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Research Papers: Hydrodynamic Lubrication

Geometry Optimization of Textured Three-Dimensional Micro- Thrust Bearings

[+] Author and Article Information
C. I. Papadopoulos, E. E. Efstathiou, L. Kaiktsis

School of Naval Architecture and Marine Engineering, National Technical University of Athens,15710 Zografos, Greece

P. G. Nikolakopoulos

Machine Design Laboratory, Department of Mechanical Engineering and Aeronautics,  University of Patras, 26504 Patras, Greece

J. Tribol 133(4), 041702 (Oct 14, 2011) (14 pages) doi:10.1115/1.4004990 History: Received March 31, 2011; Revised July 25, 2011; Accepted August 12, 2011; Published October 14, 2011; Online October 14, 2011

This paper presents an optimization study of the geometry of three-dimensional micro-thrust bearings in a wide range of convergence ratios. The optimization goal is the maximization of the bearing load carrying capacity. The bearings are modeled as micro-channels, consisting of a smooth moving wall (rotor), and a stationary wall (stator) with partial periodic rectangular texturing. The flow field is calculated from the numerical solution of the Navier-Stokes equations for incompressible isothermal flow; processing of the results yields the bearing load capacity and friction coefficient. The geometry of the textured channel is defined parametrically for several width-to-length ratios. Optimal texturing geometries are obtained by utilizing an optimization tool based on genetic algorithms, which is coupled to the CFD code. Here, the design variables define the bearing geometry and convergence ratio. To minimize the computational cost, a multi-objective approach is proposed, consisting in the simultaneous maximization of the load carrying capacity and minimization of the bearing convergence ratio. The optimal solutions, identified based on the concept of Pareto dominance, are equivalent to those of single-objective optimization problems for different convergence ratio values. The present results demonstrate that the characteristics of the optimal texturing patterns depend strongly on both the convergence ratio and the width-to-length ratio. Further, the optimal load carrying capacity increases at increasing convergence ratio, up to an optimal value, identified by the optimization procedure. Finally, proper surface texturing provides substantial load carrying capacity even for parallel or slightly diverging bearings. Based on the present results, we propose simple formulas for the design of textured micro-thrust bearings.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Three-dimensional textured converging slider geometry (parallel slider for H1  = H0 , diverging slider for H1  < H0 ). (b) Geometry of dimples. (c) Typical thrust bearing application with partial texturing.

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Figure 2

Half-slider top view, in which three x-y cross-sections are indicated

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Figure 3

Validation of present CFD results against literature data: (a) Computed non-dimensional pressure distribution versus non-dimensional streamwise coordinate for a converging micro-bearing with texturing. (b) Computed non-dimensional load carrying capacity versus convergence ratio of smooth rectangular sliders, for a number of B/L ratios.

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Figure 4

(a) Sketch of Pareto front concept for a minimization problem with two objective functions. (b) Optimization flow chart of the present study. (c) Non-dimensional load carrying capacity versus convergence ratio for infinite width untextured and textured sliders, and corresponding Pareto front.

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Figure 5

Optimal non-dimensional load carrying capacity, W* , versus convergence ratio, k, for textured sliders of different B/L ratios (N = 5, ρT = 0.83). Results for smooth converging channels and optimal step bearings are also presented.

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Figure 6

Optimal micro-bearing geometries for various B/L ratios. Cases of k = 0 and k = kopt are presented. (Domain is compressed by a factor of 33% in the x direction.)

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Figure 7

Optimal values of luo and s versus k, for textured sliders of different B/L ratios (N = 5, ρT = 0.83). Line fits to the computed data are also included.

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Figure 8

Optimal bearings with B/L = 2.0, N = 5 and ρT = 0.83: variation of load carrying capacity versus the design variables, in the regime of the optimum

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Figure 9

B/L = inf, N = 5, ρT = 0.83: distributions of non-dimensional pressure on the moving wall of the slider, for different values of non-dimensional untextured outlet length, luo , and relative dimple height, s. Graphs (a) and (b) correspond to parallel sliders (k = 0). Graphs (c) and (d) correspond to convergent sliders of k = kopt . The solid lines correspond to optimal points of the Pareto front.

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Figure 10

B/L = 2.0, k = 0, N = 5, ρT = 0.83: (a)-(c) Color-coded contours of non-dimensional pressure on the moving wall of the slider, for different values of non-dimensional untextured outlet length, luo . (d)-(f) Corresponding distribution of non-dimensional pressure at three cross-sections of the moving wall, depicted in Fig. 2.

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Figure 11

B/L = 2.0, k = 0, N = 5, ρT = 0.83: (a)-(c) Color-coded contours of non-dimensional pressure on the moving wall of the slider for different values of relative dimple height, s. (d)-(f) Corresponding distribution of non-dimensional pressure at three cross-sections of the moving wall, depicted in Fig. 2.

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Figure 12

B/L = 2.0, k = 0.91, N = 5, ρT = 0.83: (a)-(c) Color-coded contours of non-dimensional pressure on the moving wall of the slider for different values of non-dimensional untextured outlet length, luo ; (d)-(f) Corresponding distribution of non-dimensional pressure at three cross-sections of the moving wall, depicted in Fig. 2.

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Figure 13

Streamlines for optimized parallel bearings with N = 5, ρT = 0.83, released at different y-levels of the inlet plane, coded with velocity magnitude: top view, and cross section at the symmetry plane, for (a) B/L = 2.0 and (b) B/L = 1.0. (In the x-y plane, domain is compressed by a factor of 5 in the x direction.)

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Figure 14

Color-coded contours of non-dimensional w-velocity, for optimal bearings with N = 5, ρT = 0.83, at a x-z plane located at y = -0.8Hmin , and at the x-y plane corresponding to the bearing side (z = −B/2), for: (a) B/L = 2.0, k = 0, (b) B/L = 1.0, k = 0, (c) B/L = 2.0, k = 0.91, and (d) B/L = 1.0, k = 1.1. (In the x-y plane, domain is compressed by a factor of 3 in the x direction.)

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Figure 15

(a) Non-dimensional load carrying capacity and (b) friction coefficient, versus convergence ratio, for texture geometries based on the fitted equations presented in Fig. 7 For all cases, N = 5, ρT = 0.83

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Figure 16

B/L = 1.0: non-dimensional load carrying capacity, W* , versus convergence ratio, k, for (a) different values of texture density, ρT, and (b) different number of dimples, N. Variables luo and s are derived from the proposed formulas of Fig. 7.

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Figure 17

N = 5, ρT = 0.83: normalized non-dimensional load carrying capacity, W* /W* Re = 1 , versus Reynolds number, Re, for different values of convergence ratio, k, for (a) B/L = inf, (b) B/L = 2.0, (c) B/L = 1.0

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Figure 18

B/L = 1.0, N = 5, ρT = 0.83: (a) non-dimensional load carrying capacity, W* , versus convergence ratio, k, for different values of Reynolds number, Re. (b) distribution of non-dimensional pressure at the bearing symmetry plane for k = 0, for different Re values.

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