Modeling of dynamic characteristic of the aerostatic bearing spindle in an ultra-precision fly cutting machine

Axis orientation stability of aerostatic bearing spindles has great influence on machining precision of ultra-precision fly cutting machines used for processing ultra-precision optical components of large diameter. Mid-spatial frequency errors (amplitude<0.1 μm, wavelength about 100 nm) always existed on the machined surfaces along feeding direction. Generally, the waviness errors on processed surfaces will impact the performance of workpiece used as optical components greatly, and the tilting motions of spindles were believed to be the main source which produced the waviness errors. In this paper, to study the tilting motions of spindles, the Euler dynamic equations of angular displacements of spindles were proposed, and analytic solutions of the equations were also presented. At the same time, the 3D surface profile simulations of workpieces based on analytic solutions of Euler equations were achieved. The simulation results have been verified by lots of experiments on an ultra-precision fly cutting machine. At last, the inertia tensor criterion which can decrease the waviness errors of machining surface was represented, and it can be applied to instruct the structure design of aerostatic bearing spindles.