Influence of Spindle Wobble in a Lathe on the Tool’s Deformational-Displacement Trajectory

Abstract

Attention focuses here on the conversion of the trajectory of spindle-group wobble in a lathe into deformational displacement of the tool and the associated modification of the shaping trajectory. This process depends on the change in dynamic properties of the system due to the wobble. On the basis of simulation and digital experiments, it may be concluded that the wobble changes the stability of the trajectories and that various attractive sets are formed in the system (such as limit cycles, invariant tori, and chaotic attractors). The wobble does not change the shaping trajectory directly, but rather through the formation of attractive deformational-displacement sets. Therefore, the attractive sets affect the geometric topology of the workpiece surface and the limiting feasible manufacturing precision.