Abstract

A first-ever friction–wear model for four-ball extreme pressure (EP) lubrication is developed in this work based on 12 oil samples comprising minerals, esters, and other formulated lubricants. The model considers the rate of entropy generation and dissipation within the lubricated tribosystem to describe the interaction between the friction and the wear behaviors at extreme pressure conditions. The model can be used to calculate the probability to pass or fail at a specific load to estimate the weld point of a lubricant. The calculated probability exhibited a similar trend as a load-wear index from the ASTM D2783 EP test method. Besides, the model is able to estimate the EP performance of an unknown lubricant based on the model parameter, namely the dissipative coefficient. This parameter describes the proportionality between the friction and the wear phenomena from the perspective of thermodynamic analysis. This work provides useful tools to better understand the fundamentals of EP lubrication and to characterize the lubricants without overly relying on tribotest machines.

References

1.
Vakis
,
A. I.
,
Yastrebov
,
V. A.
,
Scheibert
,
J.
,
Nicola
,
L.
,
Dini
,
D.
,
Minfray
,
C.
,
Almqvist
,
A.
,
Paggi
,
M.
,
Lee
,
S.
,
Limbert
,
G.
,
Molinari
,
J. F.
,
Anciaux
,
G.
,
Aghababaei
,
R.
,
Echeverri Restrepo
,
S.
,
Papangelo
,
A.
,
Cammarata
,
A.
,
Nicolini
,
P.
,
Putignano
,
C.
,
Carbone
,
G.
,
Stupkiewicz
,
S.
,
Lengiewicz
,
J.
,
Costagliola
,
G.
,
Bosia
,
F.
,
Guarino
,
R.
,
Pugno
,
N. M.
,
Müser
,
M. H.
, and
Ciavarella
,
M.
,
2018
, “
Modeling and Simulation in Tribology Across Scales: An Overview
,”
Tribol. Int.
,
125
, pp.
169
199
. 10.1016/j.triboint.2018.02.005
2.
Vanossi
,
A.
,
Manini
,
N.
,
Urbakh
,
M.
,
Zapperi
,
S.
, and
Tosatti
,
E.
,
2013
, “
Colloquium: Modeling Friction: From Nanoscale to Mesoscale
,”
Rev. Mod. Phys.
,
85
(
2
), pp.
529
552
. 10.1103/RevModPhys.85.529
3.
Chan
,
C.-H.
,
Tang
,
S. W.
,
Mohd
,
N. K.
,
Lim
,
W. H.
,
Yeong
,
S. K.
, and
Idris
,
Z.
,
2018
, “
Tribological Behavior of Biolubricant Base Stocks and Additives
,”
Renewable Sustainable Energy Rev.
,
93
, pp.
145
157
. 10.1016/j.rser.2018.05.024
4.
Evans
,
H. P.
,
Snidle
,
R. W.
, and
Sharif
,
K. J.
,
2009
, “
Deterministic Mixed Lubrication Modelling Using Roughness Measurements in Gear Applications
,”
Tribol. Int.
,
42
(
10
), pp.
1406
1417
. 10.1016/j.triboint.2009.05.025
5.
Larsson
,
R.
,
2009
, “
Modelling the Effect of Surface Roughness on Lubrication in all Regimes
,”
Tribol. Int.
,
42
(
4
), pp.
512
516
. 10.1016/j.triboint.2008.07.007
6.
Li
,
S.
, and
Kahraman
,
A.
,
2009
, “
A Mixed EHL Model With Asymmetric Integrated Control Volume Discretization
,”
Tribol. Int.
,
42
(
8
), pp.
1163
1172
. 10.1016/j.triboint.2009.03.020
7.
Allmaier
,
H.
,
Priestner
,
C.
,
Six
,
C.
,
Priebsch
,
H. H.
,
Forstner
,
C.
, and
Novotny-Farkas
,
F.
,
2011
, “
Predicting Friction Reliably and Accurately in Journal Bearings—A Systematic Validation of Simulation Results With Experimental Measurements
,”
Tribol. Int.
,
44
(
10
), pp.
1151
1160
. 10.1016/j.triboint.2011.05.010
8.
Allmaier
,
H.
,
Priestner
,
C.
,
Reich
,
F. M.
,
Priebsch
,
H. H.
,
Forstner
,
C.
