Abstract

In this study, a multimesh gear system subjected to torque fluctuations is employed as an example to study vibro-impacts of multidegree-of-freedom systems having multiple clearances. Such rotational systems are common in various automotive geared drivetrains where external torque fluctuations lead to contact loss at gear mesh interfaces to result in sequences of impacts. The specific configuration considered here is a three-axis, two-gear mesh drivetrain that is commonly used in engine timing gear systems, known for its vibro-impacts resulting in rattling noise. On the theoretical side, a discrete torsion model is developed and solved using a piecewise-linear solution method. Its predictions are compared to measurements from a three-axis geartrain to demonstrate its accuracy. The validated model is employed to characterize the sensitivity of vibro-impact motions and associated nonlinear behavior to key excitation parameters for two kinematic configurations. For the idler configuration where the middle gear is not subject to any external disturbance, double-sided impacts of one gear mesh were shown to induce separation on the other gear mesh such that vibro-impacts are localized in a single mesh. For the torque-split configuration, the ratio of the torques carried by the outputs was identified as a major parameter defining regions and types of rattle motions.

References

1.
Wagg
,
D. J.
, and
Bishop
,
S. R.
,
2004
, “
Dynamics of a Two Degree of Freedom Vibro-Impact System With Multiple Motion Limiting Constraints
,”
Int. J. Bifurcation Chaos
,
14
(
1
), pp.
119
140
.10.1142/S0218127404009223
2.
Shaw
,
J.
, and
Shaw
,
S. W.
,
1989
, “
The Onset of Chaos in a Two-Degree-of-Freedom Impacting System
,”
ASME J. Appl. Mech.
,
56
(
1
), pp.
168
174
.10.1115/1.3176040
3.
Luo
,
G. W.
,
2004
, “
Period-Doubling Bifurcations and Routes to Chaos of the Vibratory Systems Contacting Stops
,”
Phys. Lett. A
,
323
(
3–4
), pp.
210
217
.10.1016/j.physleta.2004.01.071
4.
Comparin
,
R. J.
, and
Singh
,
R.
,
1990
, “
Frequency Response Characteristics of a Multi-Degree-of-Freedom System With Clearances
,”
J. Sound Vib.
,
142
(
1
), pp.
101
124
.10.1016/0022-460X(90)90585-N
5.
Singh
,
R.
,
Xie
,
H.
, and
Comparin
,
R. J.
,
1989
, “
Analysis of Automotive Neutral Gear Rattle
,”
J. Sound Vib.
,
131
(
2
), pp.
177
196
.10.1016/0022-460X(89)90485-9
6.
Theodossiades
,
S.
,
De La Cruz
,
M.
, and
Rahnejat
,
H.
,
2015
, “
Prediction of Airborne Radiated Noise From Lightly Loaded Lubricated Meshing Gear Teeth
,”
Appl. Acoust.
,
100
, pp.
79
86
.10.1016/j.apacoust.2015.06.014
7.
Fernandez-Del-Rincon
,
A.
,
Diez-Ibarbia
,
A.
, and
Theodossiades
,
S.
,
2019
, “
Gear Transmission Rattle: Assessment of Meshing Forces Under Hydrodynamic Lubrication
,”
Appl. Acoust.
,
144
, pp.
85
95
.10.1016/j.apacoust.2017.04.001
8.
Rocca
,
E.
, and
Russo
,
R.
,
2011
, “
Theoretical and Experimental Investigation Into the Influence of the Periodic Backlash Fluctuations on the Gear Rattle
,”
J. Sound Vib.
,
330
(
20
), pp.
4738
4752
.10.1016/j.jsv.2011.04.008
9.
Pfeiffer
,
F.
, and
Prestl
,
W.
,
1994
, “
Hammering in Diesel-Engine Driveline Systems
,”
Nonlinear Dyn.
,
5
(
4
), pp.
477
492
.10.1007/BF00052455
10.
Joshi
,
Y. V.
, and
Kelleher
,
J. E.
,
2014
, “
Gear Train Mesh Efficiency Study: The Effects of an Anti-Backlash Gear
,”
SAE Int. J. Commer. Veh.
,
7
(
1
), pp.
271
277
.10.4271/2014-01-1769
11.
Huang
,
J. C.
, and
Abram
,
K. R.
,
1999
, “
Cummins 4B Noise Reduction Anti-Backlash Camshaft Gear
,”
SAE
Paper No. 1999-01-1761.10.4271/1999-01-1761
12.
Zhao
,
H. A.
, and
Reinhart
,
T. E.
,
1999
, “
The Influence of Diesel Engine Architecture on Noise Levels
,”
SAE
Paper No. 1999-01-1747.10.4271/1999-01-1747
13.
Esmaeli
,
M.
,
2011
, “
Engine Timing Geartrain Concepts and Proposals for Gear Rattle Noise Reduction in Commercial Vehicles
