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Load Capacity Analysis of Gas Foil Bearing (GFB) for Different Foil Materials

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Proceedings of International Conference on Advances in Tribology and Engineering Systems

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

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Abstract

There is a significant attention on GFBs in recent times owing to its oil free technology and suitability over a wide array of operating conditions. However GFBs have considerably low load carrying capacity compared to normal GFBs. The present paper investigated the load capacity of the bump-type GFBs for a simple model considering only deflection of bump foils. The load capacity of GFBs with different foil materials has been inspected in view of comparing the load capacity. Also the variations of GFBs load performance with respect to the compliance of the foil have been reviewed.

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Abbreviations

C :

Bearing radial clearance (m)

D :

Diameter of journal (m)

e :

Bearing eccentricity (m)

\( E_{b} \) :

Young’s modulus of bump foil

\( E_{t} \) :

Young’s modulus of top foil \( ({\text{N}}/{\text{m}}^{2} ) \)

\( F_{X} ,F_{Y} \) :

Vertical and horizontal components of hydrodynamic forces (N)

\( \bar{F}_{X} ,\bar{F}_{Y} \) :

Non-dimensional vertical and horizontal components of hydrodynamic forces: \( \frac{{F_{X} }}{{p_{a} R^{2} }}, \frac{{F_{Y} }}{{p_{a} R^{2} }} \)

\( F_{X0} ;F_{Y0} \) :

Vertical and horizontal steady state components of hydrodynamic forces (N)

\( \bar{F}_{X0} ,\bar{F}_{Y0} \) :

Non-dimensional vertical and horizontal steady state components of hydrodynamic forces: \( \frac{{F_{X0} }}{{p_{a} R^{2} }}; \) \( \frac{{F_{Y0} }}{{p_{a} R^{2} }} \)

h :

Film thickness (m)

\( h_{o} \) :

Initial bump height (m)

\( h_{\hbox{min} } \) :

Minimum film thickness (m)

H :

Non-dimensional film thickness

\( H_{\hbox{min} } \) :

Non-dimensional minimum film thickness

i, j :

Grid location in circumferential and axial directions of FDM mesh

\( K_{f} \) :

Bump foil structural stiffness per unit area \( ( {\text{N/m}}^{ 2} ) \)

\( l_{o} \) :

Half bump length (m)

\( l_{s} \) :

Length of segment between the bumps (m)

L:

Bearing length (m)

m :

Number of divisions along j direction of FDM mesh

n :

Number of divisions along i direction of FDM mesh

O :

Centre of bearing

\( O^{\prime} \) :

Centre of journal

\( p \) :

Hydrodynamic pressure in gas film \( ( {\text{N/m}}^{ 2} ) \)

\( p_{a} \) :

Atmospheric pressure in gas film \( ( {\text{N/m}}^{ 2} ) \)

\( \bar{P} \) :

Arithmetic mean pressure along bearing length \( ( {\text{N/m}}^{ 2} ) \)

\( P \) :

Non-dimensional hydrodynamic pressure

\( \bar{p} \) :

Non-dimensional arithmetic mean pressure along bearing length

R :

Radius of journal (m)

s :

Bump foil pitch (m)

\( S \) :

Compliance number: \( \frac{{p_{a} }}{{CK_{f} }} \)

\( t \) :

Time (s)

\( t_{b} \) :

Bump foil thickness (m)

\( t_{t} \) :

Top foil thickness (m)

\( w_{t} \) :

Top foil transverse deflection (m)

\( W \) :

Non-dimensional top foil transverse deflection

\( W_{0} \) :

Steady state load carrying capacity (N)

\( \bar{W}_{0} \) :

Non-dimensional steady state load carrying capacity

\( x,y,z \) :

Coordinate system on the plane of bearing

\( Z \) :

Non-dimensional axial coordinate of bearing: \( \frac{z}{R} \)

\( \alpha \) :

