This paper presents a systematic approach for the design, generation and analysis of conical worm gear drives. The approach is based on the mathematical formulations on the mesh, tooth generation process and conditions for the appearance of contact envelope and tooth undercutting of this type of worm drives. The formulation is implemented by a computer model developed in MatLab environment. By model simulation on worm gear mesh or generation, the conditions for the formation of contact envelope and tooth undercutting are accurately determined for the proper design of worm gear blank and tooth geometry. The computer model can also be used to calculate worm gear tooth geometry and create solid models for the worm gear drives. Numerical examples on conical worm gear drive design, analysis on the problems of contact envelope, limit line and limit point are included in the paper.

Issue Section:
Technical Papers
Keywords:
mechanical engineering computing, CAD/CAM
Topics:
Design, Worm gears, Geometry, Gears
1.
Colbourne, J. R., 1989, The Use of Oversize Hobs to Cut Worm Gears, AGMA, Virginia.
2.
Fang
,
H. S.
, and
Tsay
,
C. B.
,
1996
, “
Effects of The Hob Cutter Regrinding and Setting on ZE-Type Worm Gear Manufacture
,”
Int. J. Mach. Tools Manuf.
,
36
(
10
), pp.
1123
–
1135
.
3.
Zhang
,
Y.
, and
Wu
,
Z.
,
1997
, “
Offset Face Gear Drives: Tooth Geometry and Contact Analysis
,”
ASME J. Mech. Des.
,
119
(
1
), pp.
114
–
119
.
4.
Seol
,
I. H.
, and
Litvin
,
F. L.
,
1996
, “
Computerized Design, Generation and Simulation of Meshing and Contact of Worm-Gear Drives with Improved Geometry
,”
Computer Methods in Applied Mechanics and Engineering
,
138
, pp.
73
–
103
.
5.
Zheng
,
C.
,
Lei
,
J.
, and
Savage
,
M.
,
1989
, “
A General Method for Computing Worm Gear Conjugate Mesh Property: Part I, The Generating Surface
,”
ASME J. Mech. Des.
,
111
, pp.
143
–
147
.
6.
Litvin
,
F. L.
, and
Kin
,
V.
,
1992
, “
Computerized Simulation of Meshing and Bearing Contact for Single-enveloping Worm-gear Drives
,”
ASME J. Mech. Des.
,
114
, pp.
313
–
316
.
7.
Simon, V., 1992, “Study of Characteristics of Double-Enveloping Worm-gear Drives,” ASME International Power Transmission Gearing Conference. Vol. 1, pp. 73–76.
8.
Litvin
,
F. L.
, and
Hsiao
,
C. L.
,
1993
, “
Computerized Simulation of Meshing and Contact of Enveloping Gear Tooth Surfaces
,”
Comput. Methods Appl. Mech. Eng.
,
102
, pp.
337
–
366
.
9.
Seol
,
I. H.
,
2000
, “
The Design, Generation, and Simulation of Worm-Gear Drive With Longitudinally Localized Contacts
,”
ASME J. Mech. Des.
,
122
, pp.
201
–
206
.
10.
Litvin
,
F. L.
,
Peng
,
A.
, and
Wang
,
A.
,
1999
, “
Limitation of Gear Tooth Surfaces by Envelopes to Contact Lines and Edge of Regression
,”
Mech. Mach. Theory
,
34
(
6
), pp.
889
–
902
.
11.
Litvin
,
F. L.
,
Kin
,
V.
, and
Zhang
,
Y.
,
1990
, “
Limitations of Conjugate Gear Tooth Surfaces
,”
ASME J. Mech. Des.
,
112
, pp.
230
–
236
.
12.
Chen
,
N. X.
,
2000
, “
Edges of Regression and Limit Normal Point of Conjugate Surfaces
,”
ASME J. Mech. Des.
,
122
, pp.
419
–
425
.
13.
Litvin
,
F. L.
,
Egelja
,
A. M.
, and
De Donno
,
M.
,
1998
, “
Computerized Determination of Singularities and Envelopes to Families of Contact Lines on Gear Tooth Surfaces
,”
Comput. Methods Appl. Mech. Eng.
,
158
(
1–2
), pp.
23
–
34
.
14.
Sarri, O. E., Speed-Reduction Gearing, Patent No. 2,696,125, United States patent Office, 1954.
15.
Goldfarb, V., 1995, “Theory of Design and Practice of Development of Spiroid Gearing,” Proc. Of Congress Gear Transmissions’95, Sofia, Vol. 2, pp. 1–5.
16.
Abadjiev
,
V.
, and
Petrova
,
D.
,
1997
, “
Testing of the Kinematic Conjugation of the Flanks Active Surface of Gear-Pairs of Type Spiroid
,”
Mech. Mach. Theory
,
32
(
3
), pp.
343
–
348
.
17.
Litvin
,
F. L.
, and
De Donno
,
M.
,
1998
, “
Computerized Design and Generation of Modified Spiroid Worm-gear Drive with Low Transmission Errors and Stabilized Bearing Contact
,”
Comput. Methods Appl. Mech. Eng.
,
162
, pp.
187
–
201
.
18.
Litvin
,
F. L.
,
Argentieri
,
G.
,
De Donno
,
M.
, and
Hawkins
,
M.
,
2000
, “
Computerized Design, Generation and Simulation of Meshing and Contact of Face Worm Gear Drives
,”
Comput. Methods Appl. Mech. Eng.
,
189
, pp.
785
–
801
.
19.
Su, Daizhong, Song, Yongle, and Gentle, Richard C., 2000, “A Novel Approach of Obtaining Localized Tooth Contact for Spiroid Gear Drives,” ASME 2000 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Baltimore, September 10–13.
20.
Litvin, F. L., 1994, Gear Geometry and Applied Theory, Prentice Hall, New Jersey.
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