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Comparative evaluation on probabilistic performance of journal bearing: a surrogate-based approach

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Abstract

This paper presents a comparative assessment of surrogate models in probabilistic analysis of finite plain journal bearing. Traditional Monte Carlo simulation (MCS) is employed dealing with a large number of data for validating the constructed surrogate model dealing with a limited number of data. In the case of a complex engineering system like journal bearing with finite length wherein no analytical solution exists and the system needs to be solved based on expensive numerical techniques such as finite difference and finite element method due to unavailability of a large number of experimental data. Hence, surrogate models show their computational efficiency complying with the accuracy of the models. Thus, the present study aims to investigate the applicability of five surrogate models such as moving least square, support vector machine, radial basis function, polynomial neural network and multivariate adaptive regression splines in terms of their efficiency and accuracy. A probabilistic analysis approach combining the finite difference method, surrogate models and MCS is presented in this work. The validation and parametric results corresponding to the comparison of the constructed surrogate models are presented. Substantial intuitive new results are conferred in the probabilistic surrogate schemes.

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Abbreviations

\(B_{xx} ,B_{xy} ,B_{yx} ,B_{yy}\) :

Damping coefficients (N s/m)

\(\overline{B}_{xx} ,\overline{B}_{xy} ,\overline{B}_{yx} ,\overline{B}_{yy}\) :

Non-dimensional damping coefficients, \(B_{ij} = \frac{{12\eta R^{3} L}}{{c^{3} }}\overline{B}_{ij}\)

c :

Radial clearance (m)

e :

Eccentricity (m)

\(\varepsilon\) :

Eccentricity ratio, \(\varepsilon = \frac{e}{c}\)

\(K_{xx} ,K_{xy} ,K_{yx} ,K_{yy}\) :

Stiffness coefficients (N/m)

\(\overline{K}_{xx} ,\overline{K}_{xy} ,\overline{K}_{yx} ,\overline{K}_{yy}\) :

Non-dimensional stiffness coefficients, \(K_{ij} = \frac{{6\eta UR^{2} L}}{{c^{3} }}\overline{K}_{ij}\)

L :

Length of bearing (m)

p :

Local film pressure (Pa)

\(p_{0}\) :

Steady-state pressure (Pa)

\(\overline{p}_{0}\) :

Non-dimensional steady-state pressure, \(\overline{p}_{0} = \frac{{p_{0} c^{2} }}{6\eta UR}\)

\(p_{x} ,p_{y}\) :

Pressure derivatives with respect to position, \(p_{K} = \frac{\partial p}{{\partial K}}\;({\text{Pa}}/{\text{m}})\)

\(p_{{\dot{x}}} ,p_{{\dot{y}}}\) :

Pressure derivatives with respect to velocity, \(p_{{\dot{K}}} = \frac{\partial p}{{\partial \dot{K}}}\) (Pa s/m)

\(\overline{p}_{x} ,\overline{p}_{y}\) :

Non-dimensional pressure derivatives with respect to position, \(\overline{p}_{k} = \frac{{p_{k} c^{3} }}{6\eta UR}\)

\(\overline{p}_{{\dot{x}}} ,\overline{p}_{{\dot{y}}}\) :

Non-dimensional pressure derivatives with respect to velocity, \(\overline{p}_{{\dot{k}}} = \frac{{p_{{\dot{k}}} c^{3} }}{{12\eta R^{2} }}\)

Q :

Side leakage (m3/s)

\(\overline{Q}\) :

Non-dimensional side leakage, \(\overline{Q} = \frac{2Q}{{UR^{2} Lc}}\)

R :

Radius of the journal (m)

W :

Load bearing capacity (N)

\(\overline{W}\) :

Non-dimensional load bearing capacity

\(\overline{W}_{x} ,\overline{W}_{y}\) :

Non-dimensional load component along x and y direction, \(\overline{W}_{k} = \frac{{c^{2} }}{{6\eta UR^{2} L}}W_{k}\)

x, y, z :

Rectangular coordinates in x, y, z directions

\(\overline{z}\) :

Dimensionless coordinate in the z direction, \(\overline{z} = \frac{z}{L/2}\)

\(\varepsilon\) :

Eccentricity ratio, \(\varepsilon = \frac{e}{c}\)

\(\overline{\nu }\) :

Whirl ratio

\(\phi\) :

Attitude angle

\(\theta\) :

Circumferential coordinate, \(x = R\theta\)

\(\eta\) :

