的权利要求的精神和范围之中。
Claims (10)
1.一种涡轮叶片(16),该叶片包括一翼面(38)、一平台(30)、一叶根(32)和一楔形榫(34),该翼面具有一个与表I中列出的X、Y和Z笛卡儿坐标值基本上一致的内部标称核心轮廓(40),其中Z值是无量纲值,可通过将Z值乘以以英寸为单位的翼面高度将Z转换成以英寸为单位的Z长度,并且其中X和Y是以英寸为单位的长度,当用平滑连续的弧将所述X和Y相连结时,就会沿着翼面在各Z值处形成内部核心轮廓截面,将各Z值处的轮廓截面彼此互相平滑地连结,以形成翼面内部核心轮廓。
2.如权利要求1所述的涡轮叶片,其特征在于所述翼面具有侧壁(48)和在侧壁间延伸的肋(46),所述肋在介于翼面的前缘和后缘之间彼此间隔开,并与所述侧壁的内壁表面一起确定出沿着翼面长度方向的内部冷却通道(35),所述平滑连续的弧沿着冷却通道的内壁表面并介于沿着所述侧壁的相邻通道之间延伸。
3.如权利要求2所述的涡轮叶片,其特征在于所述的平滑连续的弧穿过介于肋和每个侧壁之间的连结部分。
4.如权利要求1所述的涡轮叶片,其特征在于所述叶片翼面具有一外部翼面形状(38),所述内部核心轮廓截面在叶片翼面内部具有基本上翼面形状的部分,并且基本上与叶片翼面的所述外部翼面形状的轮廓截面减去其间的壁厚相一致。
5.如权利要求1所述的涡轮叶片,其特征在于该叶片构成涡轮的第一级的一部分。
6.如权利要求1所述的涡轮叶片,其特征在于所述的内部核心轮廓位于一个包络中,该包络是在垂直于任何内部核心表面位置的方向上±0.050英寸范围内。
7.一种涡轮叶片(16),该叶片包括一翼面(38)、一平台(30)、一叶根(32)和一楔形榫(34),所述翼面具有一个与表I中列出的X、Y和Z笛卡儿坐标值基本上一致的内部标称核心轮廓(40),其中Z值是无量纲值,可通过将Z值乘以以英寸为单位的翼面高度将Z转换成以英寸为单位的Z长度,并且其中X和Y是以英寸为单位的长度,当用平滑连续的弧将所述X和Y相连结时,就会沿着翼面在每个Z值处形成内部核心轮廓截面,将各Z值处的轮廓截面彼此互相平滑地连结,以形成所述叶片翼面内部核心轮廓,其中X、Y和Z值作为相同常数或数值的函数可按比例变化,从而提供按比例扩大或缩小的内部核心轮廓。
8.如权利要求7所述的涡轮叶片,其特征在于所述翼面具有侧壁(48)和在侧壁间延伸的肋(46),所述肋在介于翼面的前缘和后缘之间彼此间隔开,并与所述侧壁的内壁表面一起确定出沿着翼面长度方向的内部冷却通道(35),所述平滑连续的弧沿着冷却通道的内壁表面并介于沿着所述侧壁的相邻通道之间延伸。
9.如权利要求7所述的涡轮叶片,其特征在于所述的平滑连续的弧穿过介于肋和每个侧壁之间的连结部分。
10.如权利要求7所述的涡轮叶片,其特征在于所述叶片翼面(38)具有一外部翼面形状,所述内部核心轮廓截面在叶片翼面内部具有基本上翼面形状的部分,并且基本上与叶片翼面的所述外部翼面形状的轮廓截面减去其间的壁厚相一致。
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US10/684,402 US6893210B2 (en) | 2003-10-15 | 2003-10-15 | Internal core profile for the airfoil of a turbine bucket |
US10/684402 | 2003-10-15 |
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CN101446209A (zh) * | 2007-11-28 | 2009-06-03 | 通用电气公司 | 涡轮机叶片护罩内核轮廓 |
CN101446210A (zh) * | 2007-11-29 | 2009-06-03 | 通用电气公司 | 用于涡轮机叶片的柄部形状及结合该柄部形状的涡轮机 |
CN101624920A (zh) * | 2008-07-08 | 2010-01-13 | 通用电气公司 | 用于涡轮机楔形榫的曲径密封件 |
CN101644172A (zh) * | 2008-07-08 | 2010-02-10 | 通用电气公司 | 用于涡轮机楔形榫的弹性密封件 |
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US6994520B2 (en) * | 2004-05-26 | 2006-02-07 | General Electric Company | Internal core profile for a turbine nozzle airfoil |
US7632074B2 (en) * | 2006-11-28 | 2009-12-15 | Pratt & Whitney Canada Corp. | HP turbine blade airfoil profile |
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-
2003
- 2003-10-15 US US10/684,402 patent/US6893210B2/en not_active Expired - Lifetime
-
2004
- 2004-10-14 EP EP04256334A patent/EP1524408A3/en not_active Withdrawn
- 2004-10-15 JP JP2004300865A patent/JP2005121025A/ja not_active Withdrawn
- 2004-10-15 CN CNB2004100951215A patent/CN100419217C/zh not_active Expired - Fee Related
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CN101644172A (zh) * | 2008-07-08 | 2010-02-10 | 通用电气公司 | 用于涡轮机楔形榫的弹性密封件 |
CN101624920B (zh) * | 2008-07-08 | 2016-02-10 | 通用电气公司 | 用于涡轮机楔形榫的曲径密封件及密封间隙的方法 |
Also Published As
Publication number | Publication date |
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JP2005121025A (ja) | 2005-05-12 |
CN100419217C (zh) | 2008-09-17 |
US20050084372A1 (en) | 2005-04-21 |
US6893210B2 (en) | 2005-05-17 |
EP1524408A3 (en) | 2012-05-23 |
EP1524408A2 (en) | 2005-04-20 |
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