Dynamic Influence of Spindle Wobble in a Lathe on the Workpiece Geometry

Abstract

The influence of spindle wobble in a lathe on the geometry of the machined surface is not direct. The intermediate stages involve conversion of the wobble to forces and elastic deformations. Together with the elastic deformation, wobble modifies the shaping trajectories, which are mainly responsible for the geometry of the final product. Wobble induces periodic variation in the parameters of the dynamic system. It leads not only to parametric self-excitation but also, in a nonlinear dynamic system, to the formation of various attractive deformational-displacement sets. The present work is devoted to mathematical modeling of the influence of wobble on the workpiece geometry. Cases in which various types of attractive sets are formed in the system (such as limit cycles, invariant tori, and chaotic attractors) are considered.