Frezeleme İşleminde Kesme Kuvveti Katsayısı Değişiminin İncelenmesi

Abstract

Bu çalışma, frezeleme işlemlerinde kesme kuvveti katsayılarının (CFC'ler) değişimini ve bunun kuvvet tahminleri ile kararlılık analizine etkisini incelemektedir. CFC'ler genellikle basitlik adına sabit varsayılmasına rağmen, gerçekte diş başına ilerleme ve kesme hızı gibi parametrelere bağlı olarak değişkenlik göstermektedir. Bu durum, talaşlı imalat dinamiklerinde belirsizliklere yol açmaktadır. Eğik dönüşüm modeli kullanılarak, CFC'ler talaş kalınlığı ve kesme hızı dikkate alınarak ortogonal kesme veritabanından tahmin edilmektedir. Sonuçlar, CFC’lerdeki değişimlerin kesme kuvveti tahminlerini önemli ölçüde etkilediğini ve bu etkinin kararlılık lobu diyagramına (SLD) dayalı kararlılık öngörülerini de etkilediğini göstermektedir. CFC’lerin sabit kabul edilmesi, yanlış kuvvet tahminlerine, hatalı kararlılık limitlerine ve artan titreşim (tırlama) riskiyle sonuçlanabilir. Bu durum, aşırı kesme kuvvetleri, hızlanan takım aşınması, zayıf yüzey kalitesi ve hurdaya ayrılabilecek parçalarla sonuçlanabilir. Bu çalışmada, sabit ve değişken CFC modelleri kullanılarak yapılan kuvvet tahminleri, kesme kuvveti tahminleriyle karşılaştırılmış ve değişken modellere dayalı tahminlerin dinamik frezeleme koşullarında daha isabetli sonuçlar verdiği görülmüştür. Kesme hızı ve diş başına ilerlemenin, teğetsel, radyal ve eksenel kuvvet bileşenlerine etkisi sistematik olarak analiz edilmiştir. Yüksek kesme hızlarının, termal yumuşama etkisi nedeniyle CFC değerlerini azalttığı, buna karşılık artan ilerlemenin talaş yükünü artırarak kuvvet katsayılarını yükselttiği gözlemlenmiştir. CFC değişimlerini dikkate alan bir kararlılık modeli, işlem dinamiklerini daha doğru temsil edebilir. Çalışma, talaşlı imalat simülasyonlarında uyarlanabilir kuvvet ve kararlılık modellerinin önemini vurgulamaktadır. Bu bulgular, süreç parametrelerinin optimizasyonu, kararlı kesme koşullarının seçimi ve endüstriyel uygulamalarda tırlama önleyici stratejilerin geliştirilmesi açısından kritik bilgiler sunmaktadır.

Keywords

• Kesme kuvveti katsayısı
• kesme kuvveti
• titreşim kararlılığı
• belirsizlik.

Investigation of Cutting Force Coefficient Variation in Milling

Abstract

This study investigates the variation of cutting force coefficients (CFCs) in milling operations and their impact on force predictions and stability analysis. While CFCs are often assumed constant for simplicity, they are inherently dependent on feed per tooth and cutting speed, introducing uncertainties in machining dynamics. Using an oblique transformation model, CFCs are predicted from an orthogonal cutting database, considering chip thickness and cutting speed. The results indicate that variations in CFCs significantly influence cutting force estimations, affecting stability predictions based on the stability lobe diagram (SLD). Assuming constant CFCs may lead to inaccurate force predictions, miscalculated stability limits, and increased risk of chatter. This can result in excessive forces, accelerated tool wear, poor surface quality, and potential scrap part. In this study, cutting forces are compared against predictions from both constant and variable CFC models, revealing the improved accuracy of the latter in dynamic milling conditions. The influence of cutting speed and feed per tooth on tangential, radial, and axial force components is systematically analysed. It is observed that higher cutting speeds tend to reduce CFC values due to thermal softening effects, whereas increased feed per tooth generally amplifies force coefficients because of increased chip loads. A stability model incorporating CFC variations may provide a more accurate representation of process dynamics. The study emphasises the necessity of adaptive force and stability models in machining simulations to enhance predictive accuracy. These findings offer critical insights for optimising process parameters, selecting stable cutting conditions, and designing chatter avoidance strategies in industrial applications.

