Skip to main content
SpringerLink
Log in

On the Reynolds Equation and the Load Problem in Lubrication: Literature Review and Mathematical Modelling

  • Chapter
  • First Online:
Mathematics Applied to Engineering, Modelling, and Social Issues

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 200))

Abstract

In this chapter, we provide a literature review concerning the theory of hydrodynamic lubrication, especially applied to journal bearings. The device consists of an external cylinder surrounding a rotating shaft, both separated by a lubricant to prevent contact. In particular, we derive the fluid film thickness model for journal bearings, considering both the parallel and the misaligned case. The hydrodynamic Reynolds equation with cavitation phenomenon, through both Reynolds and Elrod-Adams models are fully derived in this chapter. Subsequently, we pose two suitable variational formulations for the hydrodynamic problem considering both cavitation models. In addition, we present the admissible range of misalignment angle projections for prescribed values of the shaft eccentricity and angular coordinate. Finally, we properly state the problem of a loaded misaligned journal bearing for stationary regime, considering the balance of force and torque components involved.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    It represents the lubricant concentration.

  2. 2.

    “D” stands for diversity.

References

  1. Abass, B.A., Sahib, M.M.: Effect of bearing compliance on thermo-hydrodynamic lubrication of high speed misaligned journal bearing lubricated with bubbly oil. Ind. Eng. Lett 3, 48–60 (2013)

    Google Scholar 

  2. Álvarez, S.J.: Problemas de frontera libre en teoría de lubrificación. Ph.D. thesis. Universidad Complutense de Madrid (1986)

    Google Scholar 

  3. Asanabe, S., Akakoski, M., Asai, R.: Theoretical and experimental investigation on misaligned journal bearing performance. Ind. Lubr. Tribol. 23(6), 208 (1971)

    Google Scholar 

  4. Bayada, G., Chambat, M.: Sur quelques modélizations de la zone de cavitation en lubrification hydrodynamique. J. Theor. Appl. Mech. 5(5), 703–729 (1986)

    MATH  Google Scholar 

  5. Bayada, G., Chambat, M.: The transition between the Stokes equation and the Reynolds equation: a mathematical proof. Appl. Math. Opt. 14(1), 73–93 (1986)

    MathSciNet  MATH  Google Scholar 

  6. Bayada, G., Chambat, M., Vázquez, C.: Characteristics method for the formulation and computation of a free boundary cavitation problem. J. Comput. Appl. Math. 98(2), 191–212 (1998)

    MathSciNet  MATH  Google Scholar 

  7. Bayada, G., Martin, S., Vázquez, C.: An average flow model of the Reynolds roughness including a mass-flow preserving cavitation model. J. Tribol-T. ASME. 127(4), 793–802 (2005)

    Google Scholar 

  8. Bayada, G., Martin, S., Vázquez, C.: Homogenization of a nonlocal elastohydrodynamic lubrication problem: a new free boundary model. Math. Mod. Meth. Appl. S. 15(12), 1923–1956 (2005)

    MathSciNet  MATH  Google Scholar 

  9. Bayada, G., Martin, S., Vázquez, C.: Homogneisation du modèle d’Elrod-Adams hydrodynamique. Asymptotic. Anal. 44, 75–110 (2005)

    MathSciNet  Google Scholar 

  10. Bayada, G., Martin, S., Vázquez, C.: Two-scale homogenization of a hydrodynamic Elrod-Adams model. Asymptotic. Anal. (2005)

    Google Scholar 

  11. Bayada, G., Martin, S., Vázquez, C.: Micro-roughness effects in (elasto) hydrodynamic lubrication including a mass-flow preserving cavitation model. Tribol. Int. 39(12), 1707–1718 (2006)

    Google Scholar 

  12. Bayada, G., Vázquez, C.: A survey on mathematical aspects of lubrication problems. Boletín SeMA 39, 37–74 (2007)

    MATH  Google Scholar 

  13. Bermúdez, A., Durany, J.: Numerical solution of cavitation problems in lubrication. Comput. Methods Appl. Mech. Eng. 75, 455–466 (1989)

