Abstract

The relative sliding at the meshing point directly affects the contact and lubrication characteristics of the gear pair and is an important factor of gear wear and power loss. In this study, for investigation of a new type of low sliding ratio (LSR) gear pair whose tooth profile is constructed by a cubic function, a three-dimensional (3D) mixed elastohydrodynamic lubrication (EHL) line contact model was established with consideration of the effect of tooth profile geometry, transient motion characteristics, load distribution, and machining roughness. The distribution of the center film thickness of the LSR gear along the meshing line was predicted through an example the result of which was compared with a typical line contact EHL formula to verify the model. In addition, the difference was investigated in film thickness distribution of friction coefficient and temperature rise between LSR spur gears and involute spur gears. Hence, the effect of 3D rough tooth surface on the contact lubrication characteristics of LSR gears was discussed. The results demonstrated that the minimum center film thickness of the LSR gear appeared at the alternating point of the concave and convex tooth surfaces. At the same time, compared with the involute gear, the LSR gear significantly increased the film thickness at the start and ending points of the meshing and reduced the friction coefficient and the flash temperature rise.

References

1.
Akbarzadeh
,
S.
, and
Khonsari
,
M.
,
2009
, “
Prediction of Steady State Adhesive Wear in Spur Gears Using the EHL Load Sharing Concept
,”
ASME J. Tribol.
,
131
(
2
), p.
024503
.
2.
Wang
,
J.
,
Luo
,
S.
, and
Wu
,
R.
,
2010
, “
A Method for the Preliminary Geometric Design of Gear Tooth Profiles With Small Sliding Coefficients
,”
ASME J. Mech. Des.
,
132
(
5
), p.
054501
.
3.
Park
,
D.
,
Kolivand
,
M.
, and
Kahraman
,
A.
,
2014
, “
An Approximate Method to Predict Surface Wear of Hypoid Gears Using Surface Interpolation
,”
Mech. Mach. Theory
,
71
, pp.
64
78
.
4.
Liu
,
L.
,
Meng
,
F.
, and
Ni
,
J.
,
2019
, “
A Novel Non-Involute Gear Designed Based on Control of Relative Curvature
,”
Mech. Mach. Theory
,
140
, pp.
144
158
.
5.
Mo
,
S.
,
Yue
,
Z.
,
Feng
,
Z.
,
Shi
,
L.
,
Zou
,
Z.
, and
Dang
,
H.
,
2019
, “
Analytical Investigation on Load-Sharing Characteristics for Multi-Power Face Gear Split Flow System
,”
Proc. Inst. Mech. Eng., Part C
,
234
(
2
), pp.
676
692
.
6.
Chang
,
H.
, and
Tsai
,
Y.-C.
,
1992
, “
A Mathematical Model of Parametric Tooth Profiles for Spur Gears
,”
ASME J. Mech. Des.
,
114
(
1
), pp.
8
16
.
7.
Jing
,
L.
,
2009
, “
A Pressure Angle Function Method for Describing Tooth Profiles of Planar Gears
,”
ASME J. Mech. Des.
,
131
(
5
), p.
051005
.
8.
Matkovič
,
S.
, and
Kalin
,
M.
,
2021
, “
Effects of Slide-to-Roll Ratio and Temperature on the Tribological Behaviour in Polymer-Steel Contacts and a Comparison With the Performance of Real-Scale Gears
,”
Wear
,
477
, p.
203789
.
9.
Zhou
,
C.
, and
Wang
,
H.
,
2018
, “
An Adhesive Wear Prediction Method for Double Helical Gears Based on Enhanced Coordinate Transformation and Generalized Sliding Distance Model
,”
Mech. Mach. Theory
,
128
, pp.
58
83
.
10.
He
,
S.
,
Cho
,
S.
, and
Singh
,
R.
,
2008
, “
Prediction of Dynamic Friction Forces in Spur Gears Using Alternate Sliding Friction Formulations
,”
J. Sound Vib.
,
309
(
3
), pp.
843
851
.
11.
Xu
,
L.
,
Li
,
S.
, and
Wang
,
W.
,
2017
, “
Sliding Ratio for Novel Cycloidal Gear Drive
,”
Proc. Inst. Mech. Eng., Part C
,
232
(
21
), pp.
3954
3963
.
12.
Bobach
,
L.
,
Beilicke
,
R.
,
Bartel
,
D.
, and
Deters
,
L.
,
2012
, “
Thermal Elastohydrodynamic Simulation of Involute Spur Gears Incorporating Mixed Friction
,”
Tribol. Int.
,
48
, pp.
191
206
.
13.
Barbieri
,
M.
,
Lubrecht
,
A. A.
, and
Pellicano
,
F.
,
2013
, “
Behavior of Lubricant Fluid Film in Gears Under Dynamic Conditions
,”
Tribol. Int.
,
62
, pp.
37
48
.
14.
Beilicke
,
R.
,
Bobach
,
L.
, and
Bartel
,
D.
,
2016
, “
Transient Thermal Elastohydrodynamic Simulation of a DLC Coated Helical Gear Pair Considering Limiting Shear Stress Behavior of the Lubricant
,”
Tribol. Int.
