叶片前缘高精度重建方法研究

张力宁; 张定华

叶片前缘高精度重建方法研究

张力宁^1,2,
张定华¹

1.
西北工业大学现代设计与集成制造技术教育部重点实验室, 西安 710072
2.
西北工业大学理学院应用数学系, 陕西西安 710072

基金项目: 航空科学基金(00H53076);国家教委博士点基金(20006992)

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出版历程
- 收稿日期: 2005-07-22
- 修回日期: 2006-05-18
- 刊出日期: 2006-08-28

High-precision reconstruction of blade leading edge

ZHANG Li-ning^1,2,
ZHANG Ding-hua¹

1.
Key Lab of Contemporary Design and Integrated Manufacturing Technology, Ministry of Education, Northwestern Polytechnical University, Xi'an 710072, China
2.
Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an 710072, China

摘要

摘要: 叶片前后缘的形状对发动机的气动性能有非常重要的影响。对叶片前后缘的精确建模是高质量加工的前提。现有的叶片前缘大多为圆弧或椭圆弧。为了实现精确建模,本文首先运用一种基于带约束的最小二乘方法对数据点进行拟合,然后用拟合的结果作为初值,根据椭圆的极线性质进行更精确地求解。实例表明本文的方法在对椭圆弧的拟合中具有比Fitzgibbon方法更好的鲁棒性及更高的精确度。在重建前缘时,一些事先难以排除的出格点极大地影响了拟合精度,鉴于本文方法具有较好的鲁棒性,本文提出了以前缘点为中心,对于逐次增加数据点多次运用本文的拟合方法,最终排除出格点的方案。数据实验验证了这一方案的有效性。总之,本文提出的拟合方法非常适合于在逆向工程中对叶片前缘的重建。
- 航空、航天推进系统 /
- 椭圆拟合 /
- 叶片前缘 /
- 最小二乘 /
- 逆向工程
Abstract: The shape of leading/trailing edge is very important to the performance of the turbine blade.Precise description is the premise for turbine blade machining.Generally,the leading/trailing edge is a circular arc or elliptic arc.In order to reconstruct them accurately,a method for fitting the ellipse based on the principle of conditional least square was applied at first,and then its fitting result was used as an initial value to find a more precise result according to the polar line geometrical properties of the ellipse.Some examples were given to prove the good robustness and high accuracy of this fitting method,especially for a part of ellipse.During the reconstruction of the blade,some outliers which are difficult to exclude beforehand may influence the accuracy of fitting result greatly.Because of our method's good robustness,this fitting method was applied to the progressively increasing number of data centered at leading edge for several times to exclude outliers.Numerical experiments show the effectiveness of this scheme.In conclusion,the method presented is suitable for the reconstruction of blade in the reverse engineering.
- aerospace propulsion system /
- ellipses fitting /
- blade leading edge /
- least square method /
- reverse engineering

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参考文献(5)

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