Paper:

# Support Placement for Machine Tools Using Stiffness Model

## Kotaro Mori, Daisuke Kono, Iwao Yamaji, and Atsushi Matsubara

Kyoto University

Kyotodaigaku-Katsura, Nishikyo-ku, Kyoto 615-8540, Japan

The support stiffness model and the stiffness tuning technique are applied to a practical situation. The support stiffness model is integrated with finite element analysis (FEA) to simulate the rocking vibration mode. The support stiffness of a machining center prototype is calculated based on the support stiffness model. The stiffness tuning technique is used to determine the placement of support structures in the simulation. The calculated support stiffness is integrated into a three dimensional model as springs. Rocking vibration modes are obtained from simulations by using the support stiffness model. To compare the results, a simulation without the support stiffness model is conducted. An experiment is also conducted on the same machining center that is used in the simulation. Without the support stiffness model, the difference between the experimental and simulation natural frequencies was above 19%. In contrast, the difference is under 10% when the support stiffness model is included. The experimental and the simulation results were in good agreement with respect to the rocking vibration modes. These results demonstrate that incorporating the support stiffness model into finite element analysis increases the calculation accuracy of the rocking-vibration-mode natural frequencies. Consequently, the support stiffness model and the stiffness tuning technique are effective for designing the support systems of machine tools.

*Int. J. Automation Technol.*, Vol.9, No.6, pp. 680-688, 2015.

- [1] E. I. Rivin, “Vibration isolation of precision equipment,” Precis. Eng. pp. 41-56, 1995.
- [2] F. Koenigsberger and J. Tlusty, “Machine Tool Structures,” Elsevier, 1970.
- [3] K. Yoshida, H. Shimura, H. Yahagi, and J. Yoshioka, “Effects of Mounting Conditions of Surface Griding Machines upon Their Rocking Mode Vibrations,” Proc 6 I.C.P.E., pp. 477, 1995.
- [4] K. Yoshida, H. Shimura, H. Yahagi, and J. Yoshioka, “Effects of mounting elements of surface grinding machines upon their relative receptances between grinding wheel and work table,” J. Mech. Working Technol., Vol.17, pp. 377-386, 1988.
- [5] D. B. DeBra, “Vibration Isolation of Precision Machine Tools and Instruments,” Annals of the CIRP 41, pp. 711-718, 1992.
- [6] Z. Yu, K. Nakamoto, T. Ishida, and Y. Takeuchi, “Interactive design-assistance system of machine tool structure in conceptual and Fundamental design stage,” Int. J. Autom. Technol., Vol.4, pp. 303-311, 2010.
- [7] Z. Yu, K. Nakamoto, and Y. Takeuchi, “Development of an Interactive Assistance System for Machine Tool Structure Design of Sliding Joint Damping,” Int. J. Autom. Technol. Vol.5, pp. 722-728, 2011.
- [8] M. Nakaminami, T. Tokuma, T. Moriwaki, and K. Nakamoto, “Optimal Structure Design Methodology for Compound Multiaxis Machine Tools – I,” Int. J. Autom. Technol., Vol.1, pp. 78-86, 2007.
- [9] M. Nakaminami, T. Tokuma, K. Matsumoto, S. Sakashita, T. Moriwaki, and K. Nakamoto, “Optimal Structure Design Methodology for Compound Multiaxis Machine Tools – II,” Int. J. Autom. Technol., Vol.1, pp. 87-93, 2007.
- [10] D. Huo, K. Cheng, and F. Wardle, “A holistic dynamic design and modeling approach applied development of ultraprecision micro-milling machines,” Int. J. Mach. Tools Manuf., Vol.50, pp. 335-343, 2010.
- [11] B. Li, J. Hong, and Z. Liu, “Stiffness design of machine tool structures by a biologically inspired topology optimization method,” Int. J. Mach. Tools Manuf., Vol.84, pp. 33-44, 2014.
- [12] H. Ohmori and Y. Uehara, “Development of a Desktop Machine Tool for Mirror Surface Griding,” Int. J. Autom. Technol., Vol.4, pp. 88-96, 2010.
- [13] G. Bianchi, F. Paolucci, P. Van den Braembussche, H. Van Brussel, and F. Jovane, “Towards virtual engineering in machine tool design,” CIRP Annals-Manufacturing Technology, Vol.45, No.1, pp. 381-384, 1996.
- [14] D. Kono, S. Weikert, A. Matsubara, and K. Yamazaki, “Estimation of Dynamic Mechanical Error for Evaluation of Machine Tool Structures,” Int. J. Autom. Technol., Vol.6, pp. 147-153, 2012.
- [15] J. Chang and J. Hung, “Analytical and Finite Element Modeling of the Dynamic Characteristics of a Linear Feeding Stage with Different Arrangements of Rolling Guides,” Mathematical Problems in Engineering, 454156, 2014.
- [16] C. Mingjun, Y. Lin, L. Henan, and C. Wanqun, “The Analysis on Dynamic Characteristics and the Structual Optimization of HCG Polishing Machine Tool,” Materials Science Forum, Vol.770, pp. 54-58, 2014.
- [17] G. Bianchi, S. Cagna, N. Cau, and F. Paolucci, “Analysis of vibration damping in machine tools,” Procedia CIRP 21, pp. 367-372, 2014.
- [18] S. K. Hong, H. Kato, Y. Nakano, and Y. Tomita, “ Installation of Cylindrical Griding Machine by Using Load – Sensible Mounting Elements Relation between Mounting Load and Dynamic Stiffness,” J. of J.S.P.E 57, pp. 664-668,1991.
- [19] C. E. Okwudire and J. Lee, “Minimization of the residual vibrations of ultra-precision manufacturing machines via optimal placement of vibration isolators,” Precis. Eng. Vol.37, pp. 425-432, 2013.
- [20] L. Mi, et al., “Effects of preloads on joints on dynamic stiffness of whole machine tool structure,” J. Mech. Sci. and Technol., Vol.26, No.2, pp. 495-508, 2012.
- [21] Y. Lin, et al., “A Method of Identifing Interface Characteristic for Machine Tools Design,” J. of Sound and Vibration 255, pp. 481-487, 2002.
- [22] D. Kono, T. Inagaki, A. Matsubara, and I. Yamaji, “Stiffness model of machine tool supports using contact stiffness,” Precis. Eng., Vol.37, pp. 650-657, 2013.
- [23] D. Kono, S. Nishio, I. Yamaji, and A. Matsubara, “A method for stiffness tuning of machine tool supports considering contact stiffness,” Int. J. Mach. ToolsManuf., Vol.90, pp. 50-59, 2015.

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