修正加速勾配法を用いた摩擦係数の最小化を目的としたテクスチャの形状最適化解析

Abstract

In this study, we proposed a new acceleration gradient method that introduces the concept of Taylor expansion into Nesterov's acceleration gradient method. The proposed method is called the modified acceleration gradient method. A texture shape optimization analysis is performed using the proposed method to minimize the friction coefficient. The gradient of the Lagrange function with respect to the design variables used in the proposed method can be obtained by the adjoint variable method. The equation of state used in the analysis is the Reynolds equation that determines the pressure on the oil film. As a result, the number of iterations can be significantly reduced in comparison to Nesterov's acceleration gradient method. The optimal oil film thickness distribution in the textured area was also calculated. The texture shape after convergence was asymmetric in the flow direction. This pattern was similar to that observed in shape optimization using Nesterov's acceleration gradient method. Numerical experiments performed to validate the proposed method are described.