Keywords

• Cutting force coefficient
• cutting force
• chatter stability
• uncertainty.

References

1. G. Campatelli, A. Scippa, Prediction of milling cutting force coefficients for Aluminum 6082-T4, Procedia CIRP 1 (2012) 563–568. https://doi.org/10.1016/j.procir.2012.04.100
2. W.S. Yun, D.W. Cho, Accurate 3-D cutting force prediction using cutting condition independent coefficients in end milling, International Journal of Machine Tools and Manufacture 41(4) (2001) 463–478.
3. G. Rozza, Fundamentals of reduced basis method for problems governed by parametrized PDEs and applications, in: Separated Representations and PGD-Based Model Reduction: Fundamentals and Applications, Springer, Vienna, 2014, pp. 153–227. https://doi.org/10.1007/978-3-7091-1794-1_4
4. P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems, SIAM Review 57(4) (2015) 483–531. https://doi.org/10.1137/130932715
5. F. Chinesta, A. Huerta, G. Rozza, K. Willcox, Model reduction methods, Encyclopedia of Computational Mechanics, 2nd ed., Wiley, 2017, pp. 1–36. https://doi.org/10.1002/9781119176817.ecm2110
6. A. De Bartolomeis, S.T. Newman, A. Shokrani, High-speed milling Inconel 718 using electrostatic minimum quantity lubrication (EMQL), Procedia CIRP 101 (2021) 354–357. https://doi.org/10.1016/j.procir.2021.02.038
7. F. Wang, Y. Wang, Effect of cryogenic cooling on deformation of milled thin-walled titanium alloy parts, The International Journal of Advanced Manufacturing Technology 122(9) (2022) 3683–3692.
8. J.C. Su, K.A. Young, K. Ma, S. Srivatsa, J.B. Morehouse, S.Y. Liang, Modeling of residual stresses in milling, International Journal of Advanced Manufacturing Technology 65 (2013) 717–733.

