Analytical time-domain model for tool point dynamics in turning

An analytical time domain solution is developed to model the dynamic response of a tool during a simple turning operation. The time domain solution developed in this paper relies on the superposition principal under the linear assumption to construct the time response of single mode, single degree of freedom cutting tool. The results from the analytical solution are compared with those generated using numerical time domain simulations and it is found that the two solutions converge as the time step used in the numerical simulation decreases.