Lubrication is essential to minimize wear and friction between contacting surfaces in relative motion. Oil based lubricants are often enhanced via polymer additives to minimize self-degradation due to the shear thinning effect. Therefore, an accurate estimate of the load carrying capacity of the thin lubricating film requires careful modeling of shear thinning. Available models such as the generalized Reynolds equation (GR) and the approximate shear distribution have drawbacks such as large computational time and poor accuracy, respectively. In this work, we present a new approach, i.e., the modified viscosity (MV) model, based on calculating the strain rate only in one point along the vertical direction. We investigate, for both MV and GR, the load, the maximum pressure, and the computational time for (i) sliding (non-cavitating) contacts, (ii) cavitating, and (iii) squeezing contacts. We observe that the computational time is reduced (i) considerably for non-cavitating sliding and rolling contacts and (ii) by several orders of magnitudes for cavitating and squeezing contacts. Furthermore, the accuracy of MV is comparable with the GR model within an appreciable range of bearing numbers. Finally, for each type of boundary motion, we have determined the optimal vertical location to calculate the shear strain rate for MV; while this optimal value is close to half the height of the contact for sliding configurations, for rolling dominated and squeezing contacts it is around one quarter (or three quarter) of their height. We finally provide an analysis to a priori estimate the optimal location of the strain rate.
References
1.
R. M.
Mortier
, S. T.
Orszulik
, and M. F.
Fox
, Chemistry and Technology Lubricants
(Springer
, 2010
), Vol. 107115
.2.
N. S.
Ahmed
and A. M.
Nassar
, “Lubricating oil additives
,” in Tribology—Lubricants and Lubrication
(IntechOpen
, 2011
), pp. 249
–626
.3.
Y.-R.
Jeng
, B. J.
Hamrock
, and D. E.
Brewe
, “Piezoviscous effects in nonconformal contacts lubricated hydrodynamically
,” ASLE Trans.
30
, 452
–464
(1986
).4.
P. W.
Bridgman
, The Effect of Pressure on the Viscosity of Forty-Three Pure Liquids
(Harvard University Press
, 2013
).5.
C.
Barus
, “Note on the dependence of viscosity on pressure and temperature
,” Proc. Am. Acad. Arts Sci.
27
, 13
–18
(1891
).6.
B. J.
Hamrock
, S. R.
Schmid
, and B. O.
Jacobson
, Fundamentals of Fluid Film Lubrication
(CRC Press
, 2004
).7.
Y.
Liu
, Q. J.
Wang
, S.
Bair
, and P.
Vergne
, “A quantitative solution for the full shear-thinning EHL point contact problem including traction
,” Tribol. Lett.
28
, 171
–181
(2007
).8.
A. Z.
Szeri
, Fluid Film Lubrication
(Cambridge University Press
, 2010
).9.
W.-Z.
Wang
, Y.-C.
Liu
, H.
Wang
, and Y.-Z.
Hu
, “A computer thermal model of mixed lubrication in point contacts
,” J. Tribol.
126
, 162
–170
(2004
).10.
D.
Dowson
, “A generalized Reynolds equation for fluid-film lubrication
,” Int. J. Mech. Sci.
4
, 159
–170
(1962
).11.
Y.
Peiran
and W.
Shizhu
, “A generalized Reynolds equation for non-Newtonian thermal elastohydrodynamic lubrication
,” J. Tribol.
112
, 631
–636
(1990
).12.
R.
Hewson
, N.
Kapur
, and P.
Gaskell
, “Analytical and numerical solutions of thin lubricating films for differing shear-thinning viscosity models
,” Proc. Inst. Mech. Eng., Part J
221
, 355
–366
(2007
).13.
A.
Rastogi
and R.
Gupta
, “Accounting for lubricant shear thinning in the design of short journal bearings
,” J. Rheol.
35
, 589
–603
(1991
).14.
T. F.
Conry
, S.
Wang
, and C.
Cusano
, “A Reynolds–Eyring equation for elastohydrodynamic lubrication in line contacts
,” J. Tribol.
109
, 648
–654
(1987
).15.
J.
Shukla
, S.
Kumar
, and P.
Chandra
, “Generalized Reynolds equation with slip at bearing surfaces: Multiple-layer lubrication theory
,” Wear
60
, 253
–268
(1980
).16.
R.
Wolff
and A.
Kubo
, “A generalized non-Newtonian fluid model incorporated into elastohydrodynamic lubrication
,” J. Tribol.
118
, 74
–82
(1996
).17.
M.
Kumar
and P. K.
Mondal
, “Bejan's flow visualization of buoyancy-driven flow of a hydromagnetic Casson fluid from an isothermal wavy surface
,” Phys. Fluids
33
, 093113
(2021
).18.
P.
Kaushik
, P. K.
Mondal
, and S.
Chakraborty
, “Flow dynamics of a viscoelastic fluid squeezed and extruded between two parallel plates
,” J. Non-Newtonian Fluid Mech.
227
, 56
–64
(2016
).19.
L.
Biancofiore
, L.
Brandt
, and T. A.
