Study on model for cutting force when milling SCM440 steel

Keywords: SCM440 steel milling, Cutting force, Box-Cox transformation, Johnson transformation, t-test


This article presents empirical study results when milling SCM440 steel. The cutting insert to be used was a TiN coated cutting insert with tool tip radius of 0.5 mm. Experimental process was carried out with 18 experiments according to Box-Behnken matrix, in which cutting speed, feed rate and cutting depth were selected as the input parameters of each experiment. In addition, cutting force was selected as the output parameter. Analysis of experimental results has determined the influence of the input parameters as well as the interaction between them on the output parameters. From the experimental results, a regression model showing the relationship between cutting force and input parameters was built. Box-Cox and Johnson data transformations were applied to construct two other models of cutting force. These three regression models were used to predict cutting force and compare with experimental results. Using parameters including coefficient of determination (R-Sq), adjusted coefficient of determination (R-Sq(adj)) and percentage mean absolute error (% MAE) between the results predicted by the models and the experimental results are the criteria to compare the accuracy of the cutting force models. The results have determined that the two models using two data transformations have higher accuracy than model not using two data transformations. A comparison of the model using the Box-Cox transformation and the model using the Johnson transformation was made with a t-test. The results confirmed that these two models have equal accuracy. Finally, the development direction for the next study is mentioned in this article


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Author Biographies

Nguyen Van Thien, Hanoi University of Industry

Faculty of Mechanical Engineering

Do Duc Trung, Hanoi University of Industry

Faculty of Mechanical Engineering


Budak, E. (2006). Analytical models for high performance milling. Part I: Cutting forces, structural deformations and tolerance integrity. International Journal of Machine Tools and Manufacture, 46 (12-13), 1478–1488. doi:

Dang, J.-W., Zhang, W.-H., Yang, Y., Wan, M. (2010). Cutting force modeling for flat end milling including bottom edge cutting effect. International Journal of Machine Tools and Manufacture, 50 (11), 986–997. doi:

Narita, H. (2013). A determination method of cutting coefficients in ball end milling forces model, International journal of Automation Technology, 7 (1), 39–44.

Gao, G., Wu, B., Zhang, D., Luo, M. (2013). Mechanistic identification of cutting force coefficients in bull-nose milling process. Chinese Journal of Aeronautics, 26 (3), 823–830. doi:

Guo, M., Wei, Z., Wang, M., Li, S., Liu, S. (2018). An identification model of cutting force coefficients for five-axis ball-end milling. The International Journal of Advanced Manufacturing Technology, 99 (1-4), 937–949. doi:

Wan, M., Zhang, W.-H., Dang, J.-W., Yang, Y. (2010). A novel cutting force modelling method for cylindrical end mill. Applied Mathematical Modelling, 34 (3), 823–836. doi:

Šajgalík, M., Kušnerová, M., Harničárová, M., Valíček, J., Czán, A., Czánová, T. et. al. (2020). Analysis and Prediction of the Machining Force Depending on the Parameters of Trochoidal Milling of Hardened Steel. Applied Sciences, 10 (5), 1788. doi:

Muthusamy Subramanian, A. V., Nachimuthu, M. D. G., Cinnasamy, V. (2017). Assessment of cutting force and surface roughness in LM6/SiC p using response surface methodology. Journal of Applied Research and Technology, 15 (3), 283–296. doi:

Salguero, J., Calamaz, M., Batista, M., Girot, F., Marcos Bárcena, M. (2014). Cutting Forces Prediction in the Dry Slotting of Aluminium Stacks. Materials Science Forum, 797, 47–52. doi:

Constantin, C., Constantin, G. (2013). Empirical model of the cutting forces in milling. Proceedings in Manufacturing Systems, 8 (4), 205–212.

Bağci, E. (2017). Experimental investigation of effect of tool path strategies and cutting parameters using acoustic signal in complex surface machining. Journal of Vibroengineering, 19 (7), 5571–5588. doi:

Biró, I., Czampa, M., Szalay, T. (2015). Experimental Model for the Main Cutting Force in Face Milling of a High Strength Structural Steel. Periodica Polytechnica Mechanical Engineering, 59 (1), 16–22. doi:

Günay, M., Kaçal, A., Turgut, Y. (2011). Optimization of machining parameters in milling of Ti-6Al-4V alloy using Taguchi method. e-Journal of New World Sciences Academy - Engineering Sciences, 6 (1), 428–440.

