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Friction 2023, 11(6): 992-1013 https://doi.org/10.1007/s40544-022-0641-6
Research Article | Open Access | Issue | Published: 12 June 2022

Predicting EHL film thickness parameters by machine learning approaches

Show Author's Information Max MARIAN1( ),  Jonas MURSAK2,  Marcel BARTZ2,  Francisco J. PROFITO3,  Andreas ROSENKRANZ4,  Sandro WARTZACK2
Department of Mechanical and Metallurgical Engineering, School of Engineering, Pontificia Universidad Católica de Chile, Santiago 6904411, Chile
Engineering Design, Friedrich-Alexander-University Erlangen-Nuremberg (FAU), Erlangen 91058, Germany
Department of Mechanical Engineering, Polytechnic School of the University of São Paulo, São Paulo 05508-030, Brazil
Department of Chemical Engineering, Biotechnology and Materials (DIQBM), FCFM, Universidad de Chile, Santiago 8370456, Chile
Keywords:
machine learning, artificial neural network, support vector machine, film thickness, elastohydrodynamic lubrication, Gaussian process regression
Cite this article:
MARIAN M, MURSAK J, BARTZ M, et al. Predicting EHL film thickness parameters by machine learning approaches. Friction, 2023, 11(6): 992-1013. https://doi.org/10.1007/s40544-022-0641-6
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Abstract Full text About this article

Non-dimensional similarity groups and analytically solvable proximity equations can be used to estimate integral fluid film parameters of elastohydrodynamically lubricated (EHL) contacts. In this contribution, we demonstrate that machine learning (ML) and artificial intelligence (AI) approaches (support vector machines, Gaussian process regressions, and artificial neural networks) can predict relevant film parameters more efficiently and with higher accuracy and flexibility compared to sophisticated EHL simulations and analytically solvable proximity equations, respectively. For this purpose, we use data from EHL simulations based upon the full-system finite element (FE) solution and a Latin hypercube sampling. We verify that the original input data are required to train ML approaches to achieve coefficients of determination above 0.99. It is revealed that the architecture of artificial neural networks (neurons per layer and number of hidden layers) and activation functions influence the prediction accuracy. The impact of the number of training data is exemplified, and recommendations for a minimum database size are given. We ultimately demonstrate that artificial neural networks can predict the locally-resolved film thickness values over the contact domain 25-times faster than FE-based EHL simulations (R² values above 0.999). We assume that this will boost the use of ML approaches to predict EHL parameters and traction losses in multibody system dynamics simulations.


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Predicting EHL film thickness parameters by machine learning approaches

Show Author's information Max MARIAN1( ), Jonas MURSAK2, Marcel BARTZ2, Francisco J. PROFITO3, Andreas ROSENKRANZ4, Sandro WARTZACK2
Department of Mechanical and Metallurgical Engineering, School of Engineering, Pontificia Universidad Católica de Chile, Santiago 6904411, Chile
Engineering Design, Friedrich-Alexander-University Erlangen-Nuremberg (FAU), Erlangen 91058, Germany
Department of Mechanical Engineering, Polytechnic School of the University of São Paulo, São Paulo 05508-030, Brazil
Department of Chemical Engineering, Biotechnology and Materials (DIQBM), FCFM, Universidad de Chile, Santiago 8370456, Chile

Abstract

Non-dimensional similarity groups and analytically solvable proximity equations can be used to estimate integral fluid film parameters of elastohydrodynamically lubricated (EHL) contacts. In this contribution, we demonstrate that machine learning (ML) and artificial intelligence (AI) approaches (support vector machines, Gaussian process regressions, and artificial neural networks) can predict relevant film parameters more efficiently and with higher accuracy and flexibility compared to sophisticated EHL simulations and analytically solvable proximity equations, respectively. For this purpose, we use data from EHL simulations based upon the full-system finite element (FE) solution and a Latin hypercube sampling. We verify that the original input data are required to train ML approaches to achieve coefficients of determination above 0.99. It is revealed that the architecture of artificial neural networks (neurons per layer and number of hidden layers) and activation functions influence the prediction accuracy. The impact of the number of training data is exemplified, and recommendations for a minimum database size are given. We ultimately demonstrate that artificial neural networks can predict the locally-resolved film thickness values over the contact domain 25-times faster than FE-based EHL simulations (R² values above 0.999). We assume that this will boost the use of ML approaches to predict EHL parameters and traction losses in multibody system dynamics simulations.

