@{MTMT:1875898,
	title = {State dependent regenerative effect in milling processes},
	url = {https://m2.mtmt.hu/api/publication/1875898},
	author = {Bachrathy, Dániel and Stépán, Gábor},
	booktitle = {Proceedings of the 7th European Nonlinear Dynamics Conference},
	unique-id = {1875898},
	year = {2011},
	orcid-numbers = {Bachrathy, Dániel/0000-0003-1491-1852; Stépán, Gábor/0000-0003-0309-2409}
}

@article{MTMT:1875862,
	title = {State dependent regenerative effect in milling processes},
	url = {https://m2.mtmt.hu/api/publication/1875862},
	author = {Bachrathy, Dániel and Stépán, Gábor and Turi, János},
	doi = {10.1115/1.4003624},
	journal-iso = {J COMPUT NONLIN DYN},
	journal = {JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS},
	volume = {6},
	unique-id = {1875862},
	issn = {1555-1415},
	abstract = {The governing equation of milling processes is generalized with the help of accurate chip thickness derivation resulting in a state dependent delay model. This model is valid for large amplitude machine tool vibrations and uses accurate nonlinear screen functions describing the entrance and exit positions of the cutting edges of the milling tool relative to the workpiece. The periodic motions of this nonlinear system are calculated by a shooting method. The stability calculation is based on the linearization around these periodic solutions by means of the semidiscretization method applied for the corresponding time-periodic delay system. Predictor-corrector method is developed to continue the periodic solutions as the bifurcation parameter, that is, the axial immersion is varied. It is observed that the influence of the state dependent delay on linear stability can be significant close to resonance where large amplitude forced vibrations occur. The existence of an unusual fold bifurcation is shown where a kind of hysteresis phenomenon appears between two different stable periodic motions.},
	year = {2011},
	eissn = {1555-1423},
	orcid-numbers = {Bachrathy, Dániel/0000-0003-1491-1852; Stépán, Gábor/0000-0003-0309-2409}
}

@article{MTMT:1454448,
	title = {On the Global Dynamics of Chatter in the Orthogonal Cutting Model},
	url = {https://m2.mtmt.hu/api/publication/1454448},
	author = {Dombóvári, Zoltán and Barton, David and Wilson, Eddie and Stépán, Gábor},
	doi = {10.1016/j.ijnonlinmec.2010.09.016},
	journal-iso = {INT J NONLINEAR MECH},
	journal = {INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS},
	volume = {46},
	unique-id = {1454448},
	issn = {0020-7462},
	abstract = {The large-amplitude motions of a one degree-of-freedom model of orthogonal cutting are analysed. The model takes the form of a delay differential equation which is non-smooth at the instant at which the tool loses contact with the workpiece, and which is coupled to an algebraic equation that stores the profile of the cut surface whilst the tool is not in contact. This system is approximated by a smooth delay differential equation without algebraic effects which is analysed with numerical continuation software. The grazing bifurcation that defines the onset of chattering motion is thus analysed as are secondary (period-doubling, etc.) bifurcations of chattering orbits, and convergence of the bifurcation diagrams is established in the vanishing limit of the smoothing parameters. The bifurcation diagrams of the smoothed system are then compared with initial value simulations of the full non-smooth delay differential algebraic equation. These simulations mostly validate the smoothing technique and show in detail how chaotic chattering dynamics emerge from the non-smooth bifurcations of periodic orbits. © 2010 Elsevier Ltd. All rights reserved.},
	year = {2011},
	eissn = {1878-5638},
	pages = {330-338},
	orcid-numbers = {Dombóvári, Zoltán/0000-0003-2591-3220; Stépán, Gábor/0000-0003-0309-2409}
}

@article{MTMT:1247389,
	title = {Surface properties of the machined workpiece for helical mills},
	url = {https://m2.mtmt.hu/api/publication/1247389},
	author = {Bachrathy, Dániel and Insperger, Tamás and Stépán, Gábor},
	doi = {10.1080/10910340903012167},
	journal-iso = {MACH SCI TECHNOL},
	journal = {MACHINING SCIENCE AND TECHNOLOGY},
	volume = {13},
	unique-id = {1247389},
	issn = {1091-0344},
	abstract = {Stability and surface errors are investigated numerically for milling
		operations with a helical tool. A detailed two degree of freedom
		mechanical model is derived that includes both surface regeneration and
		the helical teeth of the tool. The governing delay-differential
		equation is analyzed by the semi-discretization method. The surface
		errors are predicted based on the (stable) forced motion of the tool.
		New surface error parameters were introduced to characterize the
		properties of the spatial machined surface. The errors were calculated
		numerically for a given machine tool and workpiece for different axial
		depths of cut and spindle speeds. It is shown that both good surface
		properties and large material removal rate can be achieved by
		appropriate axial immersion in case of helical fluted tool. This
		phenomenon was proved analytically by means of the Fourier
		transformation of the cutting force.},
	year = {2009},
	eissn = {1532-2483},
	pages = {227-245},
	orcid-numbers = {Bachrathy, Dániel/0000-0003-1491-1852; Insperger, Tamás/0000-0001-7518-9774; Stépán, Gábor/0000-0003-0309-2409}
}

