Paper:

# Adaptive Cutting Force Prediction in Milling Processes

## Takashi Matsumura, Takahiro Shirakashi, and Eiji Usui

Tokyo Denki University, 2-2 Kanda Nishiki-cho, Chiyoda-ku, Tokyo 101-8457, Japan

An adaptive force model is presented to predict the cutting force and the chip flow direction in milling. The chip flow model in the milling process is made by piling up the orthogonal cuttings in the planes containing the cutting velocities and the chip flow velocities. The chip flow direction is determined to minimize the cutting energy. The cutting force is predicted using the determined chip flow model. The force model requires the orthogonal cutting data, which associate the orthogonal cutting models with the cutting parameters. Basically, the required data for simulation can be measured in the orthogonal cutting tests. However, it is difficult to perform the cutting tests with specialized setups in the machine shops. The paper presents the adaptive model to accumulate and update the orthogonal cutting data with referring the measured cutting forces in milling. The orthogonal cutting data are identified to minimize the error between the predicted and the measured cutting forces. Then, the cutting forces can be predicted well in many cutting operations using the identified orthogonal cutting data. The adaptive is effective not only in extending the database but also in improving the quality of the database for the accurate predictions.

*Int. J. Automation Technol.*, Vol.4, No.3, pp. 221-228, 2010.

- [1] M. E. Martellotti, “An Analysis of the Milling Process,” Trans. of the ASME, Vol.63, pp. 677-700, 1941.
- [2] S. Smith and J. Tlusty, “An Overview of Modeling and Simulation of the Milling Process,” Trans. of ASME, J. of Engineering for Industry, Vol.113, pp. 169-175, 1991.
- [3] K. F. Ehmann, S. G. Kapoor, R. E. DeVor, and I. Lazoglu, “Machining Process Modeling: A Review,” Trans. of ASME, J. of Manufacturing Science and Engineering, Vol.119, pp. 655-663, 1997.
- [4] F. Koenigsberger and A. J. P. Sabberwal, “An Investigation into the Cutting Force Pulsations during Milling Operations,” Int. J. of Machined Tool and Design Research, Vol.1, pp. 15-33, 1961.
- [5] W. A. Kline, R. E. DeVor, and J. R. Lindberg, “The Prediction of Cutting Forces in End Milling with Application to Cornering Cuts,” Int. J. of Machine Tool Design and Research, Vol.22, No.1, pp. 7-22, 1982.
- [6] E. J. A. Armarego and N. P. Deshpande, “Computerized Predictive Cutting Models for Forces in End Milling Including Eccentricity Effects,” Annals of CIRP, Vol.38, pp. 45-49, 1989.
- [7] E. J. A. Armarego and N. P. Deshpande, “Computerized End Milling Force Predictions with Cutting Models Allowing Eccentricity and Cutter Deflections,” Annals of CIRP, Vol.40, No.1, pp. 25-29, 1990.
- [8] E. Budak, Y. Altintas and E. J. A. Armarego, “Prediction of Milling Force Coefficients from Orthogonal Cutting Data,” Trans. of the ASME, J. of Manufacturing Science and Engineering, J. of Manufacturing Science and Engineering, Vol.118, pp. 216-224, 1996.
- [9] H. Z. Li, W. B. Zhang, and X. P. Li, “Modelling of Cutting Forces in Helical End Milling Using a Predictive Machining Theory,” Int. J. of Mechanical Sciences, Vol.43, pp. 1711-1730, 2001.
- [10] P. L. B. Oxley, “Mechanics of Machining. Chichester,” Ellie Horwood Limited, 1989.
- [11] M. Y. Yang and H. D. Park, “The Prediction of Cutting Force in Ball End Milling,” Int. J. of Machine Tool Design and Research, Vol.31, No.1, pp. 45-54, 1991.
- [12] G. Yucesan and Y. Altintas, “Prediction of Ball End Milling Force,” Trans. of ASME, J. of Engineering for Industry, Vol.118, pp. 95-103, 1996.
- [13] A. E. Bayoumi, G. Yucesan, and L. A. Kendall, “An Analytical Mechanistic Cutting ForceModel forMilling Operations: A Theory and Methodology,” Trans. of ASME, J. of Engineering for Industry, Vol.116, pp. 324-330, 1994.
- [14] H. S. Feng and C. H.Menq, “The Prediction of Cutting Forces in the Ball End Milling Process Model-I Formulation and Model Building Procedure,” Int. J. of Machine Tool Design and Research, Vol.34, pp. 697-710, 1994.
- [15] H. S. Feng and C. H. Menq, “The Prediction of Cutting Forces in the Ball End Milling Process Model-II Cut Geometry Analysis and Model Verification,” Int. J. of Machine Tool Design and Research, Vol.34, pp. 711-719, 1994.
- [16] P. Lee and Y. Altintas, “Prediction of Ball-End Milling Forces from Orthogonal Cutting Data,” Int. J. of Machine Tool Design and Research, Vol.36, No.9, pp. 1059-1072, 1996.
- [17] E. Usui, A. Hirota, and M.Masuko, “Analytical Prediction of Three Dimensional Cutting Process – Part1 Basic Cutting Model and Energy Approach,” Trans. of ASME, J. of Engineering for Industry, Vol.100, pp. 222-228, 1978.
- [18] A. Hirota and E. Usui, “Analytical Prediction of Cutting Forces in Plain Milling Operation,” J. of Japan Society for Precision Engineering, Vol.44, No.4, pp. 508-514, 1978 (in Japanese).
- [19] J. Mackerle, “Finite Element Analysis and Simulation of Machining: An Addendum A Bibliography (1996-2002),” Int. J. of Machine Tools and Manufacture, Vol.43, pp. 103-114, 2003.
- [20] H. Sasahara, T. Obikawa, and T. Shirakashi, “Prediction Model of Surface Residual Stress within a Machined Surface by Combining Two Orthogonal Plane Models,” Int. J. of Machine Tools and Manufacture, Vol.44, pp. 815-822, 2004.
- [21] E. Usui, T. Obikawa, H. Sasahara, and T. Shirakashi, “The Effects of Non-Linearity of Dynamic Cutting Process upon Self-Excited Chatter Vibration (2
^{nd}Report) – An Energy Approach to Dynamic Cutting Process –,” J. of Japan Society for Precision Engineering, Vol.56, No.4, pp. 661-666, 1990 (in Japanese). - [22] M. J. D. Powell, “An Efficient Method for Finding the Minmax of a Function of Several Variables without Calculating Derivatives,” The Computer Journal, Vol.7, pp. 155-162, 1964.
- [23] J. Kiefer, “Sequential Minmax Search for aMaximum,” Proc. of the American Mathematical Society, Vol.4, No.3, pp. 502-506, 1953.

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