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Research Papers

Data-Driven Model for the Dynamic Characteristics of O-Rings for Gas Bearing Supported Rotors

[+] Author and Article Information
Philipp Bättig

Department of Mechanical Engineering,
Laboratory for Applied Mechanical Design,
Ecole Polytechnique Fédérale de Lausanne,
CH-2002 Neuchâtel 2, Switzerland
e-mail: philipp.battig@epfl.ch

Jürg Schiffmann

Department of Mechanical Engineering,
Laboratory for Applied Mechanical Design,
Ecole Polytechnique Fédérale de Lausanne,
CH-2002 Neuchâtel 2, Switzerland
e-mail: jurg.schiffmann@epfl.ch

Manuscript received December 21, 2018; final manuscript received April 9, 2019; published online May 13, 2019. Assoc. Editor: Ahmet S. Yigit.

J. Appl. Mech 86(8), 081003 (May 13, 2019) (10 pages) Paper No: JAM-18-1722; doi: 10.1115/1.4043473 History: Received December 21, 2018; Accepted April 09, 2019

The measurement results of various nitrile butadiene rubber (NBR) O-Ring sizes are presented, and reduced-order models are developed in order to predict the stiffness and damping coefficient as a function of O-Ring geometry, Shore hardness, squeeze, and excitation frequency. The results show that the curvature ratio d/D needs to be considered in the reduced-order models. The assessment of the model suggests a maximum deviation of 30% in predicted stiffness compared to the measurement data. However, taking into account the typical Shore hardness tolerance given by O-Ring manufacturers and other measurement uncertainties, the proposed model enables the prediction of various O-Rings with a good accuracy in the frequency range of 1.5–3.75 kHz, which corresponds to typical gas bearing supported rotor applications.

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References

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Figures

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Fig. 1

Measurement of O-Ring supported bearing bushing amplitudes

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Fig. 2

O-Ring nomenclature

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Fig. 4

Pareto chart of relative effects on stiffness and damping for the tested NBR O-Rings

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Fig. 5

Evolution of the measured stiffness k1 as a function of excitation frequency for selected Shore 70 and 90 NBR O-Rings

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Fig. 6

Evolution of the measured damping coefficient c as a function of excitation frequency for selected Shore 70 and 90 NBR O-Rings

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Fig. 7

Identified storage modulus E’ as a function of frequency and Shore hardness

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Fig. 8

Dimensionless stiffness k as a function of d/D and squeeze δ for Shore 70

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Fig. 9

Dimensionless stiffness k as a function of d/D and squeeze δ for Shore 90

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Fig. 10

Averaged loss factor η for Shore 70 and Shore 90 NBR O-Rings including standard deviations and second-order polynomial fit for Shore 70 and Shore 90 NBR O-Rings

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Fig. 11

Comparison of predicted and measured stiffness k1

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Fig. 12

Comparison of predicted and measured damping coefficient c

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Fig. 13

Residual error of fitted surface of dimensionless stiffness versus d/D and squeeze δ

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Fig. 14

Plot of static storage modulus E0 as a function of Shore hardness according Eq. 18

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Fig. 15

Measured O-Ring stiffness compared to predicted stiffness for Shore 90, D = 20 mm, d = 2 mm, and δ=10%. Dashed lines represent measurement uncertainty, while dash-dotted lines include measurement and Shore hardness uncertainty.

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Fig. 16

Measurement results for stiffness k1 of a Shore 70 NBR O-Ring with d = 1 mm

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Fig. 17

Measurement results for stiffness k1 of a Shore 70 NBR O-Ring with d = 2 mm

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Fig. 18

Measurement results for stiffness k1 of a Shore 70 NBR O-Ring with d = 3 mm

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Fig. 19

Measurement results for stiffness k1 of a Shore 90 NBR O-Ring with d = 1 mm

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Fig. 20

Measurement results for stiffness k1 of a Shore 90 NBR O-Ring with d = 2 mm

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Fig. 21

Measurement results for stiffness k1 of a Shore 90 NBR O-Ring with d = 3 mm

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Fig. 22

Measurement results for damping coefficient c of a Shore 70 NBR O-Ring with d = 1 mm

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Fig. 23

Measurement results for damping coefficient c of a Shore 70 NBR O-Ring with d = 2 mm

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Fig. 24

Measurement results for damping coefficient c of a Shore 70 NBR O-Ring with d = 3 mm

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Fig. 25

Measurement results for damping coefficient c of a Shore 90 NBR O-Ring with d = 1 mm

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Fig. 26

Measurement results for damping coefficient c of a Shore 90 NBR O-Ring with d = 2 mm

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Fig. 27

Measurement results for damping coefficient c of a Shore 90 NBR O-Ring with d = 3 mm

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