, and
Novotny-Farkas
,
F.
,
2012
, “
Predicting Friction Reliably and Accurately in Journal Bearings—The Importance of Extensive Oil-Models
,”
Tribol. Int.
,
48
, pp.
93
101
. 10.1016/j.triboint.2011.11.009
9.
Ripoll
,
M. R.
,
Podgornik
,
B.
, and
Vižintin
,
J.
,
2011
, “
Finite Element Analysis of Textured Surfaces Under Reciprocating Sliding
,”
Wear
,
271
(
5
), pp.
952
959
. 10.1016/j.wear.2011.04.003
10.
Li
,
S.
,
Kahraman
,
A.
,
Anderson
,
N.
, and
Wedeven
,
L. D.
,
2013
, “
A Model to Predict Scuffing Failures of a Ball-on-Disk Contact
,”
Tribol. Int.
,
60
, pp.
233
245
. 10.1016/j.triboint.2012.11.007
11.
Ouyang
,
T.
,
Huang
,
H.
,
Zhang
,
N.
,
Mo
,
C.
, and
Chen
,
N.
,
2017
, “
A Model to Predict Tribo-Dynamic Performance of a Spur Gear Pair
,”
Tribol. Int.
,
116
, pp.
449
459
. 10.1016/j.triboint.2017.08.005
12.
Mukchortov
,
I.
,
Zadorozhnaya
,
E.
, and
Polyacko
,
E.
,
2017
, “
Transitional Friction Regime Modeling Under Boundary Lubrication Conditions
,”
Procedia Eng.
,
206
, pp.
725
733
. 10.1016/j.proeng.2017.10.544
13.
Hao
,
L.
, and
Meng
,
Y.
,
2015
, “
Numerical Prediction of Wear Process of an Initial Line Contact in Mixed Lubrication Conditions
,”
Tribol. Lett.
,
60
(
2
), p.
31
. 10.1007/s11249-015-0609-z
14.
Ghaffari
,
M. A.
,
Zhang
,
Y.
, and
Xiao
,
S.
,
2018
, “
Multiscale Modeling and Simulation of Rolling Contact Fatigue
,”
Int. J. Fatigue
,
108
, pp.
9
17
. 10.1016/j.ijfatigue.2017.11.005
15.
Godlevskiy
,
V. A.
, and
Blinov
,
O. V.
,
2016
, “
Computing of the Molecular Orientation State of the Lubrication Layer
,”
Procedia Eng.
,
150
, pp.
584
589
. 10.1016/j.proeng.2016.07.046
16.
Baskar
,
S.
,
Sriram
,
G.
, and
Arumugam
,
S.
,
2016
, “
The Use of D-Optimal Design for Modeling and Analyzing the Tribological Characteristics of Journal Bearing Materials Lubricated by Nano-Based Biolubricants
,”
Tribol. T.
,
59
(
1
), pp.
44
54
. 10.1080/10402004.2015.1063179
17.
Xiong
,
S.
,
Sun
,
J.
,
Xu
,
Y.
, and
Yan
,
X.
,
2015
, “
QSPR Models for the Prediction of Friction Coefficient and Maximum Non-Seizure Load of Lubricants
,”
Tribol. Lett.
,
60
(
1
), p.
13
. 10.1007/s11249-015-0590-6
18.
Simonovic
,
K.
, and
Kalin
,
M.
,
2016
, “
Methodology of a Statistical and DOE Approach to the Prediction of Performance in Tribology—A DLC Boundary-Lubrication Case Study
,”
Tribol. Int.
,
101
, pp.
10
24
. 10.1016/j.triboint.2016.04.007
19.
Weinebeck
,
A.
,
Kaminski
,
S.
,
Murrenhoff
,
H.
, and
Leonhard
,
K.
,
2017
, “
A New QSPR-Based Prediction Model for Biofuel Lubricity
,”
Tribol. Int.
,
115
, pp.
274
284
. 10.1016/j.triboint.2017.05.005
20.
Hu
,
Y.
,
Wang
,
L.
,
Politis
,
D. J.
, and
Masen
,
M. A.
,
2017
, “
Development of an Interactive Friction Model for the Prediction of Lubricant Breakdown Behaviour During Sliding Wear
,”
Tribol. Int.
