The effect of mesh stiffness on the dynamic response of face gear transmission system combining with backlash nonlinearity is studied. First, a nonlinear time-varying (NLTV) and a nonlinear time-invariant (NLTI) dynamic models of face gear transmission system with backlash nonlinearity are formulated. The 6DOF motion equations of the face gear pair considering the mesh stiffness, backlash, contact damping and supporting stiffness are proposed. Second, the effect of mesh stiffness on the dynamic response of the face gear drive system is analyzed with the numerical method, where the mesh stiffness is expressed in two patterns as time-varying form and time-invariant form. According to the comparative study, some significant phenomena as bifurcation, chaos, tooth separation and occurrence of multijump are detected. The results show that different forms of mesh stiffness generate an obvious change on the dynamic mesh force.

References

References
1.
Litvin
,
F. L.
,
Wang
,
J. C.
,
Bossler
,
J. R. B.
,
Chen
,
Y. J. D.
,
Heath
,
G.
, and
Lewicki
,
D. G.
,
1994
, “
Application of Face-Gear Drives in Helicopter Transmissions
,”
ASME J. Mech. Des.
,
116
(
3
), pp.
672
676
.10.1115/1.2919434
2.
Binney, D. A., Vinayak, H., Gmirya, Y., Zunski, L. M., Houser, D. R., and Ames, E. C., 2003, “Face Gear Transmission Development Program at Sikorsky Aircraft,” Proceedings of DETC03, Sept. 2–6, Paper no. PTG-48039.
3.
Litvin
,
F. L.
,
Fuentes
,
A.
,
Zanzi
,
C.
, and
Pontiggia
,
M.
,
2002
, “
Design, Generation, and Stress Analysis of Two Versions of Geometry of Face-Gear Drives
,”
Mech. Mach. Theory
,
37
(
10
), pp.
1179
1211
.10.1016/S0094-114X(02)00050-2
4.
Litvin
,
F. L.
, and
Fuentes
,
A.
,
2004
,
Gear Geometry and Applied Theory
,
Cambridge University Press
,
Cambridge
.
5.
Zanzi
,
C.
, and
Pedrero
,
J. I.
,
2005
, “
Application of Modified Geometry of Face Gear Drive
,”
Comput. Methods Appl. Mech. Eng.
,
194
(
27-29
), pp.
3047
3066
.10.1016/j.cma.2004.07.022
6.
Litvin
,
F. L.
,
Egelja
,
A.
,
Tan
,
J.
,
Chen
,
D. Y. D.
, and
Heath
,
G.
,
2000
, “
Handbook on Face Gear Drives With a Spur Involute Pinion
,” Technical Report No. CR-2000-209909. Available at: http://www.dtic.mil/dtic/tr/fulltext/u2/a380815.pdf
7.
Litvin
,
F. L.
,
Egelja
,
A.
,
Tan
,
J.
, and
Heath
,
G.
,
1998
, “
Computerized Design, Generation and Simulation of Meshing of Orthogonal Offset Face-Gear Drive With a Spur Involute Pinion With Localized Bearing Contact
,”
Mech. Mach. Theory
,
33
(
1-2
), pp.
87
102
.10.1016/S0094-114X(97)00022-0
8.
Litvin
,
F. L.
,
Fuentes
,
A.
, and
Howkins
,
M.
,
2001
, “
Design, Generation and TCA of New Type of Asymmetric Face-Gear Drives
,”
Comput. Methods Appl. Mech. Eng.
,
190
(
43-44
), pp.
5837
5865
.10.1016/S0045-7825(01)00201-8
9.
Litvin
,
F. L.
,
Fuentes
,
A.
,
Zanzi
,
C.
,
Pontiggia
,
M.
, and
Handschuh
,
R. F.
,
2002
, “
Face-Gear Drive With Spur Involute Pinion: Geometry, Generation by a Worm, Stress Analysis
,”
Comput. Methods Appl. Mech. Eng.
,
191
(
25-26
), pp.
2785
2813
.10.1016/S0045-7825(02)00215-3
10.
Litvin
,
F. L.
,
Gonzalez-Perez
,
I.
,
Fuentes
,
A.
,
Hayasaka
,
K.
, and
Yukishima
,
K.
,
2005
, “
Topology of Modified Surfaces of Involute Helical Gears With Line Contact Developed for Improvement of Bearing Contact, Reduction of Transmission Errors, and Stress Analysis
,”
Math. Comput. Modell.
,
42
(
9-10
), pp.
