基于概率密度最小二乘拟合的叶片后缘轮廓

Blade trailing edge contour based on probability density least-square fitting

为了解决燃气轮机叶片后缘轮廓的测量和模型化的难题,采用了基于概率密度的最小二乘圆拟合方法,通过对数据重复拟合过程若干次,求得每组的拟合圆心坐标和半径,以概率密度分布的最大值作为最优拟合值。通过数据仿真,对拟合数据误差进行了理论分析和实验验证,验证了该方法的可行性和鲁棒性。结果表明,实现了对叶片后缘轮廓的拟合和数据的参量估计,精度达到±0.01mm,求得圆拟合的最优圆心坐标和半径;对于直线段和短圆弧组合的叶片后缘,在不知切点和圆弧方程的情况下,能够对叶片后缘轮廓拟合。此方法对叶片后缘轮廓的高精度测量、加工精度以及参量的设计有着重要的指导意义。

In order to solve the problems for measurement and modeling of gas turbine blade trailing edge contour, a least-square circle fitting method based on probability density was proposed. After several times of fitting data repeatedly, each fitting center coordinate and radius was obtained. The maximum value of probability density distribution was looked as the optimal value. The errors of fitting data were analyzed by data simulation after theoretical analysis and experimental verification. The feasibility and robustness of the method were verified. The results show that the fitting of blade trailing edge contour and the estimation of parameter data are realized. The fitting error is ± 0. 01mm. The optimal center coordinates and radius of circle fitting is obtained. For the blade trailing edge composed of straight line segments and short arcs, the fitting result is effective and accurate in the case of unknowing the point of tangent and arc equation. The method has an important guiding significance to precision measurement, machining accuracy and parameter design of blade trailing edge contour.