Abstract

The traditional research on the dynamics of planetary gear transmission (PGT) is based on the assumption that the support is on the ground. However, the PGT inside the aircraft is spatially moved along with the airframe, which is not only subject to gravity, but also to additional inertia forces. These loads should affect the dynamic characteristics of the PGT. The PGT itself is a non-inertial system (NIS) and is called the internal non-inertial system (INIS). By contrast, an airframe in the aerospace environment is named an external non-inertial system (ENIS). In order to investigate the dynamic behavior of the PGT in a compound NIS, the kinematic equations of various components in arbitrary spatial motion state of the airframe are deduced. Subsequently, the coupled dynamics model of PGT in NIS is improved. The dynamic responses of PGT in different non-inertial conditions are compared based on the hovering motion of the airframe. The results indicate that INIS is the main factor affecting the trajectory of planet gear, while ENIS is the force source changing the trajectory of the central component. The aircraft’s hovering motion makes the gravity effect become a relatively time-varying excitation, but the dominant factor is still the additional inertial forces. The non-inertial effect during aerospace operation can significantly affect the bearing force, vibration and load sharing performance. It will lead to serious errors if the traditional research method is still used to obtain the dynamic behavior of PGT in the aerospace environment.

References

References
1.
Leque
,
N.
, and
Kahraman
,
A.
,
2017
, “
A Three-Dimensional Load Sharing Model of Planetary Gear Sets Having Manufacturing Errors
,”
ASME J. Mech. Des.
,
139
(
3
), p.
033302
. 10.1115/1.4035554
2.
Xun
,
C.
,
Long
,
X.
, and
Hua
,
H.
,
2018
, “
Effects of Random Tooth Profile Errors on the Dynamic Behaviors of Planetary Gears
,”
J. Sound Vib.
,
415
, pp.
91
110
. 10.1016/j.jsv.2017.11.022
3.
Zhou
,
W.
,
Zuo
,
Y.
, and
Zheng
,
M.
,
2018
, “
Analysis and Optimization of the Vibration and Noise of a Double Planetary Gear Power Coupling Mechanism
,”
Shock Vib.
,
2018
, p.
13
. 10.1155/2018/9048695
4.
Liu
,
W.
,
Shuai
,
Z.
,
Guo
,
Y.
, and
Wang
,
D.
,
2019
, “
Modal Properties of a Two-Stage Planetary Gear System With Sliding Friction and Elastic Continuum Ring Gear
,”
Mech. Mach. Theory
,
135
, pp.
251
270
. 10.1016/j.mechmachtheory.2019.01.026
5.
Krothapalli
,
K. R.
,
Prasad
,
J. V. R.
, and
Peters
,
D. A.
,
2001
, “
Helicopter Rotor Dynamic Inflow Modeling for Maneuvering Flight
,”
J. Am. Helicopter Soc.
,
46
(
2
), pp.
129
139
. 10.4050/JAHS.46.129
6.
Lin
,
F.
, and
Meng
,
G.
,
2003
, “
Study on the Dynamics of a Rotor in a Maneuvering Aircraft
,”
ASME J. Vib. Acoust.
,
125
(
3
), pp.
324
327
. 10.1115/1.1576422
7.
El-Saeidy
,
F. M. A.
, and
Sticher
,
F.
,
2010
, “
Dynamics of a Rigid Rotor Linear/Nonlinear Bearings System Subject to Rotating Unbalance and Base Excitations
,”
J. Vib. Control
,
16
(
3
), pp.
403
438
. 10.1177/1077546309103565
8.
Yang
,
Y.
,
Ren
,
X.
,
Qin
,
W.
,
Wu
,
Y.
, and
Zhi
,
X.
,
2010
, “
Analysis on the Nonlinear Response of Cracked Rotor in Hover Flight
,”
Nonlinear Dyn.
,
61
(
1–2
), pp.
183
192
. 10.1007/s11071-009-9640-7
9.
Han
,
Q.
, and
Chu
,
F.
