A time-frequency approach to ensuring stability of machining by turning





stability of the cutting process, stability lobes diagram, frequency stability criterion, machining by turning


This paper reports a new approach to ensuring the stability of the turning process, which is based on the frequency-time characteristics of the technological machining system (TMS). The approach uses a mathematical model of the turning process as a single-mass system with one degree of freedom, taking into account negative feedback on the normal coordinate and positive feedback with a delay in cutting depth. A new criterion for the stability of the cutting process as a system with a delay in positive feedback is proposed, based on the analysis of frequency characteristics in the form of a Nyquist diagram. It is proved that such a system will be stable when the chart of its Nyquist diagram does not cover a point with coordinates [+1, 0] on the complex plane. The validity of the new criterion has been confirmed by comparing the simulation results in the time range with the location of the Nyquist diagram on the complex plane. Based on the new criterion of stability, an algorithm for automatic construction of a Stability Lobes Diagram (SLD) has been developed. The necessary a priori parameters of TMS, the ranges of frequency change, and the calculation step for constructing such a characteristic in the coordinates "cutting depth – spindle rotational speed" have been determined. The adequacy of the obtained results is confirmed by a full-scale experiment to assess the roughness of machined parts under cutting modes that fall into the area of stability and instability on the SLD chart. The full-scale experiment proved the possibility of a significant reduction in roughness according to the Rz parameter, from 43 µm to 18 µm, while increasing productivity by 1.28 times. The use of a stability lobes diagram is especially effective when programming CNC lathes where it is possible to select the spindle speed in a wide range.

Author Biographies

Yuri Petrakov, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”

Doctor of Technical Sciences, Professor

Department of Mechanical Engineering Technology

Mariia Danylchenko, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”

PhD, Senior Lecturer

Department of Machine Design


  1. Kayhan, M., Budak, E. (2009). An experimental investigation of chatter effects on tool life. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 223 (11), 1455–1463. doi: https://doi.org/10.1243/09544054jem1506
  2. Quintana, G., Ciurana, J., Teixidor, D. (2008). A new experimental methodology for identification of stability lobes diagram in milling operations. International Journal of Machine Tools and Manufacture, 48 (15), 1637–1645. doi: https://doi.org/10.1016/j.ijmachtools.2008.07.006
  3. Tobias, S., Fishwick, W. (1958). Theory of Regenerative Machine Tool Chatter. The Engineer, 199–205. Available at: http://www.vibraction.fr/images/stories/Documents/1erePresentationLobesTobias.pdf
  4. Tlusty, J., Polacek, M. (1963). The Stability of Machine Tools against Self Excited Vibrations in Machining. International research in production engineering, ASME, 465–474. Available at: http://www.vibraction.fr/images/stories/Documents/2emePresentationLobesTlusty.pdf
  5. Budak, E., Altintas, Y. (1995). Modeling and avoidance of static form errors in peripheral milling of plates. International Journal of Machine Tools and Manufacture, 35 (3), 459–476. doi: https://doi.org/10.1016/0890-6955(94)p2628-s
  6. Altintas, Y., Weck, M. (2004). Chatter Stability of Metal Cutting and Grinding. CIRP Annals, 53 (2), 619–642. doi: https://doi.org/10.1016/s0007-8506(07)60032-8
  7. Quintana, G., Ciurana, J. (2011). Chatter in machining processes: A review. International Journal of Machine Tools and Manufacture, 51 (5), 363–376. doi: https://doi.org/10.1016/j.ijmachtools.2011.01.001
  8. Khasawneh, F. A. (2015). Stability Analysis of Machining Processes Using Spectral Element Approach. IFAC-PapersOnLine, 48 (12), 340–345. doi: https://doi.org/10.1016/j.ifacol.2015.09.401
  9. Yue, C., Gao, H., Liu, X., Liang, S. Y., Wang, L. (2019). A review of chatter vibration research in milling. Chinese Journal of Aeronautics, 32 (2), 215–242. doi: https://doi.org/10.1016/j.cja.2018.11.007
  10. Altintas, Y., Stepan, G., Budak, E., Schmitz, T., Kilic, Z. M. (2020). Chatter Stability of Machining Operations. Journal of Manufacturing Science and Engineering, 142 (11). doi: https://doi.org/10.1115/1.4047391
  11. Petrakov, Y. V. (2019). Chatter suppression technologies for metal cutting. Mechanics and Advanced Technologies, 86 (2). doi: https://doi.org/10.20535/2521-1943.2019.86.185849
  12. Altintas, Y., Ber, A. (2001). Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design. Applied Mechanics Reviews, 54 (5), B84–B84. doi: https://doi.org/10.1115/1.1399383
  13. Sipahi, R., Niculescu, S.-I., Abdallah, C.T., Michiels, W., Gu, K. (2011). Stability and Stabilization of Systems with Time Delay. IEEE Control Systems, 31 (1), 38–65. doi: https://doi.org/10.1109/mcs.2010.939135
  14. Petrakov, Y., Danylchenko, M., Petryshyn, A. (2019). Prediction of chatter stability in turning. Eastern-European Journal of Enterprise Technologies, 5 (1 (101)), 58–64. doi: https://doi.org/10.15587/1729-4061.2019.177291
  15. Szulewski, P., Śniegulska-Grądzka, D. (2017). Systems of automatic vibration monitoring in machine tools. Mechanik, 90 (3), 170–175. doi: https://doi.org/10.17814/mechanik.2017.3.37
A time-frequency approach to ensuring stability of machining by turning




How to Cite

Petrakov, Y., & Danylchenko, M. (2022). A time-frequency approach to ensuring stability of machining by turning. Eastern-European Journal of Enterprise Technologies, 6(2 (120), 85–92. https://doi.org/10.15587/1729-4061.2022.268637