A method for improving the capability of convergence of numerical lubrication simulation by using the PID controller

  • Yuechang Wang
  • Ying LiuEmail author
  • Yuming Wang
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


Numerically simulating lubricated components is a basic analysis method in tribology. Such kind of simulation usually requires solving a closed equation system. Iterative algorithm has been used to numerically solve it for many years. The convergence of the corresponding solution procedures is achieved by adjusting some initial parameters to satisfy the pre-defined convergence criteria. There is very little discussion about the method used to adjust the initial parameters, however it directly influence the convergence of the whole simulation. In this paper, the analogy between the solution procedures and the feedback loop was discussed. And based on such analogy, the widely used proportional-integral-derivative controller (PID controller) in the control of the feed-back loop could be also used to make the solution procedures of lubrication simulation converge. The mixed point contact EHL problem, which is rather difficult to converge in lubrication simulation, was chosen as the example to prove the validity and efficiency of using PID controller in the solution procedures. The results show that the PID controller can be easily implemented and simplify the code. And it really accelerates the convergent speed of the simulation. In some working conditions, the traditional way cannot lead to satisfied results but the PID controller can make it. The most attractive advantage of using PID controller is that it can automatically converge the solution procedure, no extra modification is needed once the simulation starts.


Lubrication simulation PID controller Efficiency 


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  1. 1.
    Huang, P.: Numerical calculation methods of elastohydrodynamic lubrication. Tsinghua University Press, Beijing (2013).Google Scholar
  2. 2.
    Kim K W, Tanaka M, Hori Y.: A 3-dimensional analysis of thermohydrodynamic performance of sector-shaped, tilting-pad thrust-bearings. Journal of Lubrication Technology-Transactions of the ASME 105(3), 406–413(1983).Google Scholar
  3. 3.
    Heinrichson N, Santos I F. :Reducing friction in tilting-pad bearings by the use of enclosed recesses. Journal of Tribology-Transactions of the ASME 130: 0110091 (2008).Google Scholar
  4. 4.
    Ouyang W, Yuan X Y, Jia Q.: Analysis of tilting-pad thrust bearing static instability and lubrication performance under the bistability. Industrial Lubrication and Tribology 66(5), 584–592 (2014).Google Scholar
  5. 5.
    Wang, Y., Liu, Y., Wang, Z., and Wang, Y.: Surface roughness characteristics effects on fluid load capability of tilt pad thrust bearings with water lubrication. Friction 5(4), 392-401 (2017).Google Scholar
  6. 6.
    Wang, Y., Liu, Y., Wang, Z., and Wang, Y.: Analysis of tilt pad thrust bearings based on PID method. Tribology 37(3), 372-378 (2017).Google Scholar
  7. 7.
    Zhu, D., Wang, J. X., and Wang, Q. J.: On the Stribeck Curves for Lubricated Counterformal Contacts of Rough Surfaces. Journal of Tribology-Transactions of the ASME 137(2) (2015).Google Scholar
  8. 8.
    Chang, L., Jeng, Y. R., and Yu, Q.: A unified mixed-lubrication model of rolling-sliding line contacts from elastohydrodynamic lubrication to boundary lubrication. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 230(9), 1056-1070, (2015)Google Scholar
  9. 9.
    Wu, J. J.: Simulation of rough surfaces with FFT, Tribology international, 33(1), 47-58, (2000).Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.State Key Laboratory of TribologyTsinghua UniversityBeijingChina

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