Numerical study on the rotational and machining accuracy of an end-milling process with spindles supported by aerostatic bearings

Aerostatic bearings are widely used for spindles in ultra-precision machining tools. These spindles consist of a pair of aerostatic thrust bearings and several aerostatic journal bearings. The rotational accuracy of aerostatic spindles depends largely on the arrangement and performance of the individual bearings, but the evaluation of the rotational accuracy is mainly carried out experimentally using a prototype machine, which poses challenges in terms of the time and cost of building a prototype. Therefore, a real need exists to evaluate the spindle characteristics by numerical calculation. In this study, we developed a method to numerically calculate the trajectory of the spindle rotator which is supported by aerostatic bearings. The method was developed to numerically investigate and determine the effects on the rotational accuracy of the spindle during end milling when the cutting force is applied to the rotating rotor. A comparison was made regarding the amount of runout of the rotating shaft when side milling was performed using a spindle with a shaft diameter of 22 mm and a small end mill with a diameter of 1 mm, concerning three different spindles with different arrangements of thrust and journal bearings. The effects of rotational speed, radial depth of cut, and the number of tool teeth on the runout of the rotating shaft were numerically verified. As a result, it was found that a spindle structure in which the thrust bearing is placed on the tool side and the journal bearing span is lengthened is desirable.