M. Abebe and F. C. Appl, A slip-line solution for negative rake angle cutting, Proc. 19th NAMRC, pp.341-348, 1981.

Y. Altintas, Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design, Applied Mechanics Reviews, vol.54, issue.5, 2000.
DOI : 10.1115/1.1399383

Y. Altintas and M. Weck, Chatter Stability of Metal Cutting and Grinding, CIRP Annals - Manufacturing Technology, vol.53, issue.2, pp.619-642, 2004.
DOI : 10.1016/S0007-8506(07)60032-8

R. N. Arnold, The mechanism of tool vibration in the cutting of steel, Proceedings of the Institution of Mechanical Engineers, pp.261-284, 1946.
DOI : 10.1243/PIME_PROC_1946_154_037_02

J. A. Bailey, Friction in metal machining???Mechanical aspects, Wear, vol.31, issue.2, pp.243-275, 1975.
DOI : 10.1016/0043-1648(75)90161-1

J. L. Battaglia, L. Puigsegur, and O. Cahuc, ESTIMATED TEMPERATURE ON A MACHINED SURFACE USING AN INVERSE APPROACH, Experimental Heat Transfer, vol.1, issue.1, pp.13-32, 2001.
DOI : 10.1007/BF02833765

P. V. Bayly, S. A. Metzler, A. J. Schaut, and K. A. Young, Theory of Torsional Chatter in Twist Drills: Model, Stability Analysis and Composition to Test, Journal of Manufacturing Science and Engineering, vol.123, issue.4, pp.552-561, 2001.
DOI : 10.1115/1.1381399

C. F. Bisu, A. Gérard, J. K-"-nevez, R. Laheurte, and O. Cahuc, Self-excited vibrations in turning: forces torsor analysis, The International Journal of Advanced Manufacturing Technology, vol.21, issue.6, pp.447-462, 2009.
DOI : 10.1007/s00170-008-1850-5

URL : https://hal.archives-ouvertes.fr/hal-00410366

C. F. Bisu, P. Darnis, A. Gérard, and J. K-"-nevez, Displacements analysis of self-excited vibrations in turning, The International Journal of Advanced Manufacturing Technology, vol.31, issue.3???4, pp.1-16, 2009.
DOI : 10.1007/s00170-008-1815-8

URL : https://hal.archives-ouvertes.fr/hal-00408724

D. Bondarenko, A. Gouskov, and H. Paris, Parameters Identification of the Ploughing Force Model by an Experimental Approach, 12th CIRP Conference on Modeling of Machining Operations, 2009.

D. Bondarenko, A. Gouskov, and H. Paris, Influence du talonnage sur la stabilité du système usinant, 19 ème Congrès Français de Mécanique, 2008.

D. Brissaud, A. Gouskov, H. Paris, and S. Tichkiewitch, The Fractional Model for the Determination of the Cutting Forces, Asian International Journal of Science and Technology ? Production and Manufacturing, vol.1, issue.1, pp.17-25, 1998.
URL : https://hal.archives-ouvertes.fr/hal-00528122

E. Budak and Y. Altintas, Analytical Prediction of Chatter Stability in Milling???Part I: General Formulation, Journal of Dynamic Systems, Measurement, and Control, vol.120, issue.1, pp.22-30, 1998.
DOI : 10.1115/1.2801317

E. A. Butcher, H. Ma, E. Bueler, V. Averina, and Z. Szabo, Stability of linear time-periodic delay-differential equations via Chebyshev polynomials, International Journal for Numerical Methods in Engineering, vol.59, issue.7, pp.895-922, 2005.
DOI : 10.1002/nme.894

O. Cahuc, J. K-"-nevez, A. Gérard, P. Darnis, G. Albert et al., Self-excited vibrations in turning: cutting moment analysis, The International Journal of Advanced Manufacturing Technology, vol.206, issue.156, pp.217-225, 2001.
DOI : 10.1007/s00170-009-2189-2

