The Optimization for the Shape Profile of the Slider Surface Under Ultra-Thin Film Lubrication Conditions by the Rarefied-Flow Model

The optimization of the surface shape for a slider to meet the specified load demands under an ultra-thin film lubrication condition has been performed in this study. The optimization process is developed based on the conjugate gradient method in conjunction with a direct problem solver, which is built based on the rarefied-flow theory. The direct problem solver is able to predict the pressure distributions of the rarefied gas flows in the slip-flow, transition-flow, and molecular-flow regimes with a wide range of characteristic inverse Knudsen number. First, the validity of the direct problem solver has been verified by a comparison with the existing information for some particular cases, and then the developed direct problem solver is incorporated with the conjugate gradient method for optimizing the shape profile of the slider surface. The performance of the present optimization approach has also been evaluated. Results show that the shape profile of the slider surface can be efficiently optimized by using the present approach. Thus, a number of cases under various combinations of influential parameters, involving the characteristic inverse Knudsen number and the bearing numbers in the $x$- and $y$-directions, are investigated.