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This thesis is mainly to study the Trosional surfaces and freeform surfaces, impeller construction and its machining methods. The mathematical model is used to calculate the centrifugal impeller,and the freeform surfaces is scanned by reverse engineering, and the machining path is set through the CATIA machining module.Moreover,the geometrical relationship between the outlet angle of the centrifugal impeller and the entry angle is obtained by the definition of the flow field parameters. The inner product relationship is obtained from the design, the spatial geometry and the analytical equation, and finally the fourth axis of the rotary axis and five-axis machining machine is rotary axis. The centrifugal impeller is a closed curved surface.In addition the side-milling and rigid-body transformation method are used to calculate the tool path and the impeller profile equation.By establishing a set of blade machining paths through the analytical equation and allows Vsual Studio C# to calculate the coordinate points of the blade curves, generate tool path trajectories, and put them into CATIA for simulated cutting to confirm the correctness of the tool path machining.In addition, the workpiece is measured by non-contact three dimensional scanning, and the point data of the solid model is obtained, and then the software of the reverse engineering is used for calculation, and the free-form surface blade is scanned by reverse engineering, and the five-axis machining module in CATIA is reconstructed to The free-form surface blade is processed by point machining.
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