Determination of Gas-Bearing Stability by Response to a Step-Jump

Abstract

The stability of a gas bearing is treated by a new procedure in which the bearing film is characterised by its responses to step-jump displacements. Duhamel’s theorem is invoked to generalize these step responses in a system of dynamical equations. Stability is determined by calculation of a “growth factor” for each degree of freedom. Results are presented for the infinitely long self-acting sleeve bearing and for a finite length two-bearing system.

Clearance Regulation of Mechanical Gas Face Seals: Part I—Modeling

“…The values for the gas film model coefficients are determined using a curve-fit procedure on step response or frequency response data computed numerically by solving the Reynolds equation. Three techniques have been presented in the literature for generating this data: the "step-jump" method (Miller and Green (11); Elrod, et al (12)), the direct numerical frequency response method (Miller and Green (11)), and the small perturbation method (16)). The small perturbation method is used in this work to compute the gas film frequency responses, from which the model coefficients in Eq.…”

“…When the gas film forces are linear in response to small step displacements in the stator position, the net gas film forces and moments can be related to the step responses and seal motion by Duhamel's integral (Miller and Green (9), Elrod, et al (12))…”

The Dynamic Properties of Annular Gas Squeeze Film Dampers

“…Elrod et al (1967) use a series of Laguerre Polynomials to model the gas film properties in a journal bearing, but Miller and Green (1997) prove that the model can violate the Second Law of Thermodynamics. Later, Miller and Green (1998) show that a Prony series is a flexible, thermodynamically valid gas film model useful for a wide range of applications.…”

“…If this linearity assumption is valid, then the gas film properties can be represented by the step response (Elrod et al, 1967) or by the frequency response (Ono, 1975, andBlech, 1985).…”

Improving the pneumatic hammer stability of aerostatic thrust bearing with recess using damping orifices

“…The dynamic stiffness and damping characteristics of a circular pad aerostatic thrust bearing are studied with dynamic grid technique of ANSYS [10]. H.G Elrod describes the dynamic stiffness and damping of the bearing by the coefficients of the Lagrange polynomial [11]. The dynamic stiffness and damping characteristics of the annular throttle [12] and Orifice [13] bearing and aerostatic bearings with stabilizing restrictors [14,15] are studied.…”