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State–space analysis of mode-coupling workpiece chatter

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Abstract

Chatter vibrations produced during turning of slender parts cause poor workpiece surface finishing and premature tool wear. In this paper, mode coupling in flexible workpiece metal cutting without tailstock is analysed in the state-space domain. The proposed mode coupling model considers mode rotation with the workpiece. Closed form equations are obtained for eigenvalues of the system formed by the cutting process and the mechanical structure, as a function of cutting conditions and workpiece modal parameters. Mode rotation and cutting speed influence on system stability is analysed and chatter-free conditions are determined. Finally, experimental tests are presented to evaluate theoretical formulations in slender workpiece facing operation. By means of a state-space domain analysis of the system formed by the cutting process and the workpiece, it is possible to obtain mathematical formulations that quantitatively relate system natural frequencies to process stability. Therefore, it is possible to detect this type of chatter vibrations before workpiece quality is affected by monitoring vibrations during machining. These formulations facilitate the development of an active vibration control system which will improve process stability.

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Funding

The research reported in this paper is supported by the Education department of Basque Government (PRE 2017 2 0016).

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Authors and Affiliations

  1. Faculty of Engineering, Mondragon University, Loramendi 4, C.P. 20500, Arrasate-Mondragon, Gipuzkoa, Spain

    X. Badiola, A. Iturrospe, J. M. Abete & P. J. Arrazola

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  1. X. Badiola
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  2. A. Iturrospe
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  3. J. M. Abete
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  4. P. J. Arrazola
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Correspondence to X. Badiola.

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Appendix: Cutting constant fitting

Appendix: Cutting constant fitting

The cutting constants were obtained experimentally. The material employed was steel C45. Several machining tests were carried out using the cutting conditions presented in Table 5. Cutting constants were calculated from Ks = F/bh. Figure 14 a and b shows the evolution of the radial and tangential cutting constants with the cutting speed for hm = 0.2 mm/rev. These were obtained in the MatLab Curve Fitting tool using a Power function defined as:

$$ K_{i}=a_{i}V_{c}^{b_{i}-1} $$
(30)
Table 5 Parameters and measuring instruments
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Fig. 14
figure 14

Evolution of cutting constants with Vc

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Badiola, X., Iturrospe, A., Abete, J.M. et al. State–space analysis of mode-coupling workpiece chatter. Int J Adv Manuf Technol 103, 2773–2781 (2019). https://doi.org/10.1007/s00170-019-03737-8

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  • DOI: https://doi.org/10.1007/s00170-019-03737-8

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