利用弦长不变特征的叶片截面轮廓匹配算法

Novel Sectional Profile Matching Algorithm for Gas Turbine Blades Based on Curve Chord-Length Invariant Feature

针对大型燃气轮机叶片型面形状加工质量高精度检测分析评价中的无基准坐标匹配问题,提出了一种利用截面轮廓曲线弦长几何不变特征的精确坐标匹配算法.该算法在获取对应截面轮廓数据后,基于叶片截面轮廓曲线对应弦长不变特征建立目标函数,并依此计算出理论轮廓曲线中与测量数据对应的坐标点,构造出坐标变换超静定方程组,然后通过豪斯荷尔德矩阵变换方法计算出该坐标变换的最小二乘最优解.采用该算法计算出叶片截面轮廓曲线的模拟测量数据与理论数据之间的坐标变换矩阵,得出了该变换矩阵下的截面轮廓评价结果,其偏差小于1.5μm,表明该算法对于自由曲面的大型燃气轮机叶片型面形状加工质量的检测评价具有较好的应用效果.

Aiming at the non-datum coordinate matching for large-scale gas turbine blade profile in high-precision detection and evaluation, an accurate coordinate matching algorithm is proposed based on the chord-length invariant feature of sectional profile. After acquiring the point data of corresponding sectional profile, the objective function is established according to the corresponding chord-length invariant feature of blade sectional profile curve. The points corresponding to the measured ones in the theoretical profile curve are calculated with the proposed algorithm. Moreover, the indeterminate equations for coordinate transformation can also be constructed. The least-square optimal solution of coordinate transformation of sectional profile can be calculated by Householder matrix transformation. As the coordinate transformations of multiple sectional profiles are calculated, the optimal coordinate transformation matrix can be obtained by linearly averaging the transformation relationships. Then, the coordinate system can be unified. The coordinate transformation matrix between simulatively measured data and theoretical data of a blade sectional profile curve is calculated with the proposed algorithm to obtain the evaluation result of sectional profile. The deviation of evaluation result gets within the acceptable range （less than 1.5μm）.