Evaluation of the minimum face clearance of a high speed gas lubricated bearing with Navier slip boundary conditions under random excitations

Bailey, N.Y.; Hibberd, S.; Power, H.; Tretyakov, M.V.

Abstract

Motivated by ongoing developments in aero-engine technology, a model for a coupled gas lubricated bearing is developed in terms of an extended dynamical system. A slip boundary condition, characterised by a slip length, is incorporated on the bearing faces which can be relevant for operation in non-ideal extreme conditions, notably where external vibrations or disturbances could destabilise the bearing. A modified Reynolds equation is formulated to model the gas flow, retaining the effects of centrifugal inertia which is increasingly important for high-speed operation, and is coupled to the structural equations; spring-mass-damper systems model the axial stator and rotor displacements. A novel model is developed corresponding to a bearing experiencing an external random force to evaluate the resulting induced displacements of the bearing components. The minimum face clearance is obtained from a mapping solver for the modified Reynolds equation and structural equations simultaneously. In the case of random excitations, the solver is combined with a Monte Carlo technique. Evaluation of the average value of the minimum gap and the probability of the gap reaching a prescribed tolerance are provided. Extensive insight is given on the effect of key bearing parameters on the corresponding bearing dynamics.

Citation

Bailey, N., Hibberd, S., Power, H., & Tretyakov, M. (2018). Evaluation of the minimum face clearance of a high speed gas lubricated bearing with Navier slip boundary conditions under random excitations. Journal of Engineering Mathematics, 112(1), 17–35. https://doi.org/10.1007/s10665-018-9963-9

• Journal Article Type: Article
• Acceptance Date: May 11, 2018
• Online Publication Date: Jun 11, 2018
• Publication Date: 2018-10
• Deposit Date: May 11, 2018
• Publicly Available Date: Jun 11, 2018
• Journal: Journal of Engineering Mathematics
• Print ISSN: 0022-0833
• Electronic ISSN: 1573-2703
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 112
• Issue: 1
• Pages: 17–35
• DOI: https://doi.org/10.1007/s10665-018-9963-9
• Keywords: coupled gas lubricated bearing, Navier slip boundary condition, random external force, Monte Carlo method
• Public URL: https://nottingham-repository.worktribe.com/output/937148
• Publisher URL: https://link.springer.com/article/10.1007/s10665-018-9963-9