The relief surfaces of the cutting teeth of a dual-cone double enveloping hourglass worm gear hob cannot be ground automatically until now because all of teeth have different profiles and different spiral angles with each other. The land width and the relief angle of the hob are two important factors when using the hob to hob a worm gear. In order to improve the precision of this type worm pair, the land width and the relief angle of the hob need to be machined accurately and effectively. For the purpose that the land width and the relief angle could be machined precisely, an incomplete design and generating theory of the relief surfaces of the dual-cone double enveloping hourglass worm gear hob is put forward in this paper. The mathematical model of the incomplete design and generating theory of the relief grinding of the hob is built. According to the model, a series of data of the motion parameters when grinding different points of the land edges of the different hob teeth are solved out. Using those data of the motion parameters on a four-axis hourglass worm-grinding machine, a machining simulation is built and the results of the simulation show that the relief surfaces of the hob can be ground continuously, and the land width and the relief angle are consistent with the design.

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