,
2013
, “
Dynamic Response of Cracked Rotor-Bearing System Under Time-Dependent Base Movements
,”
J. Sound Vib.
,
332
(
25
), pp.
6847
6870
. 10.1016/j.jsv.2013.07.025
10.
Hou
,
L.
,
Chen
,
Y.
,
Cao
,
Q.
, and
Lu
,
Z.
,
2016
, “
Nonlinear Vibration Analysis of a Cracked Rotor-Ball Bearing System During Flight Maneuvers
,”
Mech. Mach. Theory
,
105
, pp.
515
528
. 10.1016/j.mechmachtheory.2016.07.024
11.
Han
,
B.
, and
Ding
,
Q.
,
2018
, “
Forced Responses Analysis of a Rotor System With Squeeze Film Damper During Flight Maneuvers Using Finite Element Method
,”
Mech. Mach. Theory
,
122
, pp.
233
251
. 10.1016/j.mechmachtheory.2018.01.004
12.
Qian
,
P.
,
Zhang
,
Y.
,
Cheng
,
G.
,
Ge
,
S.
, and
Zhou
,
C.
,
2013
, “
Model Analysis and Verification of 2K-H Planetary Gear System
,”
J. Vib. Control
,
21
(
10
), pp.
1946
1957
. 10.1177/1077546313496575
13.
Wang
,
Z.
,
Yuan
,
Y.
,
Wang
,
Z.
,
Liu
,
W.
,
Guo
,
Y.
, and
Wang
,
D.
,
2018
, “
Lateral-Torsional Coupling Characteristics of a Two-Stage Planetary Gear Rotor System
,”
Shock Vib.
,
2018
, p.
15
. 10.1155/2018/4293475
14.
Tatar
,
A.
,
Schwingshackl
,
C. W.
, and
Friswell
,
M. I.
,
2019
, “
Dynamic Behaviour of Three-Dimensional Planetary Geared Rotor Systems
,”
Mech. Mach. Theory
,
134
, pp.
39
56
. 10.1016/j.mechmachtheory.2018.12.023
15.
Kahraman
,
A.
,
Ligata
,
H.
, and
Singh
,
A.
,
2010
, “
Influence of Ring Gear Rim Thickness on Planetary Gear Set Behavior
,”
ASME J. Mech. Des.
,
132
(
2
), p.
021002
. 10.1115/1.4000699
16.
Rezaei
,
M.
,
Poursina
,
M.
,
Jazi
,
S. H.
, and
Aboutalebi
,
F. H.
,
2018
, “
Calculation of Time Dependent Mesh Stiffness of Helical Planetary Gear System Using Analytical Approach
,”
J. Mech. Sci. Technol.
,
32
(
8
), pp.
3537
3545
. 10.1007/s12206-018-0704-9
17.
Parker
,
R. G.
, and
Lin
,
J.
,
2004
, “
Mesh Phasing Relationships in Planetary and Epicyclic Gears
,”
ASME J. Mech. Des.
,
126
(
2
), pp.
365
374
. 10.1115/1.1667892
18.
Chapron
,
M.
,
Velex
,
P.
,
Bruyere
,
J.
, and
Becquerelle
,
S.
,
2016
, “
Optimization of Profile Modifications With Regard to Dynamic Tooth Loads in Single and Double-Helical Planetary Gears With Flexible Ring-Gears
,”
ASME J. Mech. Des.
,
138
(
2
), p.
023301
. 10.1115/1.4031939
19.
Zhang
,
H.
,
Qi
,
C.
,
Fan
,
J.
,
Dai
,
S.
, and
You
,
B.
,
2018
, “
Vibration Characteristics Analysis of Planetary Gears With a Multi-Clearance Coupling in Space Mechanism
,”
Energies
,
11
(
10
), p.
2687
. 10.3390/en11102687
20.
Liu
,
C.
,
Qin
,
D.
,
Lim
,
T. C.
, and
Liao
,
Y.
