LOSS OF CONTACT AND TIME DELAY DYNAMICS OF MILLING PROCESSES

Abstract

Considering the feed motion, the dynamics of constant spindle speed (CSS) milling processes is described by a set of delay differential equations with periodic coefficients and a variable time delay associated with each cutting tooth. This model, which has been developed for the first time as a part of this dissertation, is used to study the dynamics and stability of the system. The semi-discretization scheme, a numerical scheme with an analytical basis, is refined to examine the stability of periodic solutions of this system. This scheme can be used to predict not only the stability but also the chatter frequencies for a wide variety of milling operations ranging from full-immersion to partial-immersion operations. From the results obtained thus far, it can be stated that feed-rate effects can be neglected during full-immersion and high-immersion operations, where the influence of loss of contact nonlinearities is not pronounced. However, for low-immersion milling operations, where loss of contact effects have a strong influence on system stability behavior, high feed-rate effects are pronounced and this effects can't be ignored. Along with investigations into the dynamics of CSS milling processes, in this dissertation, a better delay approximation has been used in the modeling of variable spindle speed (VSS) milling processes, and the benefits of VSS milling operations are discussed by comparing the stability charts of VSS milling operations with those obtained for CSS milling operations. The nonsmooth characteristics of milling processes are pointed out by presenting the simulated results for cutting forces. Work conducted with a nonsmooth mechanical system, a simplified system related to the milling process, is presented and the numerical results and experimental results obtained show evidence for grazing and other bifurcations in this nonsmooth system.