To five-axis point mill turbomachinery components, a least squares approximation procedure for generating tool paths in terms of parametric rational B-splines is presented. The detailed processes of using the appropriate parameters of rational B-splines that will reduce the amount of geometric deviations between the designed and machined part surfaces are proposed. Compared to a traditional linear tool path, a rational B-spline tool path can substantially reduce the number of blocks on machine controllers without compromising the accuracy. As a result, the machining efficiency and machine dynamic behavior can be improved. Numerical and experimental results are given to show such improvements. A practical application example for machining a centrifugal compressor impeller with 12 blades is also illustrated to demonstrate the reliability and usefulness of the developed procedure.

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