Feed-forward control of fast tool servo for real-time correction of spindle error in diamond turning of flat surfaces

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Abstract

A fast tool servo is designed and tested to obtain sub-micrometre form accuracy in diamond turning of flat surfaces. The thermal growth spindle error is compensated for real time using a fast tool servo driven by a piezoelectric actuator along with a capacitive displacement sensor. To overcome the inherent non-linearity of the piezoelectric actuator, Proportional Integral (PI) feedback control with a notch filter is implemented. Besides, feed-forward control based on a simple feed-forward predictor is added to achieve better tracking performance. Actual machining data are discussed in detail to prove that the proposed fast tool servo is capable of fabricating flat aluminum specimens of 100 mm in diameter to a form accuracy of 0.10 μm in peak-to-valley error value.

Introduction

The advance of diamond turning technology allows machining mirror-like surfaces with sub-micron form accuracy by use of high precision spindles and stiff hydrostatic guide ways. A recent new approach made in diamond turning is to incorporate fast tool servos (FTSs) to improve machining accuracy by reducing the surface-normal tool position errors [1]. FTSs refer to auxiliary servos that are specially adopted to activate the diamond tool with fine resolution, high stiffness and fast dynamic response. FTSs were mounted to diamond turning machines to fabricate non-rotationally symmetric surfaces by rapid actuation of tools with a sufficiently high bandwidth [2]. FTSs can also be an effective means for the fabrication of large aspheric off-axis mirrors in diamond turning machines [3], [4].

In this paper a fast tool servo is presented, which can move several micrometres in the Z-direction with a following error of 0.15 μm in the peak-to-valley value. To correct the inherent hysteresis of piezoelectric actuators, Proportional-Integral (PI) feedback control with a notch filter is implemented. And, feed-forward control based on a simple predictor is added to provide better tracking performance. Machine movement errors including the thermal growth of the spindle are measured and corrected using the FTS, which is driven by a piezoelectric actuator in a closed loop with a capacitive displacement sensor. Actual machining data prove that the proposed approach of FTS is capable of fabricating aluminum mirrors of 100 mm in diameter to a form accuracy of 0.10 μm in terms of the peak-to-valley error value.

Section snippets

Design and testing of fast tool servo

The details of the FTS designed in this investigation are shown in Fig. 1. The FTS is composed of a main body base, a tool holder, a moving body, a capacitive displacement sensor with its holder, and a piezoelectric actuator. A single diamond tool is mounted on the tool holder, which is bolted to the moving body. The piezoelectric actuator is of stacked type, 45 mm in length and 18 mm in outer diameter, which is preloaded by four flexure hinges in the main body. The actuator pushes back and

Machining experiment and discussions

Actual machining experiments of the FTS were performed with a diamond turning machine. Fig. 10 illustrates the hardware configuration of the diamond turning machine used in this investigation for the fabrication of flat Aluminum specimens. The machine is composed of three main parts; an aerostatic spindle to rotate the workpiece, an X-axis linear servo floating on a hydrostatic bearing to laterally move the spindle together with the workpiece, and a Z-axis linear hydrostatic servo to translate

Conclusions

The fast tool servo (FTS) was developed to correct the thermal growth error of the spindle. For the testing of the FTS, a test bench was built and its performance was evaluated. In order to correct the hysteresis and drift of the piezoelectric actuator used, a closed-loop control scheme including PI feedback control was used. For better tracking performance, a notch filter and a simple predictor was implemented besides the PI closed loop control scheme. As results, it was shown that the FTS can

Acknowledgements

The work presented in this paper was supported by the Ministry of Science and Technology of Korea as part of the National Research Laboratory Program. The authors appreciate Dr Seung-Woo Kim of the Korea Advanced Institute of Science and Technology for his valuable consultations exerted for the work. The authors also acknowledge Min-Gi Kim and Tae-Hyoung Kim of Daewoo Heavy Industries and Machinery, LTD for providing the ultraprecision lathe for this research.

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