Newton-GMRES-Method for the Scritinization of electric double layer and surface roughness on EHL line contact problem

Vishwanath B Awati; Parashuram Obannavar; Mahesh Kumar N

doi:10.15282/jmes.17.1.2023.7.0741

Authors

V.B. Awati Department of Mathematics, Rani Channamma University, Belagavi, Karnataka, India-591156. Phone: 0831-2565246
P. M. Obannavar Department of Mathematics, Rani Channamma University, Belagavi, Karnataka, India-591156. Phone: 0831-2565246
N. Mahesh Kumar Department of Mathematics, Rani Channamma University, Belagavi, Karnataka, India-591156. Phone: 0831-2565246

DOI:

https://doi.org/10.15282/jmes.17.1.2023.7.0741

Keywords:

Electric double layer, EHL, Thin water lubricating film, Newton-GMREs method, Daubechies D6 wavelet

Abstract

The electric double layer phenomenon exists on the solid interface under the water-liquid condition. The water molecules are ionized and adhered in the interface forming the sturn layer is a diffused layer in which molecules can move with the movement of bulk of molecules. Because of these two characteristics, the boundary layer of water molecules is called the electric double layer. The aim of present study is to explore the impact of two fraction surfaces of electric double layer (EDL) on a thin water lubricating film on an elastohydrodynamic lubrication (EHL) line contact problem with a sinusoidal surface roughness. The governing modified Reynolds and film thickness equations are based on mathematical model of electro-viscosity of asymmetrical electrical double layer is analyzed numerically. The viscosity-pressure relation of water and theoretical evaluation pertaining to the effect of electric double layer on film-thickness and pressure distribution of EHL with water film of line contact problem is discussed in detail. The effect of zeta potential on film thickness and pressure is determined using Newton’s-GMRES method with Daubechies D6 wavelet as a pre-conditioner. The results predict that, EDL has less impact on pressure distribution and significant impact on film thickness. The obtained results are compared with results of Dowson and Higginson which are comparable.

References

W.-L. Li, "Effects of electrodouble layer (EDL) and surface roughness on lubrication theory," Tribology Letters, vol. 20, pp. 53-61, 2005.

C. Terzaghi, "The static rigidity of plastic clays," Journal of Rheology, vol. 2, no. 3, pp. 253-262, 1931.

L. Ren, D. Li, and W. Qu, "Electro-viscous effects on liquid flow in microchannels," Journal of Colloid and Interface Science, vol. 233, no. 1, pp. 12-22, 2001.

L. Ren, W. Qu, and D. Li, "Interfacial electrokinetic effects on liquid flow in microchannels," International Journal of Heat and Mass Transfer, vol. 44, no. 16, pp. 3125-3134, 2001.

D. Li, "Electro-viscous effects on pressure-driven liquid flow in microchannels," Colloids and Surfaces A: Physicochemical and Engineering Aspects, vol. 195, no. 1-3, pp. 35-57, 2001.

J. Luo, S. Wen, and P. Huang, "Thin film lubrication. Part I. Study on the transition between EHL and thin film lubrication using a relative optical interference intensity technique," Wear, vol. 194, no. 1-2, pp. 107-115, 1996.

S. Wen and J. Luo, "Study on thin film lubrication in the nano scale," Journal-Tsinghua University, vol. 41, no. 4/5, pp. 63-68, 2001.

D. C. Prieve and S. G. Bike, "Electrokinetic repulsion between two charged bodies undergoing sliding motion," Chemical Engineering Communications, vol. 55, no. 1-6, pp. 149-164, 1987.

S. G. Bike and D. C. Prieve, "Electrohydrodynamic lubrication with thin double layers," Journal of Colloid and Interface Science, vol. 136, no. 1, pp. 95-112,1990.

B. Zhang and N. Umehara, "Hydrodynamic lubrication theory considering electric double layer for very thin water film lubrication of ceramics," JSME International Journal Series C Mechanical Systems, Machine Elements and Manufacturing, vol. 41, no. 2, pp. 285-290, 1998.

