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Research Article | Open Access

A new method to solve the Reynolds equation including mass-conserving cavitation by physics informed neural networks (PINNs) with both soft and hard constraints

Yinhu XI1( ), Jinhui DENG1, Yiling LI2
School of Mechanical Engineering, Anhui University of Science and Technology, Huainan 232001, China
Ericsson AB, Datalinjen 3, Linköping 58330, Sweden
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Graphical Abstract

Abstract

In this work, a new method to solve the Reynolds equation including mass-conserving cavitation by using the physics informed neural networks (PINNs) is proposed. The complementarity relationship between the pressure and the void fraction is used. There are several difficulties in problem solving, and the solutions are provided. Firstly, the difficulty for considering the pressure inequality constraint by PINNs is solved by transferring it into one equality constraint without introducing error. While the void fraction inequality constraint is considered by using the hard constraint with the max-min function. Secondly, to avoid the fluctuation of the boundary value problems, the hard constraint method is also utilized to apply the boundary pressure values and the corresponding functions are provided. Lastly, for avoiding the trivial solution the limitation for the mean value of the void fraction is applied. The results are validated against existing data, and both the incompressible and compressible lubricant are considered. Good agreement can be found for both the domain and domain boundaries.

Keywords

Reynolds equationmass-conserving cavitationphysics informed neural networkshard constraintstrivial solution

