Multi-domain stability and modal analysis applied to Gas Foil Bearings: Three approaches

The effects of air film pressure constraints and top foil detachment on the static equilibrium, stability and modal characteristics of a foil-air bearing rotor model

“…The above described approach for TNDA or SESMA, based on eq. ( 1), is referred to as "simultaneous" [10] or "(fully) coupled" [16].…”

“…There has been less take-up of the SESA/SESMA approach of [10,11,3,15], due to continued attachment to the LFCM, despite known discrepancies between its OIS prediction and the OIS determined from low-amplitude time domain integration of the nonlinear system (simultaneous or not) [7]. However, Gu et al [20] followed the SESA approach of Bonello and Pham [10] for the OIS and, 8 most recently, von Osmanski et al [16] adopted the SESMA approach of Bonello [3,15] (but with ad hoc filtering) as a benchmark for troubleshooting the application of LFCM to FABs. SESMA can be used as the benchmark linearisation method since it works directly on the Jacobian of eq.…”

“…It is noted that the works in [16,20] used the alternative implicit representation 𝐌(𝐬)𝐬 ′ = 𝛘 ̌(𝜏, 𝐬) which nonetheless can be expressed in the explicit format of eq. ( 1) in the normal case where all domains are represented by timebased differential equations [16], as was the case in [16,20].…”

“…With regard to the aforementioned problem with the LFCM, it was recently found by Pronobis and Liebich [21], and later by [16], that previous works (e.g. [4,5,7]) comparing LFCM with time domain analysis did not ensure that the damping was precisely equivalent in the two methods.…”

“…Nonetheless, discrepancies remain [21,16] and increase with decreasing foil stiffness [16]. von Osmanski et al [16] went on to extend LFCM to consider the dependency of the air pressure on foil deflection ("extended perturbation method" (EPM)).…”