    MathSciNet  MATH  Google Scholar 

  14. Bermúdez, A., Moreno, C.: Duality methods for solving variational inequalities. Comp. Math. Appl. 7, 43–58 (1981)

    MathSciNet  MATH  Google Scholar 

  15. Blum, C., Vallès, M.Y., Blesa, M.J.: An ant colony optimization algorithm for DNA sequencing by hybridization. Comput. Oper. Res. 35(11), 3620–3635 (2008)

    MATH  Google Scholar 

  16. Boedo, S., Booker, J.F.: Classical bearing misalignment and edge loading: a numerical study of limiting cases. J. Tribol-T. ASME. 126(3), 535–541 (2004)

    Google Scholar 

  17. Boucherit, H., Lahmar, M., Bou-Said, B.: Misalignment effects on steady-state and dynamic behaviour of compliant journal bearings lubricated with couple stress fluids. Lubr. Sci. 20(3), 241–268 (2008)

    Google Scholar 

  18. Bouyer, J., Fillon, M.: An experimental analysis of misalignment effects on hydrodynamic plain journal bearing performances. J. Tribol. 124(2), 313–319 (2002)

    Google Scholar 

  19. Bouyer, J., Fillon, M.: Improvement of the THD performance of a misaligned plain journal bearing. J. Tribol. 125(2), 334–342 (2003)

    Google Scholar 

  20. Brito, F.P.: Thermohydrodynamic performance of twin groove journal bearings considering realistic lubricant supply conditions: a theoretical and experimental study. Ph.D. thesis. Universidade do Minho (2009)

    Google Scholar 

  21. Calvo, N., Durany, J., Vázquez, C.: Comparación de algoritmos numéricos en problemas de lubricación hidrodinámica con cavitación en dimensión uno. Rev. Int. Metod. Numer. 13(2), 185–209 (1997)

    Google Scholar 

  22. Capriz, G., Cimatti, G.: Free boundary problems in the theory of hydrodynamic lubrication: a survey. In: Fasano, A., Primicerio, M. (eds.) Free Boundary Problems: Theory and Applications, vol. 2. Research Notes in Mathematics 79. Pitman, pp. 613–635 (1983)

    Google Scholar 

  23. Chelouah, R., Siarry, P.: Enhanced continuous tabu search: an algorithm for optimizing multiminima functions. In: Meta-Heuristics. Advances and Trends in Local Search Paradigms for Optimization (Chap. 4), pp. 49–61. Springer, Berlin (1999)

    Google Scholar 

  24. Chelouah, Rachid, Siarry, Patrick: A continuous genetic algorithm designed for the global optimization of multimodal functions. J. Heuristics 6(2), 191–213 (2000)

    MATH  Google Scholar 

  25. Christopherson, D.G.: A new mathematical method for the solution of film lubrication problems. Inst. Mech. Engrs. J. Proc. 146, 126–135 (1941)

    MathSciNet  MATH  Google Scholar 

  26. Cimatti, G.: On certain nonlinear problems arising in the theory of lubrication. Appl. Math. Opt. 11(1), 227–245 (1984)

    MathSciNet  MATH  Google Scholar 

  27. Cimatti, G.: Existence and uniqueness for nonlinear Reynolds equations. Int. J. Eng. Sci. 24(5), 827–834 (1986)

    MathSciNet  MATH  Google Scholar 

  28. Ciuperca, I.S., Hafidi, I., Jai, M.: Singular perturbation problem for the incompressible Reynolds equation. Electr. J. Differ. Equ. 2006(83), 1–19 (2006)

    MathSciNet  MATH  Google Scholar 

  29. Ciuperca, I.S., Jai, M., Tello, J.I.: On the existence of solutions of equilibria in lubricated journal bearings. SIAM J. Math. Anal. 40(6), 2316–2327 (2009)

    MathSciNet  MATH  Google Scholar 

  30. Ciuperca, I.S., Jai, M., Tello, J.I.: Equilibrium analysis for a mass-conserving model in presence of cavitation. Nonlinear Anal.: R. World Appl. 35, 250–264 (2017)