References

[1]
Dular M, Požar T, Zevnik J, Petkovšek R. High speed observation of damage created by a collapse of a single cavitation bubble. Wear 418–419: 13–23 (2019)
Crossref Google Scholar
[2]
Dowson D, Taylor C M. Cavitation in bearings. Annu Rev Fluid Mech 11: 35–65 (1979)
Crossref Google Scholar
[3]
Braun M J, Hannon W M. Cavitation formation and modelling for fluid film bearings: A review. Proc Inst Mech Eng Part J 224(9): 839–863 (2010)
Crossref Google Scholar
[4]
Geike T. Review on the bubble dynamics based cavitation dynamics for the negative squeeze motion in lubricated contacts. Front Mech Eng 6: 33 (2020)
Crossref Google Scholar
[5]
Kamat H, Kini C R, Shenoy S B. Effect of cavitation and temperature on fluid film bearing using CFD and FSI technique: A review. Arch Computat Methods Eng 30(3): 1623–1636 (2023)
Crossref Google Scholar
[6]
Wang W, He Y Y, Zhao J, Mao J Y, Hu Y T, Luo J B. Optimization of groove texture profile to improve hydrodynamic lubrication performance: Theory and experiments. Friction 8(1): 83–94 (2020)
Crossref Google Scholar
[7]
Jakobsson B, Floberg L. The finite journal bearing, considering vaporization (Das Gleitlager von endlicher Breite mit Verdampfung). Trans Chalmers University of Technology 1957: 190 (1957)
Google Scholar
[8]
Elrod H G, Adams M L. A computer program for cavitation and starvation problems. Cavitat Relat Phenom Lubr 1: 37–13 (1975)
Google Scholar
[9]
Giacopini M, Fowell M T, Dini D, Strozzi A. A mass-conserving complementarity formulation to study lubricant films in the presence of cavitation. J Tribol 132(4): 1 (2010)
Crossref Google Scholar
[10]
Bertocchi L, Dini D, Giacopini M, Fowell M T, Baldini A. 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)
Crossref Google Scholar
[11]
Almqvist A, Fabricius J, Larsson R, Wall P. A new approach for studying cavitation in lubrication. J Tribol 136(1): 011706 (2014)
Crossref Google Scholar
[12]
Silva A, Lenzi V, Cavaleiro A, Carvalho S, Marques L. FELINE: Finite element solver for hydrodynamic lubrication problems using the inexact Newton method. Comput Phys Commun 279: 108440 (2022)
Crossref Google Scholar
[13]
Geng Y, Chen W. Multiscale method of modelling surface texture with mass-conserving cavitation model. Tribol Int 173: 107663 (2022)
Crossref Google Scholar
[14]
Gropper D, Wang L, Harvey T J. Hydrodynamic lubrication of textured surfaces: A review of modeling techniques and key findings. Tribol Int 94: 509–529 (2016)
Crossref Google Scholar
[15]
Han Y X, Meng Q G, de Boer G. Two-scale homogenization of hydrodynamic lubrication in a mechanical seal with isotropic roughness based on the Elrod cavitation algorithm. Proc Inst Mech Eng Part J 236(3): 359–385 (2022)
Crossref Google Scholar
[16]
Ardah S, Profito F J, Dini D. An integrated finite volume framework for thermal elasto-hydrodynamic lubrication. Tribol Int 177: 107935 (2023)
Crossref Google Scholar
[17]
Raissi M, Perdikaris P, Karniadakis G E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys 378: 686–707 (2019)
Crossref Google Scholar
[18]
Yucesan Y A, Viana F A C. A hybrid physics-informed neural network for main bearing fatigue prognosis under grease quality variation. Mech Syst Signal Process 171: 108875 (2022)
Crossref Google Scholar
[19]
van Herten R L M, Chiribiri A, Breeuwer M, Veta M, Scannell C M. Physics-informed neural networks for myocardial perfusion MRI quantification. Med Image Anal 78: 102399 (2022)
Crossref Google Scholar
[20]
Cai S Z, Wang Z C, Wang S F, Perdikaris P, Karniadakis G E. Physics-informed neural networks for heat transfer problems. J Heat Transf 143(6): 060801 (2021)
Crossref Google Scholar
[21]
Zheng B, Li T C, Qi H J, Gao L G, Liu X Q, Yuan L. Physics-informed machine learning model for computational fracture of quasi-brittle materials without labelled data. Int J Mech Sci 223: 107282 (2022)
Crossref Google Scholar
[22]
Kovacs A, Exl L, Kornell A, Fischbacher J, Hovorka M, Gusenbauer M, Breth L, Oezelt H, Praetorius D, Suess D, et al. Magnetostatics and micromagnetics with physics informed neural networks. J Magn Magn Mater 548: 168951 (2022)
Crossref Google Scholar
[23]
Almqvist A. Fundamentals of physics-informed neural networks applied to solve the Reynolds boundary value problem. Lubricants 9(8): 82 (2021)
Crossref Google Scholar
[24]
Zhao Y, Guo L, Wong P P L. Application of physics-informed neural network in the analysis of hydrodynamic lubrication. Friction 11(7): 1253–1264 (2023)
Crossref Google Scholar
[25]
Li L L, Li Y Z, Du Q W, Liu T Y, Xie Y H. ReF-nets: Physics-informed neural network for Reynolds equation of gas bearing. Comput Meth Appl Mech Eng 391: 114524 (2022)
Crossref Google Scholar
[26]
Rom M. Physics-informed neural networks for the Reynolds equation with cavitation modeling. Tribol Int 179: 108141 (2023)
Crossref Google Scholar
[27]
Lu L, Pestourie R, Yao W J, Wang Z C, Verdugo F, Johnson S G. Physics-informed neural networks with hard constraints for inverse design. SIAM J Sci Comput 43(6): B1105–B1132 (2021)
Crossref Google Scholar
[28]
Miraskari M, Hemmati F, Jalali A, Alqaradawi M Y, Gadala M S. A robust modification to the universal cavitation algorithm in journal bearings. J Tribol 139(3): 031703 (2017)
Crossref Google Scholar
[29]
Sahlin F, Almqvist A, Larsson R, Glavatskih S. A cavitation algorithm for arbitrary lubricant compressibility. Tribol Int 40(8): 1294–1300 (2007)
Crossref Google Scholar
[30]
Manser B, Belaidi I, Hamrani A, Khelladi S, Bakir F. Texture shape effects on hydrodynamic journal bearing performances using mass-conserving numerical approach. Tribol Mater Surf Interfaces 14(1): 33–50 (2020)
Crossref Google Scholar
[31]
Shen C, Khonsari M M. On the magnitude of cavitation pressure of steady-state lubrication. Tribol Lett 51(1): 153–160 (2013)
Crossref Google Scholar
Friction
Volume 12 Issue 6,
June 2024
Pages 1165-1175
DOI: 10.1007/s40544-023-0791-1
Cite this article:
XI Y, DENG J, LI Y. A new method to solve the Reynolds equation including mass-conserving cavitation by physics informed neural networks (PINNs) with both soft and hard constraints. Friction, 2024, 12(6): 1165-1175. https://doi.org/10.1007/s40544-023-0791-1

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Received: 13 April 2023
Revised: 22 May 2023
Accepted: 21 June 2023
Published: 12 January 2024
© The author(s) 2023.

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