@book{MTMT:30178324,
	title = {Delay Differential Equations: Recent Advances and New Directions},
	url = {https://m2.mtmt.hu/api/publication/30178324},
	isbn = {9780387855943},
	doi = {10.1007/978-0-387-85595-0},
	editor = {Balachandran, Balakumar and Kalmár-Nagy, Tamás and Gilsinn, David},
	publisher = {Springer US; Springer Science and Business Media B.V.},
	unique-id = {30178324},
	abstract = {Delay Differential Equations: Recent Advances and New Directions cohesively presents contributions from leading experts on the theory and applications of functional and delay differential equations (DDEs).
		
		Students and researchers will benefit from a unique focus on theory, symbolic, and numerical methods, which illustrate how the concepts described can be applied to practical systems ranging from automotive engines to remote control over the Internet. Comprehensive coverage of recent advances, analytical contributions, computational techniques, and illustrative examples of the application of current results drawn from biology, physics, mechanics, and control theory.
		
		Students, engineers and researchers from various scientific fields will find Delay Differential Equations: Recent Advances and New Directions a valuable reference.},
	keywords = {Lambert function approach - Maple - bifurcation - bifurcations - calculus - control - control theory - delay differential equations (DDEs) - functional equations - machine tool applications - mechanics - numerical methods - stability - time delay - time},
	year = {2009},
	orcid-numbers = {Kalmár-Nagy, Tamás/0000-0003-1374-2620}
}

@article{MTMT:1148761,
	title = {On the higher-order semi-discretizations for periodic delayed systems},
	url = {https://m2.mtmt.hu/api/publication/1148761},
	author = {Insperger, Tamás and Stépán, Gábor and Turi, J},
	doi = {10.1016/j.jsv.2007.11.040},
	journal-iso = {J SOUND VIB},
	journal = {JOURNAL OF SOUND AND VIBRATION},
	volume = {313},
	unique-id = {1148761},
	issn = {0022-460X},
	abstract = {Semi-discretization techniques of periodic delayed systems are
		presented using zeroth-, first- and higher-order approximations of the
		delayed term. It is shown that if the time-periodic coefficients in the
		equation are approximated by piecewise constant functions, then there
		is no need to use higher than first-order approximations of the delayed
		term. The results are demonstrated on construction of the stability
		chart of the delayed Mathieu equation. (c) 2007 Elsevier Ltd. All
		rights reserved.},
	year = {2008},
	eissn = {1095-8568},
	pages = {334-341},
	orcid-numbers = {Insperger, Tamás/0000-0001-7518-9774; Stépán, Gábor/0000-0003-0309-2409}
}

@article{MTMT:1148749,
	title = {On stability prediction for milling},
	url = {https://m2.mtmt.hu/api/publication/1148749},
	author = {Gradisek, J and Kalveram, M and Insperger, Tamás and Weinert, K and Stépán, Gábor and Govekar, E and Grabec, I},
	doi = {10.1016/j.ijmachtools.2004.11.015},
	journal-iso = {INT J MACH TOOL MANU},
	journal = {INTERNATIONAL JOURNAL OF MACHINE TOOLS & MANUFACTURE},
	volume = {45},
	unique-id = {1148749},
	issn = {0890-6955},
	abstract = {Stability of 2-dof milling is investigated. Stability boundaries are
		predicted by the zeroth order approximation (ZOA) and the
		semi-discretization (SD) methods. While similar for high radial
		immersions, predictions of the two methods grow considerably different
		as radial immersion is decreased. The most prominent difference is an
		additional type of instability causing periodic chatter which is
		predicted only by the SD method. Experiments confirm predictions of the
		SD method, revealing three principal types of tool motion: periodic
		chatter-free, quasi-periodic chatter and periodic chatter, as well as
		some special chatter cases. Tool deflections recorded during each of
		these motion types are studied in detail. (c) 2004 Elsevier Ltd. All
		rights reserved.},
	year = {2005},
	eissn = {1879-2170},
	pages = {769-781},
	orcid-numbers = {Insperger, Tamás/0000-0001-7518-9774; Stépán, Gábor/0000-0003-0309-2409}
}