Keywords: machine learning, artificial neural network, support vector machine, film thickness, elastohydrodynamic lubrication, Gaussian process regression

References(93)

[1]
Holmberg K, Erdemir A. Influence of tribology on global energy consumption, costs and emissions. Friction 5(3): 263–284 (2017)
DOI Google Scholar
[2]
Holmberg K, Andersson P, Erdemir A. Global energy consumption due to friction in passenger cars. Tribol Int 47: 221–234 (2012)
DOI Google Scholar
[3]
Holmberg K, Andersson P, Nylund N O, Mäkelä K, Erdemir A. Global energy consumption due to friction in trucks and buses. Tribol Int 78: 94–114 (2014)
DOI Google Scholar
[4]
Marian M, Bartz M, Wartzack S, Rosenkranz A. Non-dimensional groups, film thickness equations and correction factors for elastohydrodynamic lubrication: A review. Lubricants 8(10): 95 (2020)
DOI Google Scholar
[5]
Dowson D, Higginson G R. The effect of material properties on the lubrication of elastic rollers. J Mech Eng Sci 2(3): 188–194 (1960)
DOI Google Scholar
[6]
Dowson D, Higginson G R, Whitaker A V. Elasto-hydrodynamic lubrication: A survey of isothermal solutions. J Mech Eng Sci 4(2): 121–126 (1962)
DOI Google Scholar
[7]
Moes H. Discussion on Paper D1 by D. Dowson. Proc Instn Mech Engrs 180: 244–245 (1966)
Google Scholar
[8]
Moes H. Communications. In Proc. of the Symposium on Elastohydrodynamic Lubrication, 1965: 244–245.
Google Scholar
[9]
Johnson K L. Regimes of elastohydrodynamic lubrication. J Mech Eng Sci 12(1): 9–16 (1970)
DOI Google Scholar
[10]
Habchi W, Bair S, Vergne P. On friction regimes in quantitative elastohydrodynamics. Tribol Int 58: 107–117 (2013)
DOI Google Scholar
[11]
van Leeuwen H. The determination of the pressure–viscosity coefficient of a lubricant through an accurate film thickness formula and accurate film thickness measurements. Proc Inst Mech Eng Part J J Eng Tribol 223(8): 1143–1163 (2009)
DOI Google Scholar
[12]
Dowson D. Elastohydrodynamics. Proc Inst Mech Eng 182: 151–157 (1968)
DOI Google Scholar
[13]
Jacobson B O, Hamrock B J. Non-Newtonian fluid model incorporated into elastohydrodynamic lubrication of rectangular contacts. J Tribol 106(2): 275–282 (1984)
DOI Google Scholar
[14]
Dowson D, Toyoda S. A central film thickness formula for elastohydrodynamic line contacts. In Proceedings of the 5th Leeds-Lyon Symposium on Tribology, 1978: 60–65.
[15]
Moes H. Lubrication and Beyond–University of Twente Lecture Notes code 115531. Enschede, Netherlands: University of Twente, 2000.
[16]
Hamrock BJ, Dowson D. Isothermal elastohydrodynamic lubrication of point contacts. Part III—Fully flooded results. J Lubr Technol 99(2): 264–275 (1977)
DOI Google Scholar
[17]
Chittenden R J, Dowson D, Dunn J F, Taylor C M. A theoretical analysis of the isothermal elastohydrodynamic lubrication of concentrated contacts. I. Direction of lubricant entrainment coincident with the major axis of the Hertzian contact ellipse. Proc R Soc Lond A 397(1813): 245–269 (1985)
DOI Google Scholar
[18]
Evans H P, Snidle R W. The isothermal elastohydrodynamic lubrication of spheres. J Lubr Technol 103(4): 547–557 (1981)
DOI Google Scholar
[19]
Nijenbanning G, Venner C H, Moes H. Film thickness in elastohydrodynamically lubricated elliptic contacts. Wear 176(2): 217–229 (1994)
DOI Google Scholar
[20]
Sperka P, Krupka I, Hartl M. Analytical formula for the ratio of central to minimum film thickness in a circular EHL contact. Lubricants 6(3): 80 (2018)
