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Delay equations with fluctuating delay related to the regenerative chatter II: analysis of reduced bifurcation equation |
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| Authors: | Ali Demir Alemdar Hasanov N Sri Namachchivaya |
| Institution: | 1. Applied Mathematical Sciences Research Center , Kocaeli University , Ataturk Bulvari, 41300, Izmit-Kocaeli, Turkey ademir@edu.tr;3. Applied Mathematical Sciences Research Center , Kocaeli University , Ataturk Bulvari, 41300, Izmit-Kocaeli, Turkey;4. Department of Aeronautical and Astronautical Engineering , University of Illinois at Urbana–Champaign , 104 South Wright Street, Urbana, IL 61801, USA |
| Abstract: | In this article, we study the reduced bifurcation equations of the nonlinear delay differential equations with periodic delays, which models the machine tool chatter with continuously modulated spindle speed 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. |
| Keywords: | Bifurcation equation Periodic solutions Stability boundaries AMS Subject Classifications: 34C35 34K15 34K20 |