Revealing the effect of dual-frequency vibrations in turning through waviness classification maps

Waviness marks induced by machine-tool vibrations are commonly identified as visual marks that deteriorate the surface quality. The surface waviness is formed by multiple helix patterns, whose spatial features—namely the wavelength, number of threads and orientation—are directly related to the mechanical vibration frequencies of the machine-tool. The stroboscopic sampling of the workpiece rotation applied to a single-frequency tool vibration reveals that the tool feed, aliased tool motion, and sub-Nyquist waves are reflected as different helix patterns. This work studies the influence of the frequency and amplitude ratios of a dual-frequency tool vibration on the generation of the aliased beating helix. By combining the stroboscopic sampling of the tool motion and the beating phenomenon, the spatial features of the aliased beating helix are analytically derived. Waviness classification maps are proposed to outline the frequency and amplitude ratio combinations that promote the aliased beating helix. The generation of additional helix patterns due to the interaction of two vibration frequencies of a multi-frequency spectrum is verified. The findings are numerically and experimentally validated in a cylindrical turning process where a controlled tool vibration motion with varying frequency and amplitude ratios is generated by a piezoelectric actuator. The main waviness of the experimental topographies agrees with waviness classification maps predictions. Besides, the analytic equations are successfully applied to relate the helix spatial features to the root vibration frequencies. The study provides a robust framework for diagnosing the origin of waviness marks in real industrial scenarios where multi-frequency machine-tool vibrations are commonly encountered.