Date of Award


Degree Name

Doctor of Philosophy


Engineering Science

First Advisor

Luo, Albert


In this dissertation, a 2-DOF nonlinear regenerative cutting model with forced vibration from the workpiece oscillation is established. The periodic motions in such a nonlinear time-delay system are studied through a semi-analytical method. Such a method constructs an implicit mapping structure for periodic motions through the discretization of the governing delay-differential equations. The stability and bifurcations of periodic motions are predicted from the eigenvalue analysis. The periodic motions varying with excitation frequency in linear-structural and nonlinear-structural machine-tool systems are presented. The rich dynamics of the machine-tool systems are discovered. The numerical simulations of stable periodic motions are carried out from analytical predictions. Chatter may not be the chaotic motions; in fact, it can be large- amplitude periodic motions (stable and unstable). The phase difference between horizontal and vertical displacements can be used to detect chatter in machining process.




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