航空学报 > 1981, Vol. 2 Issue (4): 88-96

叶片空间造型的计算几何方法

刘鼎元1, 赵玉琦2, 詹廷雄2, 肖宏恩2   

  1. 1. 复旦大学2. 南华动力机械研究所
  • 收稿日期:1980-07-01 修回日期:1900-01-01 出版日期:1981-12-25 发布日期:1981-12-25

A COMPUTATIONAL GEOMETRY METHOD FOR BLADE SPACE GEOMETRIC DESIGN

Liu Dingyuan1, Zhao Yuqi2, Zhan Tingxiong2, Xiao Hongen2   

  1. 1. Fudan University;2. Nanhua Power plant Research Institute
  • Received:1980-07-01 Revised:1900-01-01 Online:1981-12-25 Published:1981-12-25

摘要: 本文把新近发展起来的计算几何中的几种典型方法(包括Bézier曲面、B样条曲面和Bézier-B样条混合曲面等),同航空发动机叶片空间造型结合起来,形成一套计算机辅助叶片外形设计的新方法。扭曲叶片由三二次混合曲面片拼接而成,型面有完整的数学模型。因此有利于叶片三元流场性能和有限元强度计算分析以及与数控加工相结合。实例表明该方法简单、灵活、计算量小,对大弯度叶片设计亦行之有效。

Abstract: This paper presents a new method of computer-aided blade geometric design, which combines several typical methods of computational geometry developed recently (including Bezier patches, 5-spline patches and Bezier-B-spline mixed patches, etc. ) with the space shaping for aerojet blades.On the basis of the classic works on computational geometry[1] [2][3] and recent research results in China [4][ 5 ],the geometric design of a heavily cambered aerojet blade has been investigated.Aa the curvature of the blade surface is large chordwise but small in the radial direction, several surface patches are used chordwise and one in the radial direction to build a whole blade surface. Thus, an integral mathematical model for a blade configuration is obtained and jointed by a set of 3 times 2 order mixed surface patches with a common expression P(u,v) = [U][M]k[B][N][V] (see eq. (1) (1 a ) (1 b ) (1 c ) (1 d ))It is quite important to give the spatial position vector matrix [B] of the polygonal mesh vertices of the blade surface. In this paper the vertices are simplified to be given in three basic sections(see fig. 3 ).Present method is capable of easy moving the vertices on the screen and improving the adjustable parameters so that a desired blade surface can be formed to meet the requirements of the optimum geometric design.A practical example given in this paper has shown that the method is simple and clear, adaptable and flexible for modification, and its computational quantity is not great. It may be seen that the method is beneficial to aerodynamic calculations of three dimensional flow field in cascade and finite element strength analysis, and also it can be combined with digital control manufacture of blades. Therefore, it will make a contribution to a blade computer-aided design and manufacture system (CAD/CAM).