These slides were presented at the NAFEMS World Congress 2025, held in Salzburg, Austria from May 19–22, 2025.

Abstract

The machine tool industry increasingly demands higher precision and performance, and rotary tables with hydrostatic guideways are well-suited to meet these requirements due to their low friction, high stability, and excellent load-bearing capacity. Understanding the interplay between structural deformation and hydraulic pressure in these systems is critical for optimizing their design and performance. The structural design of the table and the hydrostatic guiding parameters play an important role in the performance of the table. Size constraints should be imposed to limit the cost of the part and hydrostatic constraints to ensure sufficient stiffness of the guiding system, which is crucial to ensure accuracy in machining. Designing these parts requires a detailed exploration of the design space, focusing on the bidirectional coupling between structural deformation and fluid pressure that governs the system'™s mechanical and hydraulic behavior. This study presents a custom-developed finite element simulation tool that integrates structural and hydraulic physics into a monolithic scheme to analyze these coupled effects. The structural components are modeled with linear elasticity, while the hydraulic pressure field is calculated using the Reynolds equation for lubrication, derived from Navier-Stokes under assumptions of a thin fluid film and laminar, incompressible flow. The model incorporates nonlinearities arising from the dependence of pressure on the gap between support surfaces and fluid viscosity changes with temperature. An iterative approach is used to linearize and solve the system of equations. The studied rotary table is made of cast iron, has a diameter of 5000 mm and two hydrostatic support rings. On the one hand, the influence of the elasticity in large hydrostatic tables is assessed by comparing the presented model with an infinitely rigid table. On the other hand, the design parameters of the hydrostatic system are analyzed to study their influence in load capacity, stiffness, gap, and pump power, and a design of experiments is conducted to detect the sensibility of each parameter in the performance of the table. This approach offers a robust framework for designing cost-effective, high-performance rotary tables tailored to specific industrial needs.