,
97
, pp.
136
150
.
15.
Cao
,
W.
,
Pu
,
W.
,
Wang
,
J.
, and
Xiao
,
K.
,
2018
, “
Effect of Contact Path on the Mixed Lubrication Performance, Friction and Contact Fatigue in Spiral Bevel Gears
,”
Tribol. Int.
,
123
, pp.
359
371
.
16.
Wang
,
Z.
,
Pu
,
W.
,
He
,
T.
,
Wang
,
J.
, and
Cao
,
W.
,
2019
, “
Numerical Simulation of Transient Mixed Elastohydrodynamic Lubrication for Spiral Bevel Gears
,”
Tribol. Int.
,
139
, pp.
67
77
.
17.
Yin
,
Z.
,
Fan
,
Z.
, and
Wang
,
M.
,
2020
, “
Thermal Elastohydrodynamic Lubrication Characteristics of Double Involute Gears at the Graded Position of Tooth Waist
,”
Tribol. Int.
,
144
, p.
106028
.
18.
Li
,
S.
, and
Kahraman
,
A.
,
2010
, “
A Transient Mixed Elastohydrodynamic Lubrication Model for Spur Gear Pairs
,”
ASME J. Tribol.
,
132
(
1
), p.
011501
.
19.
Li
,
S.
, and
Kahraman
,
A.
,
2014
, “
A Micro-Pitting Model for Spur Gear Contacts
,”
Int. J. Fatigue
,
59
, pp.
224
233
.
20.
Liu
,
H.
,
Mao
,
K.
,
Zhu
,
C.
, and
Xu
,
X.
,
2012
, “
Mixed Lubricated Line Contact Analysis for Spur Gears Using a Deterministic Model
,”
ASME J. Tribol.
,
134
(
2
), p.
021501
.
21.
Liu
,
H.
,
Mao
,
K.
,
Zhu
,
C.
,
Chen
,
S.
,
Xu
,
X.
, and
Liu
,
M.
,
2013
, “
Spur Gear Lubrication Analysis With Dynamic Loads
,”
Tribol. Trans.
,
56
(
1
), pp.
41
48
.
22.
Liu
,
H.
,
Zhu
,
C.
,
Sun
,
Z.
, and
Song
,
C.
,
2016
, “
Starved Lubrication of a Spur Gear Pair
,”
Tribol. Int.
,
94
, pp.
52
60
.
23.
Liu
,
H.
,
Liu
,
H.
,
Zhu
,
C.
,
Wei
,
P.
, and
Tang
,
J.
,
2019
, “
Tribological Behavior of Coated Spur Gear Pairs With Tooth Surface Roughness
,”
Friction
,
7
(
2
), pp.
117
128
.
24.
Ziegltrum
,
A.
,
Lohner
,
T.
, and
Stahl
,
K.
,
2017
, “
TEHL Simulation on the Influence of Lubricants on Load-Dependent Gear Losses
,”
Tribol. Int.
,
113
, pp.
252
261
.
25.
Peng
,
Y.
,
Zhao
,
N.
,
Zhang
,
M.
,
Li
,
W.
, and
Zhou
,
R.
,
2018
, “
Non-Newtonian Thermal Elastohydrodynamic Simulation of Helical Gears Considering Modification and Misalignment
,”
Tribol. Int.
,
124
, pp.
46
60
.
26.
Shi
,
X.
,
Sun
,
W.
,
Lu
,
X.
,
Ma
,
X.
,
Zhu
,
D.
,
Zhao
,
B.
, and
He
,
T.
,
2019
, “
Three-Dimensional Mixed Lubrication Analysis of Spur Gears With Machined Roughness
,”
Tribol. Int.
,
140
, p.
105864
.
27.
Diab
,
Y.
,
Ville
,
F.
, and
Velex
,
P.
,
2006
, “
Investigations on Power Losses in High-Speed Gears
,”
Proc. Inst. Mech. Eng., Part J
,
220
(
3
), pp.
191
198
.
28.
Sheng
,
W.
,
Li
,
Z.
,
Zhang
,
H.
, and
Zhu
,
R.
,
2021
, “
Geometry and Design of Spur Gear Drive Associated With Low Sliding Ratio
,”
Adv. Mech. Eng.
,
13
(
4
), pp.
1
12
.
29.
Litvin
,
F. L.
and
Fuente
,
A.
,
2004
,
Gear Geometry and Applied Theory
,
Cambridge University Press
,
Cambridge, UK
.
30.
Guiggiani
,
M.
,
2008
, “
Gear Geometry and Applied Theory, F.L. Litvin, A. Fuentes, Second ed., Cambridge University Press, Cambridge (2004)
,”
Mech. Mach. Theory
,
43
(
3
), p.
390
.
31.
Pei
,
J.
,
Han
,
X.
,
Tao
,
Y.
, and
Feng
,
S.
,
2020
, “
Mixed Elastohydrodynamic Lubrication Analysis of Line Contact With Non-Gaussian Surface Roughness
,”
Tribol. Int.
