In this paper, we first set up the cutting mechanism of a CNC
hobbing machine and mathematical model of a hob cutter. The
kinematic relationship can be obtained on the basis of the cutting
mechanism and transformation matrices. Based on the cutting
mechanism, generation concept with multi-degree of freedom,
and theory of mechanisms, a general mathematical model for
the gear hobbing simulation on a 6-axis CNC hobbing machine
can be developed. By properly selecting the parameters of the
developed general gear mathematical model, the equations of
the tooth surfaces for different types of gears can be obtained
and the respective gear tooth surfaces can also be cut by using
the CNC hobbing machine.
The crossed helical-gear is used in crossed axes power trans-
mission. However, the load capacity of the crossed helical-gear
is comparatively lower than the hypoid gear due to its point 本文来自优*文!论(文&网，
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contact and low contact ratio. In this paper, we propose a general
gear mathematical model to derive a novel type of gear named
"Helipoid" (as invented by the third author Professor Nagata).
An illustrative example demonstrates the effectiveness of the
proposed mathematical model and a gear cut by a CNC hobbing
machine with multi-degree of freedom.
The general gear mathematical model, capable of simulating
the gear cutting process of CNC hobbing, can facilitate the
manufacturer in gear design and manufacturing. The general
gear mathematical model can also be applied to the design
and manufacturing of spur, helical, worm gears and noncircular
gears. Results shown in this study also provide the industry an
important software for design, analysis, and manufacturing of
various types of gears.
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