Abstract

This study proposes a modification of the Matsumoto equation using a directional parameter of tooth surfaces to adapt various gear finishing processes. The directional parameters of a contact surface, which affect oil film formations, have been discussed in the field of tribology; but this effect has been undetermined on the meshing gear tooth surfaces having directional machining marks. Thus, this paper investigates the relationship between the gear frictional coefficients and the directional parameters (based on ISO25178) of their tooth surfaces with the various finishing processes and modifies the Matsumoto equation by introducing a new directional parameter to augment the various gear finishing processes. Our findings indicate that through optimizing the coefficient of the correction term that include the new directional parameter, the calculated friction values using the modified Matsumoto equation correlate more highly to the experimental friction values than that using the unmodified Matsumoto equation.

References

1.
Misharin
,
J. A.
,
1958
, “
Influence of the Friction Conditions on the Magnitude of the Friction Coefficient in the Case of Rolling With Sliding
,”
Instn. Mech. Engrs., Proc. Int. Conf. Gearing
,
London, UK
,
Sept. 23–25
.
2.
Benedict
,
G.
, and
Kelley
,
B.
,
1961
, “
Instantaneous Coefficients of Gear Tooth Friction
,”
ASLE Trans.
,
4
(
1
), pp.
59
70
.
3.
Kelley
,
B.
, and
Lemanski
,
A.
,
1967
, “
Lubrication of Involute Gearing
,”
Proceedings of the Institution of Mechanical Engineers, Conference Proceedings
, Vol.
182
,
SAGE Publications
,
Sage UK: London, England
, pp.
173
184
.
4.
Drozdov
,
Y. N.
, and
Gavrikov
,
Y. A.
,
1968
, “
Friction and Scoring Under the Conditions of Simultaneous Rolling and Sliding of Bodies
,”
Wear
,
11
(
4
), pp.
291
302
.
5.
Trachman
,
E. G.
,
1978
, “
A Simplified Technique for Predicting Traction in Elastohydrodynamic Contacts
,”
ASLE Trans.
,
21
(
1
), pp.
53
62
.
6.
Martin
,
K.
,
1978
, “
A Review of Friction Predictions in Gear Teeth
,”
Wear
,
49
(
2
), pp.
201
238
.
7.
Dudley
,
D. W.
,
1984
,
Handbook of Practical Gear Design
,
McGraw-Hill Book Company
,
New York
, p.
656
.
8.
Buckingham
,
E.
,
1988
,
Analytical Mechanics of Gears
,
Courier Corporation
,
North Chelmsford, MA
.
9.
Ariura
,
Y.
,
Ueno
,
T.
,
SunAGA
,
T.
, and
Sunamoto
,
S.
,
1973
, “
The Lubricant Churning Loss in Spur Gear Systems
,”
Bull. JSME
,
16
(
95
), pp.
881
892
.
10.
Dawson
,
P.
,
1984
, “
Windage Loss in Larger High-speed Gears
,”
Proc. Inst. Mech. Eng., Part A: Power Process Eng.
,
198
(
1
), pp.
51
59
.
11.
O’donoghue
,
J.
, and
Cameron
,
A.
,
1966
, “
Friction and Temperature in Rolling Sliding Contacts
,”
ASLE Trans.
,
9
(
2
), pp.
186
194
.
12.
Xu
,
H.
,
Kahraman
,
A.
,
Anderson
,
N.
, and
Maddock
,
D.
,
2007
, “
Prediction of Mechanical Efficiency of Parallel-Axis Gear Pairs
,”
ASME J. Mech. Des.
,
129
(
1
), pp.
58
68
.
13.
Schoeder
,
W.
, and
Leimann
,
D.O.
,
1980
, “
Emrmittlung der getriebe verlustleistung
,”
Antirebstechnik
,
19
(
11
), pp.
532
535
.
14.
Michaelis
,
K.
,
Höhn
,
B.-R.
, and
Doleschel
,
A.
,
2009
, “
Lubricant Influence on Gear Efficiency
,”
Proceedings of ASME2009 International Design Engineering Technical Conferences, DETC2009
,
San Diego, CA
,
Aug. 30–Sept. 2
, pp.
71
80
.
15.
Matsumoto
,
S.
, and
Morikawa
,
K.
,
2014
, “
The New Estimation Formula of Coefficient of Friction in Rolling-Sliding Contact Surface Under Mixed Lubrication Condition for the Power Loss Reduction of Power Transmission Gears
,”
Proceedings of International Gear Conference
,
Lyon, France
,
Aug. 26–28
, Vol. 2014, pp.
1078
1088
.
16.
Fernandes
,
C. M.
,
Martins
,
R. C.
, and
Seabra
,
J. H.
,
2016
, “
Coefficient of Friction Equation for Gears Based on a Modified Hersey Parameter
,”
Tribol. Int.
,
100
(
101
), pp.
