Optimization tools in the analysis of micro-textured lubricated devices

Figures & data

Figure 1. Schematic view of a slider.

Figure 2. Schematic view of the dimples and an individual cell with its system of coordinates.

Figure 3. Flow chart of the genetic algorithm.

Figure 4. Non-dimensional Rayleigh step.

Figure 5. Results of the GENESIS code compared to the optimal Rayleigh step. Left: Case 1, Right: Case 2.

Table 1. Results of the GENESIS code compared to the exact ones, indicating the number of evaluations (Case 3).

Parameter	hleft	hright	D
Exact	1.8660	1	0.7182
100 Eval.	1.8756	1.00044	0.7029
500 Eval.	1.8662	1.00048	0.7029
4000 Eval.	1.8662	1.00039	0.7154
10,000 Eval.	1.8662	1	0.7174

Table 2. Relative load capacity obtained with the GENESIS code using 50, 100 and 200 variables to define the film thickness h.

Nvar	Relative load capacity
50	0.9991
100	0.9921
200	0.9629

Figure 6. History of the objective function along algorithmic iterations (relative to the exact optimum). The mutation rate constant is set to the default value of the GENESIS code, 0.001. The tics in the vertical axis have a spacing of 0.1.

Figure 7. History of the objective function along algorithmic iterations (relative to the exact optimum). The mutation rate constant is set to 0.01.

Figure 8. History of the objective function along algorithmic iterations (relative to the exact optimum). The mutation rate constant is set to 0.1, a value that is too high to attain convergence.

Figure 9. Friction force and minimum film thickness derivatives along the slider.

Figure 10. Relative friction force and minimum film thickness. Evolution along the optimization process. Notice that a 4% decrease in friction, together with a 2% increase in minimum film thickness, is attained.

Figure 11. Optimized textures for two different non-dimensional loads: 0.06 (top) and 0.006 (bottom).

Figure 12. Scheme showing the region in which dimples are introduced in the finite-width case.

Figure 13. Pressure distribution when a uniform texture is introduced in the region indicated in figure 12.

Figure 14. A 3D view of depth distribution of the optimized texture after 3000 evaluations of the objective function. The maximum depth is 1.292, the minimum one is 0.085.

Figure 15. Two 3D views of depth distribution of the optimized texture obtained after 18,000 evaluations of the objective function. The maximum depth is 1.294, the minimum one is 0.0025.

Figure 16. Optimized texture with the depth shown by means of color zones. The maximum depth is 1.294 (brighter), the minimum one is 0.0025 (darker).