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Numerical investigation of influence sensitivity of a gas foil bearing parameters on the dynamic coefficients

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Abstract

Most studies on dynamic coefficients of bearings are focused on evaluation using different analytical methods. Minimal emphasis is given to the level of influence of each geometrical variable, the corresponding range of these variables for optimum stiffness and damping and the measure of performance of the analytical method used. The objective of this paper was to study the influence and sensitivity of length-to-diameter ratio, eccentricity ratio, bearing number, whirl ratio, and bearing compliance on the stiffness and damping of gas foil bearing. A numerical model is developed by utilizing the finite difference method to evaluate the dynamic coefficients. The results reveal that the normalized stiffness increases with the bearing number and decreases with increased bearing compliance whereas the normalized damping shows an opposite nature. Further, the stiffness coefficients tend to increase and the damping coefficients tend to decrease corresponding to increase in speed up to 240 krpm. The characteristic data sets obtained from the analysis is used to train an artificial neural network (ANN). Performance of ANN network is evaluated though computation of root-mean-square error (RSME) and regression coefficient (R2) and Mean Absolute Error (MAE). Utilizing the neural network results, a Sobol’s sensitivity test is carried out to identify most effective parameters which have a significant influence on the dynamic coefficients of gas foil bearing. After that, an adaptive neurofuzzy interface system (ANFIS) is established to determine the optimum range of data for which maximum stiffness and damping can be obtained. The results deduce that the neural network shows high efficacy in predicting the output variables correctly with a regression of more than 95%. It is also observed that the variation of dynamic coefficients is the highest for eccentricity ratio whereas lowest for whirl ratio. The maximum stiffness and damping coefficients are also obtained for a wide range of geometrical variables which can help in designing the gas foil bearing.

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Abbreviations

R :

Radius of the journal (mm)

h :

Film thickness (mm)

h b :

Bump height (mm)

R b :

Bump radius (mm)

C :

Radial clearance (mm)

p :

Aerodynamic pressure (N/m 2)

s :

Pitch of bump (mm)

P :

Atmospheric pressure (N/m 2)

2 l :

Length of bump (mm)

E :

Young's modulus (N/m 2)

t b :

Bump foil thickness (mm)

\(\overline{p}\) :

Non-dimensional pressure (p/p a)

C :

Nominal bearing clearance (mm)

\(\overline{h}\) :

Non-dimensional film thickness (h/C)

\(\overline{t}\) :

Normalized time variable (ν t)

L/D :

Length-to-diameter ratio

\(\overline{h}_{0}\) , \(\overline{h}_{x}\) , \(\overline{h}_{y}\) , \(\overline{h}_{{\mathop 0\limits^{.} }}\) , \(\overline{h}_{{\mathop x\limits^{.} }}\) , \(\overline{h}_{{\mathop y\limits^{.} }}\) :

Perturbation components of \(\overline{h}\)

Δ x, Δ y :

Normalized perturbations

\(\overline{p}_{0}\) , \(\overline{p}_{x}\) , \(\overline{p}_{y}\) , \(\overline{p}_{{\mathop 0\limits^{.} }}\) , \(\overline{p}_{{\mathop x\limits^{.} }}\) , \(\overline{p}_{{\mathop y\limits^{.} }}\) :

Perturbation components of \(\overline{p}\)

\(\overline{K}_{mn}\) :

Normalized stiffness of bearing (\(c\overline{K}_{mn} /p_{a} R^{2}\))

\(\overline{C}_{mn}\) :

Normalized damping of bearing (\(c\omega \overline{C}_{mn} /p_{a} R^{2}\))

\(\overline{k}\) :

Normalized stiffness of the foundation (\(kc/p_{a}\))

\(\overline{u}\) :

Normalized foil deflection (u/c)

\(F_{x}\) , \(F_{y}\) :

Resultant forces in x and y directions

\(\overline{W}\) :

Normalized bearing load (\(W/p_{a} R^{2}\))

\(\overline{z}\) :

Normalized axial coordinate

θ :

Circumferential coordinate

Α :

Compliance number (\(p_{a} /ck\))

γ :

Whirl frequency ratio (ν/ω)

Λ :

Bearing number (\(6\mu \omega R^{2} /p_{a} c^{2}\))

Ε:

Eccentricity ratio

μ :

Lubricant viscosity

ν :

Whirl frequency

ω :

Rotor angular velocity

MLP:

Multi-layer perceptron

MF:

Membership function

MAE:

Mean absolute error

RMSE:

Root-mean-squared error

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Authors and Affiliations

  1. Department of Mechanical Engineering, NIT Rourkela, Rourkela, Odisha, 769008, India

    Debanshu S. Khamari, Jitesh Kumar & Suraj K. Behera

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  1. Debanshu S. Khamari
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  2. Jitesh Kumar
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  3. Suraj K. Behera
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Correspondence to Debanshu S. Khamari.

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Khamari, D.S., Kumar, J. & Behera, S.K. Numerical investigation of influence sensitivity of a gas foil bearing parameters on the dynamic coefficients. J Braz. Soc. Mech. Sci. Eng. 43, 167 (2021). https://doi.org/10.1007/s40430-021-02874-0

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  • DOI: https://doi.org/10.1007/s40430-021-02874-0

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