Compliance of the bump foil \( ({\text{m}}^{3} /{\text{N}}):\frac{1}{{K_{f} }} \)

\( \varepsilon \) :

Eccentricity ratio

\( \Uplambda \) :

Bearing number: \( \frac{6\mu \omega }{{p_{a} }}\left( \frac{R}{C} \right)^{2} \)

\( \mu \) :

Gas viscosity \( ( {\text{N - s/m}}^{ 2} ) \)

\( \phi \) :

Attitude angle \( ( {\text{rad)}} \)

\( \theta \) :

Angular coordinate of bearing (rad): \( \frac{x}{R} \)

\( \theta_{o} \) :

Half bump angle (rad)

\( \upsilon \) :

Poisson’s ratio

\( \tau \) :

Non-dimensional time: \( \omega t \)

\( \omega \) :

Rotor angular velocity \( ( {\text{rad/s)}} \)

\( \Updelta \theta ,\Updelta Z \) :

Non-dimensional mesh size of FDM mesh

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Acknowledgments

This work has been carried out in the Department of Mechanical Engineering, Indian Institute of Technology, Guwahati, India, under the supervision of Prof. S. K. Kakoty.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, 781039, India

    T. M. Jamir & S. K. Kakoty

Authors
  1. T. M. Jamir
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  2. S. K. Kakoty
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Corresponding author

Correspondence to T. M. Jamir .

Editor information

Editors and Affiliations

  1. Department of Mathematics, L.D. College of Engineering, Ahmedabad, Gujarat, India

    Himanshu C. Patel

  2. Department of Mathematics, Sardar Patel University, Vallabh VidyaNagar, Gujarat, India

    Gunamani Deheri

  3. University Area, L.D. College of Engineering, Ahmedabad, Gujarat, India

    Harshvadan S. Patel

  4. Department of Mechanical Engineering University Area, L.D. College of Engineering, Ahmedabad, Gujarat, India

    Shreya M. Mehta

Appendix A

Appendix A

$$ K_{1} = H_{i}^{3} (C_{1} + C_{2} ) $$
$$ K_{2} = H_{i}^{3} (C_{3} + C_{4} ) $$
$$ K_{3} = C_{5} + C_{6} - C_{7} $$
$$ C_{1} = \frac{ - 2}{{(\Updelta \theta )^{2} }} $$
$$ C_{2} = \frac{ - 2}{{(\Updelta Z)^{2} }} $$
$$ C_{3} = \frac{{P_{i + 1,j} + P_{i - 1,j} }}{{(\Updelta \theta )^{2} }} $$
$$ C_{4} = \frac{{P_{i,j + 1} + P_{i,j - 1} }}{{(\Updelta Z)^{2} }} $$
$$ C_{5} = \frac{{(P_{i + 1,\,j} + P_{i - 1,\,j} )(P_{i + 1,\,j} H_{i + 1}^{3} + P_{i - 1,\,j} H_{i - 1}^{3} )}}{{4(\Updelta \theta )^{2} }} $$
$$ C_{6} = \frac{{(P_{i,\,j + 1} - P_{i,\,j - 1} )(P_{i,\,j + 1} H_{i}^{3} - P_{i,\,j - 1} H_{i}^{3} )}}{{4(\Updelta Z)^{2} }} $$
$$ C_{7} = \frac{{\Uplambda (P_{i + 1,\,j} H_{i + 1} + P_{i - 1,\,j} H_{i - 1} )}}{2(\Updelta \theta )} $$

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Jamir, T.M., Kakoty, S.K. (2014). Load Capacity Analysis of Gas Foil Bearing (GFB) for Different Foil Materials. In: Patel, H., Deheri, G., Patel, H., Mehta, S. (eds) Proceedings of International Conference on Advances in Tribology and Engineering Systems. Lecture Notes in Mechanical Engineering. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1656-8_29

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  • DOI: https://doi.org/10.1007/978-81-322-1656-8_29

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  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-1655-1

  • Online ISBN: 978-81-322-1656-8

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