Zaki
, “Streak instability in viscoelastic Couette flow
,” Phys. Rev. Fluids
2
, 043304
(2017
).20.
M. S.
Agrawal
, H. S.
Gaikwad
, P. K.
Mondal
, and G.
Biswas
, “Analysis and experiments on the spreading dynamics of a viscoelastic drop
,” Appl. Math. Modell.
75
, 201
–209
(2019
).21.
M.
Kumar
and P. K.
Mondal
, “Buoyancy driven flow of a couple stress fluid from an isothermal vertical plate: The role of spatially periodic magnetic field
,” Phys. Scr.
96
, 125014
(2021
).22.
B.
Bou-Said
and P.
Ehret
, “Inertia and shear-thinning effects on bearing behavior with impulsive loads
,” J. Tribol.
116
, 535
–540
(1994
).23.
T.
Tian
, V. W.
Wong
, and J. B.
Heywood
, “A piston ring-pack film thickness and friction model for multigrade oils and rough surfaces
,” SAE Trans.
105
, 1783
–1795
(1996
).24.
C.
Arcoumanis
, P.
Ostovar
, and R.
Mortier
, “Mixed lubrication modelling of Newtonian and shear thinning liquids in a piston-ring configuration
,” SAE Trans.
1997
, 1306
–1331
.25.
R.
Taylor
, “The inclusion of lubricant shear thinning in journal bearing models
,” Tribol. Ser.
36
, 611
–619
(1999
).26.
R.
Taylor
, “The inclusion of lubricant shear thinning in the short bearing approximation
,” Proc. Inst. Mech. Eng., Part J
213
, 35
–46
(1999
).27.
H.
Hirani
, K.
Athre
, and S.
Biswas
, “Lubricant shear thinning analysis of engine journal bearings
,” Tribol. Trans.
44
, 125
–131
(2001
).28.
S.
Akbarzadeh
and M. M.
Khonsari
, “Performance of spur gears considering surface roughness and shear thinning lubricant
,” J. Tribol.
130
, 021503
(2008
).29.
R. I.
Taylor
, “Tribology and energy efficiency: From molecules to lubricated contacts to complete machines
,” Faraday Discuss.
156
, 361
–382
(2012
).30.
L.
San Andrés
, V.
Barbarie
, A.
Bhattacharya
, and K.
Gjika
, “On the effect of thermal energy transport to the performance of (semi) floating ring bearing systems for automotive turbochargers
,” J. Eng. Gas Turbines Power
134
, 102507
(2012
).31.
D. E.
Sander
, H.
Allmaier
, H.-H.
Priebsch
, F. M.
Reich
, M.
Witt
, T.
Füllenbach
, A.
Skiadas
, L.
Brouwer
, and H.
Schwarze
, “Impact of high pressure and shear thinning on journal bearing friction
,” Tribol. Int.
81
, 29
–37
(2015
).32.
C.
Gu
, X.
Meng
, D.
Zhang
, and Y.
Xie
, “Transient analysis of the textured journal bearing operating with the piezoviscous and shear-thinning fluids
,” J. Tribol.
139
, 051708
(2017
).33.
P.
Wang
, T.
Keith
, Jr, and K.
Vaidyanathan
, “Non-Newtonian effects on the performance of dynamically loaded elliptical journal bearings using a mass-conserving finite element cavitation algorithm
,” Tribol. Trans.
44
, 533
–542
(2001
).34.
J.
Zhu
, H.
Qian
, H.
Wen
, L.
Zheng
, and H.
Zhu
, “Analysis of misaligned journal bearing lubrication performance considering the effect of lubricant couple stress and shear thinning
,” J. Mech.
37
, 282
–290
(2021
).35.
E.
Tomanik
, F. J.
Profito
, and D. C.
Zachariadis
, “Modelling the hydrodynamic support of cylinder bore and piston rings with laser textured surfaces
,” Tribol. Int.
59
, 90
–96
(2013
).36.
L.
Bertocchi
, D.
Dini
, M.
Giacopini
, M. T.
Fowell
, and A.
Baldini
, “Fluid film lubrication in the presence of cavitation: A mass-conserving two-dimensional formulation for compressible, piezoviscous and non-Newtonian fluids
,” Tribol. Int.
67
, 61
–71
(2013
).37.
V.
Jadhao
and M. O.
Robbins
, “Rheological properties of liquids under conditions of elastohydrodynamic lubrication
,” Tribol. Lett.
67
, 66
(2019
).38.
S.
Bair
and W. O.
Winer
, “A rheological model for elastohydrodynamic contacts based on primary laboratory data
,” J. Lubr. Technol.
101
, 258
–264
(1979
).39.
M.
Khonsari
and D.
Hua
, “Generalized non-Newtonian elastohydrodynamic lubrication
,” Tribol. Int.
26
, 405
–411
(1993
).40.
C. H.
Venner
and J.
Bos
, “Effects of lubricant compressibility on the film thickness in EHL line and circular contacts
,” Wear
173
, 151
–165
(1994
).41.
M. K.
Ghosh
and B. C.
Majumdar
, “Dynamic stiffness and damping characteristics of compensated hydrostatic thrust bearings
,” J. Lubr. Technol.
