A new representation with probability distribution for nanometric surface roughness in ultra-precision machining

•Ultra-precision machining (UPM) commonly produces nanometric surface roughness (NSR).•Nanometric surface roughness is govern by high-frequency components sensitive to noise.•Spacing features significantly affect optical quality by diffraction and interference.•A new representation for spacing features of NSR in UPM has been developed.

Ultra-precision machining (UPM) commonly produces nanometric surface roughness (NSR), which is governed by high-frequency components with tool marks sensitive to noise. Its spacing features (SF) majorly affect optical quality by diffraction and interference. However, the ISO SR standard cannot effectively represent SF. In this study, a new representation for SF was developed by evaluating surface derivative, as extra SR parameters. Probability distribution with the 95–99 rule was adopted to reduce noise effects. The results were found that the extra SR parameters well represents SF and are sensitive to spatial frequency. Probability distribution is an efficient means of reducing noise effects. Significantly, the proposed method is simple and efficient to represent SF of NSR in UPM.

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