Abstract
Recent experiments have shown that the elastic deformation behaviors of a polymeric material are consistent with the Cosserat elasticity under nonuniform deformation at a millimeter scale. Thus, an elastohydrodynamic lubrication model in the framework of the Cosserat continuum theory is proposed to explore the lubrication performance that deviates from the classical elastohydrodynamic lubrication theory for the small polymer journal bearings with millimeter size. The elastic deformation of the bearing sleeve made of polymeric material and the pressure distribution in a lubricating film are obtained through an iterative solution of the equation of the Cosserat elasticity and the modified Reynolds’ equations with considering the boundary slippage. The effect of bearing size and Cosserat characteristic lengths for torsion and bending on the lubrication performance of the small polymer journal bearings is studied using the proposed Cosserat elastohydrodynamic lubrication model. It was found that the small changes in film thickness due to the Cosserat effect can result in large changes in film pressure. The Cosserat characteristic length of bending possesses a significant effect on the lubrication behaviors of the journal bearings, because the size effect is mainly caused by the increased apparent modulus due to the bending elastic deformation of the bearing sleeve. The boundary slip behaviors dependent on the Cosserat characteristic length are also studied using the Cosserat elastohydrodynamic model, and the numerical results show that the Cosserat characteristic length changes the optimal geometric parameters of the slip zone in terms of load carrying capacity for the small polymer journal bearings.
References
1.
Ahn
, B. K.
, Lee
, D. W.
, Israelachvili
, J. N.
, and Waite
, J. H.
, 2014
, “Surface-Initiated Self-Healing of Polymers in Aqueous Media
,” Nat. Mater.
, 13
(9
), pp. 867
–872
. 2.
Olabisi
, O.
, and Adewale
, K.
, 2016
, Handbook of Thermoplastics
, CRC Press
, Boca Raton, FL
.3.
Zhou
, J.
, Blair
, B.
, Argires
, J.
, and Pitsch
, D.
, 2015
, “Experimental Performance Study of a High Speed Oil Lubricated Polymer Thrust Bearing
,” Lubricants
, 3
(1
), pp. 3
–13
. 4.
Su
, B. B.
, Huang
, L. R.
, Huang
, W.
, and Wang
, X. L.
, 2017
, “The Load Carrying Capacity of Textured Sliding Bearings With Elastic Deformation
,” Tribol. Int.
, 109
(5
), pp. 86
–96
. 5.
Shi
, X.
, Kida
, K.
, and Kashima
, Y.
, 2014
, “Surface Crack and Wear of PPS Polymer Thrust Bearings Under Rolling Contact Fatigue in Water
,” Mater. Res. Innov.
, 18
(sup5
), pp. 42
–47
. 6.
Repka
, M.
, Dörr
, N.
, Brenner
, J.
, Gabler
, C.
, Mcaleese
, C.
, Ishigo
, O.
, and Koshima
, M.
, 2017
, “Lubricant-Surface Interactions of Polymer-Coated Engine Journal Bearings
,” Tribol. Int.
, 109
(5
), pp. 519
–528
. 7.
Vakis
, A. I.
, Yastrebov
, V. A.
, Scheibert
, J.
, 2018
, “Modeling and Simulation in Tribology Across Scales: An Overview
,” Tribol. Int.
, 125
(9
), pp. 169
–199
. 8.
Stupkiewicz
, S.
, Lengiewicz
, J.
, Sadowski
, P.
, and Kucharski
, S.
, 2016
, “Finite Deformation Effects in Soft Elastohydrodynamic Lubrication Problems
,” Tribol. Int.
, 93
(SI
), pp. 511
–522
. 9.
Marx
, N.
, Guegan
, J.
, and Spikes
, H. A.
, 2016
, “Elastohydrodynamic Film Thickness of Soft EHL Contacts Using Optical Interferometry
,” Tribol. Int.
, 99
(7
), pp. 267
–277
. 10.
Rueger
, Z.
, and Lakes
, R. S.
, 2018
, “Strong Cosserat Elasticity in a Transversely Isotropic Polymer Lattice
,” Phys. Rev. Lett.
, 120
(6
), p. 065501
. 11.
Lakes
, R. S.
