Analytical time-domain turning model with multiple modes

An analytical time domain model is developed to predict the motion of a multi-mode cutting tool during orthogonal turning operations. This model is an extension of a single mode model that finds the solution to the governing delay differential equation (DDE) as a combination of constituent curves (sequential responses) which are independent of the delay term, τ. In the current model, the delay independent constituent curves are found through a recursive state-space solution wherein the individual modal displacements are determined for each sequential response. In this paper, the solution process is described in detail for a two mode system and the resulting analytical time responses are compared with numerical simulations.