On the dynamic stability of high-speed gas bearings: stability study and experimental validation

Abstract

For high-speed applications, gas lubricated bearings offer very specific advantages over other,more conventional bearing technologies: a clean and oil-free solution, virtually wear-free operation, lowfrictional losses, wide operating temperature range, etc. However, the principal drawback involved in theapplication of high-speed gas bearings concerns the dynamic stability problem. Successful applicationtherefore requires control of the rotor-bearing dynamics so as to avoid instabilities.After a detailed study of the dynamic stability problem and the formulation of a convenient stability criterium,a brief overview is given of the currently existing bearing types and configurations for improving the stability.In addition, three strategies are introduced: (i) optimal design of plain aerostatic bearings; (ii) modification ofthe bearing geometry to counteract the destabilising effects in the gas film; and (iii) introduction of dampingexternal to the gas film as to compensate for the destabilising effects.These strategies are worked out into detail leading to the formulation of a series of design rules. Theireffectiveness is validated experimentally at a miniature scale. In recent experiments a rotational speed of1.2 million rpm has been achieved with a 6 mm rotor on aerodynamic journal bearings, leading to a recordDN-number of 7.2 million.

Aerodynamic journal bearing with a flexible, damped support operating at 7.2 million DN

“…However, they must be regarded as a rule of thumb rather than as a guarantee for stability. In its final stage, the design process should therefore be backed by a more extensive stability evaluation for various operation conditions and by taking into account the frequency-dependent gas film behaviour (see for example [20]). • As for the optimal choice of support parameters m b , k e and c e given the dynamic gas film properties and rotor mass m, the following qualitative guidelines hold true: (i) in order to obtain a wide region of stable behaviour in terms of support stiffness and damping, try to keep the bush mass m b ten times smaller than the rotor mass m, i.e.…”

“…with ρ being the density of the gas, r the radius of the rotor, L the axial length and ω the rotational speed. C d is the so-called skin friction coefficient which is obtained from the following empirical equation: 1 √ C d = 2.04 + 1.768 ln (Re C d ), (19) with the Reynolds number Re defined as Re = ρcrω μ , (20) in which c equals the radial gap and μ the dynamic viscosity of the gas. Equation ( 18) has been evaluated for increasing values of the rotational speed ω.…”

Lumped parameters models for the stability analysis of rotors supported on gas bearings

“…The second method is based on the linearization of the bearings forces around a given operational point [4] and on the solution of the eigenproblem resulting from the rotor equations of motion [5], [6]. The linearized stiffness and damping coefficients are computed with the so-called perturbation method [7].…”

Stability analysis on gas-lubricated bearing for high speed cryogenic turbo-expander

“…However, it becomes more susceptible to vibration and instability problems now. There are mainly two types of dynamic instability, [1] namely: pneumatic hammering and sub-synchronous whirl, both of which are self-excited whirl. The former one has been researched extensively over the past century, while the second type is still under study.…”