DOI Google Scholar
[21]
Wolf M, Solovyev S, Arshia F. Film thickness in elastohydrodynamically lubricated slender elliptic contacts: Part I—Numerical studies of central film thickness. Proc Inst Mech Eng Part J J Eng Tribol 236(6): 1043–1055 (2022)
DOI Google Scholar
[22]
Moes H. Optimum similarity analysis with applications to elastohydrodynamic lubrication. Wear 159(1): 57–66 (1992)
DOI Google Scholar
[23]
Greenwood J A, Kauzlarich J J. Inlet shear heating in elastohydrodynamic lubrication. J Lubr Technol 95(4): 417–423 (1973)
DOI Google Scholar
[24]
Murch L E, Wilson W R D. A thermal elastohydrodynamic inlet zone analysis. J Lubr Technol 97(2): 212–216 (1975)
DOI Google Scholar
[25]
Jackson A. A simple method for determining thermal EHL correction factors for rolling element bearings and gears. S L E Trans 24(2): 159–163 (1981)
DOI Google Scholar
[26]
Wilson W R D, Sheu S. Effect of inlet shear heating due to sliding on elastohydrodynamic film thickness. J Lubr Technol 105(2): 187–188 (1983)
DOI Google Scholar
[27]
Pandey R K, Ghosh M K. Thermal effects on film thickness and traction in rolling/sliding EHL line contacts—An accurate inlet zone analysis. Wear 192(1–2): 118–127 (1996)
DOI Google Scholar
[28]
Hamrock B J, Dowson D. Isothermal elastohydrodynamic lubrication of point contacts: Part IV—starvation results. J Lubr Technol 99(1): 15–23 (1977)
DOI Google Scholar
[29]
Wedeven L D, Evans D, Cameron A. Optical analysis of ball bearing starvation. J Lubr Technol 93(3): 349–361 (1971)
DOI Google Scholar
[30]
Wiśniewski M. Einfluß eines begrenzten Ölangebotes auf die elastohydrodynamische Schmierung von Zahnrädern. Tribologie und Schmierungstechnik 30: 270–277 (1983)
Google Scholar
[31]
Habchi W, Bair S. Quantitative compressibility effects in thermal elastohydrodynamic circular contacts. J Tribol 135(1): 011502 (2013)
DOI Google Scholar
[32]
Venner C H, Bos J. Effects of lubricant compressibility on the film thickness in EHL line and circular contacts. Wear 173(1–2): 151–165 (1994)
DOI Google Scholar
[33]
Bair S. Shear thinning correction for rolling/sliding elastohydrodynamic film thickness. Proc Inst Mech Eng Part J J Eng Tribol 219(1): 69–74 (2005)
DOI Google Scholar
[34]
Jang J Y, Khonsari M M, Bair S. Correction factor formula to predict the central and minimum film thickness for shear-thinning fluids in EHL. J Tribol 130(2): 024501 (2008)
DOI Google Scholar
[35]
Habchi W, Bair S, Qureshi F, Covitch M. A film thickness correction formula for double-Newtonian shear-thinning in rolling EHL circular contacts. Tribol Lett 50(1): 59–66 (2013)
DOI Google Scholar
[36]
Kumar P, Jain S C, Ray S. Study of surface roughness effects in elastohydrodynamic lubrication of rolling line contacts using a deterministic model. Tribol Int 34(10): 713–722 (2001)
DOI Google Scholar
[37]
Masjedi M, Khonsari M M. On the effect of surface roughness in point-contact EHL: Formulas for film thickness and asperity load. Tribol Int 82: 228–244 (2015)
DOI Google Scholar
[38]
Masjedi M, Khonsari M M. Film thickness and asperity load formulas for line-contact elastohydrodynamic lubrication with provision for surface roughness. J Tribol 134(1): 11503 (2012)
DOI Google Scholar
[39]
Rosenkranz A, Marian M, Profito F J, Aragon N, Shah R. The use of artificial intelligence in tribology—A perspective. Lubricants 9(1): 2 (2020)
DOI Google Scholar
[40]
