Foil Bearing Design Guidelines for Improved Stability

[+] Author and Article Information
J. Schiffmann

e-mail: jurg.schiffmann@epfl.ch

Z. S. Spakovszky

e-mail: zolti@mit.edu
Gas Turbine Laboratory
Massachusetts Institute of Technology
Cambridge, MA 02139

1Currently at Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.

Contributed by the Tribology Division of ASME for publication in the Journal of Tribology. Manuscript received February 10, 2012; final manuscript received September 8, 2012; published online December 20, 2012. Assoc. Editor: Luis San Andres.

J. Tribol 135(1), 011103 (Dec 20, 2012) (11 pages) Paper No: TRIB-12-1022; doi: 10.1115/1.4007759 History: Received February 10, 2012; Revised September 08, 2012

Experimental evidence in the literature suggests that foil bearing-supported rotors can suffer from subsynchronous vibration. While dry friction between top foil and bump foil is thought to provide structural damping, subsynchronous vibration is still an unresolved issue. The current paper aims to shed new light onto this matter and discusses the impact of various design variables on stable foil bearing-supported rotor operation. It is shown that, while a time domain integration of the equations of motion of the rotor coupled with the Reynolds equation for the fluid film is necessary to quantify the evolution of the rotor orbit, the underlying mechanism and the onset speed of instability can be predicted by coupling a reduced order foil bearing model with a rigid-body, linear, rotordynamic model. A sensitivity analysis suggests that structural damping has limited effect on stability. Further, it is shown that the location of the axial feed line of the top foil significantly influences the bearing load capacity and stability. The analysis indicates that the static fluid film pressure distribution governs rotordynamic stability. Therefore, selective shimming is introduced to tailor the unperturbed pressure distribution for improved stability. The required pattern is found via multiobjective optimization using the foil bearing-supported rotor model. A critical mass parameter is introduced as a measure for stability, and a criterion for whirl instability onset is proposed. It is shown that, with an optimally shimmed foil bearing, the critical mass parameter can be improved by more than two orders of magnitude. The optimum shim patterns are summarized for a variety of foil bearing geometries with different L/D ratios and different degrees of foil compliance in a first attempt to establish more general guidelines for stable foil bearing design. At low compressibility (Λ < 2), the optimum shim patterns vary little with bearing geometry; thus, a generalized shim pattern is proposed for low compressibility numbers.

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Fig. 1

Bump foil gas bearing nomenclature

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Fig. 2

Rotordynamic model for rigid body analysis

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Fig. 3

Whirl speed map for cylindrical and conical modes for the reference rotor-bearing system (Table 1): onset of instability occurs at Λ = 0.43

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Fig. 4

Critical mass for reference rotor-bearing system (Table 1): onset of instability occurs at Λ = 0.43

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Fig. 5

Static eccentricity as a function of attitude angle and amplitude for reference journal bearing (Table 1) operating at Λ = 4

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Fig. 6

Critical mass as a function of attitude angle and amplitude for reference bearing (Table 1) operating up to Λ = 4

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Fig. 7

Critical mass as a function of compressibility, static load, and compliance for reference bearing (Table 1) with no structural damping

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Fig. 8

Critical mass as a function of compressibility, static load, and structural damping for reference bearing (Table 1) at α = 0.67

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Fig. 12

Critical mass as a function of the highest operating compressibility number for optimized circumferential selective shim distributions

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Fig. 9

Pareto curves for reference bearing (Table 1) for different structural damping γ

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Fig. 10

Improvement in threshold speed at instability onset for: original reference bearing (solid); optimum selective shim pattern (dotted); and three equal shim pattern (Kim and San Andrés [34], dashed)

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Fig. 11

Pareto-optimum shim distribution as a function of logarithmic decrement Γ for γ = 0, α = 0.67

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Fig. 13

Optimum selective shim patterns as a function of bearing compliance α, L/D ratio, and compressibility Λ

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Fig. 14

Generalized selective shim pattern (Table 3) compared with individually optimized selective shim pattern




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