,
110
, pp.
370
377
. 10.1016/j.triboint.2016.11.005
21.
Zhou
,
C.
,
Hu
,
B.
,
Qian
,
X.
, and
Han
,
X.
,
2018
, “
A Novel Prediction Method for Gear Friction Coefficients Based on a Computational Inverse Technique
,”
Tribol. Int.
,
127
, pp.
200
208
. 10.1016/j.triboint.2018.06.005
22.
Chong
,
W. W. F.
, and
Ng
,
J. H.
,
2016
, “
An Atomic-Scale Approach for Biodiesel Boundary Lubricity Characterisation
,”
Int. Biodeterior. Biodegrad.
,
113
, pp.
34
43
. 10.1016/j.ibiod.2016.03.029
23.
Ghanbarzadeh
,
A.
,
Wilson
,
M.
,
Morina
,
A.
,
Dowson
,
D.
, and
Neville
,
A.
,
2016
, “
Development of a New Mechano-Chemical Model in Boundary Lubrication
,”
Tribol. Int.
,
93
, pp.
573
582
. 10.1016/j.triboint.2014.12.018
24.
Lyashenko
,
I. A.
, and
Khomenko
,
A. V.
,
2012
, “
Thermodynamic Theory of Two Rough Surfaces Friction in the Boundary Lubrication Mode
,”
Tribol. Lett.
,
48
(
1
), pp.
63
75
. 10.1007/s11249-012-9939-2
25.
Li
,
S.
, and
Anisetti
,
A.
,
2017
, “
A Tribo-Dynamic Contact Fatigue Model for Spur Gear Pairs
,”
Int. J. Fatigue
,
98
, pp.
81
91
. 10.1016/j.ijfatigue.2017.01.020
26.
Zhang
,
J.-G.
,
Liu
,
S.-J.
, and
Fang
,
T.
,
2017
, “
On the Prediction of Friction Coefficient and Wear in Spiral Bevel Gears With Mixed TEHL
,”
Tribol. Int.
,
115
, pp.
535
545
. 10.1016/j.triboint.2017.06.035
27.
Gao
,
L.
,
Hua
,
Z.
, and
Hewson
,
R.
,
2018
, “
“Can a “Pre-Worn” Bearing Surface Geometry Reduce the Wear of Metal-on-Metal Hip Replacements?—A Numerical Wear Simulation Study
,”
Wear
,
406–407
, pp.
13
21
. 10.1016/j.wear.2018.03.010
28.
Bosman
,
R.
, and
Schipper
,
D. J.
,
2011
, “
Mild Wear Prediction of Boundary-Lubricated Contacts
,”
Tribol. Lett.
,
42
(
2
), pp.
169
178
. 10.1007/s11249-011-9760-3
29.
Bosman
,
R.
, and
Schipper
,
D. J.
,
2012
, “
Mild Wear Maps for Boundary Lubricated Contacts
,”
Wear
,
280–281
, pp.
54
62
. 10.1016/j.wear.2012.01.019
30.
Mishina
,
H.
, and
Hase
,
A.
,
2013
, “
Wear Equation for Adhesive Wear Established Through Elementary Process of Wear
,”
Wear
,
308
(
1
), pp.
186
192
. 10.1016/j.wear.2013.06.016
31.
Tan
,
Y.
,
Zhang
,
L.
, and
Hu
,
Y.
,
2015
, “
A Wear Model of Plane Sliding Pairs Based on Fatigue Contact Analysis of Asperities
,”
Tribol. T.
,
58
(
1
), pp.
148
157
. 10.1080/10402004.2014.956907
32.
Cao
,
S.
,
Guadalupe Maldonado
,
S.
, and
Mischler
,
S.
,
2015
, “
Tribocorrosion of Passive Metals in the Mixed Lubrication Regime: Theoretical Model and Application to Metal-on-Metal Artificial Hip Joints
,”
Wear
,
324–325
, pp.
55
63
. 10.1016/j.wear.2014.12.003
33.
Meng
,
H. C.
, and
Ludema
,
K. C.
,
1995
, “
Wear Models and Predictive Equations: Their Form and Content
,”
Wear
,
181–183
, pp.
443
457
. 10.1016/0043-1648(95)90158-2
34.
Banjac
,
M.
,
Vencl
,
A.
