Abstract
In this chapter, the passability of a flow to the separation boundary for two friction-induced oscillators is presented for a better understanding of cutting mechanism in manufacturing. The friction-induced oscillator with a constant velocity belt is presented first. Through this practical example, the theory for flow singularity and passability in discontinuous dynamical systems is understandable. To further build the basic concepts and knowledge of discontinuous dynamical systems for cutting dynamics, the friction-induced oscillator with a time-varying velocity belt is addressed. From the theory of discontinuous dynamical systems, the analytical conditions for stick and grazing motions to the velocity boundary are presented, and intuitive illustrations are used to help one understand the physical meaning of the mathematical conditions.
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References
Gegg, B.C., Luo, A.C.J. and Suh, S.C., 2008, Grazing phenomena in a friction-induced oscillator with dry-friction on a sinusoidally time-varying, traveling surface, Nonlinear Analysis: Real Word Applications, 9, 2156–2174.
Gegg, B.C., Luo, A.C.J. and Suh, S.C., 2009, Sliding motions on a periodically time-varying boundary for a friction-induced oscillator, Journal of Vibration and Control, 15(5), 671–703.
Luo, A.C.J., 2005, A theory for non-smooth dynamical systems on connectable domains, Communication in Nonlinear Science and Numerical Simulation, 10, 1–55.
Luo, A.C.J., 2006, Singularity and Dynamics on Discontinuous Vector Fields, Elsevier: Amsterdam.
Luo, A.C.J., 2008a, On the differential geometry of flows in nonlinear dynamical systems, ASME Journal of Computational and Nonlinear Dynamics, 3, 021104 (1–10).
Luo, A.C.J., 2008b, A theory for flow switchability in discontinuous dynamical systems, Nonlinear Analysis: Hybrid Systems, 2(4), 1030–1061.
Luo, A.C.J., 2009, Discontinuous Dynamical Systems on Time-varying Domains, HEP-Springer: Heidelberg.
Luo, A.C.J., 2011, Discontinuous Dynamical Systems, HEP- Springer: Heidelberg.
Luo, A.C.J. and Gegg, B.C., 2006a, On the mechanism of stick and non-stick, periodic motions in a forced linear oscillator including dry friction, ASME Journal of Vibration and Acoustics, 128, 97–105.
Luo, A.C.J. and Gegg, B.C., 2006b, Stick and non-stick, periodic motions of a periodically forced, linear oscillator with dry friction, Journal of Sound and Vibration, 291, 132–168.
Luo, A.C.J. and Gegg, B.C., 2006c, Grazing phenomena in a periodically forced, friction-induced, linear oscillator, Communications in Nonlinear Science and Numerical Simulation, 11, 777–802.
Luo, A.C.J. and Gegg, B.C., 2006d, Periodic motions in a periodically forced oscillator moving on an oscillating belt with dry friction, ASME Journal of Computational and Nonlinear Dynamics, 1, 212–220.
Luo, A.C.J. and Gegg, B.C., 2006e, Dynamics of a periodically excited oscillator with dry friction on a sinusoidally time-varying, traveling surface, International Journal of Bifurcation and Chaos, 16, 3539–3566.
Luo, A.C.J. and Gegg, B.C., 2007, An analytical prediction of sliding motions along discontinuous boundary in non-smooth dynamical systems, Nonlinear Dynamics, 49, 401–424.
Luo, A.C.J. and Zwiegart Jr., P., 2008, Existence and analytical prediction of periodic motions in a periodically forced, nonlinear friction oscillator, Journal of Sound and Vibration, 309, 129–149.
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Gegg, B.C., Suh, C.S., Luo, A.C.J. (2011). Friction-Induced Oscillators. In: Machine Tool Vibrations and Cutting Dynamics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9801-9_3
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DOI: https://doi.org/10.1007/978-1-4419-9801-9_3
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