, and Drugan
, W.
, 2015
, “Bending of a Cosserat Elastic Bar of Square Cross Section: Theory and Experiment
,” ASME J. Appl. Mech.
, 82
(9
), p. 091002
. 12.
Rueger
, Z.
, and Lakes
, R. S.
, 2017
, “Strong Cosserat Elastic Effects in a Unidirectional Composite
,” Z. Angew. Math. Phys
, 68
(3
), pp. 54
–63
. 13.
Johnson
, K. L.
, 1970
, “Regimes of Elastohydrodynamic Lubrication
,” SAGE J. Mech. Eng. Sci.
, 12
(1
), pp. 9
–16
. 14.
Hamrock
, B. J.
, and Dowson
, D.
, 1979
, “Minimum Film Thickness in Elliptical Contacts for Different Regimes of Fluid Film Lubrication
,” Proc. Fifth Leeds-Lyon Symp. on Tribo. on “Elastohydrodynamics and Related Topics”
, Burry St. Edmunds, Suffolk
, Oct. 1
, pp. 22
–27
. Mechanical Engineering Publications.15.
Esfahanian
, M.
, and Hamrock
, B. J.
, 1991
, “Fluid-Film Lubrication Regimes Revisited
,” Tribol. Trans.
, 34
(4
), pp. 628
–632
. 16.
Hamrock
, B. J.
, 1994
, Fundamentals of Fluid Film Lubrication
, McGraw-Hill Inc
, New York
.17.
Hooke
, C. J.
, 1988
, “Calculation of Clearances in Soft Point Contacts
,” ASME J. Tribol.
, 110
(1
), pp. 167
–173
. 18.
Hooke
, C. J.
, 1995
, “The Elastohydrodynamic Lubrication of Elliptical Point Contacts Operating in the Isoviscous Region
,” Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol.
, 209
(4
), pp. 225
–234
. 19.
Dowson
, D.
, and Ehret
, P.
, 1999
, “Present and Future Studies in Elastohydrodynamics
,” Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol.
, 213
(J5
), pp. 317
–333
. 20.
Etsion
, I.
, 2013
, “Modeling of Surface Texturing in Hydrodynamic Lubrication
,” Friction
, 1
(3
), pp. 195
–209
. 21.
Yagi
, K.
, and Sugimura
, J.
, 2013
, “Elastic Deformation in Thin Film Hydrodynamic Lubrication
,” Tribol. Int.
, 59
(SI
), pp. 170
–180
. 22.
Yagi
, K.
, and Sugimura
, J.
, 2013
, “Elastohydrodynamic Simulation of Rayleigh Step Bearings in Thin Film Hydrodynamic Lubrication
,” Tribol. Int.
, 64
(8
), pp. 204
–214
. 23.
Shinkarenko
, A.
, Kligerman
, Y.
, and Etsion
, I.
, 2009
, “The Effect of Surface Texturing in Soft Elasto-Hydrodynamic Lubrication
,” Tribol. Int.
, 42
(2
), pp. 284
–292
. 24.
Shinkarenko
, A.
, Kligerman
, Y.
, and Etsion
, I.
, 2009
, “The Effect of Elastomer Surface Texturing in Soft Elasto-Hydrodynamic Lubrication
,” Tribol. Lett.
, 36
(2
), pp. 95
–103
. 25.
Myers
, T. G.
, Hall
, R. W.
, Savage
, P. H.
, and Gaskell
, P. H.
, 1991
, “The Transition Region of Elastohy-Drodynamic Lubrication
,” Proc. R. Soc. Lond. Ser. A Math. Phys.
, 432
(1886
), pp. 467
–479
. 26.
de Vicente
, J.
, Stokes
, J. R.
, and Spikes
, H. A.
, 2005
, “The Frictional Properties of Newtonian Fluids in a Rolling-Sliding Soft-EHL Contact
,” Tribol. Lett.
, 20
(3-4
), pp. 273
–285
. 27.
Lam
, D. C. C.
, Yang
, F.
, Chong
, A. C. M.
, Wang
, J.
, and Tong
, P.
, 2003
, “Experiments and Theory in Strain Gradient Elasticity
,” J. Mech. Phys. Solids
, 51
(8
), pp. 1477
–1508
. 28.
