caa a22 4500 445360682 CHVBK 20180317142914.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s11071-010-9811-6 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9811-6 Analysis of the cutting tool on a lathe [Elektronische Daten] [Ali Nayfeh, Nader Nayfeh] We use a systematic approach combining a path-following scheme, the method of multiple scales, the method of harmonic balance, Floquet theory, and numerical simulations to investigate the local and global dynamics and stability of cutting tool on a lathe due to the regenerative mechanism. First, we use the method of multiple scales to determine the normal form of the Hopf bifurcation at all of the stability boundaries and calculate the limit cycles generated by the bifurcation. Then, we use a combination of a path-following scheme and the method of harmonic balance to continue the branch of generated limit cycles. Thus, we calculate small- and large-amplitude limit cycles and ascertain their stability using Floquet theory. We validate these results using numerical simulations. Then, we search for isolated branches of large-amplitude solutions coexisting with the linearly stable trivial solution. We use all of the results to generate bifurcation diagrams consisting of multiple large-amplitude stable and unstable branches of limit cycles coexisting with the trivial response, indicating three regions of operation, as in the experimental observations. Then, we investigate bifurcation control using cubic-velocity feedback and show that the unconditionally stable region can be expanded at the expense of the conditionally stable region. Springer Science+Business Media B.V., 2010 Machine-tool chatter nationallicence Hopf bifurcation nationallicence Bifurcation control nationallicence Normal form nationallicence Method of multiple scales nationallicence Harmonic balance nationallicence Floquet theory nationallicence Nayfeh Ali Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, MC 0219, 24061, Blacksburg, VA, USA aut Nayfeh Nader Northrup Grumman, Arlington, USA aut Nonlinear Dynamics Springer Netherlands 63/3(2011-02-01), 395-416 0924-090X 63:3<395 2011 63 11071 https://doi.org/10.1007/s11071-010-9811-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9811-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Nayfeh Ali Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, MC 0219, 24061, Blacksburg, VA, USA aut NATIONALLICENCE 700 1- Nayfeh Nader Northrup Grumman, Arlington, USA aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 63/3(2011-02-01), 395-416 0924-090X 63:3<395 2011 63 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer