Paper:

# Hilbert-Huang Transform Analysis of Machining Stability in Ball-Nose End-Milling of Curved Surface

## Muizuddin Azka^{*,**}, Keiji Yamada^{*,†}, Mahfudz Al Huda^{**}, Kyosuke Mani^{***}, Ryutaro Tanaka^{*}, and Katsuhiko Sekiya^{*}

^{*}Graduate School of Engineering, Hiroshima University

1-4-1 Kagamiyama, Higashi-hiroshima, Hiroshima 739-8527, Japan

^{†}Corresponding author

^{**}Agency for the Assessment and Application of Technology (BPPT), Central Jakarta, Indonesia

^{***}Ground Systems Research Center, Acquisition, Technology & Logistics Agency (ATLA), Sagamihara, Japan

This paper investigates the machining stability in ball-end-milling of curved surface in which the inclination of tool continuously changes. Initially, the influence of inclination angle is geometrically investigated on the parameters such as immersion angle and cutting velocity. Then, the paper presents the stability lobe diagrams of the process. Curved surface milling is simulated by slot milling on a cylindrical workpiece using a ball-end-mill to obtain the cutting force and vibration, which are used for fast-Fourier transform and Hilbert-Huang transform (HHT) analyses. Experimental results show that the cutting force increases, and the stability becomes worse with the inclination angle, while the machining errors decrease with the inclination. The vibration analysis showed that the HHT can detect the transition from stable to unstable during milling of curved surface in the time-frequency plots.

*Int. J. Automation Technol.*, Vol.14, No.3, pp. 500-511, 2020.

- [1] Y. Altintas and M. Weck, “Chatter stability of metal cutting and grinding,” CIRP Annals, Vol.53, No.2, pp. 619-642, 2004.
- [2] J. Tlusty, “Dynamics of high-speed milling,” J. of Engineering for Industry, Vol.108, No.2, pp. 59-67, 1986.
- [3] Y. Altintaş and E. Budak, “Analytical prediction of stability lobes in milling,” CIRP Annals, Vol.44, No.1, pp. 357-362, 1995.
- [4] Y. Altintas, E. Shamoto, P. Lee, and E. Budak, “Analytical prediction of stability lobes in ball end milling,” J. of Manufacturing Science and Engineering, Vol.121, No.4, pp. 586-592, 1999.
- [5] Y. Altintas, “Analytical prediction of three dimensional chatter stability in milling,” JSME Int. J. Series C, Vol.44, No.3, pp. 717-723, 2001.
- [6] E. Shamoto and K. Akazawa, “Analytical prediction of chatter stability in ball end milling with tool inclination,” CIRP Annals, Vol.58, No.1, pp. 351-354, 2009.
- [7] G. U. Pelayo, “Modelling of static and dynamic milling forces in inclined operations with circle-segment end mills,” Precision Engineering, Vol.56, pp. 123-135, 2019.
- [8] G. Urbikain, D. Olvera, and L. de Lacalle, “Stability contour maps with barrel cutters considering the tool orientation,” The Int. J. of Advanced Manufacturing Technology, Vol.89, Nos.9-12, pp. 2491-2501, 2017.
- [9] E. Budak, L. T. Tunç, S. Alan, and H. N. Özgüven, “Prediction of workpiece dynamics and its effects on chatter stability in milling,” CIRP Annals – Manufacturing Technology, Vol.61, No.1, pp. 339-342, 2012.
- [10] S. Alan, E. Budak, and H. N. Özgüven, “Analytical prediction of part dynamics for machining stability analysis,” Int. J. Automation Technol., Vol.4, No.3, pp. 259-267, 2010.
- [11] W. Arai, F. Tanaka, and M. Onosato, “Error estimation of machined surfaces in multi-axis machining with machine tool errors including tool self-intersecting motion based on high-accuracy tool swept volumes,” Int. J. Automation Technol., Vol.12, No.5, pp. 680-687, 2018.
- [12] K.-D. Bouzakis, P. Aichouh, and K. Efstathiou, “Determination of the chip geometry, cutting force and roughness in free form surfaces finishing milling, with ball end tools,” Int. J. of Machine Tools and Manufacture, Vol.43, No.5, pp. 499-514, 2003.
- [13] K. Shimana, E. Kondo, H. Karashima, and N. Kawagoishi, “Fast detection of chatter in end-milling using pseudo auto-correlation function,” Int. J. Automation Technol., Vol.6, No.6, pp. 728-735, 2012.
- [14] Y. Altintas, G. Stepan, D. Merdol, and Z. Dombovari, “Chatter stability of milling in frequency and discrete time domain,” CIRP J. of Manufacturing Science and Technology, Vol.1, No.1, pp. 35-44, 2008.
- [15] T. Kalvoda and Y.-R. Hwang, “A cutter tool monitoring in machining process using Hilbert-Huang transform,” Int. J. of Machine Tools and Manufacture, Vol.50, No.5, pp. 495-501, 2010.
- [16] N. Mehala and R. Dahiya, “A comparative study of FFT, STFT and wavelet techniques for induction machine fault diagnostic analysis,” Proc. of the 7th WSEAS Int. Conf. on Computational Intelligence, Man-Machine Systems and Cybernetics, pp. 203-208, 2008.
- [17] A. Susanto, C.-H. Liu, K. Yamada et al., “Milling process monitoring based on vibration analysis using Hilbert-Huang transform,” Int. J. Automation Technol., Vol.12, No.5, pp. 688-698, 2018.
- [18] A. Susanto, C.-H. Liu, K. Yamada et al., “Application of Hilbert-Huang transform for vibration signal analysis in end-milling,” Precision Engineering, Vol.53, pp. 263-277, 2018.
- [19] H. Cao, Y. Lei, and Z. He, “Chatter identification in end milling process using wavelet packets and Hilbert-Huang transform,” Int. J. of Machine Tools and Manufacture, Vol.69, pp. 11-19, 2013.
- [20] N. E. Huang and S. S. P. Shen (Eds.), “Hilbert-Huang Transform and its Applications,” World Scientific, 2005.
- [21] X. Zhou, M. Luo, D. Zhang, and W. Liu, “Cutting force prediction in four-axis milling of curved surfaces with bull-nose end mill,” Procedia CIRP, Vol.56, pp. 100-104, 2016.
- [22] Y. Altintas, “Manufacturing automation: metal cutting mechanics, machine tool vibrations, and CNC design – second edition,” pp. 92-98, Cambridge University Press, 2012.
- [23] Z. Li, Z. Wang, and X. Shi, “Fast prediction of chatter stability lobe diagram for milling process using frequency response function or modal parameters,” The Int. J. of Advanced Manufacturing Technology, Vol.89, pp. 2603-2612, 2017.
- [24] J. Gradisěk, M. Kalveram, and K. Weinert, “Mechanistic identification of specific force coefficients for a general end mill,” Int. J. of Machine Tools and Manufacture, Vol.44, pp. 401-414, 2004.
- [25] Q. Cao, J. Zhao et al., “Force coefficients identification considering inclination angle for ball-end finish milling,” Precision Engineering, Vol.36, No.2, pp. 252-260, 2012.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.