Marian M, Tremmel S. Current trends and applications of machine learning in tribology—A review. Lubricants 9(9): 86 (2021)
DOI Google Scholar
[41]
Bell J. Machine Learning: Hands-On for Developers and Technical Professionals. Hoboken: Wiley, 2014.
DOI
[42]
Müller AC, Guido S. Introduction to machine learning with Python: A guide for data scientist. Beijing: O'Reilly, 2016.
[43]
Schölkopf B, Smola A J. Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. Cambridge, Mass.: MIT Press, 2002.
[44]
Hasan M S, Kordijazi A, Rohatgi P K, Nosonovsky M. Triboinformatic modeling of dry friction and wear of aluminum base alloys using machine learning algorithms. Tribol Int 161: 107065 (2021)
DOI Google Scholar
[45]
Hasan M S, Kordijazi A, Rohatgi P K, Nosonovsky M. Triboinformatics approach for friction and wear prediction of Al-graphite composites using machine learning methods. J Tribol 144(1): 011701 (2022)
DOI Google Scholar
[46]
Yin Y, Liu X F, Huang W F, Liu Y, Hu S T. Gas face seal status estimation based on acoustic emission monitoring and support vector machine regression. Adv Mech Eng 12(5): 168781402092132 (2020)
DOI Google Scholar
[47]
Timur M, Ayding F. Anticipating the friction coefficient of friction materials used in automobiles by means of machine learning without using a test instrument. Turk J Elec Eng & Comp Sci: 1440–1454 (2013)
DOI Google Scholar
[48]
Das B, Pal S, Bag S. Torque based defect detection and weld quality modelling in friction stir welding process. J Manuf Process 27: 8–17 (2017)
DOI Google Scholar
[49]
Egala R, Jagadeesh G V, Setti S G. Experimental investigation and prediction of tribological behavior of unidirectional short castor oil fiber reinforced epoxy composites. Friction 9(2): 250–272 (2021)
DOI Google Scholar
[50]
Vinoth A, Datta S. Design of the ultrahigh molecular weight polyethylene composites with multiple nanoparticles: An artificial intelligence approach. J Compos Mater 54(2): 179–192 (2020)
DOI Google Scholar
[51]
Gangwar S, Pathak V K. Dry sliding wear characteristics evaluation and prediction of vacuum casted marble dust (MD) reinforced ZA-27 alloy composites using hybrid improved bat algorithm and ANN. Mater Today Commun 25: 101615 (2020)
DOI Google Scholar
[52]
Subrahmanyam M, Sujatha C. Using neural networks for the diagnosis of localized defects in ball bearings. Tribol Int 30(10): 739–752 (1997)
DOI Google Scholar
[53]
Canbulut F, Yildirim Ş, Sinanoğlu C. Design of an artificial neural network for analysis of frictional power loss of hydrostatic slipper bearings. Tribol Lett 17(4): 887–899 (2004)
DOI Google Scholar
[54]
Senatore A, D'Agostino V, Giuda R D, Petrone V. Experimental investigation and neural network prediction of brakes and clutch material frictional behaviour considering the sliding acceleration influence. Tribol Int 44(10): 1199–1207 (2011)
DOI Google Scholar
[55]
Aleksendrić D, Barton D C. Neural network prediction of disc brake performance. Tribol Int 42(7): 1074–1080 (2009)
DOI Google Scholar
[56]
König F, Sous C, Chaib A O, Jacobs G. Machine learning based anomaly detection and classification of acoustic emission events for wear monitoring in sliding bearing systems. Tribol Int 155: 106811 (2021)
DOI Google Scholar
[57]
Dewan M W, Huggett D J, Liao T W, Wahab M A, Okeil A M. Prediction of tensile strength of friction stir weld joints with adaptive neuro-fuzzy inference system (ANFIS) and neural network. Mater Des 92: 288–299 (2016)
DOI Google Scholar
