On the Integration of Hot Foil Bearings Into Gas Turbine Engines: Theoretical Treatment
Authors: Heshmat Hooshang , Walton James F. 
Published: November 2019

Abstract
To achieve high power density Gas Turbine Engines (GTEs), R&D efforts have strived to develop machines that spin faster and run hotter. One method to achieve that goal is to use high temperature capable foil bearings. In order to successfully integrate these advanced foil bearings into GTE systems, a theoretical understanding of both bearing and rotor system integration is essential. Without a fundamental understanding and sound theoretical modeling of the foil bearing coupled with the rotating system such an approach would prove application efforts fruitless. It is hoped that the information provided in this paper will open up opportunistic doors to designs presently thought to be impossible.
In this paper an attempt is made to describe how an advanced foil bearing is modeled for extreme high temperature operation in high performance turbomachinery including GTEs, Supercritical CO2 turbine generators and others. The authors present the advances in foil bearing capabilities that were crucial to achieving high temperature operation. Achieving high performance in a compliant foil bearing under the wide extremes of operating temperatures, pressures and speeds, requires a bearing system design approach that accounts for the highly interrelated compliant surface foil bearing elements such as: the structural stiffness and frictional characteristics of the underlying compliant support structure across the operating temperature and pressure spectrum; and the coupled interaction of the structural elements with the hydrodynamic pressure generation. This coupled elasto-hydrodynamic-Finite Element highly non-linear iterative methodology will be used by the authors to present a series of foil bearing design evaluations analyzing and modeling the foil bearing under extreme conditions. The complexity of the problem of achieving foil bearing system operation beyond 870°C (1600°F) requires as a prerequisite the attention to the tribological details of the foil bearing. For example, it is necessary to establish how both the frictional and viscous damping coefficient elements as well as the structural and hydrodynamic stiffness are to be combined. By combining these characteristics the influence of frictional coefficients of the elastic and an-elastic materials on bearing structural stiffness and hence the bearing effective coupled elasto-hydrodynamic stiffness coefficients will be shown.
Given that the bearing dynamic parameters — stiffness and damping coefficients — play a major role in the control of system dynamics, the design approach to successfully integrate compliant foil bearings into complex rotating machinery systems operating in extreme environments is explored by investigating the effects of these types of conditions on rotor-bearing system dynamics. The proposed rotor/bearing model is presented to describe how system dynamics and bearing structural properties and operating characteristics are inextricably linked together in a manner that results in a series separate but intertwined iterative solutions. Finally, the advanced foil bearing modeling and formulation in connection with resulting rotor dynamics of the system will be carried out for an experimental GTE simulator test rig. The analytical results will be compared with the experiments as presented previously to demonstrate the effectiveness of the developed method in a real world application [1].