Harmonically Excited Delay Equation for Machine Tool Vibrations

Lelkes, János ✉ [Lelkes, János (Áramlástan és hőtan), author] Department of Fluid Mechanics (BUTE / FME); Kalmár-Nagy, Tamás [Kalmár-Nagy, Tamás (Áramlástan, Elmél...), author] Department of Fluid Mechanics (BUTE / FME)

English Scientific Conference paper (Chapter in Book)
      A machining tool can be subject to different kinds of excitations. The forcing may have external sources (such as rotating imbalance or misalignment of the workpiece) or it can arise from the cutting process itself (e.g. chip formation). We investigate the classical tool vibration model which is a delay-differential equation with a quadratic and cubic nonlinearity and periodic forcing. The method of multiple scales was used to derive the slow flow equations. The resonance curves of the system are similar to those for the Duffing-equation, having a hardening characteristic. Stability analysis for the fixed points of the slow-flow equations was performed. Local and global bifurcations were studied and illustrated with phase portraits and direct numerical integration of the original equation. Subcritical Hopf saddle-node and heteroclinic bifurcations were found.
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      2021-12-04 21:21