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Research Papers: Gas Turbines: Structures and Dynamics

# Identification of Rotordynamic Force Coefficients of a Metal Mesh Foil Bearing Using Impact Load Excitations

[+] Author and Article Information
Luis San Andrés

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

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

The EOMs assume the system is linear and omit, for simplicity in the description, the effects of mass imbalance. In the frequency domain identification procedure, components with frequencies synchronous with journal speed and higher frequencies are conveniently filtered.

See Ref. 29 for a definition of this graphical output in commercial DAQ software.

J. Eng. Gas Turbines Power 133(11), 112501 (May 13, 2011) (9 pages) doi:10.1115/1.4002658 History: Received April 24, 2010; Revised May 06, 2010; Published May 13, 2011; Online May 13, 2011

## Abstract

Metal mesh foil bearings (MMFBs) are inexpensive compliant gas bearing type that aim to enable high speed, high temperature operation of small turbomachinery. A MMFB with an inner diameter of 28.00 mm and length of 28.05 mm is constructed with low cost and common materials. The bearing incorporates a copper mesh ring, 20% in compactness, and offering large material damping beneath a 0.127 mm thick preformed top foil. Prior experimentations (published papers) provide the bearing structure force coefficients and the break away torque for bearing lift off. Presently, the MMFB replaces a compressor in a small turbocharger driven test rig. Impact load tests aid to identify the direct and cross-coupled rotor dynamic force coefficients of the floating MMFB while operating at a speed of 50 krpm. Tests conducted with and without shaft rotation show the MMFB direct stiffness is less than its structural (static) stiffness, $∼25%$ lower at an excitation frequency of 200 Hz. The thin air film acting in series with the metal mesh support and separating the rotating shaft and the bearing inner surface while airborne reduces the bearing stiffness. The equivalent viscous damping is nearly identical with and without shaft rotation. The identified loss factor, best representing the hysteretic type damping from the metal mesh, is high at $∼0.50$ in the frequency range 0–200 Hz. This magnitude reveals large mechanical energy dissipation ability from the MMFB. The measurements also show appreciable cross directional motions from the unidirectional impact loads, thus generating appreciable cross-coupled force coefficients. Rotor speed coast down measurements reveal pronounced subsynchronous whirl motion amplitudes locked at distinct frequencies. The MMFB stiffness hardening nonlinearity produces the rich frequency forced response. The synchronous as well as subsynchronous motions peak while the shaft traverses its critical speeds. The measurements establish reliable operation of the test MMFB while airborne.

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## Figures

Figure 1

Photograph of prototype metal mesh foil bearing

Figure 2

Schematic view of MMFB mounted on shaft of turbocharger drive system. Inset shows a positioning table applying a horizontal static load on the MMFB.

Figure 3

Rotor speed and bearing torque versus time during a lift-off test cycle with an applied static load of 17.8 N (4 lb). Speed—up to 65 krpm, operation at constant speed of 65 krpm, and deceleration to rest. Taken from Ref. 3.

Figure 4

MMFB power loss versus rotor speed for increasing static loads

Figure 5

MMFB drag friction coefficient f versus rotor speed for increasing static loads. Steady-state operation with bearing airborne. Taken from Ref. 3.

Figure 6

Reference coordinate system (X,Y), depiction of impact forces acting on test bearing, and idealized representation of force coefficients. Bearing weight is along −Y direction.

Figure 7

Typical bearing Y displacement with respect to shaft versus time. Motion due to an impact force along vertical direction. Journal not rotating.

Figure 8

DFT amplitude of bearing Y displacement with respect to shaft due to impact forces along vertical direction. Average of ten impacts. Journal not rotating.

Figure 9

DFT amplitudes of acceleration of bearing cartridge (measured and derived from displacement) versus frequency. Average of ten impacts. Journal not rotating.

Figure 10

(Force/displacement) versus (acceleration/displ.) and linear fit identifying the MMFB structural stiffness and mass coefficients. Average of ten impacts. Journal not rotating.

Figure 11

Identified MMFB structural stiffness K=KYY=KXX versus frequency. Journal not rotating.

Figure 12

Identified MMFB equivalent viscous damping C=CYY=CXX versus frequency. Journal not rotating.

Figure 13

DFT amplitude of bearing displacements (x,y) with respect to journal. Baseline response. Journal speed=50 krpm (834 Hz).

Figure 14

Typical bearing (filtered) displacements with respect to shaft due to a Y-impact load. Time domain data show the bearing response to one of ten impact loads. Journal speed=50 krpm (834 Hz). Motions with frequency components above >200 Hz filtered.

Figure 15

DFT amplitude of bearing displacements with respect to the shaft due to the impact force along vertical direction (Y). Average of ten impacts. Journal sped=50 krpm (834 Hz).

Figure 16

Identified MMFB direct (K) and cross-coupled (k) stiffnesses versus frequency. Journal speed=50 krpm (834 Hz). Direct stiffness for condition of no journal rotation (Fig. 1) included for comparison.

Figure 17

Identified MMFB direct (C) and cross-coupled (c) equivalent viscous damping coefficients versus frequency. Journal speed=50 krpm (834 Hz). Direct damping for condition of no journal rotation (Fig. 1) included for comparison.

Figure 18

Identified MMFB loss factor (γ) versus excitation frequency for stationary journal and for journal spinning at 50 krpm (834 Hz)

Figure 19

Full spectra cascade of MMFB orbit relative to shaft. Rotor decelerates from 60 krpm (1 kHz). Applied static load=3.5 N in horizontal direction. Bearing weight of 3.5 N.

Figure 20

Full spectra cascade plot of MMFB orbit relative to shaft. Rotor decelerates from 60 krpm (1 kHz). Applied static load=18 N in horizontal direction. Bearing weight=3.5 N.

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