Parametric excitation of a rotating ring subject to moving time-varying stiffnesses has previously been investigated and given as closed-form expressions in the system parameters. These conditions are applied to identify ring gear parametric instabilities in a planetary gear system. Certain mesh phasing and contact ratio conditions suppress parametric instabilities, and these conditions are presented with examples.

1.
Ozguven
,
N. H.
, and
Houser
,
D. R.
, 1988, “
Mathematical Models Used in Gear Dynamics
,”
J. Sound Vib.
0022-460X,
121
(
3
), pp.
383
411
.
2.
Parker
,
R. G.
,
Vijayakar
,
S. M.
, and
Imajo
,
T.
, 2000, “
Non-Linear Dynamic Response of a Spur Gear Pair: Modelling and Experimental Comparisons
,”
J. Sound Vib.
0022-460X,
237
(
3
), pp.
435
455
.
3.
Blankenship
,
W. G.
, and
Kahraman
,
A.
, 1996,
Gear Dynamics Experiments, Part I: Characterization of Forced Response
,
Proceedings of the ASME Power Transmission and Gearing Conference
,
ASME
,
San Diego
, pp.
373
380
.
4.
Ambarisha
,
V. K.
, and
Parker
,
R. G.
, 2007, “
Nonlinear Dynamics of Planetary Gears Using Analytical and Finite Element Models
,”
J. Sound Vib.
0022-460X,
302
(
3
), pp.
577
595
.
5.
Hidaka
,
T.
,
Terauchi
,
Y.
, and
Nagamura
,
K.
, 1979, “
Dynamic Behavior of Planetary Gear (Sixth Report: Influence of Meshing-Phase)
,”
Bull. JSME
0021-3764,
22
(
169
), pp.
1026
1033
.
6.
Parker
,
R. G.
, 2000, “
A Physical Explanation for the Effectiveness of Planet Phasing to Suppress Planetary Gear Vibration
,”
J. Sound Vib.
0022-460X,
236
(
4
), pp.
561
573
.
7.
Lin
,
J.
, and
Parker
,
R. G.
, 2002, “
Planetary Gear Parametric Instability Caused by Mesh Stiffness Variation
,”
J. Sound Vib.
0022-460X,
249
(
1
), pp.
129
145
.
8.
Seager
,
D. L.
, 1975, “
Conditions for the Neutralization of Excitation by the Teeth in Epicyclic Gearing
,”
J. Mech. Eng. Sci.
0022-2542,
17
, pp.
293
298
.
9.
Kahraman
,
A.
, and
Blankenship
,
W. G.
, 1994, “
Planet Mesh Phasing in Epicyclic Gear-Sets
,”
Proceedings of the International Gearing Conference Newcastle
, pp.
99
104
.
10.
Ambarisha
,
V. K.
, and
Parker
,
R. G.
, 2006, “
Suppression of Planet Mode Response in Planetary Gear Dynamics Through Mesh Phasing
,”
ASME J. Vibr. Acoust.
0739-3717,
128
, pp.
133
142
.
11.
Kahraman
,
A.
,
Kharazi
,
A. A.
, and
Umrani
,
M.
, 2003, “
A Deformable Body Dynamic Analysis of Planetary Gears with Thin Rims
,”
J. Sound Vib.
0022-460X,
262
, pp.
752
768
.
12.
Abousleiman
,
V.
, and
Velex
,
P.
, 2006, “
A Hybrid 3D Finite Element∕Lumped Parameter Model for Quasi-Static and Dynamic Analyses of Planetary∕Epicyclic Gear Sets
,”
Mech. Mach. Theory
0094-114X,
41
, pp.
725
748
.
13.
Vangipuram Canchi
,
S.
, and
Parker
,
R. G.
, 2006, “
Parametric Instability of a Circular Ring Subjected to Moving Springs
,”
J. Sound Vib.
0022-460X,
293
, pp.
360
379
.
14.
Vangipuram Canchi
,
S.
, and
Parker
,
R. G.
, 2006, “
Parametric Instability of a Rotating Ring with Moving, Time-Varying Springs
,”
ASME J. Vibr. Acoust.
0739-3717,
128
, pp.
231
243
.
15.
Talbert
,
P. B.
, 2004, “
Generalized Excitation of Traveling Wave Vibration in Gears
,”
American Gear Manufacturers Association Conference
, Technical Paper No. 04FTM08.
16.
Parker
,
R. G.
, and
Lin
,
J.
, 2004, “
Mesh Phasing Relationships in Planetary and Epicyclic Gears
,”
ASME J. Mech. Des.
1050-0472,
126
, pp.
365
370
.
17.
Johnson
,
D. C.
, 1952, “
Free Vibrations of a Rotating Elastic Body
,”
Aircr. Eng.
0002-2667,
24
, pp.
234
236
.
18.
Endo
,
M.
,
Hatamura
,
K.
,
Sakata
,
M.
, and
Taniguchi
,
O.
, 1984, “
Flexural Vibration of a Thin Rotating Ring
,”
J. Sound Vib.
0022-460X,
92
(
2
), pp.
261
272
.
19.
Huang
,
S. C.
, and
Soedel
,
W.
, 1987, “
Response of Rotating Rings to Harmonic and Periodic Loading and Comparison With the Inverted Problem
,”
J. Sound Vib.
0022-460X,
118
(
2
), pp.
253
270
.
You do not currently have access to this content.