, and
Otović
,
S.
,
2014
, “
Friction and Wear Processes—Thermodynamic Approach
,”
Tribol. Ind.
,
36
(
4
), pp.
341
347
.
35.
Ramalho
,
A.
, and
Miranda
,
J. C.
,
2006
, “
The Relationship Between Wear and Dissipated Energy in Sliding Systems
,”
Wear
,
260
(
4–5
), pp.
361
367
. 10.1016/j.wear.2005.02.121
36.
Fox-Rabinovich
,
G.
,
Veldhuis
,
S. C.
,
Kovalev
,
A. I.
,
Wainstein
,
D. L.
,
Gershman
,
I. S.
,
Korshunov
,
S.
,
Shuster
,
L. S.
, and
Endrino
,
J. L.
,
2007
, “
Features of Self-Organization in Ion Modified Nanocrystalline Plasma Vapor Deposited AlTiN Coatings Under Severe Tribological Conditions
,”
J. Appl. Phys.
,
102
(
7
), p.
074305
. 10.1063/1.2785947
37.
Abdel-Aal
,
H. A.
,
2010
, “
Influence of Frictional Energy Dissipation on Wear Regime Transition in Dry Tribo-Systems
,”
Int. J. Mater. Prod. Technol.
,
38
(
1
), pp.
78
92
. 10.1504/IJMPT.2010.031897
38.
Amiri
,
M.
, and
Khonsari
,
M. M.
,
2010
, “
On the Thermodynamics of Friction and Wear—A Review
,”
Entropy
,
12
(
5
), p.
1021
. 10.3390/e12051021
39.
Gershman
,
I.
,
Gershman
,
E.
,
Mironov
,
A.
,
Fox-Rabinovich
,
G.
, and
Veldhuis
,
S.
,
2016
, “
Application of the Self-Organization Phenomenon in the Development of Wear Resistant Materials—A Review
,”
Entropy
,
18
(
11
), p.
385
. 10.3390/e18110385
40.
Fox-Rabinovich
,
G.
, and
Totten
,
G. E.
,
2006
,
Self-Organization During Friction: Advanced Surface-Engineered Materials and Systems Design
,
CRC Press
,
New York
.
41.
Fox-Rabinovich
,
G.
,
Gershman
,
I.
,
Yamamoto
,
K.
,
Biksa
,
A.
,
Veldhuis
,
S.
,
Beake
,
B.
, and
Kovalev
,
A.
,
2010
, “
Self-Organization During Friction in Complex Surface Engineered Tribosystems
,”
Entropy
,
12
(
2
), p.
275
. 10.3390/e12020275
42.
Jing
,
H.-D.
,
Zhang
,
X.-J.
,
Tian
,
Y.
, and
Meng
,
Y.-G.
,
2015
, “
Thermodynamic Analysis of Lubrication Considering Solid-Liquid Interface Interaction
,”
Acta Phys. Sin.
,
64
(
16
), p.
0168101
.
43.
Bryant
,
M. D.
,
2009
, “
Entropy and Dissipative Processes of Friction and Wear
,”
FME Trans.
,
37
, pp.
55
60
.
44.
Nosonovsky
,
M.
, and
Mortazavi
,
V.
,
2013
,
Friction-Induced Vibrations and Self-Organization: Mechanics and Non-Equilibrium Thermodynamics of Sliding Contact
,
CRC Press
,
Boca Raton
.
45.
Nosonovsky
,
M.
,
2010
, “
Entropy in Tribology: In the Search for Applications
,”
Entropy
,
12
(
6
), p.
1345
. 10.3390/e12061345
46.
Nosonovsky
,
M.
,
2010
, “
Self-Organization at the Frictional Interface for Green Tribology
,”
Philos. Trans. Royal Soc. A
,
368
(
1929
), pp.
4755
4774
. 10.1098/rsta.2010.0179
47.
ASTM D2783
,
2014
,
Standard Test Method for Measurement of Extreme-Pressure Properties of Lubricating Fluids (Four-Ball Method)
,
ASTM International
,
West Conshohocken, PA
.
48.
Dodiya
,
V. K.
, and
Parmar
,
J. P.
,
2016
, “
A Study of Various Wear Mechanism and Its Reduction Method
,”
Int. J. Innov. Res. Sci. Eng. Technol.
