On the Stability of Gas Lubricated Triboelements Using the Step Jump Method

Abstract

The step jump method was developed approximately three decades ago to help determine the stability of gas lubricated triboelements. In the approach, the force contribution from the gas layer is characterized by its step response, which is the transient force response resulting from pressure diffusion in the gas film after a step increase in film thickness. The procedure is broadened by implementing Duhamel’s theorem to yield the system characteristic equation. Since its inception in the literature, the step response has been approximated in the equations of motion using a series of Laguerre polynomials, which allows for a closed form analysis. This paper will prove that using Laguerre polynomials can violate the second law of thermodynamics, and a test case will show that stability results predicted by this approach can be inaccurate. It will be proven that a mathematical correlation exists between the dynamic behavior of the gas film and the dynamic behavior of a linear viscoelastic medium. This correlation is advantageous since much of the viscoelastic theory can be applied to the dynamic analysis of gas lubricated triboelements.