[58]
Sahraoui T, Guessasma S, Fenineche N E, Montavon G, Coddet C. Friction and wear behaviour prediction of HVOF coatings and electroplated hard chromium using neural computation. Mater Lett 58(5): 654–660 (2004)
DOI Google Scholar
[59]
Cetinel H. The artificial neural network based prediction of friction properties of Al2O3–TiO2 coatings. Ind Lubr Tribol 64(5): 288–293 (2012)
DOI Google Scholar
[60]
Kalliorinne K, Larsson R, Pérez-Ràfols F, Liwicki M, Almqvist A. Artificial neural network architecture for prediction of contact mechanical response. Front Mech Eng 6: 579825 (2021)
DOI Google Scholar
[61]
Humelnicu C, Ciortan S, Amortila V. Artificial neural network-based analysis of the tribological behavior of vegetable oil–diesel fuel mixtures. Lubricants 7(4): 32 (2019)
DOI Google Scholar
[62]
Bhaumik S, Pathak S D, Dey S, Datta S. Artificial intelligence based design of multiple friction modifiers dispersed castor oil and evaluating its tribological properties. Tribol Int 140: 105813 (2019)
DOI Google Scholar
[63]
Krogh A. What are artificial neural networks? Nat Biotechnol 26(2): 195–197 (2008)
DOI Google Scholar
[64]
Almqvist A. Fundamentals of physics-informed neural networks applied to solve the Reynolds boundary value problem. Lubricants 9(8): 82 (2021)
DOI Google Scholar
[65]
Kügler P, Marian M, Schleich B, Tremmel S, Wartzack S. tribAIn—Towards an explicit specification of shared tribological understanding. Appl Sci 10(13): 4421 (2020)
DOI Google Scholar
[66]
de la Guerra Ochoa E, Echávarri Otero J, Chacón Tanarro E, Lafont Morgado P, Lantada A D, Munoz-Guijosa J M, Sanz J M. Optimising lubricated friction coefficient by surface texturing. Proc Inst Mech Eng C J Mech Eng Sci 227(11): 2610–2619 (2013)
DOI Google Scholar
[67]
Marian M, Grützmacher P, Rosenkranz A, Tremmel S, Mücklich F, Wartzack S. Designing surface textures for EHL point-contacts—Transient 3D simulations, meta-modeling and experimental validation. Tribol Int 137: 152–163 (2019)
DOI Google Scholar
[68]
Wirsching S, Marian M, Bartz M, Stahl T, Wartzack S. Geometrical optimization of the EHL roller face/rib contact for energy efficiency in tapered roller bearings. Lubricants 9(7): 67 (2021)
DOI Google Scholar
[69]
Siebertz K, van Bebber D, Hochkirchen T. Statistische Versuchsplanung: Design of Experiments (DoE). Berlin: Springer, 2010.
DOI
[70]
Gohar R. Elastohydrodynamics. Chichester: Halsted Press, 1988.
[71]
Johnson M E, Moore L M, Ylvisaker D. Minimax and maximin distance designs. J Stat Plan Inference 26(2): 131–148 (1990)
DOI Google Scholar
[72]
Reynolds O. On the theory of lubrication and its application to Mr. Beauchamp tower's experiments, including an experimental determination of the viscosity of olive oil. Phil Trans R Soc 177: 157–234 (1886)
DOI Google Scholar
[73]
Dowson D, Higginson GR. Elasto-Hydrodynamic Lubrication: The Fundamentals of Roller and Gear Lubrication. Oxford: Pergamon Press, 1966.
[74]
Roelands C. Correlational aspects of the viscosity-temperature-pressure relationship of lubricating oils. Ph.D. Thesis. Delft University of Technology, 1966.
[75]
Marian M, Weschta M, Tremmel S, Wartzack S. Simulation of microtextured surfaces in starved EHL contacts using commercial FE software. Matls Perf Charact 6(2): MPC20160010 (2017)
DOI Google Scholar
[76]
Habchi W, Eyheramendy D, Vergne P, Morales-Espejel G. A full-system approach of the elastohydrodynamic line/point contact problem. J Tribol 130(2): 021501/1-9 (2008)
