Conventional hydrostatic bearings are not suited to use on surfaces with changing curvature which limits their applicability. To improve on this, deformable hydrostatic bearings are currently being researched. The goal of this work is to develop hydrostatic bearings with a single fluid supply that work for sinusoidal counter surfaces.

The bearing pad of a deformable hydrostatic bearing must be able to conform to the shape of the sinusoidal counter surface at any position while being able to carry high loads. Previous research has also pointed out that a deformable hydrostatic bearing should have a triangular contact pressure profile for compression against a flat surface. This way a bearing without preference towards either the concave or convex part on a sinusoidal counter surface should be obtained.

The design problem is translated into a problem formulation for the synthesis of compliant mechanisms with topology optimization. In this formulation strain energies of the design domain under different load cases are utilized to achieve selective stiffness. In an extension of the formulation, the reaction forces under uniform vertical compression of the structure are required to attain a triangular shaped profile. This requirement is relaxed in the second extension where the reaction forces are only required to monotonically decrease from the middle to the sides.

Optimizations without requirement on the reaction profile yield interesting structures with clear-cut boundaries. When implementing the requirement on the reaction profile, there appears to be a trade-off between achieving the prescribed shape and the presence of grey area and artifacts in the designs. The optimizer tends to employ distributed compliance to meet the requirement, which can compromise the load-bearing capabilities of the structures.

Evaluation of selected results with a contact model predicts that numerous obtained designs could function as a hydrostatic bearing on a sinusoidal counter surface with an amplitude of 11.3 mm. Additional effort with a more realistic evaluation model is required to draw a definite conclusion on the performance.