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The curvature variation regularity of the blade surface is complex and requires a high level of machining accuracy. In order to research the influence of interpolation tolerance on the machining accuracy of blade surface at different positions, the non-uniform rational b-spline was used to build the blade surface and analyze the curvature variation regularity at different positions, and the distribution regularity of interpolation tolerance at different curvature positions on interpolation moving points was explored based on the NC (Numerical Control) program. In addition, the NC interpolation principle is used to analyze the effect of different interpolation tolerance parameters on the machining accuracy of blade surfaces, and the appropriate interpolation moving point coordinates were obtained through the five-axis coordinate system transformation theory, and the five-axis cutting simulation and experiment were carried out. The results show that there are many interpolation moving points at the position with large curvature. With interpolation tolerances of 0.1 mm, 0.03 mm and 0.003 mm, the interpolation errors obtained in the regions with large curvature are 0.005 mm, 0.0034 mm and 0.0025 mm, respectively. The smaller the interpolation tolerance, the smaller the interpolation error. What is more, the smaller the interpolation tolerance is, the more obvious the improvement of interpolation accuracy will be when the interpolation tolerance is reduced. Besides, when sampling length of 250 μm, the surface roughness (Ra) detected at the small curvature position and the large curvature position are 0.434 and 1.070μm respectively. The surface roughness is better in position with smaller curvature, however, it is worse in position with larger curvature. The analytical regularity is in good agreement with both simulation and experiment values. It provides a reference for improving NC machining accuracy for similar blade surfaces.

In order to avoid the problem that the support points selected by the traditional single absolute error criterion are not interpolated accurately when the heat flux is small the radial basis function is used for hypersonic heat flux interpolation. In this paper, a radial basis function interpolation procedure with double error criterion is proposed. In this process, the absolute error criterion is used to select a certain number of support points, and then the relative error criterion is used to select another part of points. The numerical experiments show that the double error criterion can ensure the interpolation accuracy at both large and small heat flux and can avoid the problem of negative heat flux which is easy to appear in the interpolation results caused by the traditional single absolute error criterion.