Coefficient of viscosity of lubricant (Pa s)

\(\mu ,\overline{\mu }\) :

Coefficient of friction, \(\overline{\mu } = \frac{\mu R}{c}\)

\(\tilde{\omega }\) :

Variation parameter

References

  1. Petrov NP (1883) Friction in machines and the effect of the lubricant. Inzh. Zh, St-Peterb

    Google Scholar 

  2. Tower B (1883) First report on friction experiments. Proc Inst Mech Eng 34(1):632–659

    Article  Google Scholar 

  3. Cavalini AA Jr, Lara-Molina FA, Sales TD, Koroishi EH, Steffen V Jr (2015) Uncertainty analysis of a flexible rotor supported by fluid film bearings. Latin Am J Solids Struct 12(8):1487–1504

    Article  Google Scholar 

  4. Ap Cavalini A, Silva AD, Lara-Molina FA, Steffen V (2017) Dynamic analysis of a flexible rotor supported by hydrodynamic bearings with uncertain parameters. Meccanica 52(11–12):2931–2943

    Article  MathSciNet  Google Scholar 

  5. Ruiz RO, Diaz SE (2016) Effect of uncertainties in the estimation of dynamic coefficients on tilting pad journal bearings. In: Proceedings of the ASME international mechanical engineering congress and exposition, Phoenix, Arizona, USA (ISBN: 9780791850657)

  6. Cavalini AA, Dourado AG, Lara-Molina FA, Steffen V (2016) Uncertainty analysis of a tilting-pad journal bearing using fuzzy logic techniques. J Vibr Acoust 138(6):061016

  7. Cavalini Jr AA, Lara-Molina FA, Dourado A, Steffen Jr V (2015) Fuzzy uncertainty analysis of a tilting-pad journal bearing. In: International design engineering technical conferences and computers and information in engineering conference, vol 57181, p V008T13A076. American Society of Mechanical Engineers

  8. Da Silva HA, Nicoletti R (2019) Design of tilting-pad journal bearings considering bearing clearance uncertainty and reliability analysis. J Tribol 141(1):011703

  9. Ramos DJ, Ferraz AR, Daniel GB, Ritto TG (2018) Dynamic analysis of rotating systems considering uncertainties in the bearings’ parameters. In: International conference on rotor dynamics, pp 460–474. Springer, Cham

  10. Maharshi K, Mukhopadhyay T, Roy B, Roy L, Dey S (2018) Stochastic dynamic behaviour of hydrodynamic journal bearings including the effect of surface roughness. Int J Mech Sci 1(142):370–383

    Article  Google Scholar 

  11. Reynolds O (1886) IV. On the theory of lubrication and its application to Mr. Beauchamp tower’s experiments, including an experimental determination of the viscosity of olive oil. Philos Trans R Soc Lond. 31(177):157–234

    MATH  Google Scholar 

  12. Ocvirk FW Short-bearing approximation for full journal bearings

  13. Sommerfeld A. Zur hydrodynamischen theorie der schmiermittelreibung. Zs. math. and phys 1904, (Vol. 50 (1), p.97–155).

  14. Pinkus O, Sternlicht B (1961) Theory of hydrodynamic lubrication. McGra-Hill Book Company, Inc, New York

    MATH  Google Scholar 

  15. Lund JW, Thomsen KK (1978) A calculation method and data for the dynamic coefficients of oil-lubricated journal bearings. Topics in fluid film bearing and rotor bearing system design and optimization, p 1000118

  16. Brito FP, Miranda AS, Fillon M (2016) Analysis of the effect of grooves in single and twin axial groove journal bearings under varying load direction. Tribol Int 1(103):609–619

    Article  Google Scholar 

  17. Majumdar BC, Pai R, Hargreaves DJ (2004) Analysis of water-lubricated journal bearings with multiple axial grooves. Proc Inst Mech Eng Part J J Eng Tribol 218(2):135–146

    Article  Google Scholar 

  18. Roy L, Laha SK (2009) Steady state and dynamic characteristics of axial grooved journal bearings. Tribol Int 42(5):754–761

    Article  Google Scholar 

  19. Roy L, Kakoty SK (2013) Optimum groove location of hydrodynamic journal bearing using genetic algorithm. Adv Tribol 1:2013

    Google Scholar 

  20. Roy L (2015) Effect of axial groove on steady state and stability characteristics of finite two-lobe hybrid journal bearing. J Appl Mech Eng 4:1–7