    MathSciNet  MATH  Google Scholar 

  31. Ciuperca, I.S., Tello, J.I.: Lack of contact in a lubricated system. Q. Appl. Math. 69(2), 357–378 (2011a)

    MathSciNet  MATH  Google Scholar 

  32. Ciuperca, I.S., Tello, J.I.: On a variational inequality on elasto-hydrodynamic lubrication. J. Math. Anal. Appl. 383(2), 597–607 (2011b)

    MathSciNet  MATH  Google Scholar 

  33. Cryer, C.W.: The method of Christopherson for solving free boundary problems for infinite journal bearings by means of finite differences. Math. Comput. 25(115), 435–443 (1971)

    MathSciNet  MATH  Google Scholar 

  34. Cuvelier, C.: A free boundary problem in hydrodynamic lubrication including surface tension. In: Cabannes, H., Holt, M., Rusanov, V. (eds.) Sixth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol. 90, pp. 143–148. Springer, Berlin (1979)

    Google Scholar 

  35. Das, S., Guha, S.K., Chattopadhyay, A.K.: On the steady-state performance of misaligned hydrodynamic journal bearings lubricated with micropolar fluids. Tribol. Int. 35(4), 201–210 (2002)

    Google Scholar 

  36. Díaz, J.I., Tello, J.I.: A note on some inverse problems arising in lubrication theory. Differ. Integral. Equ. 17, 583–592 (2004)

    MathSciNet  MATH  Google Scholar 

  37. Díaz, M., Lombera, H., et al.: An approach for assembly sequence planning based on MAX-MIN Ant System. IEEE Latin Am. Trans. 13(4), 907–912 (2015)

    Google Scholar 

  38. Dorigo, M.: Optimization, learning and natural algorithms. Italian. Ph.D. thesis. Dipartimento di Elettronica, Politecnico di Milano, Milan, Italy (1992)

    Google Scholar 

  39. Dorigo, M., Maniezzo, V., Colorni, A.: Ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 26(1), 29–41 (1996)

    Google Scholar 

  40. Dowson, D.: A generalized Reynolds equation for fluid film lubrication. Int. J. Mech. Sci. 4, 159–170 (1962)

    Google Scholar 

  41. Dubois, G.B., Mabie, H.H., Ocvirk, F.W.: Experimental investigation of oil film pressure distribution for misaligned plain bearings. Technical Report. National Advisory Committee for Aeronautics, KittyHawk, NC, USA (1951)

    Google Scholar 

  42. Durany, J., García, G., Vázquez, C.: Numerical simulation of a lubricated hertzian contact problem under imposed load. Finite. Elem. Anal. Des. 38(7), 645–658 (2002)

    MathSciNet  MATH  Google Scholar 

  43. Durany, J., Pereira, J., Varas, F.: Numerical solution to steady and transient problems in thermohydrodynamic lubrication using a combination of finite element, finite volume and boundary element methods. Finite. Elem. Anal. Des. 44(11), 686–695 (2008)

    MathSciNet  Google Scholar 

  44. Durany, J., Pereira, J., Varas, F.: Dynamical stability of journal-bearing devices through numerical simulation of thermohydrodynamic models. Tribol. Int. 43, 1703–1718 (2010)

    Google Scholar 

  45. Durany, J., Vázquez, C.: Numerical approach of lubrication problems in journal bearing devices with axial supply. Numer. Methods Eng. 92, 839–844 (1992)

    Google Scholar 

  46. El Alaoui Talibi, M., Bayada, G.: Une méthode du type caractéristique pour la résolution d’un problème de lubrification hydrodynamique en régime transitoire. ESAIM-Math. Model. Num. 25(4), 395–423 (1991)

    MATH  Google Scholar 

  47. Elrod, H.G., Adams, M.L.: A computer program for cavitation and starvation problems. Cavitation and related phenomena in lubrication: proceedings of the 1st Leeds-Lyon Symposium on Tribology. Mech. Eng. Publ. pp. 37–42 (1975)

