Stability properties of regenerative cutting processes, based on impulse response functions expressed in the impulse dynamic subspace

Abstract An extensive study on the implementation of the convolution based impulse dynamic subspace (IDS) concept for machining applications is presented in this paper. The suggested method is adequate to avoid modeling based on modal parameters. Instead of parameter driven dynamical modeling, the impulse response functions (IRFs) are used for the IDS decomposition and for constructing the corresponding delayed and, on occasion, time periodic equations of motion of regenerative cutting processes. This approach makes possible to use measured frequency response functions (FRFs) in time domain based methods. This is achieved by establishing the connection between the IRF and the fundamental matrix of the corresponding linearized generally time periodic delayed system. It is shown that the concept provides the well-known analytic solution of the orthogonal turning model, demonstrating the applicability of the proposed methodology, while a specially tailored high-order semidiscretization scheme is tested on milling models.