,” M.Sc. thesis,
Chalmers University of Technology
, Sweden.
14.
Croker
,
M. D.
,
Amphlett
,
S. A.
, and
Barnard
,
A. I.
,
1995
, “
Heavy Duty Diesel Engine Gear Train Modelling to Reduce Radiated Noise
,”
SAE
Paper No. 951315.10.4271/951315
15.
Carbonelli
,
A.
,
Perret-Liaudet
,
J.
, and
Rigaud
,
E.
,
2014
, “
Hammering Noise Modelling – Nonlinear Dynamics of a Multi-Stage Gear Train
,”
International Gear Conference 2014
, Lyon, Elsevier, Aug. 26–28, pp.
447
456
.
16.
Donmez
,
A.
, and
Kahraman
,
A.
,
2022
, “
A Generalized Torsional Dynamics Formulation for Multi-Mesh Gear Trains With Clearances and Torque Fluctuations
,”
18th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
, St. Louis, MO, Aug. 14–17, Paper No. DETC2022-88988.
17.
Donmez
,
A.
, and
Kahraman
,
A.
,
2022
, “
Characterization of Nonlinear Rattling Behavior of a Gear Pair Through a Validated Torsional Model
,”
ASME J. Comput. Nonlinear Dyn.
,
17
(
4
), p.
041006
.10.1115/1.4053367
18.
Padmanabhan
,
C.
,
Barlow
,
R. C.
,
Rook
,
T. E.
, and
Singh
,
R.
,
1995
, “
Computational Issues Associated With Gear Rattle Analysis
,”
ASME J. Mech. Des.
,
117
(
1
), pp.
185
192
.10.1115/1.2826105
19.
Brogliato
,
B.
,
2016
, “
Nonsmooth Mechanics: Models
,”
Dynamics and Control
, 3rd ed.,
Springer International Publishing
, Cham,
Switzerland
.
20.
Ziegler
,
P.
, and
Eberhard
,
P.
,
2008
, “
Simulative and Experimental Investigation of Impacts on Gear Wheels
,”
Comput. Methods Appl. Mech. Eng.
,
197
(
51–52
), pp.
4653
4662
.10.1016/j.cma.2008.06.007
21.
Donmez
,
A.
, and
Kahraman
,
A.
,
2022
, “
Influence of Various Manufacturing Errors on Gear Rattle
,”
Mech. Mach. Theory
,
173
, p.
104868
.10.1016/j.mechmachtheory.2022.104868
22.
Russo
,
R.
,
Brancati
,
R.
, and
Rocca
,
E.
,
2009
, “
Experimental Investigations About the Influence of Oil Lubricant Between Teeth on the Gear Rattle Phenomenon
,”
J. Sound Vib.
,
321
(
3–5
), pp.
647
661
.10.1016/j.jsv.2008.10.008
23.
Brancati
,
R.
,
Rocca
,
E.
, and
Russo
,
R.
,
2005
, “
A Gear Rattle Model Accounting for Oil Squeeze Between the Meshing Gear Teeth
,”
Proc. Inst. Mech. Eng., Part D
,
219
(
9
), pp.
1075
1083
.10.1243/095440705X34757
24.
Wolf
,
A.
,
Swift
,
J. B.
,
Swinney
,
H. L.
, and
Vastano
,
J. A.
,
1985
, “
Determining Lyapunov Exponents From a Time Series
,”
Phys. D.
,
16
(
3
), pp.
285
317
.10.1016/0167-2789(85)90011-9
25.
Halse
,
C. K.
,
Wilson
,
R. E.
,
Di Bernardo
,
M.
,
Homer
,
M. E.
,
Technology
,
R.
, and
House
,
R.
,
2007
, “
Coexisting Solutions and Bifurcations in Mechanical Oscillators With Backlash
,”
J. Sound Vib.
,
305
(
4–5
), pp.
854
885
.10.1016/j.jsv.2007.05.010
26.
Rigaud
,
E.
, and
Perret-Liaudet
,
J.
,
2020
, “
Investigation of Gear Rattle Noise Including Visualization of Vibro-Impact Regimes
,”
J. Sound Vib.
,
467
, p.
115026
.10.1016/j.jsv.2019.115026
27.
Donmez
,
A.
, and
Kahraman
,
A.
,
2022
, “
Experimental and Theoretical Investigation of Vibro-Impact Motions of a Gear Pair Subjected to Torque Fluctuations to Define a Rattle Noise Severity Index
,”
ASME J. Vib. Acoust.
,
144
(
4
), p.
041001
.10.1115/1.4053264
28.
Wagg
,
D. J.
,
2005
, “
Periodic Sticking Motion in a Two-Degree-of-Freedom Impact Oscillator
,”
Int. J. Non. Linear Mech.
,
40
(
8
), pp.
1076
1087
.10.1016/j.ijnonlinmec.2005.03.002
29.
Nordmark
,
A. B.
,
1991
, “
Non-Periodic Motion Caused by Grazing Incidence in an Impact Oscillator
,”
J. Sound Vib.
,
145
(
2
), pp.
279
297
.10.1016/0022-460X(91)90592-8
30.
Shaw
,
S. W.
, and
Holmes
,
P. J.
,
1983
, “
A Periodically Forced Impact Oscillator With Large Dissipation
,”
ASME J. Appl. Mech.
,
50
(
4a
), pp.
849
857
.10.1115/1.3167156
31.
Foale
,
S.
, and
Bishop
,
S. R.
,
1994
, “
Bifurcations in Impact Oscillations
,”
Nonlinear Dyn.
,
6
(
3
), pp.
285
299
.10.1007/BF00053387
You do not currently have access to this content.