A perturbation method is presented which makes it possible to obtain approximate closed-form expressions for profile relief that minimize the fluctuations of quasi-static transmission errors under load. A number of results are displayed which prove the theoretical effectiveness of the proposed solutions for low-contact ratio (LCR) and high-contact ratio (HCR) spur and helical gears. It is also shown that the corresponding relief performance is not significantly downgraded by center-distance (CD) variations. Finally, a number of practical considerations are brought up and commented.

References

References
1.
Walker
,
H.
,
1938
, “
Gear Tooth Deflection and Profile Modification
,”
Engineer
,
166
, pp.
409
412
.
2.
Niemann
,
G.
, and
Baethge
,
J.
,
1970
, “
Drehwegfehler, Zahnfederhärte und Geräusch bei Stirnrädern
,”
VDI-Z.
,
112
, pp.
205
276
, 495–499.
3.
Gregory
,
R. W.
,
Harris
,
S. L.
, and
Munro
,
R. G.
,
1963
, “
Dynamic Behaviour of Spur Gears
,”
Proc. Inst. Mech
. Eng., IMechE Int. Conf. Gearing
,
178
, pp.
261
266
.
4.
Terauchi
,
Y.
,
Nadano
,
H.
, and
Nohara
,
M.
,
1982
, “
On the Effect of the Tooth Profile Modification on the Dynamic Load and the Sound Level of a Spur Gear
,”
Bull. JSME
,
25
(
207
), pp.
1474
1481
.10.1299/jsme1958.25.1474
5.
Sato
,
T.
,
Umezawa
,
K.
, and
Ishikawa
,
J.
,
1983
, “
Effects of Contact Ratio and Profile Correction on Gear Rotational Vibration
,”
Bull. JSME
,
26
(
221
), pp.
2010
2016
.10.1299/jsme1958.26.2010
6.
Smith
,
J. D.
,
1983
,
Gears and Their Vibration
,
Marcel Dekker
,
New-York, London
.
7.
Tavakoli
,
M.
, and
Houser
,
D. R.
,
1986
, “
Optimum Profile Modifications for the Minimization of Static Transmission Errors of Spur Gears
,”
ASME J. Mech., Transm., Autom. Des.
,
108
, pp.
86
95
.10.1115/1.3260791
8.
Houser
,
D. R.
,
1991
, “
Gear Noise
,”
Dudley's Gear Handbook
,
P. S.
Townsend
, ed.,
McGraw-Hill
,
New York
, pp.
14.1
14.32
.
9.
Lee
,
C.
,
Lin
,
H. H.
,
Oswald
,
F. B.
, and
Townsend
,
D. P.
,
1991
, “
Influence of Linear Profile Modification and Loading Conditions on The Dynamic Tooth Load and Stress of High-Contact-Ratio Spur Gears
,”
ASME J. Mech. Des.
,
113
(
4
), pp.
473
480
.10.1115/1.2912807
10.
Munro
,
R. G.
,
1990
, “
A Review of the Theory and Measurement of Gear Transmission Error
,”
Proceedings of the First International Conference on Gearbox Noise and Vibration
,
Cambridge
, pp.
3
10
.
11.
Munro
,
R. G.
,
Yildirim
,
N.
, and
Hall
,
D. M.
,
1990
, “
Optimum Profile Relief and Transmission Error in Spur Gears
,”
Proceedings of the First International Conference on Gearbox Noise and Vibration
,
Cambridge
, pp.
35
41
.
12.
Lin
,
H. H.
,
Oswald
,
F. B.
, and
Townsend
,
D. P.
,
1994
, “
Dynamic Loading of Spur Gears With Linear or Parabolic Tooth Profile Modifications
,”
Mech. Mach. Theory
,
29
(
8
), pp.
1115
1129
.10.1016/0094-114X(94)90003-5
13.
Matsumura
,
S.
,
Umezawa
,
K.
, and
Houjoh
,
H.
,
1996
, “
Performance Diagram of a Helical Gear Pair Having Tooth Surface Deviation During Transmission on Light Load
,”
Proceedings of the 7th ASME International Power Transmission and Gearing Conference
, Oct. 6–9,
San Diego
, pp.