    Google Scholar 

  21. Tala-Ighil N, Maspeyrot P, Fillon M, Bounif A (2007) Effects of surface texture on journal-bearing characteristics under steady-state operating conditions. Proc Inst Mech Eng Part J J Eng Tribol 221(6):623–633

    Article  Google Scholar 

  22. Ma C, Zhu H (2011) An optimum design model for textured surface with elliptical-shape dimples under hydrodynamic lubrication. Tribol Int 44(9):987–995

    Article  Google Scholar 

  23. Kango S, Singh D, Sharma RK (2012) Numerical investigation on the influence of surface texture on the performance of hydrodynamic journal bearing. Meccanica 47(2):469–482

    Article  Google Scholar 

  24. Patir N, Cheng HS (1978) An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication. J Lubr Tech 100(1):12–17

  25. Guha SK (1993) Analysis of dynamic characteristics of hydrodynamic journal bearings with isotropic roughness effects. Wear 167(2):173–179

    Article  Google Scholar 

  26. Bhaskar SU, Hussain MM, Ali MY (2013) Stability analysis on plain journal bearing with effect of surface roughness. Int J Sci Eng Res 4(3):1–8

    Google Scholar 

  27. Dubois GB, Ocvirk FW, Wehe RL (1960) Study of effect of a non-Newtonian oil on friction and eccentricity ratio of a plain journal bearing. National Aeronautics and Space Administration

  28. Guha SK (2004) A theoretical analysis of dynamic characteristics of finite hydrodynamic journal bearings lubricated with coupled stress fluids. Proc Inst Mech Eng Part J J Eng Tribol 218(2):125–133

    Article  Google Scholar 

  29. Guha SK (2012) On the steady-state performance of hydrodynamic flexible journal bearings of finite width lubricated by ferro fluids with micro-polar effect. Int J Mech Eng Robot Res 1(2):32–49

  30. Sinha P, Singh C, Prasad KR (1981) Effect of viscosity variation due to lubricant additives in journal bearings. Wear 66(2):175–188

    Article  Google Scholar 

  31. Laghrabli S, El Khlifi M, Nabhani M, Bou-Saïd B (2017) Static characteristics of ferrofluid finite journal bearing considering rotational viscosity effect. Lubr Sci 29(4):203–226

    Article  Google Scholar 

  32. Vladescu SC, Marx N, Fernández L, Barceló F, Spikes H (2018) Hydrodynamic friction of viscosity-modified oils in a journal bearing machine. Tribol Lett 66(4):127

    Article  Google Scholar 

  33. Costa L, Miranda AS, Fillon M, Claro JC (2003) An analysis of the influence of oil supply conditions on the thermohydrodynamic performance of a single-groove journal bearing. Proc Inst Mech Eng Part J J Eng Tribol 217(2):133–144

    Article  Google Scholar 

  34. Brito FP, Miranda AS, Bouyer J, Fillon M (2006) Experimental investigation of the influence of supply temperature and supply pressure on the performance of a two axial groove hydrodynamic journal bearing. In: International joint tribology conference, vol 42592, pp 319–327

  35. Ahmad MA, Kasolang S, Dwyer-Joyce R, Abdullah NR (2013) The effect of oil supply pressure on the circumferential pressure profile in hydrodynamic journal bearing. In: Applied mechanics and materials, vol 315, pp 809–814. Trans Tech Publications Ltd

  36. Ulam SM, Richtmyer RD, Von Neumann J. Statistical methods in neutron diffusion. Report, Los Alamos Scientific Laboratory LAMS-551

  37. Shinozuka M (1972) Monte Carlo solution of structural dynamics. Comput Struct 2(5–6):855–874

    Article  Google Scholar 

  38. Salehi R, Dehghan M (2013) A moving least square reproducing polynomial meshless method. Appl Numer Math 1(69):34–58

    Article  MathSciNet  Google Scholar 

  39. Li X (2016) Error estimates for the moving least-square approximation and the element-free Galerkin method in n-dimensional spaces. Appl Numer Math 1(99):77–97

    Article  MathSciNet  Google Scholar 

  40. Mukhopadhyay T, Karsh PK, Basu B, Dey S (2020) Machine learning based stochastic dynamic analysis of functionally graded shells. Compos Struct 1(237):111870

    Google Scholar 

  41. Trivedi SK, Dey S (2013) Effect of various kernels and feature selection methods on SVM performance for detecting email spams. Int J Comput Appl 66(21):18–23

