# CNC滚齿机切削的通用数学模型英文文献和翻译

CNC滚齿机切削的通用数学模型英文文献和翻译 A General Mathematical Model
for Gears Cut by GNC
Mobbing Machines
A hobbing machine's cutting mechanism is a mechanism with multi-degree of freedom
during the cutting process. In this paper, we propose a general gear mathematical
model simulating the generation process of a 6-axis CMC hobbing machine based
on the cutting mechanism of CNC hobbing machine and worm-type hob cutter. The
proposed gear mathematical model can be applied to simulate different types of gear
cutting. Some examples are included to verify the mathematical model. Also, a novel
type of gear named "Helipoid" which can be used in crossed axes transmission is
proposed. The proposed general gear mathematical model can facilitate a more
thorough understanding of generation processes and toward the development of novel
types of gears.
Introduction
Hobbing, shaping, and other special purpose machines are
widely used in industry to manufacture different types of gears.
Owing to easy tool setting, high efficiency and reliable quality,
the hobbing machine is conventionally used in manufacturing
spur, helical, and worm gears. The development of CNC hob-
bing machines has recendy made it possible for cutting gears
using the CNC hobbing machine with different manufacturing
processes, gears with novel shapes can be manufactured for
power transmissions in parallel, intersected and crossed axes.
However, the CNC hobbing process is complicated owing to
its complex tool geometry, tool setting, and the cutting motion
of multi-degree of freedom. Until now, this topic has received
only limited attention. Most investigations involving tooth ge-
ometry have based on the rack cutter generation with one degree
of freedom (Litvin and Tsay, 1985; Litvin, 1989). The genera-
tion with multi-degree of freedom has been seldom studied.
Litvin et al. (1975, 1994) proposed the concept of multi-degree
of freedom to apply to the theory of gearing. Chakraborty and
Dhande (1977) investigated the geometry of spatial cams with
two degrees of freedom, i.e., Camoid and Conoid. Also, Tsay
and Hwang (1994) applied the envelope theory to study the
geometry of Camoid. Moreover, Mitome (1981) used the enve-
lope theory to study the hobbing of a conical gear. Wu (1982)
investigated the hobbing process of a hobbing machine with
multi-degree of freedom. However, the above models can not
be applied to a 6-axis CNC hobbing machine and therefore, can
not adequately simulate and develop new types of gears. 3153

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