P. L. Wong, P. Huang, and Y. Meng, "The effect of the electric double layer on a very thin water lubricating film," Tribology Letters, vol. 14, pp. 197-203, 2003.

S. Bai, P. Huang, Y. Meng, and S. Wen, "Modeling and analysis of interfacial electro-kinetic effects on thin film lubrication," Tribology International, vol. 39, no. 11, pp. 1405-1412, 2006.

B. Shaoxian and H. Ping, "Experimental and numerical study on influence of electro-viscosity of electric double layerin thin film lubrication," Chinese Journal of Mechanical Engineering, vol. 40, no. 5, pp. 34-38, 2004.

X.-J. Wang, S.-X. Bai, and P. Huang, "Theoretical analysis and experimental study on the influence of electric double layer on thin film lubrication," Frontiers of Mechanical Engineering in China, vol. 1, pp. 370-373, 2006.

S. Z. Wen, P. Huang, "Interface Science and Technology," Beijing: Tsing Hua University press, 2011, pp. 403-11.

Q. Zuo, P. Huang, and F. Su, "Theory analysis of asymmetrical electric double layer effects on thin film lubrication," Tribology International, vol. 49, pp. 67-74, 2012.

Q. Zuo, T. Lai, and P. Huang, "The effect of the electric double layer on very thin thermal elastohydrodynamic lubricating film," Tribology Letters, vol. 45, pp. 455-463, 2012.

Y. Chen, Q. Zuo, and P. Huang, "Influence of electric double layers on elastohydrodynamic lubricating water film in line contact," Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanoengineering and Nanosystems, vol. 227, no. 4, pp. 196-198, 2013.

P. D. S. Clermont, T. Paillat, and P. Leblanc, "Numerical study on the impact of a temperature step on the electrical double layer," Journal of Electrostatics, vol. 95, pp. 13-23, 2018.

A. A. Lubrecht, W. E. Ten Napel, and R. Bosma, "Multigrid, an alternative method of solution for two-dimensional elastohydrodynamically lubricated point contact calculations," Journal of Tribology, vol. 109, no. 3, pp. 437-443, 1987.

Z. Yang, "A study of grease film thickness in elastohydrodynamic rolling point contacts," in I. Mech. E. Conference Publication, vol. 1, pp. 97, 1987.

C. Venner, "Multilevel solution of the EHL line and point contact problems," Ph.D Thesis, University of Twente, Netherland, 1991.

G. Nijenbanning, C. H. Venner, and H. Moes, "Film thickness in elastohydrodynamically lubricated elliptic contacts," Wear, vol. 176, no. 2, pp. 217-229, 1994.

H. Lu, M. Berzins, C. E. Goodyer, and P. Jimack, "High order discontinuous Galerkin method for EHL line contact problems," Communications in Numerical Methods in Engineering, vol. 21, no. 11, pp. 643 -650, 2005.

P. M. Lugt and G. E. Morales-Espejel, "A review of elasto-hydrodynamic lubrication theory," Tribology Transactions, vol. 54, no. 3, pp. 470-496, 2011.

J. M. Ford, "Wavelet-based preconditioning of dense linear systems," Ph.D. Thesis, University of Liverpool, Liverpool, UK, 2001.

K. Chen, "Matrix preconditioning techniques and applications," Cambridge University Press, 2005.

J. Ford and K. Chen, "Wavelet-based preconditioners for dense matrices with non-smooth local features," BIT Numerical Mathematics, vol. 41, pp. 282-307, 2001.

V. B. Awati and S. Naik, "Multigrid method for the solution of EHL point contact with bio-based oil as lubricants for smooth and rough asperity," Industrial Lubrication and Tribology, vol. 70, no. 4, pp. 599-611, 2018.

