Tribology Letters

, 58:18 | Cite as

Efficient Solution to the Cavitation Problem in Hydrodynamic Lubrication

  • Tomasz WoloszynskiEmail author
  • Pawel Podsiadlo
  • Gwidon W. Stachowiak
Original Paper


Hydrodynamic lubrication is present in the majority of machinery where load is transmitted between two contacting surfaces in relative motion. Cavitation in liquid lubricating films is common and directly affects the pressure distribution and subsequently the load-carrying capacity and friction force transmitted across the contact. By reformulating the Elrod–Adams implementation of the Jakobsson–Floberg–Olsson cavitation conditions, we developed an efficient algorithm, called Fischer-Burmeister-Newton-Schur (FBNS), for calculating the pressure distribution that combines two attractive properties. First, the system of discretized equations arising from the reformulation is continuously differentiable and unconstrained, thus allowing for the use of gradient-based methods to solve it. Second, the computational cost of solving the system is similar to that when cavitation is not considered. With the new algorithm, the transient analysis and optimisation of contacts with complex shapes becomes computationally feasible. A comparison of the FBNS with the established algorithms and an application to the transient analysis of a hydrodynamic contact with surface texturing are reported. The results show that the FBNS yields roughly two orders of magnitude reduction in computational time when compared against other algorithms.


Hydrodynamic lubrication Cavitation Elrod–Adams Jakobsson–Floberg–Olsson Texturing 



The authors would like to thank the Department of Mechanical Engineering at Curtin University, Australia for the financial support of this study.

Supplementary material

Supplementary material 1 (MPEG 27710 kb)


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Tomasz Woloszynski
    • 1
    Email author
  • Pawel Podsiadlo
    • 1
  • Gwidon W. Stachowiak
    • 1
  1. 1.Department of Mechanical EngineeringCurtin University of TechnologyPerthAustralia

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