URL : https://hal.archives-ouvertes.fr/hal-00407487

O. Cahuc, P. Darnis, P. Gérard, and J. Battaglia, Experimental and Analytical Balance Sheet in Turning Applications, The International Journal of Advanced Manufacturing Technology, vol.18, issue.9, pp.648-656, 1979.
DOI : 10.1007/s001700170025

URL : https://hal.archives-ouvertes.fr/hal-00179143

J. M. Challen and P. L. Oxley, An explanation of the different regimes of friction and wear using asperity deformation models, Wear, vol.53, issue.2, pp.229-243, 1973.
DOI : 10.1016/0043-1648(79)90080-2

N. H. Cook, Tool Wear and Tool Life, Journal of Engineering for Industry, vol.95, issue.4, pp.931-938, 1973.
DOI : 10.1115/1.3438271

N. H. Cook, Self-excited vibration in metal cutting, Trans. ASME, Journal of Engineering for Industry, vol.81, pp.183-186, 1959.

J. P. Costes, Y. Guillet, G. Poulachon, and M. Dessoly, Tool-life and wear mechanisms of CBN tools in machining of Inconel 718, International Journal of Machine Tools and Manufacture, vol.47, issue.7-8, pp.1081-1087, 2007.
DOI : 10.1016/j.ijmachtools.2006.09.031

URL : https://hal.archives-ouvertes.fr/hal-01088213

M. K. Das and S. A. Tobias, The relation between the static and the dynamic cutting of metals, International Journal of Machine Tool Design and Research, vol.7, issue.2, pp.63-89, 1967.
DOI : 10.1016/0020-7357(67)90026-1

A. Dugas, J. J. Lee, M. Terrier, and J. Y. Hascoët, Development of a machining simulator considering machine behavior, Proceedings of the Institution of Mechanical Engineers, 1995.

W. J. Endres, R. E. Devor, and S. G. Kapoor, A Dual-Mechanism Approach to the Prediction of Machining Forces, Part 1: Model Development, Journal of Engineering for Industry, vol.117, issue.4, pp.526-533, 1995.
DOI : 10.1115/1.2803530

M. Eynian and Y. Altintas, Chatter Stability of General Turning Operations With Process Damping, Journal of Manufacturing Science and Engineering, vol.131, issue.4, 2005.
DOI : 10.1115/1.3159047

N. Fang and P. Dewhurst, Slip-line modeling of built-up edge formation in machining, International Journal of Mechanical Sciences, vol.47, issue.7, pp.1079-1098, 2002.
DOI : 10.1016/j.ijmecsci.2005.02.008

M. S. Fofana, Aspects of stable and unstable machining by Hops bifurcation, Applied Mathematical Modeling, vol.2610, pp.953-973, 2002.

M. S. Fofana and P. B. Ryba, Parametric stability of non-linear time delay equations, International Journal of Non-Linear Mechanics, vol.39, issue.1, pp.79-91, 2004.
DOI : 10.1016/S0020-7462(02)00139-7

M. Fontaine, A. Moufki, A. Devillez, and D. Dudzinski, Modelling of cutting forces in ball-end milling with tool???surface inclination, Journal of Materials Processing Technology, vol.189, issue.1-3, pp.73-84, 2007.
DOI : 10.1016/j.jmatprotec.2007.01.006

URL : https://hal.archives-ouvertes.fr/hal-00261032

M. Fontaine, A. Moufki, A. Devillez, and D. Dudzinski, Modelling of cutting forces in ball-end milling with tool???surface inclination, Journal of Materials Processing Technology, vol.189, issue.1-3, pp.85-96, 2007.
DOI : 10.1016/j.jmatprotec.2007.01.007

URL : https://hal.archives-ouvertes.fr/hal-00261032

G. Fromentin and G. Poulachon, Modeling of interferences during thread milling operation, The International Journal of Advanced Manufacturing Technology, vol.46, issue.1, pp.41-51, 2010.
DOI : 10.1007/s00170-009-2372-5

URL : https://hal.archives-ouvertes.fr/hal-00880753

G. Fromentin and G. Poulachon, Geometrical analysis of thread milling???part 1: evaluation of tool angles, The International Journal of Advanced Manufacturing Technology, vol.39, issue.1, pp.73-80, 2010.
DOI : 10.1007/s00170-009-2402-3

