Gegg, Brandon C. (2009-05). An Investigation of the Complex Motions Inherent to Machining Systems via a Discontinuous Systems Theory Approach. Doctoral Dissertation. Thesis uri icon


  • 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 [1]. 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 [1]. 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.

publication date

  • May 2009