Constitutive Equations and the Correspondence Principle for the Dynamics of Gas Lubricated Triboelements

Abstract

A new method for characterizing the dynamic behavior of gas films in triboelements is developed. The new method is based on an expansion of the step jump method. In this method, the dynamic character of the gas film is preserved in the form of its force response to a step jump stimulus. Transforming this step response into the frequency domain yields the frequency dependent stiffness and damping properties of the gas film. By approximating the step response with analytic constitutive models and using the elastic-gas film correspondence principle, it is possible to determine the system characteristic equation in analytic form and to find closed-form solutions for stability, transient and forced responses. Requirements are given for choosing constitutive models that comply with the second law of thermodynamics. The new analytical solution method offers a significant time savings compared to direct numerical methods, and it is much more conducive to parametric studies.