Determination of Dynamic Coefficients of Air-Ring Bearings
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ORIGINAL PAPER
Determination of Dynamic Coefficients of Air‑Ring Bearings Muruganandam Muthanandam1 · Sridhar Thyageswaran1 Received: 2 October 2019 / Revised: 24 March 2020 / Accepted: 25 March 2020 © Krishtel eMaging Solutions Private Limited 2020
Abstract Purpose An externally-pressurized journal air bearing (AB) with an air-ring (AR), or air-ring bearing (ARB), for a balanced, rigid and light-weight rotor is studied. An elastic structure in the form of an AR is provided between the bearing-bushing and the casing. The ARB is analyzed to determine the dynamic coefficients (DC) at various angular velocities and angular frequencies of vibration of the journal in its range of operation. These DC can then be used to predict the dynamic stability of the rotor ARB system against self-excited (SE) vibration. A numerical simulation procedure is followed to determine the DC. Methods The ARB is modeled as a two-degrees of freedom system. During the simulation, the journal follows a prescribed harmonic motion. Self-exciting forces due to flow dynamics inside an ARB induce this motion. Three-dimensional (3-D) flow equations are solved on a moving/deformable grid using ANSYS®, to compute the pressure (p) distribution in the ARB. Unlike in previous studies, in this study the bushing displacement is determined by the instantaneous p-distribution in the ARB. DC of both AB and AR are determined simultaneously by considering the interaction between the AR and the AB regions through the feed-holes in the bushing. Results Time-dependent displacement, velocity, and load-carrying capacity obtained by numerical simulation are used to evaluate the DC. Conclusion Incorporation of an AR around an AB can prevent SE vibration due to positive values of direct damping coefficients of AR. A 3-D flow analysis can reveal the realistic nature of flow in an ARB. Keywords Journal bearings · Externally-pressurized air bearings · Dynamic coefficients · Self-excited whirl · Steady-state simulation · Transient-state simulation Abbreviations AB Air-bearing AR Air-ring ARB Air-ring bearing CG Geometric center CFD Computational fluid dynamics DC Dynamic coefficients FC Face centroid FH Feed-hole GCI Grid convergence indicator LHS Left-hand side RARBS Rotor air-ring bearing system RE Reynolds equation RHS Right-hand side * Muruganandam Muthanandam [email protected] Sridhar Thyageswaran [email protected] 1
Department of Mechanical Engineering, Coimbatore Institute of Technology, Coimbatore 641 014, India
RPM Revolutions per minute SE Self-excited SEP Static equilibrium position SHM Simple harmonic motion SSS Steady-state simulation TSS Transient-state simulation UDF User-defined function 1-DOF Single-degree of freedom 2-DOF Two-degrees of freedom List of symbols A Amplitude of vibration (m) a A coefficient (see Eq. 5) b Reference cell size (m); time step size (s); a coefficient (see Eq. 6) C Damping coefficient (N s m−1) c Radial clearance (m); specific heat (J kg−1 K−1) D Diameter (m) d Diameter (m) E
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