TY - GEN
T1 - Nonlinear delay equations with fluctuating delay
T2 - Application to regenerative chatter
AU - Demir, Ali
AU - Sri Namachchivaya, N.
AU - Langford, W. F.
PY - 2002
Y1 - 2002
N2 - The mathematical models representing machine tool chatter dynamics have been cast as differential equations with delay. The suppression of regenerative chatter by spindle speed variation is attracting increasing attention. In this paper, we study nonlinear delay differential equations with periodic delays which models the machine tool chatter with continuously modulated spindle speed. The explicit time-dependent delay terms, due to spindle speed modulation, are replaced by state dependent delay terms by augmenting the original equations. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. We make use of Lyapunov-Schmidt Reduction method to determine the periodic solutions and analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions close to the new stability boundary.
AB - The mathematical models representing machine tool chatter dynamics have been cast as differential equations with delay. The suppression of regenerative chatter by spindle speed variation is attracting increasing attention. In this paper, we study nonlinear delay differential equations with periodic delays which models the machine tool chatter with continuously modulated spindle speed. The explicit time-dependent delay terms, due to spindle speed modulation, are replaced by state dependent delay terms by augmenting the original equations. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. We make use of Lyapunov-Schmidt Reduction method to determine the periodic solutions and analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions close to the new stability boundary.
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U2 - 10.1115/IMECE2002-32389
DO - 10.1115/IMECE2002-32389
M3 - Conference contribution
AN - SCOPUS:78249249302
SN - 0791836282
SN - 9780791836286
T3 - ASME International Mechanical Engineering Congress and Exposition, Proceedings
SP - 311
EP - 321
BT - Design Engineering
PB - American Society of Mechanical Engineers (ASME)
ER -