DOI Google Scholar
[77]
Habchi W. Finite Element Modelling of Elastohydrodynamic Lubrication Problems. Chichester, UK: John Wiley & Sons Ltd, 2018
DOI
[78]
Hughes T J R, Franca L P, Hulbert G M. A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations. Comput Methods Appl Mech Eng 73(2): 173–189 (1989)
DOI Google Scholar
[79]
Zienkiewicz OC, Taylor RL, Nithiarasu P. The Finite Element Method for Fluid Dynamics. 7th edn. Oxford: Elsevier Butterworth-Heinemann, 2014.
DOI
[80]
Lohner T, Ziegltrum A, Stemplinger J P, Stahl K. Engineering software solution for thermal elastohydrodynamic lubrication using multiphysics software. Adv Tribol 2016: 6507203 (2016)
DOI Google Scholar
[81]
Tan X C, Goodyer C E, Jimack P K, Taylor R I, Walkley M A. Computational approaches for modelling elastohydrodynamic lubrication using multiphysics software. Proc Inst Mech Eng Part J J Eng Tribol 226(6): 463–480 (2012)
DOI Google Scholar
[82]
Mathworks Matlab. Understanding support vector machine regression: Mathematical formulation of SVM regression. Available at https://de.mathworks.com/help/stats/understanding-support-vector-machine-regression.html,October08, 2021
[83]
Chicco D, Warrens M J, Jurman G. The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation. PeerJ Comput Sci 7: e623 (2021)
DOI Google Scholar
[84]
Glantz SA, Slinker BK. Primer of Applied Regression and Analysis of Variance. New York, NY: McGraw-Hill, 1990.
[85]
Montgomery D C, Runger G C. Applied Statistics and Probability for Engineers 6th Edition. Wiley, 2014.
[86]
Vapnik V N. The Nature of Statistical Learning Theory. New York: Springer, 2000.
DOI
[87]
Huang T-M, Kecman V, Kopriva I. Kernel Based Algorithms for Mining Huge Data Sets: Supervised, Semi-supervised, and Unsupervised Learning. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2006.
[88]
Mathworks Matlab. Gaussian process regression models. Available at https://de.mathworks.com/help/stats/gaussian-process-regression-models.html,October08, 2021
[89]
Levenberg K. A method for the solution of certain non-linear problems in least squares. Quart Appl Math 2(2): 164–168 (1944)
DOI Google Scholar
[90]
Marquardt D W. An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math 11(2): 431–441 (1963)
DOI Google Scholar
[91]
Wilamowski B M, Yu H. Improved computation for levenberg–marquardt training. IEEE Trans Neural Netw 21(6): 930–937 (2010)
DOI Google Scholar
[92]
Lämmel U, Cleve J. Künstliche Intelligenz: Wissensverarbeitung - neuronale Netze. 5th edn. Munich, Germany: Hanser, 2020.
DOI
[93]
Bhattacharyya S. Deep Learning. Research and Applications. 1st edn. Boston, United States: ‎De Gruyter, 2020.
DOI
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Publication history

Received: 24 November 2021
Revised: 09 March 2022
Accepted: 21 April 2022
Published: 12 June 2022
Issue date: June 2023

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© The author(s) 2022.

Acknowledgements

M. Marian greatly acknowledges the support from Pontificia Universidad Católica de Chile. A. Rosenkranz gratefully acknowledges the financial support given by ANID (Chile) in the framework of the Fondecyt projects (Nos. 11180121 and EQM190057). Additionally, A. Rosenkranz acknowledges the financial support given by the VID of the University of Chile within the project U-Moderniza (No. UM-04/19).

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