Analytical solution of gas lubricated slider microbearing |
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Authors: | Nevena D Stevanovic |
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Affiliation: | (1) Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia |
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Abstract: | The analytical solution of a two-dimensional, isothermal, compressible gas flow in a slider microbearing is presented. A higher
order accuracy of the solution is achieved by applying the boundary condition of Kn
2 order for the velocity slip on the wall, together with the momentum equation of the same order (known as the Burnett equation).
The analytical solution is obtained by the perturbation analysis. The order of all terms in continuum and momentum equations
and in boundary conditions is evaluated by incorporating the exact relation between the Mach, Reynolds and Knudsen numbers
in the modelling procedure. Low Mach number flows in microbearing with slowly varying cross-sections are considered, and it
is shown that under these conditions the Burnett equation has the same form as the Navier–Stokes equation. Obtained analytical
results for pressure distribution, load capacity and velocity field are compared with numerical solutions of the Boltzmann
equation and some semi-analytical results, and excellent agreement is achieved. The model presented in this paper is a useful
tool for the prediction of flow conditions in the microbearings. Also, its results are the benchmark test for the verifications
of various numerical procedures. |
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Keywords: | Slip flow Slider microbearing Low Mach number Analytical solution |
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