104
, 491
–496
(1982
).42.
R.
Ausas
, P.
Ragot
, J.
Leiva
, M.
Jai
, G.
Bayada
, and G. C.
Buscaglia
, “The impact of the cavitation model in the analysis of microtextured lubricated journal bearings
,” J. Tribol.
129
, 868
–875
(2007
).43.
L.
Biancofiore
, M.
Giacopini
, and D.
Dini
, “Interplay between wall slip and cavitation: A complementary variable approach
,” Tribol. Int.
137
, 324
–339
(2019
).44.
T.
Woloszynski
, P.
Podsiadlo
, and G. W.
Stachowiak
, “Efficient solution to the cavitation problem in hydrodynamic lubrication
,” Tribol. Lett.
58
, 18
(2015
).45.
M.
Giacopini
, M. T.
Fowell
, D.
Dini
, and A.
Strozzi
, “A mass-conserving complementarity formulation to study lubricant films in the presence of cavitation
,” J. Tribol.
132
, 041702
(2010
).46.
A. A.
Lubrecht
, W. E.
ten Napel
, and R.
Bosma
, “Multigrid, an alternative method of solution for two-dimensional elastohydrodynamically lubricated point contact calculations
,” J. Tribol.
109
, 437
–443
(1987
).47.
A. A.
Lubrecht
, C. H.
Venner
, W. E.
ten Napel
, and R.
Bosma
, “Film thickness calculations in elastohydrodynamically lubricated circular contacts, using a multigrid method
,” J. Tribol.
110
, 503
–507
(1988
).48.
M.
Arghir
, A.
Alsayed
, and D.
Nicolas
, “The finite volume solution of the Reynolds equation of lubrication with film discontinuities
,” Int. J. Mech. Sci.
44
, 2119
–2132
(2002
).49.
R. F.
Ausas
, M.
Jai
, and G. C.
Buscaglia
, “A mass-conserving algorithm for dynamical lubrication problems with cavitation
,” J. Tribol.
131
, 031702
(2009
).50.
S.
Gamaniel
, D.
Dini
, and L.
Biancofiore
, “The effect of fluid viscoelasticity in lubricated contacts in the presence of cavitation
,” Tribol. Int.
160
, 107011
(2021
).51.
J. H.
Ferziger
, M.
Perić
, and R. L.
Street
, Computational Methods for Fluid Dynamics
(Springer
, 2002
), Vol. 3
.52.
H. G.
Elrod
, “A cavitation algorithm
,” J. Lubr. Technol.
103
, 350
–354
(1981
).53.
D.
Vijayaraghavan
and T. G.
Keith
, “An efficient, robust, and time accurate numerical scheme applied to a cavitation algorithm
,” J. Tribol.
112
, 44
–51
(1990
).54.
W. L.
Briggs
, V. E.
Henson
, and S. F.
McCormick
, A Multigrid Tutorial
(SIAM
, 2000
).55.
H. A.
Van der Vorst
, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems
,” SIAM J. Sci. Stat. Comput.
13
, 631
–644
(1992
).56.
T.
Almqvist
and R.
Larsson
, “Some remarks on the validity of Reynolds equation in the modeling of lubricant film flows on the surface roughness scale
,” J. Tribol.
126
, 703
–710
(2004
).57.
P.
Ehret
, D.
Dowson
, and C. M.
Taylor
, “On lubricant transport conditions in elastohydrodynamic conjuctions
,” Proc. R. Soc. London, Ser. A: Math., Phys. Eng. Sci.
454
, 763
–787
(1998
).58.
A.
Waseem
, I.
Temizer
, J.
Kato
, and K.
Terada
, “Micro-texture design and optimization in hydrodynamic lubrication via two-scale analysis
,” Struct. Multidiscip. Optim.
56
, 227
–248
(2017
).59.
C.
Putignano
, L.
Afferrante
, G.
Carbone
, and G.
Demelio
, “A new efficient numerical method for contact mechanics of rough surfaces
,” Int. J. Solids Struct.
49
, 338
–343
(2012
).60.
S.
Balasubramanian
, P.
Kaushik
, and P. K.
Mondal
, “Dynamics of viscoelastic fluid in a rotating soft microchannel
,” Phys. Fluids
32
, 112003
(2020
).61.
S. R.
Gorthi
, S. K.
Meher
, G.
Biswas
, and P. K.
Mondal
, “Capillary imbibition of non-Newtonian fluids in a microfluidic channel: Analysis and experiments
,” Proc. R. Soc. A
476
, 20200496
(2020
).62.
P.
Abhimanyu
, P.
Kaushik
, P. K.
Mondal
, and S.
Chakraborty
, “Transiences in rotational electro-hydrodynamics microflows of a viscoelastic fluid under electrical double layer phenomena
,” J. Non-Newtonian Fluid Mech.
231
, 56
–67
(2016
).63.
H.
Ahmed
and L.
Biancofiore
, “A new approach for modeling viscoelastic thin film lubrication
,” J. Non-Newtonian Fluid Mech.
292
, 104524
(2021
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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