204
217
.
17.
Patir
,
N.
, and
Cheng
,
H.
,
1978
, “
An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication
,”
ASME J. Lubr. Technol.
,
100
(
1
), pp.
12
17
.
18.
Patir
,
N.
, and
Cheng
,
H.
,
1979
, “
Application of Average Flow Model to Lubrication Between Rough Sliding Surfaces
,”
ASME J. Lubr. Technol.
,
101
(
2
), pp.
220
230
.
19.
Zhu
,
D.
, and
Cheng
,
H.
,
1988
, “
Effect of Surface Roughness on the Point Contact EHL
,”
ASME J. Tribol.
,
110
(
1
), pp.
32
37
.
20.
Masjedi
,
M.
, and
Khonsari
,
M.
,
2014
, “
Mixed Elastohydrodynamic Lubrication Line-Contact Formulas With Different Surface Patterns
,”
Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
,
228
(
8
), pp.
849
859
.
21.
Letalleur
,
N.
,
Plouraboué
,
F.
, and
Prat
,
M.
,
2002
, “
Average Flow Model of Rough Surface Lubrication: Flow Factors for Sinusoidal Surfaces
,”
ASME J. Tribol.
,
124
(
3
), pp.
539
546
.
22.
Wu
,
S.
, and
Cheng
,
H.
,
1991
, “
A Friction Model of Partial-EHL Contacts and Its Application to Power Loss in Spur Gears
,”
Tribol. Trans.
,
34
(
3
), pp.
398
407
.
23.
Epstein
,
D.
,
Yu
,
T.
,
Wang
,
Q. J.
,
Keer
,
L. M.
,
Cheng
,
H. S.
,
Liu
,
S.
,
Harris
,
S. J.
, and
Gangopadhyay
,
A.
,
2003
, “
An Efficient Method of Analyzing the Effect of Roughness on Fatigue Life in Mixed-EHL Contact
,”
Tribol. Trans.
,
46
(
2
), pp.
273
281
.
24.
Wang
,
Q. J.
,
Zhu
,
D.
,
Cheng
,
H. S.
,
Yu
,
T.
,
Jiang
,
X.
, and
Liu
,
S.
,
2004
, “
Mixed Lubrication Analyses by a Macro-Micro Approach and a Full-Scale Mixed EHL Model
,”
ASME J. Tribol.
,
126
(
1
), pp.
81
91
.
25.
ISO 4287: Geometrical Product Specification (GPS). Surface Texture. Profile Method. Terms, Definitions and Surface Texture Parameters
.
26.
ISO 25178: Geometric Product Specifications (GPS). Surface Texture: areal
.
27.
Petry-Johnson
,
T. T.
,
Kahraman
,
A.
,
Anderson
,
N.
, and
Chase
,
D.
,
2008
, “
An Experimental Investigation of Spur Gear Efficiency
,”
ASME J. Mech. Des.
,
130
(
6
), p.
062601
.
28.
Diab
,
Y.
,
Ville
,
F.
,
Velex
,
P.
, and
Changenet
,
C.
,
2004
, “
Windage Losses in High Speed Gears—Preliminary Experimental and Theoretical Results
,”
ASME J. Mech. Des.
,
126
(
5
), pp.
903
908
.
29.
Kubo
,
A.
,
1978
, “
Stress Condition, Vibrational Exciting Force, and Contact Pattern of Helical Gears with Manufacturing and Alignment Error
,”
ASME J. Mech. Des.
,
100
(
1
), pp.
77
84
.
30.
Dowson
,
D.
,
1967
, “
Paper 10: Elastohydrodynamics
,”
Proceedings of the Institution of Mechanical Engineers, Conference Proceedings
, Vol.
182
,
SAGE Publications
,
Sage UK: London, England
, pp.
151
167
.
31.
Wu
,
C.
,
Klaus
,
E.
, and
Duda
,
J.
,
1989
, “
Development of a Method for the Prediction of Pressure-Viscosity Coefficients of Lubricating Oils Based on Free-Volume Theory
,”
ASME J. Tribol.
,
111
(
1
), pp.
121
128
.
32.
ASTM D2160: Standard Test Method for Thermal Stability of Hydraulic Fluids (Withdrawn1997)
.
33.
Tallian
,
T.
,
1967
, “
On Competing Failure Modes in Rolling Contact
,”
ASLE Trans.
,
10
(
4
), pp.
418
439
.
34.
Peklenik
,
J.
,
1967
, “
New Developments in Surface Characterization and Measurements by Means of Random Process Analysis
,”
Proceedings of the Institution of Mechanical Engineers, Conference Proceedings
, Vol.
182
,
SAGE Publications
,
Sage UK: London, England
, pp.
108
126
.
35.
Yoshizaki
,
M.
,
Naruse
,
C.
,
Nemoto
,
R.
, and
Haizuka
,
S.
,
1991
, “
Study on Frictional Loss of Spur Gears (Concerning the Influence of Tooth Form, Load, Tooth Surface Roughness, and Lubricating Oil)
,”
Tribol. Trans.
,
34
(
1
), pp.
138
146
.
36.
Ikejo
,
K.
, and
Nagamura
,
K.
,
2003
, “
Power loss of spur gear drive lubricated with traction oil
,”
Proceeding of International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Vol.
37025
, pp.
1079
1084
.
You do not currently have access to this content.