Abstract

A concentric face gear torque split system used in the helicopter main transmission to transfer more power and reduce the structure weight is introduced. A mathematical model is proposed to analyze the vibration characteristics as well as load sharing performances of the torque split system. The excitations including mesh stiffness, backlash, static transmission error, and system work torque are considered in the model. The vibration property, dynamic displacement responses, and the system factors which affect the load sharing capacity of the system are studied based on the numerical analysis results. The results show that vibration forms of the system can be classified into three categories: pinion vibration mode, face gear vibration mode, and pinion coupled face gear mode. Resonance peaks and jump phenomena are detected around rotation speed 5772 rpm and 10,250 rpm, mainly related to the coupled translational–rotational–axial of face gears vibration modes. In addition, appropriate gear pair backlash and pinion distribution angle parameters are significant to improve the dynamic load sharing capacity. The increase of the pinion bearings' supporting stiffness will generate worse load sharing characteristics and a relative flexible bearing is recommended to the pinions' supporting.

References

1.
Litvin
,
F.
,
Zhang
,
Y.
,
Wang
,
J. C.
,
Bossler
,
R.
, Jr.
, and
Chen
,
Y. J. D.
,
1992
, “
Design and Geometry of Face-Gear Drives
,”
ASME J. Mech. Des.
,
114
(
4
), pp.
642
647
.10.1115/1.2917055
2.
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
3.
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
4.
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
5.
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
6.
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
7.
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
8.
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
9.
Li
,
Z.
,
Fan
,
J.
, and
Zhu
,
R.
,
2018
, “
Construction of Tooth Modeling Solutions of Face Gear Drives With an Involute Pinion
,”
Iranian J. Sci. Technol., Trans. Mech. Eng.
,
42
(
1
), pp.
35
39
.10.1007/s40997-017-0074-4
10.
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
11.
Wang
,
Y.
,
Hou
,
L.
,
Lan
,
Z.
, and
Zhang
,
G.
,
2016
, “
Precision Grinding Technology for Complex Surface of Aero Face-Gear
,”
Int. J. Adv. Manuf. Technol.
,
86
(
5–8
), pp.
1263
1272
.10.1007/s00170-015-8241-5
12.
Wang
,
Y.
,
Chu
,
X.
,
Huang
,
Y.
,
Su
,
G.
, and
Liu
,
D.
,
2019
, “
Surface Residual Stress Distribution for Face Gear Under Grinding With a Long-Radius Disk Wheel
,”
Int. J. Mech. Sci.
,
159
, pp.
260
266
.10.1016/j.ijmecsci.2019.06.004
13.
Guo
,
H.
,
Peng
,
X.
,
Zhao
,
N.
, and
Zhang
,
S.
,
2015
, “
A CNC Grinding Method and Envelope Residual Model for Face Gear
,”
Int. J. Adv. Manuf. Technol.
,
79
(
9–12
), pp.
1689
1698
.10.1007/s00170-015-6915-7
14.
Shen
,
Y.
,
Liu
,
X.
,
Li
,
D.
, and
Li
,
Z.
,
2018
, “
A Method for Grinding Face Gear of Double Crowned Tooth Geometry on a Multi-Axis CNC Machine
,”
Mech. Mach. Theory
,
121
, pp.
460
474
.10.1016/j.mechmachtheory.2017.11.007
15.
Tang
,
J.
,
Yin
,
F.
, and
Chen
,
X.
,
2013
, “
The Principle of Profile Modified Face-Gear Grinding Based on Disk Wheel
,”
Mech. Mach. Theory
,
70
, pp.
1
15
.10.1016/j.mechmachtheory.2013.06.013
16.
Yang
,
X.
, and
Tang
,
J.
,
2014
, “
Research on Manufacturing Method of CNC Plunge Milling for Spur Face-Gear
,”
J. Mater. Proc. Technol.
,
214
(
12
), pp.
3013
3019
.10.1016/j.jmatprotec.2014.07.010
17.
Zhou
,
Y.
,
Tang
,
J.