B. V. Awati and S. Naik, "A multigrid method for EHL line contact problem with Grease as lubricant," Mathematical Models in Engineering, vol. 3, no. 2, pp. 126-134, 2017.

V. B. Awati, M. Kumar N, and N. M. Bujurke, "Numerical solution of thermal EHL line contact with bio-based oil as lubricant," Australian Journal of Mechanical Engineering, vol. 20, no. 1, pp. 231-244, 2022.

K. Chen, L. Zeng, Z. Wu, and F. Zheng, "Elastohydrodynamic lubrication in point contact on the surfaces of particle-reinforced composite," AIP Advances, vol. 8, no. 4, p. 045213, 2018.

Z. Xiao and X. Shi, "Investigation on stiffness and damping of transient non-newtonian thermal elastohydrodynamic point contact for crowned herringbone gears," Tribology International, vol. 137, pp. 102-112, 2019.

Y. Zhao and P. L. Wong, "Thermal-EHL analysis of slip/no-slip contact at high slide-to-roll ratio," Tribology International, vol. 153, p. 106617, 2021.

V. B. Awati, M. Kumar, "Newton-GMRES method for the solution of piezo-viscous line contact problem with Daubechies wavelet as a preconditioner," Journal of Modern Industry and Manufacturing, vol. 1, pp. 1-4, 2022.

G. Meurant, J. D. Tebbens, "Krylov methods for non-symmetric linear systems: From theory to computations," Springer, 2020.

G. M. D. Carso, O. Menchi and F. Romani, "Krylov subspace methods for solving linear systems," Technical Report, University of Pisa, pp. 1-28, 2015.

N. M. Nachtigal, S. C. Reddy, and L. N. Trefethen, "How fast are nonsymmetric matrix iterations?," SIAM Journal on Matrix Analysis and Applications, vol. 13, no. 3, pp. 778-795, 1992.

A. Greenbaum, "Iterative methods for solving linear systems,"Society for Industrial and Applied Mathematics (SIAM), USA 1997.

J. Drkošová, A. Greenbaum, M. Rozložník, and Z. Strakoš, "Numerical stability of GMRES," BIT Numerical Mathematics, vol. 35, no. 3, pp. 309-330, 1995.

L. G. Houpert and B. J. Hamrock, "Fast approach for calculating film thicknesses and pressures in elastohydrodynamically lubricated contacts at high loads," Journal of Tribology, vol. 108, pp. 411-420, 1986.

C. J. A. Roelands, W. O. Winer, and W. A. Wright, "Correlational aspects of the viscosity-temperature-pressure relationship of lubricating oils," Journal of Lubrication Technology, vol. 93, no. 1, pp. 209-210, 1971.

D. Dowson and G. R. Higginson, " Elasto-hydrodynamic lubrication," Pergamon Press, Oxford, 1977.

M. J. Zahr and P.-O. Persson, "Performance tuning of Newton-GMRES methods for discontinuous Galerkin discretizations of the Navier-Stokes equations," in 21st AIAA Computational Fluid Dynamics Conference, San Diego, June 24 -27, 2013.

J. Ford, K. Chen, and L. Scales, "A new wavelet transform preconditioner for iterative solution of elastohydrodynamic lubrication problems," International Journal of Computer Mathematics, vol. 75, no. 4,pp. 497-513, 2000.

J. M. Ford and K. Chen, "Speeding up the solution of thermal EHL problems," International Journal for Numerical Methods in Engineering, vol. 53, no. 10, pp. 2305-2310, 2002.

N. M. Bujurke and M. H. Kantli, "Numerical simulation of influence of surface features on the elastohydrodynamic lubrication of sliding line contact using Krylov subspace method," Computational Mathematics and Modeling, vol. 32, no. 2, pp. 198-220, 2021.

D. Dowson and G. R. Higginson, "The effect of material properties on the lubrication of elastic rollers," Journal of Mechanical Engineering Science, vol. 2, no. 3, pp. 188-194, 1960.