Elastomer end-milling has attracted attention for use in the small-lot production of elastomeric fragments because the technique is an applicable method for a large variety of materials and does not require the preparation of expensive and time-consuming moulds. In order to effectively utilize elastomer end-milling, it is necessary to ensure the machining accuracy of elastomeric parts machined through this technique. However, the control method of machining error in the elastomer end-milling has not been presented since most machining services of the elastomeric part are based on enterprise-dependent dexterities or know-how. The objective of this paper is to construct and utilize a machining error model for elastomer end-milling. A statistical model based upon physical states and machining conditions is introduced and investigated. In this paper, a framework for modelling the machining error in elastomer end-milling is also proposed. In the framework, the candidates of model variables are evaluated based on the preliminary experiments. Moreover, a statistical model is constructed by using the selected variables. Candidate variables are cutting conditions and predictable physical state variables such as workpiece deformation and cutting force. The framework is investigated by evaluating error prediction with the experimental results. An identified error model from limited machining cases can estimate the machining error of different machining cases. The results indicate that the proposed modelling method is capable of supporting to achieve model-based precision elastomer end-milling.

1. [1] R. G. Landers, B. K. Min, and Y. Koren, “Reconfigurable Machine Tools,” CIRP Annals, Vol.50, No.1, pp. 269-274, 2001.
2. [2] Y. Altintas, “Manufacturing Automation,” Cambridge University Press, 2000.
3. [3] K. Morikawa, K. Takahashi, and D. Hirotani, “Make-to-stock policies for a multistage serial system under a make-to-order production environment,” Int. J. Production Economics, Vol.147, pp. 30-37, 2014.
4. [4] M. Jin and M. Murakawa, “High-Speed Milling of Rubber (1st Report), Fundamental Experiments and Considerations for Improvement of Work Accuracy,” J. Japan Society for Precision Engineering, Vol.64, No.6, pp. 897-901, 1998 (in Japanese).
5. [5] A. J. Shih, M. A. Lewis, and J. S. Strenkowski, “End Milling of Elastomers – Fixture Design and Tool Effectiveness for Material Removal,” J. Manufacturing Science and Engineering, Vol.126, pp. 115-123, 2004.
6. [6] T. Matsumura, T. Obikawa, T. Shirakashi, and E. Usui, “Autonomous Turning Operation Planning with Adaptive Prediction of Tool Wear and Surface Roughness,” J. Machining Systems, Vol.12, No.3, pp. 253-262, 1993.
7. [7] E. A. Rahim and H. Sasahara, “Investigation of Tool Wear and Surface Integrity on MQL Machining of Ti-6AL-4V using Biodegradable Oil,” Proc. of the Institution of Mechanical Engineers, Part B: J. Engineering Manufacture, Vol.225, No.9, pp. 1505-1511, 2011.
8. [8] Y. Altintas, P. Kersting, D. Biermann, E. Budak, B. Denkena, and I. Lazoglu, “Virtual Process Systems for Part Machining Operation,” CIRP Annals, Vol.63, No.2, pp. 585-605, 2014.
9. [9] K. Teramoto, Y. Kuroishi, and M. Yamashita, “A Framework for Machining of Soft Objects,” Proc. of the 5th Int. Conf. Leading Edge Manufacturing in 21st Century (LEM21), pp. 365-368, 2009.
10. [10] S. Takata, “Generation of Machining Scenario and Its Applications to Intelligent Machining Operation,” CIRP Annals, Vol.42, No.1, pp. 531-534, 1993.
11. [11] K. Teramoto, J. Kaneko, T. Ishida, and Y. Takeuchi, “A Framework of Compositional Machining Simulation for Versatile Machining Simulation,” J. Advanced Mechanical Design, Systems, and Manufacturing, Vol.2, No.4, pp. 668-674, 2008.
12. [12] A. Chainawakul, K. Teramoto, Z. Wu, and T. Katsube, “Proposal of a Framework for Empirical Modeling of Complex Machining Phenomena,” Proc. of the 18th Int. Conf. Precision Engineering (ICPE 2020), pp. 47-48, 2020.