G. Fromentin and G. Poulachon, Geometrical analysis of thread milling???part 2: calculation of uncut chip thickness, The International Journal of Advanced Manufacturing Technology, vol.14, issue.7, pp.81-87, 2007.
DOI : 10.1007/s00170-009-2401-4

URL : https://hal.archives-ouvertes.fr/hal-00880765

V. Gagnol, B. C. Bouzgarrou, P. Ray, and C. Barra, Model-based chatter stability prediction for high-speed spindles, International Journal of Machine Tools and Manufacture, vol.47, issue.7-8, pp.1176-1186, 1979.
DOI : 10.1016/j.ijmachtools.2006.09.002

A. Gouskov, V. Svetlitsky, and S. Voronov, Transverse self-vibration excitation of tool used for deep hole drilling, Collection of Papers Raschety na Prochnost, Mashinostroenie, pp.172-182, 1979.

A. Gouskov and S. Voronov, Dynamic models generalization of manufacturing systems with single-point cutting considering equations of new surface formation, Nonlinear Dynamics and Control of Mechanical Processing, 2 nd Workshop in COST Action P4, Hungary, 2001.

A. Gouskov, Dinamika dvuhrezcovogo tochenia, Stanki i instrumenti, pp.3-8, 2004.

A. Gouskov, S. Voronov, and A. Kvashnin, Vlianie krutilnih kolebaniy na proces sverlenia s vibrovozbuditelem, Nauka i obrazovanie, Inzenernoe obrazovanie, E-Journal, vol.12, 2007.

J. Gradisek, M. Kalveram, T. Insperger, K. Weinert, G. Stepan et al., On stability prediction for milling, International Journal of Machine Tools and Manufacture, vol.45, issue.7-8, pp.769-781, 2005.
DOI : 10.1016/j.ijmachtools.2004.11.015

N. Guibert, Etude et modélisation des phénomènes de coupe sur les performances du forage vibratoire, Doctor of Philosophy in Engineering Mechanics Thesis, 2004.

Y. B. Guo and Y. K. Chou, The determination of ploughing force and its influence on material properties in metal cutting, Journal of Materials Processing Technology, vol.148, issue.3, pp.368-375, 1974.
DOI : 10.1016/j.jmatprotec.2004.02.052

N. H. Hanna and S. A. Tobias, A Theory of Nonlinear Regenerative Chatter, Journal of Engineering for Industry, vol.96, issue.1, pp.247-255, 1974.
DOI : 10.1115/1.3438305

D. H. Hodges, Torsion of Pretwisted Beams Due to Axial Loading, Journal of Applied Mechanics, vol.47, issue.2, pp.393-397, 1966.
DOI : 10.1115/1.3153675

T. C. Hsu, A Study of the Normal and Shear Stresses on a Cutting Tool, Journal of Engineering for Industry, vol.88, issue.1, pp.51-54, 1966.
DOI : 10.1115/1.3670890

T. Insperger, G. Stepan, and J. Turi, On the higher-order semi-discretizations for periodic delayed systems, Journal of Sound and Vibration, vol.313, issue.1-2, pp.334-341, 2002.
DOI : 10.1016/j.jsv.2007.11.040

T. Insperger and G. Stepan, Semi-discretization method for delayed systems, International Journal for Numerical Methods in Engineering, vol.33, issue.1, pp.503-518, 2002.
DOI : 10.1002/nme.505

T. Insperger, B. P. Mann, G. Stepan, and P. V. Bayly, Stability of up-milling and down-milling, part 1: alternative analytical methods, International Journal of Machine Tools and Manufacture, vol.43, issue.1, pp.25-34, 2003.
DOI : 10.1016/S0890-6955(02)00159-1

T. Insperger and G. Stepan, Updated semi-discretization method for periodic delay-differential equations with discrete delay, International Journal for Numerical Methods in Engineering, vol.61, issue.1, pp.117-141, 2004.
DOI : 10.1002/nme.1061

T. Kalmar-nagy, G. Stepan, and F. C. Moon, Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations, Nonlinear Dynamics, vol.26, issue.2, pp.121-142, 2001.
DOI : 10.1023/A:1012990608060

E. Kamnev, Contribution à la modélisation et à l " industrialisation du perçage vibratoire, Doctor of Philosophy in Engineering Mechanics Thesis, 2003.