,
151
, p.
106449
.
32.
Patir
,
N.
, and
Cheng
,
H.
,
1978
, “
An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication
,”
ASME J. Tribol.
,
100
, pp.
12
17
.
33.
Zhu
,
D.
, and
Hu
,
Y. Z.
,
2001
, “
A Computer Program Package for the Prediction of EHL and Mixed Lubrication Characteristics, Friction, Subsurface Stresses and Flash Temperatures Based on Measured 3-D Surface Roughness
,”
Tribol. Trans.
,
44
(
3
), pp.
383
390
.
34.
Hu
,
Y. Z.
, and
Zhu
,
D.
,
1999
, “
A Full Numerical Solution to the Mixed Lubrication in Point Contacts
,”
ASME J. Tribol.
,
122
(
1
), pp.
1
9
.
35.
Ren
,
N.
,
Zhu
,
D.
,
Chen
,
W.
,
Liu
,
Y.
, and
Wang
,
Q.
,
2009
, “
A Three-Dimensional Deterministic Model for Rough Surface Line-Contact EHL Problems
,”
ASME J. Tribol.
,
131
(
1
), p.
011501
.
36.
Hu
,
Y. Z.
,
Wang
,
H.
,
Wang
,
W. Z.
, and
Zhu
,
D.
,
2001
, “
A Computer Model of Mixed Lubrication in Point Contacts
,”
Tribol. Int.
,
34
(
1
), pp.
65
73
.
37.
Liu
,
S.
,
Wang
,
Q.
, and
Liu
,
G.
,
2000
, “
A Versatile Method of Discrete Convolution and FFT (DC-FFT) for Contact Analyses
,”
Wear
,
243
(
1
), pp.
101
111
.
38.
Chen
,
W. W.
,
Liu
,
S.
, and
Wang
,
Q. J.
,
2008
, “
Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts of Nominally Flat Surfaces
,”
ASME J. Appl. Mech.
,
75
(
1
), p.
011022
.
39.
Roelands
,
C. J. A.
,
1966
,
Correlation Aspects of Viscosity-Temperature-Pressure Relationship of Lubricating Oils
,
Delft University of Technology
,
Delft, The Netherlands
.
40.
Ma
,
M. T.
,
1997
, “
An Expedient Approach to the Non-Newtonian Thermal EHL in Heavily Loaded Point Contacts
,”
Wear
,
206
(
1
), pp.
100
112
.
41.
Zhu
,
D.
, and
Cheng
,
H.
,
1989
, “
An Analysis and Computational Procedure for EHL Film Thickness, Friction and Flash Temperature in Line and Point Contacts
,”
Tribol. Trans.
,
32
(
3
), pp.
364
370
.
42.
Zhao
,
J.
,
Li
,
Z.
,
Zhang
,
H.
, and
Zhu
,
R.
,
2021
, “
Prediction of Contact and Lubrication Characteristics of Micro-Textured Surface Under Thermal Line Contact EHL
,”
Front. Mech. Eng.
,
7
, pp.
1
19
.
43.
Yang
,
Y.
,
2019
, “
On the Mixed EHL Characteristics, Friction and Flash Temperature in Helical Gears With Consideration of 3D Surface Roughness
,”
Ind. Lubr. Tribol.
,
71
(
1
), pp.
10
21
.
44.
Liu
,
S.
, and
Wang
,
Q.
,
2002
, “
Studying Contact Stress Fields Caused by Surface Tractions With a Discrete Convolution and Fast Fourier Transform Algorithm
,”
ASME J. Tribol.
,
124
(
1
), pp.
36
45
.
45.
Ai
,
X. L.
,
1993
,
Numerical Analyses of Elastohydrodynamically Lubricated Line and Point Contacts With Rough Surfaces by Using Semi-System and Multigrid Methods
,
Northwestern University
,
Evanston, IL
.
46.
Zhu
,
D.
, and
Ai
,
X.
,
1997
, “
Point Contact EHL Based on Optically Measured Three-Dimensional Rough Surfaces
,”
ASME J. Tribol.
,
119
(
3
), pp.
375
384
.
47.
Zhu
,
D.
, and
Jane Wang
,
Q.
,
2013
, “
Effect of Roughness Orientation on the Elastohydrodynamic Lubrication Film Thickness
,”
ASME J. Tribol.
,
135
(
3
), p.
031501
.
48.
Zhu
,
D.
,
Ren
,
N.
, and
Wang
,
Q. J.
,
2009
, “
Pitting Life Prediction Based on a 3D Line Contact Mixed EHL Analysis and Subsurface von Mises Stress Calculation
,”
ASME J. Tribol.
,
131
(
4
), p.
041501
.
49.
Cao
,
W.
,
Ren
,
S.
,
Pu
,
W.
, and
Xiao
,
K.
,
2020
, “
Microstress Cycle and Contact Fatigue of Spiral Bevel Gears by Rolling-Sliding of Asperity Contact
,”
Friction
,
8
(
6
), pp.
1083
1101
.
You do not currently have access to this content.