Interpolation using non-uniform rational B-spline for the smooth milling of ruled-surface impeller blades

Abstract

The integral impeller is a complex part characterized by highly curved surfaces. Modeling and interpolation methods for manufacturing integral impellers are currently the subject of intensive research. In this study, to represent the shape of the ruled-surface blades, third-order non-uniform rational B-splines are constructed from data points for the hub and shoulder on the pressure and suction sides of the blade. Various methods for determining the tool axis vector offset and the location of the tool center for a cylindrical ball cutter are developed and verified with simulations of machining operations. To obtain a smooth interpolation and high accuracy in machining, a third-order non-uniform rational B-spline interpolation algorithm for ruled-surface blades is developed. This method can create a smooth transition between the hub and the blade shoulders. The method is implemented in an open-architecture computer numerical control controller. Simulations and experimental tests of machining tasks are performed to verify the non-uniform rational B-spline interpolation method. The test results show that this interpolation technique can produce a smooth and continuous path along the axes of motion. The new technique has the advantages of requiring fewer lines of numerical control code and producing higher machining accuracy.