F. A. Khasawneh, B. P. Mann, T. Insperger, and G. Stepan, Increased Stability of Low-Speed Turning Through a Distributed Force and Continuous Delay Model, Journal of Computational and Nonlinear Dynamics, vol.4, issue.4, 2009.
DOI : 10.1115/1.3187153

R. Laheurte, O. Cahuc, P. Darnis, and A. Gérard, Behaviour law for cutting process, The International Journal of Advanced Manufacturing Technology, vol.62, issue.1-2, pp.17-33, 2006.
DOI : 10.1007/s00170-004-2498-4

URL : https://hal.archives-ouvertes.fr/hal-00179131

S. Laporte, J. K-"-nevez, O. Cahuc, and P. Darnis, Phenomenological model for drilling operation, The International Journal of Advanced Manufacturing Technology, vol.58, issue.1996, 2009.
DOI : 10.1007/s00170-007-1305-4

V. Lazarev, Ustoychivost processa rezania metalov, Vyshaia shkola, 1973.

C. R. Liu and T. M. Liu, Automated Chatter Suppression by Tool Geometry Control, Journal of Engineering for Industry, vol.107, issue.2, pp.95-98, 1985.
DOI : 10.1115/1.3185989

A. M. Lyapunov, The general problem of the stability of motion, International Journal of Control, vol.553, pp.531-534, 1992.

B. P. Mann, T. Insperger, P. V. Bayly, and G. Stepan, Stability of up-milling and down-milling, part 2: experimental verification, International Journal of Machine Tools and Manufacture, vol.43, issue.1, pp.35-40, 2003.
DOI : 10.1016/S0890-6955(02)00160-8

J. Manjunathaiah and W. J. Endres, A New Model and Analysis of Orthogonal Machining With an Edge-Radiused Tool, Journal of Manufacturing Science and Engineering, vol.122, issue.3, pp.384-390, 1945.
DOI : 10.1115/1.1285886

M. E. Merchant, Mechanics of the Metal Cutting Process. II. Plasticity Conditions in Orthogonal Cutting, Journal of Applied Physics, vol.16, issue.6, pp.318-324, 1945.
DOI : 10.1063/1.1707596

H. E. Merrit, Theory of Self-Excited Machine-Tool Chatter: Contribution to Machine-Tool Chatter Research???1, Journal of Engineering for Industry, vol.87, issue.4, pp.447-454, 1965.
DOI : 10.1115/1.3670861

I. E. Minis and R. Yanushevsky, A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling, Journal of Engineering for Industry, vol.115, issue.1, pp.1-8, 1993.
DOI : 10.1115/1.2901633

F. C. Moon and T. Kalmar-nagy, Nonlinear models for complex dynamics in cutting material, Philosophical Transactions of the, pp.695-711, 2001.

G. F. Moraru, Etude du comportement du système pièce ? outil ? machine en régime de coupe vibratoire, Doctor of Philosophy in Engineering Mechanics Thesis Arts et Métiers, 2002.

P. Naisson and L. Grenier, Reconception du porte outil vibratoire dans le cadre du projet FGVV, évolution v1, 1979.

H. Nyquist, Regeneration theory, Bell System Technical Journal, pp.126-147, 1932.

P. L. Oxley, The mechanics of machining, 1989.

H. Paris, D. Brissaud, A. Gouskov, N. Guibert, and J. Rech, Influence of the ploughing effect on the dynamic behavior of the self-vibratory drilling head, CIRP Annals ? Manufacturing Technology, vol.57, issue.1, 2008.

G. Peigné, Etude et simulation des effets dynamiques de la coupe sur la stabilité de la coupe et la qualité géométrique de la surface usinée : application au fraisage de profil, Doctor of Philosophy in Engineering Mechanics Thesis, 2003.

