Abstract
In this work, the stability of a flexible thin cylindrical workpiece in turning is analyzed. A process model is derived based on a finite element representation of the workpiece flexibility and a nonlinear cutting force law. Repeated cutting of the same surface due to overlapping cuts is modeled with the help of a time delay. The stability of the so obtained system of periodic delay differential equations is then determined using an approximation as a time-discrete system and Floquet theory. The time-discrete system is obtained using the semi-discretization method. The method is implemented to analyze the stability of two different workpiece models of different thicknesses for different tool positions with respect to the jaw end. It is shown that the stability chart depends on the tool position as well as on the thickness.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Taylor, F.: On the art of cutting metals. Transactions of the ASME 28, 31–350 (1907)
Arnold, R.: The mechanism of tool vibration in the cutting of steel. Proceedings of the Institution of Mechanical Engineers 154, 261–284 (1946)
Tobias, S.A.: Machine-Tool Vibration. Blackie and Sons, London (1965)
Merrit, H.E.: Theory of self-excited machine-tool chatter. Journal of Engineering for Industry 87, 447–454 (1965)
Tlusty, J., Polacek, M.: The stability of machine tools against self-excited vibrations in machining. ASME International Research in Production Engineering 1, 465–474 (1963)
Clancy, B.E., Shin, Y.C.: A comprehensive chatter prediction model for face turning operation including tool wear effect. International Journal of Machine Tools and Manufacture 42, 1035–1044 (2002)
Ozlu, E., Budak, E.: Analytical modeling of chatter stability in turning and boring operations. Part I: Model development. Journal of Manufacturing Science and Engineering 129, 726–732 (2007)
Ozlu, E., Budak, E.: Comparison of one-dimensional and multi-dimensional models in stability analysis of turning operations. International Journal of Machine Tools and Manufacture 49, 1042–1047 (2009)
Li, Z.Q., Liu, Q.: Solution and analysis of chatter stability for end milling in the time-domain. Chinese Journal of Aeronautics 21, 169–178 (2008)
Srinivas, J., Kotaiah, K.: A study of bifurcation behaviour in oblique turning operation. International Journal of Machine Tools and Manufacture 49, 1042–1047 (2009)
Mehdi, K., Rigal, J., Play, D.: Dynamic behavior, thin walled cylindrical workpiece during the turning process. Part 2: Cutting process simulation. Transactions of ASME, Journal of Manufacturing Science and Engineering 124, 532–568 (2002)
Mehdi, K., Rigal, J., Play, D.: Dynamic behavior, thin walled cylindrical workpiece during the turning process. Part 2: Experimental approach and validation. Transactions of ASME, Journal of Manufacturing Science and Engineering 124, 569–580 (2002)
Bayly, L.K., Davis, M.A.: Stability of interrupted cutting by temporal finite element analysis. Journal ofManufacturing Science and Engineering 125, 220–225 (2003)
Insperger, T., Stépán, G.: Semi-discretization method for delayed systems. International Journal for Numerical Methods in Engineering 55, 503–518 (2002)
Insperger, T., Stépán, G.: Updated semi-discretization method for periodic delay-differential equations with discrete delay. International Journal for Numerical Methods in Engineering 61, 117–141 (2004)
Henninger, C., Eberhard, P.: Improving the computational efficiency and the accuracy of the semi-discretization method for periodic delay-differential equations. European Journal of Mechanics A/Solids 27, 975–985 (2008)
Gawronski, W.K.: Advanced Structural Dynamics and Active Control of Structures. Springer, New York (2004)
König, K., Essel, W., Witte, L.: Spezifische Schnittkraftwerte für die Zerspanung metallischer Werkstoffe Verein Deutscher Eisenhüttenleute. Verlag Stahleisen mbH, Düsseldorf (1982) (in German)
Paucksch, E., Holsten, S., Linß, M., et al.: Zerspantechnik. Vieweg+Teubner, Wiesbaden (2008) (in German)
Henninger, C.: Methoden zur simulationsbasierten Analyse der dynamischen Stabilität von Frässprozessen, doctoral thesis, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, Shaker Verlag, Aachen (2009) (in German)
Hartung, F., Insperger, T., Stépán, G., et al.: Approximate stability charts for milling processes using semi-discretization. Applied Mathematics and Computation 174, 51–73 (2006)
Hale, J.K., Lunel, S.M.V.: Introduction to Functional Differential Equations. Springer, New York (1993)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chanda, A., Fischer, A., Eberhard, P. et al. Stability analysis of a thin-walled cylinder in turning operation using the semi-discretization method. Acta Mech Sin 30, 214–222 (2014). https://doi.org/10.1007/s10409-013-0097-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10409-013-0097-z