  42. Karsh PK, Kumar RR, Dey S (2020) Radial basis function-based stochastic natural frequencies analysis of functionally graded plates. Int J Comput Methods 17(09):1950061

    Article  MathSciNet  Google Scholar 

  43. Kumar RR, Karsh PK, Pandey KM, Dey S (2019) Stochastic natural frequency analysis of skewed sandwich plates. Eng Comput

  44. Karsh PK, Raturi HP, Kumar RR, Dey S (2020) Parametric uncertainty quantification in natural frequency of sandwich plates using polynomial neural network. In: IOP conference series: materials science and engineering, vol 798, No. 1, p 012036. IOP Publishing

  45. Kumar RR, Mukhopadhya T, Pandey KM, Dey S (2020) Prediction capability of polynomial neural network for uncertain buckling behavior of sandwich plates. In: Handbook of probabilistic models, pp 131–140. Butterworth-Heinemann

  46. Karsh PK, Kumar RR, Dey S (2019) Stochastic impact responses analysis of functionally graded plates. J Braz Soc Mech Sci Eng 41(11):501

    Article  Google Scholar 

  47. Karsh PK, Mukhopadhyay T, Dey S (2020) A stochastic investigation of effect of temperature on natural frequencies of functionally graded plates. In: Advances in structural engineering and rehabilitation, pp 41–53. Springer, Singapore

  48. Lancaster P, Salkauskas K (1981) Surfaces generated by moving least squares methods. Math Comput 37(155):141–158

    Article  MathSciNet  Google Scholar 

  49. Levin D (1998) The approximation power of moving least-squares. Math Comput 67(224):1517–1531

    Article  MathSciNet  Google Scholar 

  50. Garimella RV (2017) A Simple Introduction to Moving Least Squares and Local Regression Estimation. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

  51. Friedman JH (1991) Multivariate adaptive regression splines. Ann Stat 1:1–67

    MathSciNet  MATH  Google Scholar 

  52. Cheng MY, Cao MT (2014) Accurately predicting building energy performance using evolutionary multivariate adaptive regression splines. Appl Soft Comput 1(22):178–188

    Article  Google Scholar 

  53. Craven P, Wahba G (1979) Smoothing noisy data with spline functions. Estimating the correct degree of smoothing by the method of generalized cross-validation. Numer Math 31:377–403

    Article  MathSciNet  Google Scholar 

  54. Burges CJ (1998) A tutorial on support vector machines for pattern recognition. Data Min Knowl Disc 2(2):121–167

    Article  Google Scholar 

  55. Vapnik V (2013) The nature of statistical learning theory. Springer

  56. Viana FA, Gogu C, Haftka RT (2010) Making the most out of surrogate models: tricks of the trade. In: International design engineering technical conferences and computers and information in engineering conference, vol 44090, pp 587–598

  57. Dey S, Naskar S, Mukhopadhyay T, Gohs U, Spickenheuer A, Bittrich L, Sriramula S, Adhikari S, Heinrich G (2016) Uncertain natural frequency analysis of composite plates including effect of noise—a polynomial neural network approach. Compos Struct 20(143):130–142

    Article  Google Scholar 

  58. Ivakhnenko AG (1968) The group method of data of handling; a rival of the method of stochastic approximation. Soviet Autom Control 13:43–55

    Google Scholar 

  59. Anastasakis L, Mort N (2001) The development of self-organization techniques in modelling: a review of the group method of data handling (GMDH). Research Report-University of Sheffield Department of Automatic Control and Systems Engineering

  60. Kitayama S, Srirat J, Arakawa M, Yamazaki K (2013) Sequential approximate multi-objective optimization using radial basis function network. Struct Multidiscip Optim 48(3):501–515

    Article  MathSciNet  Google Scholar 

  61. Dey S, Mukhopadhyay T, Adhikari S (2017) Metamodel based high-fidelity stochastic analysis of composite laminates: a concise review with critical comparative assessment. Compos Struct 1(171):227–250

    Article  Google Scholar 

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Acknowledgments

The first author acknowledges the financial support received from the Ministry of Education (MoE), Govt. of India, during the period of this research work.

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  1. Department of Mechanical Engineering, National Institute of Technology Silchar, Silchar, India

    B. Roy & S. Dey

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Roy, B., Dey, S. Comparative evaluation on probabilistic performance of journal bearing: a surrogate-based approach. J Braz. Soc. Mech. Sci. Eng. 43, 299 (2021). https://doi.org/10.1007/s40430-021-02926-5

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