Applied Engineering Sciences Deng (Ed.)
© 2015 Taylor & Francis Group, London, 978-1-138-02649-0
Tooth width design of the arc tooth face-gear
Y.M. Cui, L.P. Wang & X.Z. Feng
School of Mechatronics Engineering, Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou, China
ABSTRACT: The arc tooth face-gear was processed by the generating method, avoidance of undercutting and
pointing in the toe and heel of the arc tooth face-gear The non-undercutting and avoiding pointing conditions for
the face- gear were established based on meshing principle, differential geometry and geometry principle. The
geometry principle of non-pointing conditions has solved the maximum outer radius. The MATLAB has built
the precise model for the arc tooth face-gear. It ensures the precision of the generating method in processing
the arc tooth face-gear. The method provides a theoretical and tentative basis for the analysis of tooth surface
contact stress, tooth root bending stress and dynamics, and further furnishes systematic theoretical direction for
experiment and application.
Arc tooth face-gear transmission is a stable transmis-
sion of high carrying capacity, low meshing noise and
simplified structure, which is widely used in trans-
mission systems in aviation, vessel and automobile
industries. As the arc tooth face-gear is a point-
contact-local conjugate gear pair, which adopts paired
processing and application, the geometry of tooth sur-
face is complex and it’s difficult to adjust the machine
tool and hard to establishthe accurate geometric model
of tooth surface
. Litvin and his research institution
have made great contributions to the research on linear
tooth-surface gear
and represented new comput-
erised developments in design, generation, simulation
of meshing, and stress analysis of gear drives. They
proposed a novel profile modification methodology
for the moulded face-gear drive to enhance the con-
trollability of the contact pattern and the transmission
characteristics. The goal
was to propose a simple
formula in order to predict the width of the wheel
as a function of the main design parameters. This
method was able to simulate the geometry and the
quasistatic loaded behavior of a face gear. A genetic
was used to determine the robust areas for
tooth modifications. They
research on the face-
gears in modeling, meshing, computer simulation of
contact trace, integrated approach of localised tooth
contact, and manufacture. The generating method in
this paper ensures the correct transmission of arc
tooth face-gear pairs. To prevent transmission fail-
ure from undercutting the inner end dedendum and
pointing the outer end addendum, tooth width of the
arc tooth face-gear is designed using the meshing
principle, the differential geometry and the geome-
try principle. The precise modelling of the arc tooth
face-gear is realised using MATLAB programming,
which offers theoretical basis for the analysis on tooth
surface contact stress, tooth root bending stress, and
For the arc tooth face-gear pairs to be processed, the
generating gear was assumed to conjugate arc tooth
cylinder gear and arc tooth face-gear in order to ensure
the processed arc tooth face-gear can correctly mesh
with the arc tooth cylinder gear
. Owing to the limit
of tooth undercut and steeple top for face- gear in
generating the processing of arc tooth face-gear, tooth
width of tooth face-gear has to be properly designed.
Based on meshing principle and differential geome-
try, the non-undercut conditions have been established
so that the minimum inner radius of face gear with-
out undercut is solved. Furthermore, according to the
geometry principle, the geometrical model with gear
avoiding steeple top for face- gear is deduced to ensure
the maximum outer radius without steeple top of
2.1 Methods of judging the non-undercut
When processing the conjugate arc tooth face-gear
using the gear cutters, assuming the tooth surface
of the cutters is smooth with no singular points, the
curve group of the tooth surface the envelope ridge
line would be formed by curve group of the tooth sur-
face connecting with the contacting lines of arc tooth
face-gear in the conjugate movement of the tooth sur-
face and arc tooth face-gear. It is called the undercut
curve emerging in arc tooth face-gear. The points in
the curve are called the undercut points, namely the

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