Applied Engineering Sciences

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.

1 INTRODUCTION

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

[1−6]

. Litvin and his research institution

have made great contributions to the research on linear

tooth-surface gear

[7−11]

and represented new comput-

erised developments in design, generation, simulation

of meshing, and stress analysis of gear drives. They

[12]

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

[13]

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

algorithm

[4]

was used to determine the robust areas for

tooth modifications. They

[15,16]

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

dynamics.

2 TOOTH WIDTH DESIGNING OF ARC

TOOTH FACE-GEAR

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

[17]

. 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

face-gear.

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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