Bifurcation analysis of a forced delay equation for machine tool vibrations

A machining tool can be subject to different kinds of excitations. The forcing may have external sources (such as rotating imbalance, misalignment of the workpiece or ultrasonic excitation), or it can arise from the cutting process itself (e.g., periodic chip formation). We investigate the classical one-degree-of-freedom tool vibration model, a delay-differential equation with quadratic and cubic nonlinearity, and periodic forcing. The method of...