Topography lobes diagram applied to identify waviness features induced by a single-frequency tool vibration in turning

In finishing processes, such as grinding and hard turning, the surface texture is a key aspect that influences the functionality of the part. Thus, the appearance of waviness marks, commonly associated with machine-tool vibrations, means the rejection of high added value parts. Although machine-tool vibrations are often monitored, it is challenging to pinpoint which vibration frequency, of the complete spectrum, is responsible for creating the waviness marks. This study investigates the impact of a single-frequency tool vibration on surface waviness in cylindrical turning operations. By considering the rotational sampling of the tool motion along the feed direction, it is demonstrated that the aliased tool motion, tool interference, and sub-Nyquist waves are decisive in the formation of the surface topography. Based on a frequency and an amplitude non-dimensional parameter, the main surface topography helix is identified. Besides, the number of threads, orientation, and wavelength of the multiple surface topography helixes are determined analytically. To validate the results, calculated surface topographies are successfully compared to experimental topographies generated in cylindrical turning experiments where a controlled tool vibration is generated by a piezoelectric actuator. These findings are essential to identify the surface waviness features that relate to the machine-tool vibration generating poor surface quality. • The surface topography induced by a single-frequency vibration reveals multiple helix patterns related to the tool feed, aliased vibration, and sub-Nyquist artefacts. • The main waviness pattern is identified at the feed direction profile’s wavelength and the angular profile’s wave spectrum. • The identification of the main waviness pattern according to the frequency and amplitude ratios is essential to relate the surface topography to the machine-tool vibration. • The analytical equations defining the wavelength, number of threads, and orientation of the tool feed, aliased and sub-Nyquist helixes can be applied to determine the frequency ratio of the excited tool vibration.