McFarland
, A. W.
, and Colton
, J. S.
, 2005
, “Role of Material Microstructure in Plate Stiffness With Relevance to Microcantilever Sensors
,” J. Micromech. Microeng.
, 15
(5
), pp. 1060
–1067
. 29.
Bucsek
, A. N.
, Alisafaei
, F.
, Han
, C. S.
, and Lakhera
, N.
, 2016
, “On Thresholds in the Indentation Size Effect of Polymers
,” Polym. Bull.
, 73
(3
), pp. 763
–772
. 30.
Zhang
, S.
, Xie
, Z. Q.
, Chen
, B. S.
, and Zhang
, H. W.
, 2013
, “Finite Element Analysis of 3D Elastic-plastic Frictional Contact Problem for Cosserat Materials
,” Comput. Mech.
, 51
(6
), pp. 911
–925
. 31.
Bigoni
, D.
, and Drugan
, W. J.
, 2007
, “Analytical Derivation of Cosserat Moduli Via Homogenization of Heterogeneous Elastic Materials
,” ASME J. Appl. Mech.
, 74
(4
), pp. 741
–753
. 32.
Nikolov
, S.
, Han
, C. S.
, and Raabe
, D.
, 2007
, “On the Origin of Size Effects in Small-Strain Elasticity of Solid Polymers
,” Int. J. Solids Struct.
, 44
(5
), pp. 1582
–1592
. 33.
Yang
, Z.
, SanAndres
, L.
, and Childs
, D. W.
, 1995
, “Thermohydrodynamic Analysis of Process-Liquid Hydrostatic Journal Bearings in Turbulent Regime, Part II: Numerical Solution and Results
,” ASME J. Appl. Mech.
, 62
(3
), pp. 679
–684
. 34.
Trachsel
, M.
, Pittini
, R.
, and Dual
, J.
, 2018
, “Evaluation and Quantification of Friction Using Ionic Liquids in Small, Self Lubricating Journal Bearings
,” Tribol. Int.
, 122
(6
), pp. 15
–22
. 35.
Trachsel
, M.
, Pittini
, R.
, and Dual
, J.
, 2016
, “Friction and 2D Position Measurements in Small Journal Bearings
,” Tribol. Int.
, 102
(10
), pp. 555
–560
. 36.
Wu
, C. W.
, Ma
, G. J.
, Zhou
, P.
, and Wu
, C. D.
, 2006
, “Low Friction and High Load Support Capacity of Slider Bearing With a Mixed Slip Surface
,” ASME J. Tribol.
, 128
(4
), pp. 904
–907
. 37.
Aurelian
, F.
, Patrick
, M.
, and Mohamed
, H.
, 2011
, “Wall Slip Effects in (Elasto) Hydrodynamic Journal Bearings
,” Tribol. Int.
, 44
(7-8
), pp. 868
–877
. 38.
Senatore
, A.
, and Rao
, T. V. V. L. N.
, 2018
, “Partial Slip Texture Slider and Journal Bearing Lubricated With Newtonian Fluids: A Review
,” ASME J. Tribol.
, 140
(4
), p. 040801
. 39.
Fortier
, A. E.
, and Salant
, R. F.
, 2005
, “Numerical Analysis of a Journal Bearing With a Heterogeneous Slip/No-Slip Surface
,” ASME J. Tribol.
, 127
(4
), pp. 820
–825
. 40.
Zhu
, B.
, Yang
, H. W.
, and Chen
, J. F.
, 2015
, “A Novel Finite Element Time Domain Method for Nonlinear Maxwell’s Equations Based on the Parametric Quadratic Programming Method
,” Microw. Opt. Technol. Lett.
, 57
(7
), pp. 1640
–1645
. 41.
Ma
, G. J.
, Wu
, C. W.
, and Zhou
, P.
, 2007
, “Multi-Linearity Algorithm for Wall Slip in Two-Dimensional Gap Flow
,” Int. J. Numer. Methods Eng.
, 69
(12
), pp. 2469
–2484
. 42.
Zhu
, B.
, Li
, Y. P.
, Wang
, W. G.
, and Lei
, M. K.
