The vibration modal properties of double-helical planetary gear (DHPG) system with three-dimensional motion are investigated with a combined use of numerical and analytical approach in this paper. The lumped-parameter model of the DHPG considering stiffness coupled between the left gear and the right gear is developed. Load-sharing with journal bearings is accepted in this planetary gear system, so that four stiffness coefficients can be applied to describe the dynamic behavior between the planet gear and the carrier. The model has three planar degrees of freedom for the carrier and an added axial degree of freedom for all gears, considering the effect of axial dynamic forces. The vibration equations are obtained according to Lagrange equation. A modal type distribution map is plotted initially to simplify modal classification. With the application of this modal type distribution map, all vibration modes are categorized distinctly into three essentially different types of modes including planet mode (PM), rotational-axial mode (RAM), and planer-translational mode (PTM). Unique characteristics of these vibration modes, such as, eigenvalue number, multiplicity of natural frequencies and deflection relations, are deduced and proved analytically. For each type of vibration modes, the reduced-order eigenvalue problems are derived.

References

References
1.
Cunliffe
,
F.
,
Smith
,
J.
, and
Welbourn
,
D.
,
1974
, “
Dynamic Tooth Loads in Epicyclic Gears
,”
J. Eng. Ind.
,
5
(
95
), pp.
578
584
.10.1115/1.3438367
2.
Botman
,
M.
,
1976
, “
Epicyclic Gear Vibrations
,”
J. Eng. Ind.
,
98
(
3
), pp.
811
815
.10.1115/1.3439034
3.
Lin
,
J.
, and
Parker
,
R. G.
,
1999
, “
Analytical Characterization of the Unique Properties of Planetary Gear Free Vibration
,”
ASME J. Vib. Acoust.
,
121
(
3
), pp.
316
321
.10.1115/1.2893982
4.
Wu
,
X.
, and
Parker
,
R. G.
,
2008
, “
Modal Properties of Planetary Gears With an Elastic Continuum Ring Gear
,”
ASME J. Appl. Mech.
,
75
(
3
), pp.
1
12
.10.1115/1.2839892
5.
Parker
,
R. G.
, and
Wu
,
X.
,
2010
, “
Vibration Modes of Planetary Gears With Unequally Spaced Planets and an Elastic Ring Gear
,”
J. Sound Vib.
,
329
(
11
), pp.
2265
2275
.10.1016/j.jsv.2009.12.023
6.
Ambarisha
,
V. K.
, and
Parker
,
R. G.
,
2005
, “
Suppression of Planet Mode Response in Planetary Gear Dynamics Through Mesh Phasing
,”
ASME J. Vib. Acoust.
,
128
(
2
), pp.
133
142
.10.1115/1.2171712
7.
Parker
,
R. G.
,
2000
, “
A Physical Explanation for the Effectiveness of Planet Phasing to Suppress Planetary Gear Vibration
,”
J. Sound Vib.
,
236
(
4
), pp.
561
573
.10.1006/jsvi.1999.2859
8.
Tongqiang
,
Y.
,
Yimin
,
S.
, and
Ce
,
Z.
,
2005
, “
Property Analysis of Free Vibration of Helical Planetary Gear Trains
,”
Chin. J. Mech. Eng.
,
41
(
7
), pp.
50
55
.
9.
Eritenel
,
T.
, and
Parker
,
R. G.
,
2009
, “
Modal Properties of Three-Dimensional Helical Planetary Gears
,”
J. Sound Vib.
,
325
(
1
), pp.
397
420
.10.1016/j.jsv.2009.03.002
10.
Bu
,
Z.
,
Liu
,
G.
, and
Wu
,
L.
,
2012
, “
Modal Analyses of Herringbone Planetary Gear Train With Journal Bearings
,”
Mech. Mach. Theory
,
54
, pp.
99
115
.10.1016/j.mechmachtheory.2012.03.006
11.
Friswell
,
M.
,
Penny
,
J. E.
,
Garvey
,
S. D.
, and
Lees
,
A. W.
,
2010
,
Dynamics of Rotating Machines
,
Cambridge University
,
Cambridge, UK
.
12.
Smith
,
D. M. L.
,
1969
,
Journal Bearings in Turbomachinery
,
Chapman & Hall
,
London, UK
.
13.
Cheng
,
Y.
, and
Lim
,
T. C.
,
2003
, “
Dynamics of Hypoid Gear Transmission With Nonlinear Time-Varying Mesh Characteristics
,”
ASME J. Mech. Des.
,
125
(
2
), pp.
373
382
.10.1115/1.1564064
You do not currently have access to this content.