Stabilization in a State-Dependent Model of Turning Processes

dc.contributor.ISNI0000 0001 1616 0605 (Krawcewicz, W)
dc.contributor.ISNI0000 0000 4128 774X (Turi, J)
dc.contributor.LCNA89645792 (Krawcewicz, W)
dc.contributor.LCNA88656618 (Turi, J)
dc.contributor.authorHu, Qingwenen_US
dc.contributor.authorKrawcewicz, Wieslawen_US
dc.contributor.authorTuri, Jànosen_US
dc.contributor.utdAuthorHu, Qingwenen_US
dc.contributor.utdAuthorKrawcewicz, Wieslawen_US
dc.contributor.utdAuthorTuri, Jànosen_US
dc.date.accessioned2014-02-27T23:36:28Z
dc.date.available2014-02-27T23:36:28Z
dc.date.created2012-01-03en_US
dc.date.issued2012-01-03en_US
dc.description.abstractWe consider a two-degree-of-freedom model for turning processes which involves a system of differential equations with state-dependent delay. Depending on process parameters (e.g., spindle speed, depth of cut) the cutting tool can exhibit unwanted vibrations, resulting in a nonsmooth surface of the workpiece. In this paper we propose a feedback law to stabilize the turning process for a large range of system parameters. The feedback law introduces a generic nonhyperbolic stationary point into the model, which generates the main technical challenge of this work. We establish the stability equivalence between the differential equations with state-dependent delay and a corresponding nonlinear system with the delay fixed at its stationary value. Then we show the stability of that nonlinear system with constant delay by computing its normal form. Finally, we obtain conditions on system parameters which guarantee the stability of the state-dependent delay model at the nonhyperbolic stationary point. ©2012 Society for Industrial and Applied Mathematics.en_US
dc.identifier.bibliographicCitationHu, Q., W. Krawcewicz, and J. Turi. 2012. "Stabilization in a state-dependent model of turning processes." SIAM Journal on Applied Mathematics 72(1): doi:10.1137/110823468en_US
dc.identifier.issn0036-1399en_US
dc.identifier.issue1en_US
dc.identifier.startpage1en_US
dc.identifier.urihttp://hdl.handle.net/10735.1/3117
dc.identifier.volume72en_US
dc.language.isoenen_US
dc.publisherSIAMen_US
dc.relation.urihttp://dx.doi.org/10.1137/110823468
dc.rights©2012 Society for Industrial and Applied Mathematicsen_US
dc.sourceSIAM Journal on Applied Mathematics
dc.subjectDifferential equationsen_US
dc.subjectNormal formen_US
dc.subjectStability equivalenceen_US
dc.subjectState-dependent delayen_US
dc.subjectTurning processesen_US
dc.titleStabilization in a State-Dependent Model of Turning Processesen_US
dc.typeTexten_US
dc.type.genreArticleen_US

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