,
Zhou
,
H.
, and
Yin
,
F.
,
2016
, “
Multistep Method for Grinding Face-Gear by Worm
,”
ASME J. Manuf. Sci. Eng.
,
138
(
7
).10.1115/1.4033387
18.
Zhou
,
Y.
,
Wang
,
S.
,
Wang
,
L.
,
Tang
,
J.
, and
Chen
,
Z. C.
,
2019
, “
CNC Milling of Face Gears With a Novel Geometric Analysis
,”
Mech. Mach. Theory
,
139
, pp.
46
65
.10.1016/j.mechmachtheory.2019.04.009
19.
Chang
,
S.-H.
,
Chung
,
T.-D.
, and
Lu
,
S.-S.
,
2000
, “
Tooth Contact Analysis of Face-Gear Drives
,”
Int. J. Mech. Sci.
,
42
(
3
), pp.
487
502
.10.1016/S0020-7403(99)00013-2
20.
Barone
,
S.
,
Borgianni
,
L.
, and
Forte
,
P.
,
2004
, “
Evaluation of the Effect of Misalignment and Profile Modification in Face Gear Drive by a Finite Element Meshing Simulation
,”
ASME J. Mech. Des.
,
126
(
5
), pp.
916
924
.10.1115/1.1767818
21.
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
22.
Tang
,
J.
, and
Liu
,
Y.
,
2013
, “
Loaded Multi-Tooth Contact Analysis and Calculation for Contact Stress of Face-Gear Drive With Spur Involute Pinion
,”
J. Central South Univ.
,
20
(
2
), pp.
354
362
.10.1007/s11771-013-1495-x
23.
Peng
,
M.
, and
DeSmidt
,
H.
,
2015
, “
Torsional Stability of a Face-Gear Drive System
,”
J. Am. Helicopter Soc.
,
60
(
4
), pp.
1
11
.10.4050/JAHS.60.042007
24.
Li
,
Z.
,
Wang
,
J.
, and
Zhu
,
R.
,
2016
, “
Influence Comparisons of Two Version Tooth Profile Modifications on Face Gear Dynamic Behaviors
,”
J. Vibroeng.
,
18
(
6
), pp.
3499
3511
.10.21595/jve.2016.17025
25.
Li
,
Z.
,
Chen
,
H.
, and
Zhu
,
R.
,
2016
, “
Study of Low-Noise Face Gear Drives Associated With Micro-Punch Webs
,”
Adv. Mech. Eng.
,
8
(
2
), p.
168781401663298
.10.1177/1687814016632989
26.
Li
,
Z.
,
Wang
,
H.
,
Zhu
,
R.
, and
Ye
,
W.
,
2017
, “
Solutions of Active Vibration Suppression Associated With Web Structures on Face Gear Drives
,”
J. Vibroeng.
,
14
, pp.
146
150
.10.21595/vp.2017.19009
27.
Li
,
Z.
,
Wang
,
H.
, and
Zhu
,
R.
,
2019
, “
Effect Predictions of Web Active Control on Dynamic Behaviors of Face Gear Drives
,”
J. Low Freq. Noise, Vib. Active Control
,
38
(
2
), pp.
753
764
.10.1177/1461348418821587
28.
Li
,
Z.
,
Liu
,
S.
,
Zhu
,
R.
, and
Xu
,
X.
,
2016
, “
Investigations of Dynamic Behaviors of Face Gear Drives Associated With Pinion Dedendum Fatigue Cracks
,”
Shock Vib.
, 2016, p.
10
.10.1155/2016/3173860
29.
Dai
,
Y.
,
Ma
,
F.
,
Zhu
,
X.
,
Su
,
Q.
, and
Hu
,
X.
,
2019
, “
Evaluation and Optimization of the Oil Jet Lubrication Performance for Orthogonal Face Gear Drive: Modelling, Simulation and Experimental Validation
,”
Energies
,
12
(
10
), p.
1935
.10.3390/en12101935
30.
Dai
,
Y.
,
Ma
,
F.
