Dynamics modeling of thermo-fluid-structure coupled aerostatic spindle considering 3D gas-film temperature field

Thermal effects in aerostatic spindles are a major source of form error in ultra-precision machining. However, most existing studies predict spindle temperature based on one-dimensional temperature approximations, with insufficient consideration of thermo-fluid-structure coupling involving the three-dimensional temperature field. This study develops a thermo-fluid-structure coupled model for a high-speed aerostatic spindle by resolving the 3D gas-film temperature field and incorporating rotor thermal expansion. The circumferential, axial, and film-thickness velocity components of the gas film are derived from the continuity condition for laminar flow and the pressure field obtained from the Reynolds equation. A steady-state energy equation is then coupled with the Reynolds equation and discretized using the finite difference method. The boundary conditions account for air supply, ambient end faces, circumferential periodicity, heat dissipation through the water-cooled bearing, and heat transfer to the rotor. The proposed model is validated through experimental data and ANSYS Fluent simulations. Based on the proposed model, the effects of key rotor–bearing parameters on the gas-film temperature distribution are first investigated. The results show that the gas-film temperature is mainly governed by the operating and geometric parameters that directly alter the film thickness, shear behavior, and heat-transfer characteristics. Rotor thermal expansion is then incorporated to examine its influence on the gas-film thickness, pressure distribution, and temperature distribution. The results show that rotor thermal expansion alters the gas-film behavior and further affects the bearing load capacity, support performance, and spindle-end vibration response. The proposed model therefore provides a useful physics-based tool for thermal design and accuracy improvement of aerostatic spindles in ultra-precision manufacturing.