    Google Scholar 

  48. Frêne, J., Nicolas, D., et al.: Hydrodynamic Lubrication: Bearings and Thrust Bearings, vol. 33. Elsevier, Amsterdam (1997)

    MATH  Google Scholar 

  49. Gambardella, L.M., Taillard, É., Agazzi, G.: MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization (Chap. 5), pp. 63–76. McGraw-Hill, London (1999)

    Google Scholar 

  50. Garcia-Najera, A., Bullinaria, J.A.: Extending ACOR to solve multi-objective problems. In: Proceedings of the UK Workshop on Computational Intelligence, London (2007)

    Google Scholar 

  51. Gómez-Mancilla, J., Nosov, V.: Short journal bearing with misaligned axes. In: Proceedings 1st International Symposium on Control of Rotating Machinery (2001)

    Google Scholar 

  52. Gómez-Mancilla, J., Nosov, V.: Perturbed pressure field solution for misaligned short journal bearings. In: Proceedings 9th International Symposium on Transport Phenomena and Rotating Machinery. ISROMAC-9, Hawaii, EU (2002)

    Google Scholar 

  53. Guha, S.K.: Analysis of steady-state characteristics of misaligned hydrodynamic journal bearings with isotropic roughness effect. Tribol. Int. 33(1), 1–12 (2000)

    MathSciNet  Google Scholar 

  54. He, Z., Zhang, J., et al.: Misalignment analysis of journal bearing influenced by asymmetric deflection, based on a simple stepped shaft model. J. Zhejiang Univ. Sci. A 13(9), 647–664 (2012)

    Google Scholar 

  55. Jang, J.Y., Khonsari, M.M.: Design of bearings on the basis of thermohydrodynamic analysis. In: Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, vol. 218, No. 5, pp. 355–363. Sage, Beverley Hills (2004)

    Google Scholar 

  56. Jang, J.Y., Khonsari, M.M.: On the characteristics of misaligned journal bearings. Lubricants 3(1), 27–53 (2015)

    Google Scholar 

  57. Jang, J.Y., Khonsari, M.M., Bair, S.: On the elastohydrodynamic analysis of shear-thinning fluids. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol. 463, No. 2088, pp. 3271–3290. The Royal Society (2007)

    Google Scholar 

  58. Khonsari, M.M., Booser, E.R.: Applied Tribology: Bearing Design and Lubrication, 2nd edn. Wiley, New York (2008). ISBN: 978-0-470-05711-7

    Google Scholar 

  59. Kumar, P., Khonsari, M.M.: Traction in EHL line contacts using free-volume pressureviscosity relationship with thermal and shear-thinning effects. J. Tribol. 131(1), 011503 (2009)

    Google Scholar 

  60. Leguizamón, G., Coello, C.A.: A study of the scalability of ACOR for continuous optimization problems. Technical report, The Evolutionary Computation Group at CINVESTAV-IPN (2010)

    Google Scholar 

  61. Leguizamón, G., Coello, C.A.: An alternative ACOR algorithm for continuous optimization problems. In: Swarm Intelligence: 7th International Conference, ANTS 2010, vol. 6234, pp. 48–59. Lecture Notes in Computer Science, Brussels, Belgium. Springer, Berlin (2010)

    Google Scholar 

  62. Liao, T.: Improved ant colony optimization algorithms for continuous and mixed discrete continuous optimization problems. MA thesis. Université Libre de Bruxelles, Belgium (2011)

    Google Scholar 

  63. Liao, T., Montes de Oca, M.A., et al.: An incremental ant colony algorithm with local search for continuous optimization. In: Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, pp. 125–132. ACM, New York (2011)

    Google Scholar 

  64. Liao, T., Stützle, T., et al.: A unified ant colony optimization algorithm for continuous optimization. Euro. J. Oper. Res. 234(3), 597–609 (2014)

    MathSciNet  MATH  Google Scholar 

  65. Liñan, A.: Curso de Mecánica de Fluidos. Technical Report, Universidad Politécnica de Madrid (1999)

    Google Scholar 

  66. Liu, G.: Dual variational principles for the free-boundary problem of cavitated bearing lubrication. In: Gao, D.Y. (ed.) Complementarity, Duality and Symmetry in Nonlinear Mechanics: Proceedings of the IUTAM Symposium, vol. 6, pp. 179–189. Springer Science & Business Media (2004)

