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

Abstract

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.

The extraction of Campbell diagrams from the dynamical system representation of a foil-air bearing rotor model

“…The relatively high stiffness value is justified for a bearing of this sizein fact, for a similar size bearing in Table 1 of reference [24], the stiffness was calculated to be 43.223 GN/m 3 using SEFM formula in eq. ( 15) of reference [15]. The radial clearance is rather low, but was chosen in [30] since it gave (linear) stability beyond 88 krpm.…”

“…applied TNDA to the complete system), and the approach has been taken up by other researchers e.g. [10,11,14,15,16]. In this case, the state vector contains state variables from all three domains (air film, foil and rotor) e.g.…”

A fully coupled air foil bearing model considering friction – Theory & experiment

“…The excessive sagging has previously been investigated in [32], where a correction factor on the top foil's Young's modulus was introduced by fitting to experimental data, but a more generic approach is desirable. A point of attention for further work should hence be the implementation of an improved top foil formulation, possibly based on shell elements as presented in [56], if not only to provide numerical stability and speed up the simulation. where…”

An efficient three-dimensional foil structure model for bump-type gas foil bearings considering friction

“…For example, the third generation GFB [5], whose bump stiffness changes in more than one direction, has a better bearing load carrying capacity. Another example is that the bump foil removed from the region of minimum film thickness improves the steady behavior of a GFB rotor system with a large unbalance [33]. Furthermore, GFBs frequently have angular misalignment due to rotor bending, unbalanced torque, or installation errors.…”