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Research Papers: Gas Turbines: Structures and Dynamics

Metal Mesh Foil Bearing: Effect of Motion Amplitude, Rotor Speed, Static Load, and Excitation Frequency on Force Coefficients

[+] Author and Article Information
Luis San Andrés

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

Thomas Abraham Chirathadam

Mechanical Engineering Department,  Texas A&M University, College Station, TX 77843-3123

The assertion applies to foil bearings and many types of seals with complicated surface textures.

The parameter derived from single input (force)-single output(displacement)

An earlier MMFB [1-3] similar in size, had a thicker mesh (6.9 mm). The current bearing having a thinner mesh thickness replicates commercial foil bearings. To manufacture the thin ring, metal mesh strips are stacked up vertically and compressed under ∼30 ton load to reach the desired density of 20% (compactness). The compressed flat strip is hand-curved and inserted into the cartridge, along with the top foil, to complete the bearing construction.

Bearing force coefficients are derived from radial (lateral) forces and ensuing bearing displacements along two orthogonal directions. Accurate and reliable parameter identification requires the test element not to displace axially; or worse yet not to pitch (or yaw), with respect to the rotor spinning axis. Hence, it is common to add external constraints, i.e., pairs of taut cables for example. The arrangement is very flexible radially yet has a high rotational stiffness to minimize pitch or yaw of the test element when excited [18].

In a 1 DOF model, combining the damping ratio, ξ = CXX /2Mωn , with the loss factor model, γ = CXX ω/KXX , gives the relationship, γ = 2 ξ (ω/ωn ).

J. Eng. Gas Turbines Power 133(12), 122503 (Aug 29, 2011) (10 pages) doi:10.1115/1.4004112 History: Received April 08, 2011; Revised April 21, 2011; Published August 29, 2011; Online August 29, 2011

Metal mesh foil bearings (MMFBs), simple to construct and inexpensive, are a promising bearing technology for oil-free microturbomachinery operating at high speed and high temperature. Prior research demonstrated the near friction-free operation of a MMFB operating to 60 krpm and showing substantial mechanical energy dissipation characteristics. This paper details further experimental work and reports MMFB rotordynamic force coefficients. The test rig comprises a turbocharger driven shaft and overhung journal onto which a MMFB is installed. A soft elastic support structure akin to a squirrel cage holds the bearing, aiding to its accurate positioning relative to the journal. Two orthogonally positioned shakers excite the test element via stingers. The test bearing comprises a cartridge holding a Copper wire mesh ring, 2.7 mm thick, and a top arcuate foil. The bearing length and inner diameter are 38 mm and 36.5 mm, respectively. Experiments were conducted with no rotation and with journal spinning at 40–50 krpm, with static loads of 22 N and 36 N acting on the bearing. Dynamic load tests spanning frequencies from 150 to 450 Hz were conducted while keeping the amplitude of bearing displacements at 20 µm, 25 µm, and 30 µm. With no journal spinning, the force coefficients represent the bearing elastic structure alone because the journal and bearing are in contact. The direct stiffnesses gradually increase with frequency while the direct damping coefficients drop quickly at low frequencies (< 200 Hz) and level off above this frequency. The damping combines both viscous and material types from the gas film and mesh structure. Journal rotation induces airborne operation with a hydrodynamic gas film separating the rotor from its bearing. Hence, cross-coupled stiffness coefficients appear although with magnitudes lower than those of the direct stiffnesses. The direct stiffnesses, 0.4 to 0.6 MN/m within 200–400 Hz, are slightly lower in magnitude as those obtained without journal rotation, suggesting the air film stiffness is quite high. Bearing direct stiffnesses are inversely proportional to the bearing motion amplitudes, whereas the direct equivalent viscous damping coefficients do not show any noticeable variation. All measurements evidence a test bearing system with material loss factor (γ) ∼ 1.0, indicating significant mechanical energy dissipation ability.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic cut view of a metal mesh foil bearing

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Figure 2

Photograph of the MMFB mounted on the test journal. Inset shows a slot in the bearing cartridge for affixing the top foil.

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Figure 3

Photograph of gas bearing test rig for dynamic load excitations

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Figure 4

Schematic view of MMFB mounted on shaft of turbocharger drive system. Inset shows two stingers for application of dynamic loads along two orthogonal directions.

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Figure 5

Typical excitation force along X direction versus time. Sine sweep 150–450 Hz.

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Figure 6

Bearing relative displacements along X and Y directions for excitation forces along X (top) and Y (bottom) directions. Rotor speed 50 krpm (833 Hz).

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Figure 7

Identified MMFB direct and cross-coupled stiffnesses versus frequency. Applied static load of 22 N. Dynamic displacement amplitude  30 μm. Rotor speeds = (a) 0 rpm, (b) 40 krpm (667 Hz), (c) 45 krpm (750 Hz), and (d) 50 krpm (833 Hz).

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Figure 8

Identified MMFB direct and cross-coupled equivalent viscous damping coefficients versus frequency. Applied static load of 22 N. Dynamic displacement amplitude 30 μm. Rotor speeds = (a) 0 rpm, (b) 40 krpm (667 Hz), (c) 45 krpm (750 Hz), and (d) 50 krpm (833 Hz).

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Figure 9

Identified MMFB direct and cross-coupled stiffnesses versus frequency. Motion amplitudes of 20 μm and 25 µm Applied static load of 22 N. Rotor speed of 50 krpm (833 Hz).

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Figure 10

Identified MMFB direct and cross-coupled equivalent viscous damping coefficients versus frequency. Bearing motion amplitudes = 20 μm and 25 μm. Applied static load = 22 N. Rotor speed = 50 krpm (833 Hz).

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Figure 11

Derived MMFB loss factor versus frequency. Dynamic displacement amplitude 30 μm. Rotor speeds = 0 rpm, 40 krpm (667 Hz), 45 krpm (750 Hz) and 50 krpm (833 Hz). Applied static loads of 22 N and 36 N (50 krpm only).

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Figure 12

Waterfall plot of (a) excitation force (150–450 Hz) along X direction and (b) bearing dynamic displacement (30 μm) along X direction. Rotor speed = 50 krpm (833 Hz). Applied static load of 22 N.

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