    Google Scholar 

  67. Lombera, H., Tello, J.I.: A numerical approach to solve an inverse problem in lubrication theory. RACSAM. Rev. R. Acad. A. 108(2), 617–631 (2014)

    MathSciNet  MATH  Google Scholar 

  68. Martin, S.: Influence of multiscale roughness patterns in cavitated flows: applications to journal bearings. Math. Probl. Eng. 2008, 1–26 (2008)

    MathSciNet  MATH  Google Scholar 

  69. Maru, M.M., Tanaka, D.K.: Consideration of stribeck diagram parameters in the investigation on wear and friction behavior in lubricated sliding. J. Braz. Soc. Mech. Sci. Eng. 29(1), 55–62 (2007)

    Google Scholar 

  70. McKee, S.A., McKee, T.R.: Pressure distribution in oil films of journal bearings. ASME 54, 149–165 (1932)

    Google Scholar 

  71. Nikolakopoulos, P.G., Papadopoulos, C.A.: Non-linearities in misaligned journal bearings. Tribol. Int. 27(4), 243–257 (1994)

    Google Scholar 

  72. Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer Science + Business Media, LLC, Berlin (2006)

    MATH  Google Scholar 

  73. Ocvirk, F.W., DuBois, G.B.: Analytical derivation and experimental evaluation of shortbearing approximation for full journal bearings. Technical Report 1157. NACA (1953)

    Google Scholar 

  74. Osman, T.A.: Misalignment effect on the static characteristics of magnetized journal bearing lubricated with ferrofluid. Tribol. Lett. 11(3–4), 195–203 (2001)

    Google Scholar 

  75. Pedraza, G., Díaz, M., Lombera, H.: An approach for assembly sequence planning by genetic algorithms. IEEE Latin Am. Trans. 14(5), 2066–2071 (2016)

    Google Scholar 

  76. Pierre, I., Bouyer, J., Fillon, M.: Thermohydrodynamic study of misaligned plain journal bearings-comparison between experimental data and theoretical results. Appl. Mech. Eng. 7(3), 949–960 (2002)

    Google Scholar 

  77. Pierre, I., de France, E., et al.: Thermohydrodynamic behavior of misaligned plain journal bearings: theoretical and experimental approaches. Tribol. Trans. 47(4), 594–604 (2004)

    Google Scholar 

  78. Piggott, R.J.S.: Bearings and lubrication. Bearing troubles traceable to design can be avoided by engineering study. Mech. Eng. 64, 259 (1942)

    Google Scholar 

  79. Piniganti, L.: A Survey of Tabu search in combinatorial optimization. MA thesis. University of Nevada, Las Vegas (2014)

    Google Scholar 

  80. Pinkus, O., Bupara, S.S.: Analysis of misaligned grooved journal bearings. J. Tribol. 101(4), 503–509 (1979)

    Google Scholar 

  81. Pinkus, O., Sternlicht, B.: Theory of Hydrodynamic Lubrication. McGraw-Hill, New York (1961)

    MATH  Google Scholar 

  82. 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. Roy. Soc. A 117, 157–234 (1886)

    MATH  Google Scholar 

  83. Rodrigues, J.F.: Remarks on the Reynolds problem of elastohydrodynamic lubrication. Eur. J. Appl. Math. 4(01), 83–96 (1993)

    MathSciNet  MATH  Google Scholar 

  84. Rohde, S.M., McAllister, G.T.: A variational formulation for a class of free boundary problems arising in hydrodynamic lubrication. Int. J. Eng. Sci. 13(9–10), 841–850 (1975)

    MATH  Google Scholar 

  85. Sharma, S.C., Jain, S.C., Nagaraju, T.: Combined influence of journal misalignment and surface roughness on the performance of an orifice compensated non-recessed hybrid journal bearing. Tribol. Trans. 45(4), 457–463 (2002)

