Envelope-approximation theory of manufacture technology for point-contact tooth surface on six-axis CNC hypoid generator

A new generation method for point-contact tooth surface is proposed based on the six-axis movement of CNC machine. The new method is derived from the idea of motion of Darboux–Frenet trihedron along a predesigned path of contact on the predesigned (theoretical) tooth surface. The generated tooth surface provided by the new method has tangency of second order with the predesigned (theoretical) surface along the predesigned path of contact and the predesigned (least) warping in regions that differ from the path of contact. This means that the new method can reliably control meshing characteristics at each contact point. In contrast, the previous method can only control meshing characteristics at a mean contact point and make correction by observing the contact-bearing condition to determine meshing characteristics at other contact points. Different from the previous CNC generation method translated from the cradle-style universal hypoid generator, the developed method directly suits the six-axis movement of CNC machine to identify the relative motion between the tool and the workpiece based on the predesigned meshing characteristics of the gear being generated. A numerical example is given to prove that the above-mentioned manufacture method is accurate and feasible.