Gegg, Brandon C. (2009-05). An Investigation of the Complex Motions Inherent to Machining Systems via a Discontinuous Systems Theory Approach. Doctoral Dissertation.
The manufacturing process has been a heavily studied area over the past century. The
study completed herein has established a foundation for the future of manufacturing
research. The next step of this industry is to become proficient at the micro and nano
scale levels of manufacturing. In order to accomplish this goal, the modeling of
machining system needs to be completely understood throughout the entire process. In
effort to attack this problem, this study will focus on the boundaries present in
machining systems; and will define and interpret the associated phenomena.
This particular focus is selected since nearly all manufacturing related studies
concentrate on continuous processes; which by definition considers only one particular
operation. There is a need to understand the phenomena corresponding to interactions of
multiple processes of manufacturing systems. As a means to this end, the nonlinear
phenomena associated in the continuous domains of machining systems will be modeled
as linear to ensure the boundary interactions are clearly observed. Interference of
additional nonlinearities is not the focus of this research. In this dissertation, the
mechanical model for a widely accepted machine-tool system is presented. The state and continuous domains are defined with respect to the boundaries in
this system (contact and frictional force acting at the point of tool and work-piece
contact). The switching sets defining plane boundaries for the continuous systems of
this machine-tool will be defined and studied herein. The forces and force products, at
the point of switching from one continuous system to another, govern the pass-ability of
the machine-tool through the respective boundary. The forces and force product
components at the switching points are derived according to discontinuous systems
theory Luo . Mapping definitions and notations are developed through the switching
sets for each of the boundaries.
A mapping structure and notation for periodic interrupted cutting, non-cutting
and chip seizure motions are defined. The interruption of the chip flow for a machining
system will be investigated through a range of system parameters. The prediction of
interrupted periodic cutting, non-cutting and chip seizure motion will be completed via
closed form solutions for this machine-tool. The state of this system is defined to utilize
the theory of Luo . This is necessary to properly handle the frictional force boundary
at the chip/tool interface, the onset of cutting boundary and the contact boundary
between the tool and work-pieces.
The predictions by this method will be verified via numerical simulation and
comparison to existing research. A goal of this research is to illustrate the effects of the
dynamical systems interacting at the frictional force (chip/tool) boundary and the chip
onset of growth and vanishing boundary. The parameter space for this machine-tool
model is studied through numerical and analytical predictions, which provide limits on
the existence of interrupted periodic cutting, non-cutting and chip seizure motions.