9. X. Jiang, X. Kong, Z. Zhang, Z. Wu, Z. Ding, M. Guo, Modeling the effects of undeformed chip volume on residual stresses during the milling of curved thin-walled parts, International Journal of Mechanical Sciences 167 (2020) 105162. https://doi.org/10.1016/j.ijmecsci.2019.105162
10. X. Jiang, X. Kong, S. He, K. Wu, Modeling the superposition of residual stresses induced by cutting force and heat during the milling of thin-walled parts, Journal of Manufacturing Processes 68 (2021) 356–370. https://doi.org/10.1016/j.jmapro.2021.05.048
11. K.H. Fuh, R.M. Hwang, A predicted milling force model for high-speed end milling operation, International Journal of Machine Tools and Manufacture 37(7) (1997) 969–979.
12. H. Dogan, M. Ozsoy, R.H. Namlu, Feasibility study of chatter suppression in milling through internal channels, The International Journal of Advanced Manufacturing Technology (2025). https://doi.org/10.1007/s00170-025-16594-5
13. M. Ozsoy, Optimizing coolant channels for improved cutting tool vibration suppression, Materials and Manufacturing Processes 40(10) (2025) 1311–1317. https://doi.org/10.1080/10426914.2025.2507068
14. M. Kaymakci, Z.M. Kilic, Y. Altintas, Unified cutting force model for turning, boring, drilling and milling operations, International Journal of Machine Tools and Manufacture 54 (2012) 34–45.
15. M. Ozsoy, N.D. Sims, E. Ozturk, Actuator saturation during active vibration control of milling, Mechanical Systems and Signal Processing (2025) 111942. https://doi.org/10.1016/j.ymssp.2024.111942
16. Y. Altintas, Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations and CNC Design, Cambridge University Press, Cambridge, 2000. https://doi.org/10.1017/CBO9780511843723
17. E. Budak, Y. Altintas, Analytical prediction of chatter stability in milling – Part I: General formulation, Journal of Dynamic Systems, Measurement, and Control 120 (1998) 22–30.
18. E. Budak, Y. Altintas, Prediction of milling force coefficients from orthogonal cutting data, ASME Production Engineering Division 64 (1993) 453–460. https://doi.org/10.1115/1.2831014
19. E.J.A. Armarego, The unified-generalized mechanics of cutting approach—a step towards a house of predictive performance models for machining operations, Machining Science and Technology 4(3) (2000) 319–362. https://doi.org/10.1080/10940340008945715
20. M. Ozsoy, N.D. Sims, E. Ozturk, Robotically assisted active vibration control in milling: A feasibility study, Mechanical Systems and Signal Processing 177 (2022) 109152. https://doi.org/10.1016/j.ymssp.2022.109152
21. M. Ozsoy, N.D. Sims, E. Ozturk, Investigation of an actively controlled robot arm for vibration suppression in milling, Proceedings of EURODYN 2020, pp. 4577–4589. https://doi.org/10.47964/1120.9372.19472
22. M. Ozsoy, N.D. Sims, E. Ozturk, Improving chatter stability of flexible structure milling in robotic assisted machining, Proceedings of ISMA 2022, pp. 109–120.
23. J. Munoa, X. Beudaert, Z. Dombovari, Y. Altintas, E. Budak, C. Brecher, G. Stépán, Chatter suppression techniques in metal cutting, CIRP Annals 65 (2016) 785–808. https://doi.org/10.1016/j.cirp.2016.06.004
24. H. Dogan, M. Ozsoy, E. Ozturk, D.J. Wagg, N.D. Sims, Analysis of virtual inerter-based passive absorber for active chatter control, Journal of Sound and Vibration 578 (2024) 118359.
25. M. Ozsoy, H. Dogan, E. Ozturk, D.J. Wagg, N.D. Sims, Active chatter suppression through virtual inerter-based passive absorber control, Proceedings of the Machining Innovations Conference for Aerospace Industry (MIC), 2022. https://doi.org/10.2139/ssrn.4259207
26. J. Monnin, F. Kuster, K. Wegener, Optimal control for chatter mitigation in milling – Part 1: Modeling and control design, Control Engineering Practice 24 (2014) 156–166.
27. H. Dogan, N.D. Sims, D.J. Wagg, Implementation of inerter-based dynamic vibration absorber for chatter suppression, Journal of Manufacturing Science and Engineering 145 (2023). https://doi.org/10.1115/1.4062118
28. M. Wang, L. Gao, Y. Zheng, An examination of the fundamental mechanics of cutting force coefficients, International Journal of Machine Tools and Manufacture 78 (2014) 1–7.
29. A. Bhattacharyya, J.K. Schueller, B.P. Mann, T.L. Schmitz, M. Gomez, Uncertainty propagation through an empirical model of cutting forces in end milling, Journal of Manufacturing Science and Engineering 143(7) (2021) 071002. https://doi.org/10.1115/1.4049508
30. A. Cornelius, J. Karandikar, T. Schmitz, Bayesian stability and force modeling for uncertain machining processes, npj Advanced Manufacturing 1 (2024) 11. https://doi.org/10.1038/s44334-024-00011-y
31. I.S. Jawahir, H. Attia, M. Dix, H. Ghadbeigi, Z. Liao, J. Schoop, A. Shokrani, Revisiting machinability assessment: Towards total machining performance, CIRP Annals (2025). https://doi.org/10.1016/j.cirp.2025.05.003
32. A. Shokrani, P.J. Arrazola, D. Biermann, P. Mativenga, I.S. Jawahir, Sustainable machining: Recent technological advances, CIRP Annals 73(2) (2024) 483–508.