Multi-axis machining of helicoids using the generating method

The geometry of helicoid with specific cross-section profile is normally generated with form-mill cutter by dedicated machine tools and software. The manufacturing cost and cycle time of development for the helicoids are high because the complicated helical surface. To improve the efficiency of development, this paper proposes an approach for multi-axis machining of helicoids using the CNC machine tool. The method of design and manufacturing of the helicoids are established based on the differential geometry, homogeneous coordinate transformation and the envelope theory. The cross-section profiles and helicoids firstly are derived according to the conjugate theory. Rapid prototyping model is fabricated from three-dimensional CAD model for concurrent development. In the multi-axis machining of helicoids, the form grinding wheel profiles are determined from the reverse enveloping theory. The cutter location and the toolpath of generating method are represented. The cutting simulations with solid model were performed to verify the proposed toolpath generation method.