,
2
(
9
), pp.
242
248
.
49.
Kato
,
K.
,
2002
, “
Classification of Wear Mechanisms/Models
,”
P. I. Mech. Eng. J-J. Eng.
,
216
, pp.
349
355
.
50.
Rudas
,
J. S.
,
Gómez
,
L. M.
,
Toro
,
A.
,
Gutiérrez
,
J. M.
, and
Corz
,
A.
,
2017
, “
Wear Rate and Entropy Generation Sources in a Ti6Al4V–WC/10Co Sliding Pair
,”
ASME J. Tribol.
,
139
(
6
), p.
061608
. 10.1115/1.4036321
51.
Deeva
,
V.
, and
Slobodyan
,
S.
,
2018
, “
Assessment of the Tribological Contact Between Sliding Surfaces Via an Entropy Approach
,”
ASME J. Tribol.
,
141
(
3
), p.
031602
. 10.1115/1.4041644
52.
Bryant
,
M. D.
,
2016
, “
On Constitutive Relations for Friction From Thermodynamics and Dynamics
,”
ASME J. Tribol.
,
138
(
4
), p.
041603
. 10.1115/1.4032821
53.
Abd Maurad
,
Z.
,
Yeong
,
S. K.
,
Idris
,
Z.
, and
and Ishak
,
S. A.
,
2018
, “
Combined Esterification and Short-Path Distillation for High-Purity Pentaerythritol Ester From Palm Kernel for Biolubricants
,”
J. Am. Oil. Chem. Soc.
,
95
(
11
), pp.
1421
1429
. 10.1002/aocs.12149
54.
Gupta
,
R. N.
, and
Harsha
,
A. P.
,
2016
, “
Synthesis, Characterization, and Tribological Studies of Calcium–Copper–Titanate Nanoparticles as a Biolubricant Additive
,”
ASME J. Tribol.
,
139
(
2
), p.
021801
. 10.1115/1.4033714
55.
Ekrem
,
M.
,
Düzcükoğlu
,
H.
,
Ali Şenyurt
,
M.
,
Sinan Şahin
,
Ö
, and
Avcı
,
A.
,
2017
, “
Friction and Wear Performance of Epoxy Resin Reinforced With Boron Nitride Nanoplatelets
,”
ASME J. Tribol.
,
140
(
2
), p.
022001
. 10.1115/1.4037698
56.
Nurul
,
M. A.
,
Shahrullalail
,
S.
, and
Teng
,
H. W.
,
2016
, “
Alternative Lubricants: Study on Palm Oil-Based Lubricants in Metal Forming Process
,”
J. Oil Palm Res.
,
28
(
1
), pp.
93
103
. 10.21894/jopr.2016.2801.11
57.
Sethuramiah
,
A.
,
2003
, “Tribological Evaluation Methodologies,”
Lubricated Wear: Science and Technology
,
42
,
A.
Sethuramiah
, ed., Elsevier Science Serials, Amsterdam, pp.
203
234
.
58.
Czichos
,
H.
, and
Kirschke
,
K.
,
1972
, “
Investigations Into Film Failure (Transition Point) of Lubricated Concentrated Contacts
,”
Wear
,
22
(
3
), pp.
321
336
. 10.1016/0043-1648(72)90392-4
59.
IP 239
,
2014
, “
Determination of Extreme Pressure and Anti-Wear Properties of Lubricating Fluids and Greases—Four Ball Method
,” Energy Institute,
London
.
60.
Wright
,
M. S.
,
Jain
,
V. K.
, and
Saba
,
C. S.
,
1989
, “
Wear Rate Calculation in the Four-Ball Wear Test
,”
Wear
,
134
(
2
), pp.
321
334
. 10.1016/0043-1648(89)90134-8
61.
I-Ming
,
F.
,
1962
, “
A New Approach in Interpreting the Four-Ball Wear Results
,”
Wear
,
5
(
4
), pp.
275
288
. 10.1016/0043-1648(62)90130-8
62.
Inman
,
M. C.
, and
Tipler
,
H. R.
,
1963
, “
Interfacial Energy and Composition in Metals and Alloys
,”
Metall. Rev.
,
8
(
1
), pp.
105
166
. 10.1179/mtlr.1963.8.1.105
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