Tool and workpiece deformation effect in the cutting speed direction on the machining dynamics

Numerous studies were devoted to studying the dynamic cutting system considered in combination of the tool and the workpiece sub-systems interacting through a dynamic connection formed by the machining process. Dynamic coupling is simulated by the cutting forces represented in the system state coordinates, which determines the system properties. Several models were proposed to describe the dynamic connection reflecting various experimentally observed effects and contributing to the self-excitation. Regenerative effect of the tool trace left on the workpiece at the previous revolution was considered. The regenerative effect was studied on the basis of assumption that the retarding argument in the forces description was remaining unchanged. The paper studies the regenerative effect influence on dynamic properties of the cutting process taking into account (unlike the known works) the retarded argument dependence on the tool deformation displacement. This could fundamentally change properties of the system under consideration in the unity of stability and the attracted formed deformation displacement sets (limit cycles, invariant tori and chaotic attractors). Results of the mathematical simulation are presented taking into account the regenerative self-excitation, where the retarded argument is the state coordinates function. Bifurcation diagrams of attracting sets of the deformation displacements are considered, and conditions for formation of their superlow-frequency components of the complex spatial-temporal structure are discussed. Research results are aimed at determining the machining conditions based on requirements for ensuring the specified quality of parts manufacturing using the longitudinal turning example.