摘要：AbstractA 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 gave an excellent approximation of the solution. The resonance curves found here are similar to those for the Duffing-equation, having a hardening characteristic. We found subcritical Hopf and saddle-node bifurcations.
关键词：Keywordsdelay-differential equationmethod of multiple scalesharmonic excitationHopf bifurcationprimary resonance
