TY - JOUR
T1 - Stability of systems with time-periodic delay
T2 - Application to variable speed boring process
AU - Vedula, L.
AU - Lingala, N.
AU - Sri Namachchivaya, N.
N1 - Funding Information:
The authors would like to acknowledge the support of the National Science Foundation under grant numbers DMS-0504581and CMMI 07-58569.
PY - 2011/10
Y1 - 2011/10
N2 - The stability of systems with fluctuating delay is studied. The aim is to demonstrate that, greater depths of cut may be achieved in a boring process, when the speed of the spindle is modulated sinusoidally instead of being kept constant. Since the variation of spindle speed is small and independent of the tool motion, by expanding the delay terms about a finite mean delay and augmenting the system, the time-dependent delay system can be written as a system of non-linear delay equations with fixed delay. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. The centre-manifold and normal form methods are then used to obtain an approximate and simpler four-dimensional system. Analysis of this simpler system shows that periodic variations in the delay lead to larger stability boundaries.
AB - The stability of systems with fluctuating delay is studied. The aim is to demonstrate that, greater depths of cut may be achieved in a boring process, when the speed of the spindle is modulated sinusoidally instead of being kept constant. Since the variation of spindle speed is small and independent of the tool motion, by expanding the delay terms about a finite mean delay and augmenting the system, the time-dependent delay system can be written as a system of non-linear delay equations with fixed delay. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. The centre-manifold and normal form methods are then used to obtain an approximate and simpler four-dimensional system. Analysis of this simpler system shows that periodic variations in the delay lead to larger stability boundaries.
KW - Boring process
KW - Centre-manifold reduction
KW - Chatter suppression
KW - Functional differential equation
KW - Spindle speed variation
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U2 - 10.1177/0954406211407249
DO - 10.1177/0954406211407249
M3 - Article
AN - SCOPUS:81255161492
SN - 0954-4062
VL - 225
SP - 2296
EP - 2311
JO - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
JF - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
IS - 10
ER -