@article{MTMT:1332633,
	title = {Linearized stability in periodic functional differential equations with state-dependent delays},
	url = {https://m2.mtmt.hu/api/publication/1332633},
	author = {Hartung, Ferenc},
	doi = {10.1016/j.cam.2004.04.006},
	journal-iso = {J COMPUT APPL MATH},
	journal = {JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS},
	volume = {174},
	unique-id = {1332633},
	issn = {0377-0427},
	abstract = {In this paper, we study stability of periodic solutions of a class of nonlinear functional differential equations (FDEs) with stare-dependent delays using the method of linearization. We show that a periodic solution of the nonlinear FDE is exponentially stable, if the zero solution of an associated linear periodic linear homogeneous FDE is exponentially stable.},
	year = {2005},
	eissn = {1879-1778},
	pages = {201-211},
	orcid-numbers = {Hartung, Ferenc/0000-0001-7953-3480}
}

@article{MTMT:1148740,
	title = {Stability analysis of turning with periodic spindle speed modulation via semidiscretization},
	url = {https://m2.mtmt.hu/api/publication/1148740},
	author = {Insperger, Tamás and Stépán, Gábor},
	doi = {10.1177/1077546304044891},
	journal-iso = {J VIB CONTROL},
	journal = {JOURNAL OF VIBRATION AND CONTROL},
	volume = {10},
	unique-id = {1148740},
	issn = {1077-5463},
	abstract = {We investigate a single-degree-of-freedom model of turning with
		sinusoidal spindle speed modulation and the corresponding
		delay-differential equation with time-varying delay. The equation is
		analyzed by the numerical semidiscretization method. Stability charts
		and chatter frequencies are constructed. Improvement in the efficiency
		of machining is found for high modulation frequency and for low spindle
		speed domain. Period-one, period-two (flip), and secondary Hopf
		bifurcations were detected by eigenvalue analysis.},
	year = {2004},
	eissn = {1741-2986},
	pages = {1835-1855},
	orcid-numbers = {Insperger, Tamás/0000-0001-7518-9774; Stépán, Gábor/0000-0003-0309-2409}
}

@article{MTMT:1148736,
	title = {Stability of up-milling and down-milling, part 1: alternative analytical methods},
	url = {https://m2.mtmt.hu/api/publication/1148736},
	author = {Insperger, Tamás and Mann, BP and Stépán, Gábor and Bayly, PV},
	doi = {10.1016/S0890-6955(02)00159-1},
	journal-iso = {INT J MACH TOOL MANU},
	journal = {INTERNATIONAL JOURNAL OF MACHINE TOOLS & MANUFACTURE},
	volume = {43},
	unique-id = {1148736},
	issn = {0890-6955},
	abstract = {The dynamic stability of the milling process is investigated through a single degree of freedom mechanical model. Two alternative analytical methods are introduced, both based on finite dimensional discrete map representations of the governing time periodic delay-differential equation.
		Stability charts and chatter frequencies are determined for partial immersion up- and down-milling, and for full immersion milling operations. A special duality property of stability regions for up- and down-milling is shown and explained. (C) 2002 Elsevier Science Ltd. All rights reserved.},
	year = {2003},
	eissn = {1879-2170},
	pages = {25-34},
	orcid-numbers = {Insperger, Tamás/0000-0001-7518-9774; Stépán, Gábor/0000-0003-0309-2409}
}

@inproceedings{MTMT:1148983,
	title = {Semi-discretization of delayed dynamical systems},
	url = {https://m2.mtmt.hu/api/publication/1148983},
	author = {Insperger, Tamás and Stépán, Gábor},
	booktitle = {18th Biennial Conference on Mechanical Vibration and Noise},
	unique-id = {1148983},
	abstract = {An efficient numerical method is presented for the stability analysis of linear retarded dynamical systems. The method is based on a special kind of discretization technique with respect to the past effect only. The resulting approximate system is delayed and time-periodic in the same time, but still, it can be transformed analytically into a high dimensional linear discrete system. The method is especially efficient for time varying delayed systems, including the case when the time delay itself varies in time. The method is applied to determine the stability charts of the delayed Mathieu equation with damping.},
	year = {2001},
	pages = {1227-1232},
	orcid-numbers = {Insperger, Tamás/0000-0001-7518-9774; Stépán, Gábor/0000-0003-0309-2409}
}

@book{MTMT:1002286,
	title = {Retarded Dynamical Systems. Stability and Characteristic Functions},
	url = {https://m2.mtmt.hu/api/publication/1002286},
	isbn = {0470213353},
	author = {Stépán, Gábor},
	publisher = {Longman Scientific & Technical},
	unique-id = {1002286},
	year = {1989},
	orcid-numbers = {Stépán, Gábor/0000-0003-0309-2409}
}