    Google Scholar 

  86. Siarry, Patrick, Berthiau, Gérard, et al.: Enhanced simulated annealing for globally minimizing functions of many-continuous variables. ACM Trans. Math. Softw. (TOMS) 23(2), 209–228 (1997)

    MathSciNet  MATH  Google Scholar 

  87. Socha, K.: Ant colony optimization for continuous and mixed-variable domains. PhD thesis. Université Libre de Bruxelles, Belgium (2008)

    Google Scholar 

  88. Socha, K., Dorigo, M.: Ant colony optimization for continuous domains. Euro. J. Oper. Res. 185(3), 1155–1173 (2008)

    MathSciNet  MATH  Google Scholar 

  89. Srinivas, M., Patnaik, L.M.: Genetic algorithms: a survey. Computer 27(6), 17–26 (1994)

    Google Scholar 

  90. Stachowiak, G., Batchelor, A.W.: Engineering Tribology. Butterworth-Heinemann, Oxford (2013)

    Google Scholar 

  91. Stieber, W.: Das Schwimmlager. Technical Report Ver. Dtsch. Ing. Berlin (1933)

    Google Scholar 

  92. Stützle, T., Hoos, H.: MAX-MIN Ant System. Futur. Gener. Comput. Syst. 16(8), 889–914 (2000)

    MATH  Google Scholar 

  93. Sun, J., Deng, M., et al.: Thermohydrodynamic lubrication. Analysis of misaligned plain journal bearing with rough surface. J. Tribol. 132(1), 011704 (2010)

    Google Scholar 

  94. Sun, J., Zhu, X., et al.: Effect of surface roughness, viscosity-pressure relationship and elastic deformation on lubrication performance of misaligned journal bearings. Ind. Lubr. Tribol. 66(3), 337–345 (2014)

    Google Scholar 

  95. Swift, H.W.: The stability of lubricating films in journal bearings. J. Inst. Civ. Eng. 233(Part 1), 267–288 (1932)

    Google Scholar 

  96. Thomsen, K., Klit, P.: Improvement of journal bearing operation at heavy misalignment using bearing flexibility and compliant liners. Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol. 226(8), 651–660 (2012)

    Google Scholar 

  97. Vijayaraghavan, D., Keith, T.G.: Effect of cavitation on the performance of a grooved misaligned journal bearing. Wear 134(2), 377–397 (1989)

    Google Scholar 

  98. Vijayaraghavan, D., Keith, T.G.: Analysis of a finite grooved misaligned journal bearing considering cavitation and starvation effects. J. Tribol-T. ASME. 112(1), 60–67 (1990)

    Google Scholar 

  99. Xu, G., Zhou, J., et al.: Research on the static and dynamic characteristics of misaligned journal bearing considering the turbulent and thermohydrodynamic effects. J. Tribol. 137(2), 024504 (2015)

    Google Scholar 

  100. Zhang, Y., Wang, S., Ji, G.: A comprehensive survey on particle swarm optimization algorithm and its applications. Math. Probl. Eng. 2015 (2015)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centro de Informática Industrial, Universidad de las Ciencias Informáticas, 19370, La Habana, Cuba

    Hassán Lombera Rodríguez

  2. Depto Matemática Aplicada a las TIC. ETSIS Sistemas Informáticos, UPM, 28037, Madrid, Spain

    J. Ignacio Tello

Authors
  1. Hassán Lombera Rodríguez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Ignacio Tello
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Ignacio Tello .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University College London, London, UK

    Frank T. Smith

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

  3. Department of Mathematics, Center for Mathematics of Uncertainty, Creighton University, Omaha, NE, USA

    John N. Mordeson

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Lombera Rodríguez, H., Tello, J.I. (2019). On the Reynolds Equation and the Load Problem in Lubrication: Literature Review and Mathematical Modelling. In: Smith, F.T., Dutta, H., Mordeson, J.N. (eds) Mathematics Applied to Engineering, Modelling, and Social Issues. Studies in Systems, Decision and Control, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-030-12232-4_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-12232-4_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12231-7

  • Online ISBN: 978-3-030-12232-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation