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Research Papers: Applications

Rotordynamic Performance of Flexure Pivot Tilting Pad Gas Bearings With Vibration Damper

[+] Author and Article Information
Aaron Rimpel

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123amrimpel@tamu.edu

Daejong Kim

Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, TX 76019daejongkim@uta.edu

Hereon, the term “vibration damper“ will be used to refer to the design configuration of an around-bearing-shell damper or flexible bearing shell support.

This reference considers the analysis of shoed brush seals, which is similar to that of an FPTPGB-C.

Note that eigenvalues are calculated from the impedance matrix premultiplied by the mass matrix; thus units of modal stiffness (denoted with prime) have units of stiffness divided by mass, e.g., N/kgm or rad/s2.

The term critical speed is used here to describe the speed where a local-maximum amplitude exists in the imbalance response plot.

For bearing shell mass case of 0.1 kg in Fig. 5, it was noted previously that the higher speed resonance region appeared to be the coalescing of at least two critical speeds. Since the trend observed that the middle (upper) critical speed increases (decreases) as the mass increases, it is reasonably assumed that the middle and upper critical speeds for the 0.1 kg case coincide at the same speed.

This is reference to the maximum amplitudes of the vibrations at bearing shell critical speeds, which were all observed to have rotor and bearing shell motions out of phase, which amplified actual eccentricities.

J. Tribol 131(2), 021101 (Mar 03, 2009) (12 pages) doi:10.1115/1.3063809 History: Received December 05, 2007; Revised November 10, 2008; Published March 03, 2009

Recently, gas-lubricated bearings have drawn enormous attention for clean energy conversion/process systems such as fuel cells, micro-gas-turbines, gas compressors, etc. Among many different types of gas bearings, tilting pad gas bearings have many attractive features such as high rotor-bearing stability and less severe thermal issues (due to multipad configurations) than foil gas bearings. However, extension of the application of the tilting pad gas bearings to flexible rotors and harsh environments with external vibrations/impacts poses significant design challenges. The design problem addressed in this paper is the vibration damper to be integrated with the flexure pivot tilting pad gas bearing (FPTPGB) with and without pad radial compliance. Linear and nonlinear dynamic models of the FPTPGB with vibration damper were developed, and rotordynamic performance was evaluated to prescribe design guidelines for the selection of bearing shell mass and damper properties. Direct numerical integration (time-domain orbit simulations) and linear analyses were employed to predict rotordynamic responses and other interesting behaviors relevant of rotor-bearing systems with the vibration damper. Rotor-bearing systems showed better performance with larger damper stiffness for both with and without radial compliance. However, bearing shell mass showed different tendencies; lower bearing shell mass was shown to be ideal for bearings with radial compliance, while the opposite trend was observed for bearings without radial compliance. Although increasing the degrees of freedom of the system by allowing the bearing shell to move introduces additional natural frequencies, careful design considerations could allow the placement of the natural frequencies outside of the operating range.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Flexure pivot tilting pad gas bearing with pad radial compliance (FPTPGB-C)

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Figure 2

FPTPGB-C supported by bump foil elastic structure as a vibration damper

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Figure 3

General rotor-bearing system model

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Figure 4

FPTPGB-C geometry

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Figure 5

Synchronous imbalance responses; bearings without radial compliance, plotted up to the speed where nonsynchronous vibrations begin to appear. Rotor response (solid line) and bearing shell response (dotted line). Fixed bearing shell support stiffness (1×107 N/m) and varying bearing shell masses (0.1 kg, 0.2 kg, and 0.3 kg). Inset shows the zoomed region by middle critical speeds.

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Figure 6

Synchronous imbalance responses; bearings without radial compliance, plotted up to the speed where nonsynchronous vibrations begin to appear. Rotor response (solid line) and bearing shell response (dotted line). Fixed bearing shell mass (0.2 kg) and varying bearing shell support stiffnesses (5×106 N/m, 1×107 N/m, and 5×107 N/m). Inset shows the zoomed region by middle critical speeds.

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Figure 7

Cascade plot of rotor vibrations for simulated case of bearings without radial compliance, bearing shell mass of 0.1 kg, and bearing shell support stiffness of 1×107 N/m. The system excited by supersynchronous natural frequency associated with critical speed at ∼100 krpm.

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Figure 8

Plots of fK(ν) versus frequency ratio to determine zero-crossing points. Cases shown for bearing without radial compliance, 0.2 kg and 5×107 N/m bearing shell mass and support stiffness, and selected rotor speeds of (a) 10 krpm, (b) 40 krpm, (c) 70 krpm, and (d) 100 krpm.

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Figure 9

Predicted natural frequencies for bearing without radial compliance and fixed bearing support stiffness 1×107 N/m; comparisons with different bearing shell masses (0.1 kg, 0.2 kg, and 0.3 kg)

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Figure 10

Predicted natural frequencies for bearing without radial compliance and fixed bearing shell mass (0.2 kg); comparisons with different bearing shell masses (5×106 N/m, 1×107 N/m, and 5×107 N/m)

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Figure 11

Trends of natural frequencies for a simple two-mass system. Mass-1 and stiffness-1 are analogous to the bearing shell mass and support stiffness. Mass-2 and stiffness-2 are analogous to the rotor mass and gas film stiffness. Analogous comparisons show effects of increasing (a) bearing shell mass, (b) bearing shell support stiffness, and (c) gas film stiffness.

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Figure 12

Effect of increasing bearing shell mass on multiple crossing points for natural frequency contours

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Figure 13

Synchronous imbalance responses; bearings with radial compliance, plotted up to the speed where nonsynchronous vibrations begin to appear. Rotor response (solid line) and bearing shell response (dotted line). Fixed damper stiffness 1×107 N/m and varying bearing shell masses (0.1 kg, 0.2 kg, and 0.3 kg).

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Figure 14

Synchronous imbalance responses; bearings with radial compliance, plotted up to the speed where nonsynchronous vibrations begin to appear. Rotor response (solid line) and bearing shell response (dotted line). Fixed bearing shell mass (0.2 kg) and varying damper stiffnesses (5×106 N/m, 1×107 N/m, and 5×107 N/m).

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Figure 15

Cascade plot of rotor vibrations for simulated case of bearings with radial compliance, bearing shell mass of 0.3 kg, and bearing shell support stiffness of 1×107 N/m. The system excited by subsynchronous natural frequencies of rotor and bearing shell, which are suppressed after 140 krpm.

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Figure 16

Predicted natural frequencies for bearing with radial compliance and fixed bearing support stiffness (1×107 N/m); comparisons with different bearing shell masses (0.1 kg, 0.2 kg, and 0.3 kg)

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Figure 17

Predicted natural frequencies for bearing with radial compliance and fixed bearing shell mass (0.2 kg); comparisons with different bearing shell masses (5×106 N/m, 1×107 N/m, and 5×107 N/m)

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Figure 18

Plots of fK(ν) versus frequency ratio for 0.1 kg and 1×107 N/m bearing shell mass and support stiffness at 130–150 krpm. Inflection in contour causes abrupt change in the zero-crossing frequency ratio.

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Figure 19

Rotor growth increases the converging wedge effect for a bearing without radial compliance. Pad with radial compliance allows more rotor growth, but eventually leads to a loss of converging wedge.

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Figure 20

Synchronous direct stiffness coefficients for various cases of bearings described in Table 1. (a) Rotor growth significantly increases direct stiffness of bearing without radial compliance. (b) Radial compliance reduces the direct stiffness of the bearing and extends maximum operating speed.

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Figure 21

Rotor growth and mean pad deflection versus rotor speed for bearing with radial compliance described in Table 1. Radial compliance allows rotor growth to exceed original set bore clearance, but mean pad deflection must be smaller than original preload radius to maintain converging wedge effect.

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Figure 22

Mean film thickness values versus rotor speed for bearing with radial compliance described in Table 1. Mean pad tilt angle increases initially to grow local film thickness at leading edge of the pad, but rotor growth causes pad angle to neutralize. Eventually film thickness reduction ratio drops to near unity, indicating loss of preload.

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