A dynamic model that includes friction and tooth profile error excitation for herringbone gears is proposed for the dynamic analysis of variable speed processes. In this model, the position of the contact line and relative sliding velocity are determined by the angular displacement of the gear pair. The translational and angular displacements are chosen as generalized coordinates to construct the dynamic model. The friction is calculated using a variable friction coefficient. The tooth profile error excitation is assumed to depend on the position along the contact line and to vary with the angular displacement of the driving gear. Thus, the proposed model can be used in the dynamic analysis of the variable speed process of a herringbone gear transmission system. An example acceleration process is numerically simulated using the model proposed in this paper. The dynamics responses are compared with those from the model utilizing a constant friction coefficient and without friction in cases where the profile error excitations are included and ignored.

References

References
1.
Wang
,
C.
,
Fang
,
Z.
, and
Jia
,
H.
,
2010
, “
Investigation of a Design Modification for Double Helical Gears Reducing Vibration and Noise
,”
J. Mar. Sci. Appl.
,
9
(
1
), pp.
81
86
.10.1007/s11804-010-8087-z
2.
Iida
,
H.
,
Tamura
,
A.
, and
Yamada
,
Y.
,
1985
, “
Vibrational Characteristics of Friction Between Gear Teeth
,”
Bull. JSME
,
28
(
241
), pp.
1512
1519
.10.1299/jsme1958.28.1512
3.
Borner
,
J.
, and
Houser
,
D. R.
,
1996
, “
Friction and Bending Moments as Gear Noise Excitations
,”
SAE Technical Paper No. 961816
,
105
(
6
), pp.
1669
1676
.10.4271/961816
4.
He
,
S.
,
Singh
,
R.
, and
Pavic
,
G.
,
2008
, “
Effect of Sliding Friction on Gear Noise Based on a Refined Vibro-Acoustic Formulation
,”
Noise Control Eng. J.
,
56
(
3
), pp.
164
175
.10.3397/1.2938737
5.
Velex
,
P.
, and
Sainsot
,
P.
,
2002
, “
An Analytical Study of Tooth Friction Excitations in Errorless Spur and Helical Gears
,”
Mech. Mach. Theory
,
37
(
7
), pp.
641
658
.10.1016/S0094-114X(02)00015-0
6.
He
,
S.
,
Gunda
,
R.
, and
Singh
,
R.
,
2007
, “
Inclusion of Sliding Friction in Contact Dynamics Model for Helical Gears
,”
ASME J. Mech. Des.
,
129
(
1
), pp.
48
–57.10.1115/1.2359474
7.
Velex
,
P.
, and
Cahouet
,
V.
,
2000
, “
Experimental and Numerical Investigations on the Influence of Tooth Friction in Spur and Helical Gear Dynamics
,”
ASME J. Mech. Des.
,
122
(
4
), pp.
515
522
.10.1115/1.1320821
8.
Xu
,
H.
,
Kahraman
,
A.
,
Anderson
,
N. E.
, and
Maddock
,
D. G.
,
2007
, “
Prediction of Mechanical Efficiency of Parallel-Axis Gear Pairs
,”
ASME J. Mech. Des.
,
129
(
1
), pp.
58
68
.10.1115/1.2359478
9.
Drozdov
,
Y. N.
, and
Gavrikov
,
Y. A.
,
1968
, “
Friction and Scoring Under the Conditions of Simultaneous Rolling and Sliding of Bodies
,”
Wear
,
11
(
4
), pp.
291
302
.10.1016/0043-1648(68)90177-4
10.
O'Donoghue
,
J. P.
, and
Cameron
,
A.
,
1966
, “
Friction and Temperature in Rolling Sliding Contacts
,”
ASLE Trans.
,
9
(
2
), pp.
186
194
.10.1080/05698196608972134
11.
Misharin
,
Y. A.
,
1958
, “
Influence of the Friction Condition on the Magnitude of the Friction Coefficient in the Case of Rollers With Sliding
,”
Proceedings of International Conference on Gearing, Mechanical Engineering
, London, pp.
159
164
.
12.
Benedict
,
G. H.
, and
Kelley
,
B. W.
,
1961
, “
Instantaneous Coefficients of Gear Tooth Friction
,”
ASLE Trans.
,
4
(
1
), pp.
59
70
.10.1080/05698196108972420
13.
ISO TC 60, DTR 13989.
14.
Vaishya
,
M.
, and
Singh
R.
,
2003
, “
Strategies for Modeling Friction in Gear Dynamics
,”
ASME J. Mech. Des.
,
125
(
2
), pp.
383
393
.10.1115/1.1564063
15.
Vaishya
,
M.
, and
Singh
,
R.
,
2001
, “
Sliding Friction-Induced Non-Linearity and Parametric Effects in Gear Dynamics
,”
J. Sound Vib.
,
248
(
4
), pp.
671
694
.10.1006/jsvi.2001.3818
16.
Vaishya
,
M.
, and
Singh
,
R.
,
2001
, “
Analysis of Periodically Varying Gear Mesh Systems With Coulomb Friction Using Floquet Theory
,”
J. Sound Vib.
,
243
(
3
), pp.
525
545
.10.1006/jsvi.2000.3419
17.
He
,
S.
,
Gunda
,
R.
, and
Singh
,
R.
,
2007
, “
Effect of Sliding Friction on the Dynamics of Spur Gear Pair With Realistic Time-Varying Stiffness
,”
J. Sound Vib.
,
301
(
3–5
), pp.
927
949
.10.1016/j.jsv.2006.10.043
18.
Yang
,
P.
, and
Yang
,
P.
,
2007
, “
Analysis on the Thermal Elastohydrodynamic Lubrication of Tapered Rollers in Opposite Orientation
,”
Tribol. Int.
,
40
(
10
), pp.
1627
1637
.10.1016/j.triboint.2007.02.018
19.
Ajmi
,
M.
, and
Velex
,
P.
,
2005
, “
A Model for Simulating the Quasi-Static and Dynamic Behaviour of Solid Wide-Faced Spur and Helical Gears
,”
Mech. Mach. Theory
,
40
(
2
), pp.
173
190
.10.1016/j.mechmachtheory.2003.06.001
20.
Xu
,
H.
,
2005
, “
Development of a Generalized Mechanical Efficiency Prediction Methodology for Gear Pairs
,” Electronic thesis or Dissertation, Ohio State University, Columbus, OH.
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