On the Dynamics of Gas Lubricated Triboelements

Gas lubricated triboelements are ubiquitous in many applications, from gas turbines seals, high speed dental drills, cryogenic refrigerators, oil-free bearings for turbo chargers, to read-write self acting heads in magnetic recording. In all these application the film must be maintained sufficiently precise especially in the presence of disturbances. Hence, it is insufficient to analyze such triboelements quasi statically, where a complete dynamic analysis of the system is needed. Numerous techniques have been developed over the past five decades, some are purely numerical, and others are semi-analytical. Complete analytical methods are practically non-existent because of the non-linear nature of the Reynolds equation. This work discusses a few of the common techniques, explores their intricate, and highlights limitations and flaws in implementation. Particularly: (1) in the so called “orbit codes” the equations of motion and the Reynolds equation must be solved simultaneously (and not “side-by-side”), (2) a common representation of linearized stiffness and damping is shown to be produce unrealistic results even in the simplest application, and (3) for the first time a mathematical justification is given for the use of Prony series representation of the hereditary stiffness in the so called “step-jump” method.