The search for the optimal bearing geometry has been on for over a century. In a publication from 1918, Lord Rayleigh revealed the infinitely wide bearing geometry that maximises the load carrying capacity under incompressible flow, i.e. the Rayleigh step bearing. Four decades ago, Rohde, who continued on the same path, revealed the finitely wide bearing geometry that maximises the load carrying capacity, referred to as the Rayleigh-pocket bearing. Since then, the numerical results have been perfected with highly refined meshes, all converging to the same Rayleigh-pocket bearing. During recent years new methods for performing topology optimisations have been developed and one of those is the method of moving asymptotes, frequently used in the area of structural mechanics. In this work, the method of moving asymptotes is employed to find optimal bearing geometries under incompressible flow, for three different objectives. Among the results obtained are (i) show new bearing geometries that maximise the load carrying capacity, which performs better than the ones available, (ii) new bearing geometries minimising the coefficient of friction and (iii) new bearing geometries minimising the friction force for a given load carrying capacity are presented as well.

寻找最佳轴承几何形状已经进行了一个多世纪。在1918年的出版物中，瑞利勋爵（Lord Rayleigh）揭示了无限宽的轴承几何形状，即在不可压缩的流动下最大化承载能力，即瑞利阶梯轴承。四十年前，沿着同一条路继续前进的罗德（Rohde）揭示了有限的轴承几何形状，该几何形状可最大化承载能力，被称为Rayleigh-pocket轴承。从那时起，数值结果已使用高度精炼的网格进行了完善，所有网格都收敛于相同的Rayleigh-pocket轴承。近年来，已经开发了用于执行拓扑优化的新方法，其中之一是移动渐近线的方法，该方法通常在结构力学领域中使用。在这项工作中 针对三个不同的目标，采用了渐近线的移动方法来寻找不可压缩流下的最佳轴承几何形状。在获得的结果中，（i）显示出最大承载能力的新型轴承几何形状，其性能要优于现有的轴承几何形状；（ii）新的轴承几何形状将摩擦系数最小化；以及（iii）新的轴承几何形状使摩擦系数最小化还给出了给定的承载能力。