Investigation on the influence of tool-tip vibration on surface roughness and its representative measurement in ultra-precision diamond turning

High frequency tool-tip vibration, in the cutting force direction, is an intrinsic feature of ultra-precision single point diamond turning (SPDT). This paper is dedicated to a study of the influence of the tool-tip vibration on surface roughness. The resulting periodic fluctuation of the surface profile is identified in a particular spatial frequency range by a tangential measurement method. The ISO standard provides merely a minimal, not an optimal requirement for surface measurement. Thus, in this paper, a more representative measurement method is proposed to better characterise the machined surface in SPDT. The conventional radial and aerial surface measurements yield a relatively biased result on surface roughness which cannot adequately reflect the detrimental effect of tool-tip vibration. Representative measurement takes account of the sample area ratios and is able to be used to objectively study the discrepancies in surface measurement. The proposed model for surface generation and representative measurement are applicable to the problems in surface generation in ultra-precision SPDT, such as the spiral turning marks and spatial errors in the radial profile measurement.