V. Poduraev, Obrabotka rezaniem s vibraciami, Mashinostroenie, 1970.

V. Poduraev and A. Kibalchenko, The technology of defense industry for manufacturing of customer goods, Rosconversia, 1993.

J. R. Pratt and A. H. Nayfeh, Vibration control for chatter suppression, Doctor of Philosophy in Engineering Mechanics Thesis, 1997.

S. Seguy, G. Dessein, L. Arnaud, and T. Insperger, Control of Chatter by Spindle Speed Variation in High-Speed Milling, Advanced Materials Research, vol.112, pp.179-186, 1969.
DOI : 10.4028/www.scientific.net/AMR.112.179

T. R. Sisson and R. L. Kegg, An Explanation of Low-Speed Chatter Effects, Journal of Engineering for Industry, vol.91, issue.4, pp.951-958, 1969.
DOI : 10.1115/1.3591778

R. Stevenson, The measurement of parasitic forces in orthogonal cutting, International Journal of Machine Tools and Manufacture, vol.38, issue.1-2, pp.113-130, 1994.
DOI : 10.1016/S0890-6955(97)00022-9

Y. S. Tarng, H. T. Young, and B. Y. Lee, An analytical model of chatter vibration in metal cutting, International Journal of Machine Tools and Manufacture, vol.34, issue.2, pp.183-197, 1907.
DOI : 10.1016/0890-6955(94)90100-7

F. Taylor, On the art of cutting metals, Trans. ASME, vol.28, pp.31-350, 1907.

V. Thevenot, L. Arnaud, G. Dessein, and G. Cazenave-larroche, Integration of dynamic behaviour variations in the stability lobes method: 3D lobes construction and application to thin-walled structure milling, The International Journal of Advanced Manufacturing Technology, vol.27, issue.7-8, pp.638-644, 1963.
DOI : 10.1007/s00170-004-2241-1

URL : https://hal.archives-ouvertes.fr/hal-00800292

J. Tlusty and M. Polacek, The stability of machine tools against self-excited vibrations in machining, International Research in Production Engineering, ASME, pp.465-474, 1958.

S. A. Tobias and W. Fishwick, Theory of regenerative machine tool chatter, 1956.

K. J. Trigger and B. T. Chao, The mechanism of crater wear of cemented carbide tools, Trans. ASME, vol.78, pp.1119-1126, 1956.

D. J. Waldorf, R. E. Devor, and S. G. Kapoor, A Slip-Line Field for Ploughing During Orthogonal Cutting, Journal of Manufacturing Science and Engineering, vol.120, issue.4, pp.693-699, 1998.
DOI : 10.1115/1.2830208

J. Wang and C. M. Zheng, An analytical force model with shearing and ploughing mechanisms for end milling, International Journal of Machine Tools and Manufacture, vol.42, issue.7, pp.761-771, 2001.
DOI : 10.1016/S0890-6955(02)00019-6

M. Wiercirgroch and E. Budak, Sources of nonlinearities, chatter generation and suppression in metal cutting, Philosophical Transactions of the, pp.663-693, 2001.

M. Wiercigroch and A. M. Krivtsov, Frictional chatter in orthogonal metal cutting, Philosophical Transactions of the, pp.713-738, 1989.

D. W. Wu, A new approach of formulating the transfer function for dynamic cutting process, Journal of Engineering for Industry, vol.11137, pp.37-47, 1988.

D. W. Wu, Application of a comprehensive dynamic cutting force model to orthogonal wavegenerating processes, International Journal of Mechanical Sciences, vol.308, 1988.

D. W. Wu and C. R. Liu, An Analytical Model of Cutting Dynamics. Part 1: Model Building, Journal of Engineering for Industry, vol.107, issue.2, pp.107-111, 1985.
DOI : 10.1115/1.3185972

F. Zemzemi, Caractérisation de modèles de frottement aux interfaces pièce-outil-copeau en usinage : application au cas de l " usinage des aciers et de l " inconnel718, Doctor of Philosophy in Engineering Mechanics Thesis, p.2007, 1986.

I. Zharkov, Vibracii pri obrabotke lezviynim instrumentom, 1986.