Patwari, M. A., Amin, A. K. M. N., Faris, W. F. (1970). Prediction of tangential cutting force in end milling of medium carbon steel by coupling design of experiment and response surface methodology. Journal of Mechanical Engineering, 40 (2), 95–103. doi:

Chuangwen, X., Ting, X., Xiangbin, Y., Jilin, Z., Wenli, L., Huaiyuan, L. (2016). Experimental tests and empirical models of the cutting force and surface roughness when cutting 1Cr13 martensitic stainless steel with a coated carbide tool. Advances in Mechanical Engineering, 8 (10), 168781401667375. doi:

Chen, J.-Y., Chan, T.-C., Lee, B.-Y., Liang, C.-Y. (2020). Prediction model of cutting edge for end mills based on mechanical material properties. The International Journal of Advanced Manufacturing Technology, 107 (7-8), 2939–2951. doi:

Arunnath, A., Masooth, P. H. S. (2021). Optimization of process parameters in CNC turning process on machining SCM440 steel by uncoated carbide and TiCN/Al2O3/TiN coated carbide tool under dry conditions. Materials Today: Proceedings, 45, 6253–6269. doi:

Thirumalai, R., Srinivas, S., Vinodh, T., Kowshik Kumar, A. L., Kumar, M. K. (2014). Optimization of Surface Roughness and Flank Wear in Turning SCM440 Alloy Steel Using Taguchi Method. Applied Mechanics and Materials, 592-594, 641–646. doi:

Reddy, N. S. K., Yang, M. (2009). Development of an electro static lubrication system for drilling of SCM 440 steel. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 224 (2), 217–224. doi:

Basar, G., Kahraman, F. (2018). Modeling and optimization of face milling process parameters for AISI 4140 steel. Tehnički Glasnik, 12 (1), 5–10. doi:

Sales, W., Becker, M., Barcellos, C. S., Landre, J., Bonney, J., Ezugwu, E. O. (2009). Tribological behaviour when face milling AISI 4140 steel with minimum quantity fluid application. Industrial Lubrication and Tribology, 61 (2), 84–90. doi:

Stipkovic, M. A., Bordinassi, É. C., Farias, A. de, Delijaicov, S. (2017). Surface Integrity Analysis in Machining of Hardened AISI 4140 Steel. Materials Research, 20 (2), 387–394. doi:

Xu, Q., Zhao, J., Ai, X. (2017). Cutting performance of tools made of different materials in the machining of 42CrMo4 high-strength steel: a comparative study. The International Journal of Advanced Manufacturing Technology, 93 (5-8), 2061–2069. doi:

Dean, A., Voss, D., Draguljić, D. (2017). Design and Analysis of Experiments. Springer, 840. doi:

Trung, D. D. (2020). Influence of Cutting Parameters on Surface Roughness during Milling AISI 1045 Steel. Tribology in Industry, 42 (4), 658–665. doi:

Dean, A., Voss, D. (Eds.) (1999). Design and Analysis of Experiments. Springer, 742. doi:

Du, N. V., Binh, N. D. (2011). Design of experiment techniques. Science and technics publishing House.

Bhardwaj, B., Kumar, R., Singh, P. K. (2014). An improved surface roughness prediction model using Box-Cox transformation with RSM in end milling of EN 353. Journal of Mechanical Science and Technology, 28 (12), 5149–5157. doi:

Bhardwaj, B., Kumar, R., Singh, P. K. (2013). Effect of machining parameters on surface roughness in end milling of AISI 1019 steel. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 228 (5), 704–714. doi:

Nguyen, N.-T., Trung, D. D. (2020). Modeling And Improvement of the Surface Roughness Model in Hole Turning Process 3x13 Stainless Steel by Using Johnson Transformation. International Journal of Mechanical and Production Engineering Research and Development, 10 (3), 12097–12110. doi:

Uyen, V. T. N., Son, N. H. (2021). Improving accuracy of surface roughness model while turning 9XC steel using a Titanium Nitride-coated cutting tool with Johnson and Box-Cox transformation. AIMS Materials Science, 8 (1), 1–17. doi:

Trung, D. D. (2021). Influence of Cutting Parameters on Surface Roughness in Grinding of 65G Steel. Tribology in Industry, 43 (1), 167–176. doi: ttps://

Sakia, R. M. (1992). The Box-Cox Transformation Technique: A Review. The Statistician, 41 (2), 169. doi:

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How to Cite
Thien, N. V., & Trung, D. D. (2021). Study on model for cutting force when milling SCM440 steel. EUREKA: Physics and Engineering, (5), 23-35.

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