Evaluation of the minimum face clearance of a high-speed gas-lubricated bearing with Navier slip boundary conditions under random excitations

Nicola Bailey, Stephen Hibberd, Henry Power, M Tretyakov

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Motivated by ongoing developments in aero-engine technology, a model for a coupled gas-lubricated bearing is developed in terms of an extended dynamical system. A slip boundary condition, characterised by a slip length, is incorporated on the bearing faces which can be relevant for operation in non-ideal extreme conditions, notably where external vibrations or disturbances could destabilise the bearing. A modified Reynolds equation is formulated to model the gas flow, retaining the effects of centrifugal inertia which is increasingly important for high-speed operation, and is coupled to the structural equations; spring-mass-damper systems model the axial stator and rotor displacements. A novel model is developed corresponding to a bearing experiencing an external random force to evaluate the resulting induced displacements of the bearing components. The minimum face clearance is obtained from a mapping solver for the modified Reynolds equation and structural equations simultaneously. In the case of random excitations, the solver is combined with a Monte Carlo technique. Evaluation of the average value of the minimum gap and the probability of the gap reaching a prescribed tolerance are provided. Extensive insight is given on the effect of key bearing parameters on the corresponding bearing dynamics.
Original languageEnglish
Pages (from-to)17-35
Number of pages19
JournalJournal of Engineering Mathematics
Issue number1
Early online date11 Jun 2018
Publication statusPublished - 1 Oct 2018



  • Coupled gas-lubricated bearing
  • Monte Carlo method
  • Navier slip boundary condition
  • Random external force

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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