1063
1078
.10.1016/j.mcm.2004.10.028
11.
Litvin
,
F. L.
,
Gonzalez-Perez
,
I.
,
Fuentes
,
A.
,
Vecchiato
,
D.
,
Hansen
,
B. D.
, and
Binney
,
D.
,
2005
, “
Design, Generation and Stress Analysis of Face-Gear Drive With Helical Pinion
,”
Comput. Methods Appl. Mech. Eng.
,
194
(
36-38
), pp.
3870
3901
.10.1016/j.cma.2004.09.006
12.
Guingand
,
M.
,
De Vaujany
,
J.-P.
, and
Jacquin
,
C.-Y.
,
2005
, “
Quasi-Static Analysis of a Face Gear Under Torque
,”
Comput. Methods Appl. Mech. Eng.
,
194
(
39-41
), pp.
4301
4318
.10.1016/j.cma.2004.10.010
13.
Chen
,
G.-Y.
,
Chen
,
G.-D.
,
Li
,
Y.-X.
, and
Zhao
,
N.
,
2009
, “
Dynamic Response Analysis of Gear Drive With Face-Gears
,”
Hangkong Dongli Xuebao/J. Aerosp. Power
,
24
(
10
), pp.
2391
2396
.
14.
Lim
,
T. C.
, and
Singh
,
R.
,
1990
, “
Vibration Transmission Through Rolling Element Bearings, Part II: System Studies
,”
J. Sound Vib.
,
139
(
2
), pp.
201
225
.10.1016/0022-460X(90)90883-2
15.
Chen, S. Y., Tang, J. Y., Luo, C. W., Wang, Q. B.,
2011
, “
Nonlinear Dynamic Characteristics of Geared Rotor Bearing Systems With Dynamic Backlash and Friction
,”
Mech. Mach. Theory
,
46
(
4
), pp.
466
478
.10.1016/j.mechmachtheory.2010.11.016
16.
Jin
,
G.
,
Zhu
,
R.
, and
Bao
,
H.
,
2010
, “
Nonlinear Dynamical Characteristics of Face Gear Transmission System
,”
J. Central South Univ. (Sci. Technol.)
,
41
(
5
), pp.
1807
1813
(in Chinese).
17.
Peng
,
M.
,
Desmidt
,
H.
,
Saribay
,
Z. B.
, and
Smith
,
E. C.
,
2011
,
Parametric Instability of Face-Gear Drives With a Spur Pinion
, Vol.
4
, American Helicopter Society,
Virginia Beach, VA
, pp.
2478
2488
.
18.
Wang
,
J.
, and
Lim
,
T. C.
,
2009
, “
Effect of Tooth Mesh Stiffness Asymmetric Nonlinearity for Drive and Coast Sides on Hypoid Gear Dynamics
,”
J. Sound Vib.
,
319
(
3-5
), pp.
885
903
.10.1016/j.jsv.2008.06.021
19.
Chowdhury, I., and Dasgupta, S. P., 1998, “Computation of Rayleigh Damping Coefficients for Large Systems,” Department of Civil Engineering, India Institute of Technology, India.
20.
Cheon
,
G.-J.
,
2007
, “
Nonlinear Behavior Analysis of Spur Gear Pairs With a One-Way Clutch
,”
J. Sound Vib.
,
304
(
1–2
), pp.
18
30
.10.1016/j.jsv.2007.01.044
21.
Kahraman
,
A.
, and
Blankenship
,
G. W.
,
1999
, “
Effect of Involute Contact Ratio on Spur Gear Dynamics
,”
ASME J. Mech. Des.
,
121
(
1
), pp.
112
118
.10.1115/1.2829411
22.
Kuang
,
J.
, and
Yang
,
Y.
,
1992
, “
An Estimate of Mesh Stiffness and Load Sharing Ratio of a Spur Gear Pair
,” Advancing Power Transmission into the 21st Century, pp.
1
9
.
23.
Chang-Jian
,
C.-W.
,
2010
, “
Nonlinear Analysis for Gear Pair System Supported by Long Journal Bearings Under Nonlinear Suspension
,”
Mech. Mach. Theory
,
45
(
4
), pp.
569
583
.10.1016/j.mechmachtheory.2009.11.001
24.
zgüven
,
H. N.
, and
Houser
,
D. R.
,
1988
, “
Dynamic Analysis of High Speed Gears by Using Loaded Static Transmission Error
,”
J. Sound Vib.
,
125
(
1
), pp.
71
83
.10.1016/0022-460X(88)90416-6
You do not currently have access to this content.