161
168
.
14.
Velex
,
P.
, and
Maatar
,
M.
1996
, “
A Mathematical Model for Analyzing the Influence of Shape Deviations and Mounting Errors on Gear Dynamics
,”
J. Sound Vib.
,
191
(
5
), pp.
629
660
.10.1006/jsvi.1996.0148
15.
Maatar
,
M.
, and
Velex
,
P.
,
1997
, “
Quasi-Static and Dynamic Analysis of Narrow-Faced Helical Gears With Profile and Lead Modifications
,”
ASME J. Mech. Des.
,
119
(
4
), pp.
474
480
.10.1115/1.2826392
16.
Houser
,
D. R.
,
Harianto
,
J.
,
Iyer
,
N.
,
Josephson
,
J.
, and
Chandrasekaren
,
B.
,
2000
, “
A Multi-Variable Approach to Determining the ‘Best’ Gear Design
,”
Proceedings of the 8th ASME International Power Transmission and Gearing Conference
, Sept. 10–13,
Baltimore
,
8
pages, Paper DETC 2000/PTG-111.
17.
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
325
.10.1115/1.2912785
18.
Sundaresan
,
S
.,
Ishii
,
K.
, and
Houser
,
D. R.
,
1992
, “
Design Optimization for Robustness Using Performance Simulation Programs
,”
Eng. Optim.
,
20
(
3
), pp.
163
178
.10.1080/03052159208941278
19.
Ghribi
,
D.
,
Bruyère
,
J.
,
Velex
,
P.
,
Octrue
,
M.
, and
Haddar
,
M.
,
2012
, “
A Contribution to the Design of Robust Profile Modifications in Spur and Helical Gears by Combining Analytical Results and Numerical Simulations
,”
ASME J. Mech. Des.
,
134
(
6
), p.
061011
.10.1115/1.4006740
20.
Velex
,
P.
,
Bruyère
,
J.
, and
Houser
,
D. R.
,
2011
, “
Some Analytical Results on Transmission Errors in Narrow-Faced Spur and Helical Gears—Influence of Profile Modifications
,”
ASME J. Mech. Des.
,
133
(
3
), p.
031010
.10.1115/1.4003578
21.
Velex
,
P.
and
Ajmi
,
M.
,
2006
, “
On the Modelling of Excitations in Geared Systems by Transmissions Errors
,”
J. Sound Vib.
,
290
(
3–5
), pp.
882
909
.10.1016/j.jsv.2005.04.033
22.
Weber
,
C.
, and
Banaschek
,
K.
,
1953
,
Formänderung und Profilrücknahme bei Gerad-und Schrägverzahnten Antriebstechnik
, Vol. 11,
Vieweg
,
Braunschweig
.
23.
Lundberg
,
G.
,
1939
, “
Elastische Berührung zweier Halbraüme
,”
Forsch. Geb. Ingenieurwes.
,
10
(
5
), pp.
201
211
.10.1007/BF02584950
24.
Sainsot
,
P.
,
Velex
,
P.
, and
Duverger
,
O.
,
2004
, “
Contribution of Gear Body to Tooth Deflections—A New Bidimensional Analytical Formula
,”
ASME J. Mech. Des.
,
126
(
4
), pp.
748
752
.10.1115/1.1758252
25.
Hinch
,
E. J.
,
1991
, “
Perturbation Methods
,”
Cambridge University Press
,
Cambridge
, pp.
1
26
.
26.
Cai
,
Y.
, and
Hayashi
,
T.
,
1992
, “
The Optimum Modification of Tooth Profile for a Pair of Spur Gears to Make its Rotational Vibration Equal Zero
,”
Proceedings of the 6th ASME International Power Transmission and Gearing Conference
,
Phoenix
, pp.
453
460
.
27.
Velex
,
P.
,
Maatar
,
M.
, and
Raclot
,
J. P.
,
1997
, “
Some Numerical Methods for the Simulation of Geared Transmission Dynamic Behavior—Formulation and Assessment
,”
ASME J. Mech. Des.
,
119
(
2
), pp.
292
298
.10.1115/1.2826250
You do not currently have access to this content.