,
Zhu
,
X.
, and
Jia
,
J.
,
2019
, “
Numerical Simulation Investigation on the Windage Power Loss of a High-Speed Face Gear Drive
,”
Energies
,
12
(
11
), p.
2093
.10.3390/en12112093
31.
Hu
,
Z.
,
Tang
,
J.
,
Chen
,
S.
, and
Lei
,
D.
,
2013
, “
Effect of Mesh Stiffness on the Dynamic Response of Face Gear Transmission System
,”
ASME J. Mech. Des.
,
135
(
7
), p.
071005
.10.1115/1.4024369
32.
Chen
,
S.
,
Tang
,
J.
,
Chen
,
W.
,
Hu
,
Z.
, and
Cao
,
M.
,
2014
, “
Nonlinear Dynamic Characteristic of a Face Gear Drive With Effect of Modification
,”
Meccanica
,
49
(
5
), pp.
1023
1037
.10.1007/s11012-013-9814-8
33.
Tang
,
J.
,
Hu
,
Z.
,
Chen
,
S.
, and
Lei
,
D.
,
2014
, “
Effects of Directional Rotation Radius and Transmission Error on the Dynamic Characteristics of Face Gear Transmission System
,”
Proc. Inst. Mech. Eng., Part C
,
228
(
7
), pp.
1108
1118
.10.1177/0954406213500745
34.
Hu
,
Z.
,
Tang
,
J.
,
Chen
,
S.
, and
Sheng
,
Z.
,
2015
, “
Coupled Translation-Rotation Vibration and Dynamic Analysis of Face Geared Rotor System
,”
J. Sound Vib.
,
351
, pp.
282
298
.10.1016/j.jsv.2015.04.033
35.
Peng
,
M.
,
DeSmidt
,
H. A.
, and
Zhao
,
J.
,
2015
, “
Parametric Instability of Face-Gear Drives Meshing With Multiple Spur Pinions
,”
ASME J. Mech. Des.
,
137
(
12
), pp.
123301
123309
.10.1115/1.4031442
36.
Li
,
Z.
,
Ye
,
W.
,
Zhang
,
L.
, and
Zhu
,
R.
,
2016
, “
Effect Predictions of Star Pinion Geometry Phase Adjustments on Dynamic Load Sharing Behaviors of Differential Face Gear Trains
,”
J. Vibroeng.
,
18
, pp.
81
92
.https://www.jvejournals.com/article/16561
37.
Zhao
,
N.
,
Li
,
W.
,
Hu
,
T.
,
Guo
,
H.
,
Zhou
,
R.
, and
Peng
,
Y.
,
2018
, “
Quasistatic Load Sharing Behaviours of Concentric Torque-Split Face Gear Transmission With Flexible Face Gear
,”
Math. Probl. Eng.
,
2018
, pp.
1
12
.10.1155/2018/6568519
38.
Dong
,
J.
,
Tang
,
J.
, and
Hu
,
Z.
,
2019
, “
Investigation of Assembly, Power Direction and Load Sharing in Concentric Face Gear Split-Torque Transmission System
,”
Meccanica
,
54
(
15
), pp.
2485
2506
.10.1007/s11012-019-01078-0
39.
Liu
,
Z.
,
Lei
,
Y.
,
Liu
,
H.
,
Yang
,
X.
, and
Song
,
W.
,
2020
, “
A Phenomenological Model for Investigating Unequal Planet Load Sharing in Epicyclic Gearboxes
,”
Mech. Syst. Signal Process.
,
135
, p.
106414
.10.1016/j.ymssp.2019.106414
40.
Xie
,
C.
,
Hua
,
L.
,
Lan
,
J.
,
Han
,
X.
,
Wan
,
X.
, and
Xiong
,
X.
,
2018
, “
Improved Analytical Models for Mesh Stiffness and Load Sharing Ratio of Spur Gears Considering Structure Coupling Effect
,”
Mech. Syst. Signal Process.
,
111
, pp.
331
347
.10.1016/j.ymssp.2018.03.037
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