The effect of parametric excitation on a dynamic system of cutting process

The problem of ensuring stability of movements of the tool about workpiece taking into account parametric self-excitation is considered. The factors causing periodic changes of parameters in dynamic system when cutting are analyzed. They are connected with spatial anisotropy of properties of elasticity in a subsystem of the processed workpiece with allowance variations on workpiece rotation perimeter, with kinematic perturbation from mechanical part of drives of executive elements of the machine, with periodic processes in a cutting zone. The generalized dynamic model of system with periodically changing parameters is given. Influence of periodically changing parameters on stability of trajectories is studied. The features of loss of stability specific to dynamic systems of cutting are disclosed. In particular, it is shown that due to parametrical effects with increasing cutting speed at increase of rotational frequency of spindle there is always a critical frequency at which the system loses stability. © The Authors, published by EDP Sciences, 2018.