Band-stop-filter-based repetitive control of fast tool servos for diamond turning of micro-structured functional surfaces

Abstract

Fast tool servo (FTS) is a promising technique for the high-speed diamond turning of micro-structured functional surfaces due to its fast response capacity. However, the inherent actuator non-linearity, the lightly damped vibration mode and the external disturbance of the FTS would degrade its tracking performance severely and thus restrict its machining ability. To overcome this limitation, a band-stop-filter-based repetitive control (BSF-RC) scheme is proposed in this article to improve the operating performance of the FTS. Firstly, the spectra of the FTS tool paths (FTS-TPs) for machining typical micro-structured functional surfaces with the cylindrical coordinate machining method are analyzed in detail. The results reveal that the frequency components concentrate on the tiny neighborhoods of the rotational frequency of the spindle and its harmonic frequencies. Afterwards, the comb-like band-stop filter used by the BSF-RC is elaborately designed via the cascade of three comb-like notch filters to generate a comb-like band-stop loop shape for covering main spectral components of the FTS-TPs. The analytical expression of the comb-like band-stop filter amplitude as well as the stability condition of the closed-loop control system are derived to provide effective criteria for the parameter selection of the BSF-RC. The experimental validation of the developed BSF-RC scheme is conducted on a five-axis ultra-precision lathe equipped with a self-developed FTS via the diamond turning of three typical micro-structured functional surfaces. The experimental results show that good surface qualities with the maximal form error of a few hundred nanometers and the surface roughness of a several nanometers are achieved for all the obtained micro-structured surfaces by using the BSF-RC scheme under a high spindle speed.