, 2019
, “Boundary Slippage Modeling and Optimization of Hydrophobic Tilting Pad Thrust Bearing With Elastic Deformation
,” Tribol. Int.
, 136
(8
), pp. 299
–316
. 43.
Huebner
, K. H.
, and Thornton
, E. A.
, 1975
, The Finite Element Method for Engineers
, Wiley
, New York
.44.
Oh
, K. P.
, and Huebner
, K. H.
, 1973
, “Solution of the Elastohydrodynamic Finite Journal Bearing Problem
,” ASME J. Lubr. Technol.
, 95
(3
), pp. 187
–194
. 45.
Cameron
, A.
, 1981
, Basic Lubrication Theory
, 3rd ed., Ellis Horwood Ltd
., Chichester
.46.
Burzynski
, S.
, Chroscielewski
, J.
, Daszkiewicz
, K.
, and Witkowski
, W.
, 2018
, “Elastoplastic Nonlinear FEM Analysis of FGM Shells of Cosserat Type
,” Compos. Part B Eng.
, 154
(12
), pp. 478
–491
. 47.
Gauthier
, R. D.
, and Jahsman
, W. E.
, 1975
, “A Quest for Micropolar Elastic Constants
,” ASME J. Appl. Mech.
, 42
(2
), pp. 369
–374
. 48.
Bair
, S.
, and Winer
, W. O.
, 1992
, “The High Pressure High Shear Stress Rheology of Liquid Lubricants
,” ASME J. Tribol.
, 114
(1
), pp. 1
–13
. 49.
Östensen
, J. O.
, Wikstrom
, V.
, and Höglund
, E.
, 1992
, “Interaction Effects Between Temperature, Pressure and Type of Base Oil on Lubricant Shear Strength Coefficient
,” Tribologia.
, 11
, pp. 123
–132
.50.
Bair
, S.
, and Winer
, W. O.
, 1979
, “Shear Strength Measurements of Lubricants at High Pressure
,” ASME J. Lubr. Technol.
, 101
(3
), pp. 251
–257
. 51.
Höglund
, E.
, 1989
, “The Relationship Between Lubricant Shear Strength and Chemical Composition of the Base Oil
,” Wear
, 130
(1
), pp. 213
–224
. 52.
Craig
, V. S. J.
, Neto
, C.
, and Williams
, D. R. M.
, 2001
, “Shear-Dependent Boundary Slip in an Aqueous Newtonian Liquid
,” Phys. Rev. Lett.
, 87
(5
), pp. 054504
. 53.
Zhu
, Y. X.
, and Granick
, S.
, 2002
, “Limits of the Hydrodynamic No-Slip Boundary Condition
,” Phys. Rev. Lett.
, 88
(10
), pp. 106102
. 54.
Bonaccurso
, E.
, Kappl
, M.
, and Butt
, H. J.
, 2002
, “Hydrodynamic Force Measurements: Boundary Slip of Water on Hydrophilic Surfaces and Electrokinetic Effects
,” Phys. Rev. Lett.
, 88
(7
), pp. 076103
. 55.
Bair
, S.
, and Winer
, W. O.
, 1990
, “The High Shear Stress Rheology of Liquid Lubricants at Pressures of 2 to 200 MPa
,” ASME J. Tribol.
, 112
(2
), pp. 246
–252
. 56.
Wikstrom
, V.
, and Höglund
, E.
, 1994
, “Investigation of Parameter Affecting the Limiting Shear Stress-Pressure Coefficient: A New Model Incorporating Temperature
,” ASME J. Tribol.
, 116
(3
), pp. 612
–620
. 57.
Wilson
, W. R. D.
, and Huang
, X. B.
, 1989
, “Viscoplastic Behavior of a Silicone Oil in a Metalforming Inlet Zone
,” ASME J. Tribol.
, 111
(4
), pp. 585
–590
. 58.
Kato
, K.
, Iwasaki
, T.
, Kato
, M.
, and Inoue
, K.
, 1993
, “Evaluation of Limiting Shear Stress of Lubricants by Roller Test
,” JSME Int. J. Ser. C
, 36
(4
), pp. 512
–522
. Copyright © 2019 by ASME
You do not currently have access to this content.
