Motion Error Compensation Method for Hydrostatic Tables Using Actively Controlled Capillaries

To compensate for the motion errors in hydrostatic tables, a method to actively control the clearance of a bearing corresponding to the amount of error using actively controlled capillaries is introduced in this paper. The design method for an actively controlled capillary that considers the output rate of a piezo actuator and the amount of error that must be corrected is described. The basic characteristics of such a system were tested, such as the maximum controllable range of the error, micro-step response, and available dynamic bandwidth when the capillary was installed in a hydrostatic table. The tests demonstrated that the maximum controllable range was $2.4\;{\mu}m$, the resolution was 27 nm, and the frequency bandwidth was 5.5 Hz. Simultaneous compensation of the linear and angular motion errors using two actively controlled capillaries was also performed for a hydrostatic table driven by a ballscrew and a DC servomotor. An iterative compensation method was applied to improve the compensation characteristics. Experimental results showed that the linear and angular motion errors were improved to $0.12{\mu}m$ and 0.20 arcsec, which were about $1/15^{th}$ and $1/6^{th}$ of the initial motion errors, respectively. These results confirmed that the proposed compensation method improves the motion accuracy of hydrostatic tables very effectively.