,
2014
, “
Dynamic Characteristics of the Herringbone Planetary Gear Set During the Variable Speed Process
,”
J. Sound Vib.
,
333
(
24
), pp.
6498
6515
. 10.1016/j.jsv.2014.07.024
21.
Liu
,
Y.
,
Lai
,
J.
,
Dong
,
P.
, and
Xu
,
X.
,
2017
, “
Dynamic Analysis of Helical Planetary Gear Sets Under Combined Force and Moment Loading
,”
Shock Vib.
, p.
4635204
. 10.1155/2017/4635204
22.
Liu
,
Z.
,
Liu
,
Z.
, and
Yu
,
X.
,
2018
, “
Dynamic Modeling and Response of a Spur Planetary Gear System With Journal Bearings Under Gravity Effects
,”
J. Vib. Control
,
24
(
16
), pp.
3569
3586
. 10.1177/1077546317707878
23.
Eritenel
,
T.
, and
Parker
,
R. G.
,
2009
, “
Modal Properties of Three-Dimensional Helical Planetary Gears
,”
J. Sound Vib.
,
325
(
1–2
), pp.
397
420
. 10.1016/j.jsv.2009.03.002
24.
Sun
,
W.
,
Ding
,
X.
,
Wei
,
J.
,
Wang
,
X.
, and
Zhang
,
A.
,
2016
, “
Hierarchical Modeling Method and Dynamic Characteristics of Cutter Head Driving System in Tunneling Boring Machine
,”
Tunnelling Underground Space Technol.
,
52
, pp.
99
110
. 10.1016/j.tust.2015.11.022
25.
Tan
,
J.
,
Zhu
,
C.
,
Song
,
C.
, and
Xu
,
X.
,
2019
, “
Study on the Dynamic Modeling and Natural Characteristics of Wind Turbine Drivetrain Considering Electromagnetic Stiffness
,”
Mech. Mach. Theory
,
134
, pp.
541
561
. 10.1016/j.mechmachtheory.2019.01.015
26.
Wei
,
J.
,
Zhang
,
A.
,
Qin
,
D.
,
Lim
,
T. C.
,
Shu
,
R.
,
Lin
,
X.
, and
Meng
,
F.
,
2017
, “
A Coupling Dynamics Analysis Method for a Multistage Planetary Gear System
,”
Mech. Mach. Theory
,
110
, pp.
27
49
. 10.1016/j.mechmachtheory.2016.12.007
27.
Wang
,
J.
,
Yang
,
J.
, and
Li
,
Q.
,
2018
, “
Quasi-Static Analysis of the Nonlinear Behavior of a Railway Vehicle Gear System Considering Time-Varying and Stochastic Excitation
,”
Nonlinear Dyn.
,
93
(
2
), pp.
463
485
. 10.1007/s11071-018-4204-3
28.
Zhang
,
A.
,
Wei
,
J.
,
Qin
,
D.
,
Hou
,
S.
, and
Lim
,
T. C.
,
2018
, “
Coupled Dynamic Characteristics of Wind Turbine Gearbox Driven by Ring Gear Considering Gravity
,”
ASME J. Dyn. Syst., Meas. Contr.
,
140
(
9
), p.
091009
. 10.1115/1.4039482
29.
Wei
,
J.
,
Zhang
,
A.
,
Wang
,
G.
,
Qin
,
D.
,
Lim
,
T. C.
,
Wang
,
Y.
, and
Lin
,
T.
,
2018
, “
A Study of Nonlinear Excitation Modeling of Helical Gears With Modification: Theoretical Analysis and Experiments
,”
Mech. Mach. Theory
,
128
, pp.
314
335
. 10.1016/j.mechmachtheory.2018.06.005
30.
Yavuz
,
S. D.
,
Saribay
,
Z. B.
, and
Cigeroglu
,
E.
,
2018
, “
Nonlinear Time-Varying Dynamic Analysis of a Spiral Bevel Geared System
,”
Nonlinear Dyn.
,
92
(
4
), pp.
1901
1919
. 10.1007/s11071-018-4170-9
You do not currently have access to this content.