This paper presents a method for vibrostability prognosis using a non-stationary model of the machine tool-cutting process system. The method employs Liapunov-Floquet theory. The method is illustrated by the example of the determination of limit cutting parameters using appropriate model reduction methods.
Hahn, W., 1961, “On difference differential equations with periodic coefficients,”Journal of Mathematical Analysis and Applications3, 70-101.
2.
Kruszewski, J., Sawiak, S., and Wittbrodt, E., 1999, “Rigid finite element method in the dynamic of constructions”, WNT Warsaw.
3.
Marchelek, K. and Tomków, J., 1998a, “Vibrostability of a multidimensional machine tool-workpiece-tool system, part I: Modeling the mechanical structure and cutting process,”Journal of Vibration and Control4, 99-112.
4.
Marchelek, K. and Tomków, J., 1998b, “Vibrostability of a multidimensional machine tool-workpiece-tool System, part II: An example of vibrostability analysis made on a vertical lathe,”Journal of Vibration and Control4, 113-130.
5.
Pajor, M., Marchelek, K., and Powałka, B., 2000, “Method of DOF number reduction of machine tool-cutting process system from the point of view of vibrostability analysis,” in Eighth Conference on Nonlinear Vibrations, Stability, and Dynamics of Structures, Blacksburg, VA, July 23-27.
6.
Spires, J. M. and Sinha, S. C., 1996, “On the response of linear time-periodic systems subjected to deterministic and stochastic excitations,”Journal of Vibration and Control2, 219-249.
7.
Sridhar, R., Hohn, R. E., and Long, G. W., 1968, “A stability algorithm for the general milling process equation - contribution to machine tool chatter research - 7,”Transactions of the ASME B90, 330-334.