Tooth surface modifications are small, micron-level intentional deviations from perfect involute geometries of spur and helical gears. Such modifications are aimed at improving contact pressure distribution, while minimizing the motion transmission error to reduce noise excitations. In actual practice, optimal modification requirements vary with the operating torque level, misalignments, and manufacturing variance. However, most gear literature has been concerned with determining optimal flank form modifications at a single design point, represented by fixed, single load and misalignment values. A new approach to the design of tooth surface modifications is proposed to handle such conditions. The problem is formulated as a robust design optimization problem, and it is solved, in conjunction with an efficient gear contact solver (Load Distribution Program (LDP)), by a direct search, global optimization algorithm aimed at guaranteeing global optimality of the obtained microgeometry solutions. Several tooth surface modifications can be used as microgeometry design variables, including profile, lead, and bias modifications. Depending on the contact solver capabilities, multiple performance metrics can be considered. The proposed method includes the capability of simultaneously and robustly handling several conflicting design objectives. In the present paper, peak contact stress and loaded transmission error amplitude are used as objective functions (to be minimized). At the end, two example optimizations are presented to demonstrate the effectiveness of the proposed method.

References

References
1.
Ghribi
,
D.
,
Bruyère
,
J.
,
Velex
,
P.
,
Octrue
,
M.
, and
Haddar
,
M.
,
2012
, “
Design Optimization for Robustness Using Quadrature Factorial Models
,”
ASME J. Mech. Des.
,
134
(
6
), p.
061011
.10.1115/1.4006740
2.
GearLab
,
Load Distribution Program Manual
,
The Ohio State University
,
Columbus, OH
.
3.
Walker
,
H.
,
1938
, “
Gear Tooth Deflection and Profile Modification
,”
Engineer
,
166
, pp.
409
412
and 434–436.
4.
Dudley
,
D. W.
,
1949
, “
Modification of Gear Tooth Profiles
,”
Prod. Eng.
, pp.
126
131
.
5.
Tavakoli
,
M. S.
, and
Houser
,
D. R.
,
1986
, “
Optimum Profile Modifications for the Minimization of Static Transmission Errors of Spur Gears
,”
ASME J. Mech. Trans.
,
108
(
1
), pp.
86
94
.10.1115/1.3260791
6.
Simon
,
V.
,
1989
, “
Optimal Tooth Modifications for Spur and Helical Gears
,”
ASME J. Mech. Trans.
,
111
(
4
), pp.
611
615
.10.1115/1.3259044
7.
Wagaj
,
P.
, and
Kahraman
,
A.
,
2002
, “
Influence of Tooth Profile Modification on Helical Gear Durability
,”
ASME J. Mech. Des.
,
124
(
3
), pp.
501
510
.10.1115/1.1485289
8.
Beghini
,
M.
,
Presicce
,
F.
, and
Santus
,
C.
,
2005
, “
Proposal for Tip Relief Modification to Reduce Noise in Spur Gears and Sensitivity to Meshing Conditions
,”
VDI-Berichte
1904
, Vol.
II
, pp.
1719
1734
.
9.
Bonori
,
G.
,
Barbieri
,
M.
, and
Pellicano
,
F.
,
2008
, “
Optimum Profile Modifications of Spur Gears by Means of Genetic Algorithms
,”
J. Sound Vib.
,
313
, pp.
603
616
.10.1016/j.jsv.2007.12.013
10.
Artoni
,
A.
,
Kolivand
,
M.
, and
Kahraman
,
A.
,
2010
, “
An Ease-Off Based Optimization of the Loaded Transmission Error of Hypoid Gears
,”
ASME J. Mech. Des.
,
132
(
1
), p.
011010
.10.1115/1.4000645
11.
Artoni
,
A.
,
Gabiccini
,
M.
,
Guiggiani
,
M.
, and
Kahraman
,
A.
,
2011
, “
Multi-Objective Ease-Off Optimization of Hypoid Gears for Their Efficiency, Noise, and Durability Performances
,”
ASME J. Mech. Des.
,
133
(
12
), p.
121007
.10.1115/1.4005234
12.
Sundaresan
,
S.
,
Ishii
,
K.
, and
Houser
,
D. R.
,
1991
, “
A Procedure Using Manufacturing Variance to Design Gears With Minimum Transmission Error
,”
ASME J. Mech. Des.
,
113
(
3
), pp.
318
324
.10.1115/1.2912785
13.
Yu
,
J.-C.
,
1998
, “
Design Optimization for Robustness Using Quadrature Factorial Models
,”
Eng. Optimiz.
,
30
, pp.
203
225
.10.1080/03052159808941244
14.
Harianto
,
J.
, and
Houser
,
D.
, Sept. 4–7,
2007
, “
A Methodology for Obtaining Optimum Gear Tooth Micro-Topographies for Noise and Stress Minimization Over a Broad Operating Torque Range
,”
Proceedings of the ASME 2007 International Design Engineering Technical Conference and Computers and Information in Engineering Conference
, Paper No. IDETC/CIE 2007.
15.
Gabiccini
,
M.
,
Bracci
,
A.
, and
Guiggiani
,
M.
,
2010
, “
Robust Optimization of the Loaded Contact Pattern in Hypoid Gears With Uncertain Misalignments
,”
ASME J. Mech. Des.
,
132
(
4
), p.
041010
.10.1115/1.4001485
16.
Houser
,
D.
,
Harianto
,
J.
, and
Talbot
,
D.
,
2006
, “
Gear Mesh Misalignment
,”
Gear Solutions
(June 2006), pp.
34
43
.
17.
Jones
,
D. R.
,
2001
, “
Direct Global Optimization Algorithm
,”
Encyclopedia of Optimization
,
C. A.
Floudas
and
P. M.
Pardalos
, eds.,
Kluwer Academic Publishers
,
Dordrecht, The Netherlands
, pp.
431
440
.
18.
Kelley
,
C. T.
, “Implicit Filtering,” Retrieved Jan. 12, 2013, www4.ncsu.edu/∼ctk/iffco.html
19.
Beyer
,
H.-G.
, and
Sendhoff
,
B.
,
2007
, “
Robust Optimization—A Comprehensive Survey
,”
Comput. Methods Appl. Mech. Eng.
,
196
, pp.
3190
3218
.10.1016/j.cma.2007.03.003
20.
Miettinen
,
K. M.
,
1999
,
Nonlinear Multiobjective Optimization
,
Kluwer Academic Publishers
,
Norwell, MA
.
21.
Deb
,
K.
,
2001
,
Multi-Objective Optimization Using Evolutionary Algorithms
,
John Wiley & Sons
,
Chichester, West Sussex, England
.
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