A general mathematical model is established to describe the geometries and geometric characteristics of tooth surfaces of straight noncircular bevel gears. One of the direction angles of the normal vector of the tooth surfaces is taken as a function of the angular position of its origin, called the direction angle function (DAF). The normal vector and DAF are introduced to characterize this model. The normal vector including its direction angles and modulus is solved first and then the corresponding tooth surfaces and their geometric properties, such as major curvatures and slide coefficients, could be generated and calculated directly, logically and systematically by using this model and defining various DAFs. This method is applicable to many types of straight noncircular bevel gears with different tooth surfaces including tooth surfaces cut by the crown rack cutter or others. In addition, by using this method, it is relatively easy to realize the desired geometrical and mechanical properties into the design.

References

References
1.
Jia
,
J. M.
,
Gao
,
B.
, and
Qiao
,
Y. W.
, 2003, “
A Study on Variable Ratio Differential for Off-Road Vehicles
,”
Automot. Eng.
,
25
(
5
), pp.
498
500
(in Chinese).
2.
Huston
,
R. L.
, and
Coy
,
J. J.
, 1981, “
Ideal Spiral Bevel Gears-A New Approach to Surface Geometry
,”
ASME J. Mech. Des.
,
103
, pp.
127
133
.
3.
Huston
,
R. L.
, and
Coy
,
J. J.
, 1982, “
Surface Geometry of Circular Cut Spiral Bevel Gears
,”
ASME J. Mech. Des.
,
104
, pp.
743
748
.
4.
Huston
,
R. L.
,
Lin
,
Y.
, and
Coy
,
J. J.
, 1983, “
Tooth Profile Analysis of Circular-Cut, Spiral-Bevel Gears
,”
ASME J. Mech., Transm., Autom. Des.
,
105
, pp.
132
137
.
5.
Tsai
,
Y. C.
, and
Chin
,
P. C.
, 1987, “
Surface Geometry of Straight and Spiral Bevel Gears
,”
ASME J. Mech., Transm., Autom. Des.
,
109
, pp.
443
449
.
6.
Litvin
,
F. L.
, 1994,
Gear Geometry and Applied Theory
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
7.
Al-Daccak
,
M. J.
,
Angeles
,
J.
, and
Gonzalez-Palacios
,
M. A.
, 1994, “
The Modeling of Bevel Gears Using the Exact Spherical Involute
,”
ASME J. Mech. Des.
,
116
, pp.
364
368
.
8.
Shunmugam
,
M. S.
,
Subba-Rao
,
B.
, and
Jayaprakash
,
V.
, 1998, “
Establishing Gear Tooth Surface Geometry and Normal Deviation, Part II-Bevel Gears
,”
Mech. Mach. Theory
,
33
, pp.
525
534
.
9.
Ollson
,
V.
, 1959,
Noncircular Bevel Gears
,
The Royal Swedish Academy of Engineering Sciences
,
Stockholm, Sweden
.
10.
Wang
,
X. C.
,
Wu
,
X. T.
, and
Peng
,
W.
, 1990, “
An Efficient Differential With Variable Transmission Ratio
,” China Patent No. 1043981A (in Chinese).
11.
Jia
,
J. M.
,
Gao
,
B.
, and
Zhao
,
D.
, 2008, “
Analysis Method for Noncircular Bevel Gearing Based on Geodesic Curvature Preserving Mapping
,”
Chin. J. Mech. Eng.
,
44
(
4
), pp.
53
57
(in Chinese).
12.
Xia
,
J.
,
Liu
,
Y.
,
Geng
,
C.
, and
Song
,
J.
, 2008, “
Noncircular Bevel Gear Transmission With Intersecting Axes
,”
ASME J. Mech. Des.
,
130
, p.
054502
.
13.
Gray
,
A.
, 1997,
Modern Differential Geometry of Curves and Surfaces With Mathematica
,
2nd ed.
,
CRC
,
Boca Raton, FL
, pp.
185
187
.
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