The forming method has been widely used for manufacturing screw rotors with helical profile. This paper takes the manufacturing of screws for screw pumps as an example and uses the cubic spline interpolation method to obtain the tooth profile of the screw forming cutter according to the tooth profile at any end section of screws composed of discrete points and based on the principle of gearing mesh. Furthermore, this paper studies the space enveloping and geometric characteristics between the screw and cutter during the manufacturing process, combines the shape of the contact line, which is generated due to the cooperative motion of the machine tool, screw, and cutter, with spatial location parameters, and thus innovatively proposes a design method for the screw forming cutter based on discrete points, namely, the form-position geometric method (FPGM). It can be seen after comparing the proposed method with the principle of gear meshing that the cutter-workpiece enveloping solution model, simplified by the FPGM, can overcome the key technical difficulty, i.e., it is difficult to accurately calculate the cusp of the tooth curve; meanwhile, the proposed method can improve the precision of the cutter tooth profile design. Finally, the feasibility and superiority of FPGM are verified by experiments.

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