Transient and steady state behaviour of elasto–aerodynamic air foil bearings, considering bump foil compliance and top foil inertia and flexibility: A numerical investigation

Bo Bjerregaard Nielsen, Ilmar F. Santos

Research output: Contribution to journalJournal articleResearchpeer-review


This work gives a theoretical contribution to the problem of modelling air foil bearings considering large sagging effects in the calculation of the non-linear transient and steady state response of a rigid rotor. This paper consists of two parts: the development of a miltiphysics model of the air foil bearing, and a numerical parameter study of a rigid journal supported in an air foil bearing with a partially supported top foil. The mathematical model of the air foil bearing is centred around the finite element models of both the air film and the top foil structure. These finite element models utilise two types of eight-node isoparametric elements. The rotor is modelled as a rigid body without rotational inertia, i.e. as a journal. The bump foil is included via a bilinear version of the simple elastic foundation model. This paper introduces the bilinear simple elastic foundation model, which combined with the top foil structure model, enables a separation of the top foil and the bump foil. A phenomenon associated within areas of the top foil is where the aerodynamic pressure is sub-ambient. The parameter study investigates the performance of three air foil bearings with partially supported top foils and one air foil bearing with a fully supported top foil. The steady state responses of a journal supported by these air foil bearings are investigated for varied rotational speeds and journal unbalances as well as the top foil sagging in the unsupported area. The study reveals that sub-harmonic vibrations associated with a large journal unbalance can be eliminated by a proper design layout of the bump foil, i.e. placement of the unsupported area. The positive effect is attributed to ‘equivalent shallow pockets’ formed by the sagging top foil.
Original languageEnglish
JournalProceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology
Issue number10
Pages (from-to)1235-1253
Publication statusPublished - 2017


  • Air foil bearing
  • Bilinear simple elastic foundation model
  • Finite element
  • Non-linear analysis
  • Reynolds equation
  • Shell structure
  • Transient response
  • Top foil flexibility

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