13. [13] S. Ratchev, W. Huang, and A. A. Becker, “Milling Error Prediction and Compensation in Machining of Low-rigidity Parts,” Int. J. Machine Tools and Manufacture, Vol.44, No.15, pp. 1629-1641, 2004.
14. [14] K. Nakamoto, T. Iizuka, and Y. Takeuchi, “Dexterous Machining of Soft Objects by Means of Flexible Clamper,” Int. J. Automation Technol., Vol.9, No.1, pp. 83-88, 2015.
15. [15] N. Takahashi and J. Shinozuka, “Contributions of High-speed Cutting and High Rake Angle to the Cutting Performance of Natural Rubber,” Int. J. Automation Technol., Vol.8, No.4, pp. 550-560, 2014.
16. [16] J. Yan and J. S. Strenkowski, “A Finite Element Analysis of Orthogonal Rubber Cutting,” J. Materials Processing Technology, Vol.174, Nos.1-3, pp. 102-108, 2006.
17. [17] J. W. Sutherland and R. E. DeVor, “An Improvement Method for Cutting Force and Surface Error Prediction in Flexible End Milling System,” J. Manufacturing Science and Engineering, Vol.108, No.4, pp. 269-279, 1986.
18. [18] M. Yang and H. Park, “The prediction of cutting force in ball-end milling,” Int. J. Machine Tools and Manufacture, Vol.31, No.1, pp. 45-54, 1991.
19. [19] K. Ichikawa, H. Saito, J. Kaneko, Y. Okuma, and K. Horio, “Estimation Method of Machining Error on Low Rigidity Workpiece for Tool Posture Planning,” Int. J. Automation Technol., Vol.11, No.6, pp. 964-970, 2017.
20. [20] C. T. McCarthy, M. Hussey, and M. D. Gilchrist, “On the Sharpness of Straight Edge Blades in Cutting Soft Solids: Part I – Indentation Experiments,” J. Engineering Fracture Mechanics, Vol.74, No.14, pp. 2205-2224, 2007.
21. [21] K. Teramoto, S. Kudo, and Y. Furuya, “In-process Observation of Workpiece Deformation in Elastomer Endmilling,” Proc. of the 7th Int. Conf. Leading Edge Manufacturing in 21st Century (LEM21), pp. 259-262, 2013.
22. [22] K. Teramoto, T. Kunishima, and H. Matsumoto, “Analysis of Cutting Force in Elastomer End-Milling,” Int. J. Automation Technol., Vol.11, No.6, pp. 958-963, 2017.
23. [23] Z. Wu, K. Teramoto, T. Araki, and H. Matsumoto, “Research on Mechanistic Modeling of Machining Error for Model-based Elastomer End-milling,” Proc. of the 9th Int. Conf. Leading Edge Manufacturing in 21st Century (LEM21), pp. 104-108, 2017.
24. [24] A. Kobayashi, “Special Machining Methods of Nonmetallic Materials,” Chijinishokan, 1965 (in Japanese).
25. [25] A. J. Shih, J. Luo, M. A. Lewis, and J. S. Strenkowski, “Chip Morphology and Force in End Milling of Elastomers,” J. Manufacturing Science and Engineering, Vol.126, No.1, pp. 124-130, 2004.
26. [26] S. R. Lavoie, R. Long, and T. Tang, “A Rate-Dependent Damage Model for Elastomers at Large Strain,” Extreme Mechanics Letters, Vol.8, pp. 114-124, 2016.
27. [27] R. Brighenti, F. J. Vernerey, and F. Artoni, “Rate-Dependent Failure Mechanism of Elastomers,” Int. J. Mechanical Sciences, Vol.130, pp. 448-457, 2017.
28. [28] Y. Furuya, K. Teramoto, and S. Kudo, “Modeling Deformation in Elastomer Endmilling,” Proc. of JSPE Autumn Conf. 2013, pp. 125-126, 2013 (in Japanese).
29. [29] I. T. Jolliffe, “Principle Component Analysis,” Springer, 2002.
30. [30] H. Narita, “A Determination Method of Cutting Coefficients in Ball End Milling Forces Model,” Int. J. Automation Technol., Vol.7, No.1, pp. 39-44, 2013.