Influence of real gas equations on the numerical modeling of porous aerostatic air bearings

  • Stellmach, Laurenz (Otto-von-Guericke Universität)
  • Nitzschke, Steffen (Otto-von-Guericke Universität)
  • Woschke, Elmar (Otto-von-Guericke Universität)

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Due to the increasing demands of the semiconductor industry on precision and feature sizes, numerical simulation of manufacturing machines and their components has become increasingly important. A key aspect in this context is the support of moving components, which is often realized by aerostatic air bearings in order to meet strict cleanliness requirements. In particular, applications operating at low rotational speeds commonly employ porous air bearings, which provide low-friction and highly precise operation through an external air supply. This contribution addresses the numerical simulation of porous aerostatic air bearings based on the coupled solution of the Reynolds and Darcy equations in conjunction with the continuity equation. The computational domain is discretized using the finite volume method. To efficiently solve the resulting nonlinear system of equations, a Newton–Raphson scheme is applied, reducing the computational effort in time-dependent simulations. Since the governing equations depend on both pressure and gas density, an appropriate equation of state is required. While the ideal gas equation is commonly employed, its validity becomes limited at elevated pressures and temperatures. In this work the influence of representative real gas equations, including the van der Waals and Soave–Redlich–Kwong models, on the numerical simulation of porous aerostatic air bearings is systematically investigated. Both stationary and dynamic operating conditions are considered, and the resulting pressure distributions and load capacities are compared with simulations based on the ideal gas equation. This allows an assessment of the operating regimes in which real gas modeling significantly affects load capacity predictions and where the additional modeling effort is justified.