Aerostatic Stiffness and Damping Analysis for High-Speed Air Bearings in Ultra-Precision Machine Tools

Abstract

The microsystems technology drives manufacturing industries with the need for smaller structures for ultra-precision requirements. Precision combined with the allowed dynamics of the moving components are basic principles. Aerostatic bearings provide smooth and contactless movements, which are key resources for ultra-precision machine tools. Providing sufficient high stiffness properties for manufacturing applications, the air gap height of gas bearings has a size of just a few micrometres and shows a clear sensitivity to temperature and, in the case of journal bearings, also to speed. An algorithm developed computes the stiffness and damping properties and performs a full sensitivity analysis investigating all physical parameters of a plain journal bearing. The advanced approach combines a 2D-Thin-Film Finite Difference Method (FDM) with the Infinitesimal Perturbation Method (IFP) to achieve an eccentricity and attitude angle-dependent pressure distribution. This study describes a fully parametrized approach to serve as a base for the sensitivity analysis during the design phase and for the model of the control system. The outlined concept is evaluated on a high-speed journal bearing with the dimensionless DN factor of 3 ∙ 106. The orifice design in combination with industry-standard inlet pressure ranges is the main design restriction. The described correlation matrices are evaluated with the Latin Hypercube Sampling Method and ensures together with the 2D Reynolds equation-based FDM algorithm a short calculation period. The proposed system is validated and further discussed through a rotor dynamic study on a high-speed aerostatic machine tool spindle.