Research Article
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Numerical Analysis of End Mill Equations of Motion in Relation to Cutting Force

Year 2024, , 14 - 22, 30.04.2024
https://doi.org/10.52795/mateca.1436817

Abstract

Due to the nature of the milling process, the loads generated in the cutting process are intermittent and periodic, and vibrations in the cutting tool operating under these loads are inevitable. However, under unsuitable cutting conditions, the loads acting on the system cannot be damped most of the time and cause chatter, which is referred to as an unstable condition. Chatter is a type of vibration that cannot be controlled. It has a negative effect on surface finish, tool life, and machine tool components. In order to eliminate or prevent this problem, it is necessary to determine the correct cutting parameters. This study presents a method to monitor the stability of the cutting tool operating under cutting forces, estimate the chatter frequencies, and determine the stable cutting conditions. The end mill is modeled as a two-degree-of-freedom system damped as a cantilever beam in the presented method. Finite difference equations are used to solve the mathematical model, and the system's response functions are calculated. Continuous time functions of the cutting forces acting on the system were obtained by Fourier approximation using experimental measurement data with an accuracy of 94.76% and 93.81% for the Fx and Fy force components, respectively. In the experiments, AISI 4140 tempered steel was used as the workpiece, and an AlCrN-coated tungsten carbide (WC) end mill with a diameter of 9.5 mm and a helix angle of 38° was used as the cutting tool. The cutting parameters selected were spindle speed 3350 rpm, feed per tooth 0.04 mm/tooth, and axial cutting depth 0.5 mm. The response functions of the system were performed in the computer environment using the Python programming language, and the results were presented graphically in the time domain. The study is a reference for developing industrial applications such as instant tool monitoring, determination of scratch frequencies, determination of stable cutting intervals with intelligent techniques, improvement of surface roughness, dimensional errors, and tool life with the presented method.

Project Number

BAP-FYL-2021-7274

References

  • 1. R. Bellman, J. Casti, Differential quadrature and long-term integration, Journal of Mathematical Analysis and Applications, 34(2):235-238, 1971.
  • 2. L. Zhu, C. Liu, Recent progress of chatter prediction. detection and suppression in milling, Mechanical Systems and Signal Processing, 143, 2020.
  • 3. F.W. Taylor, On the Art of Cutting Metals, American society of mechanical engineers, California, 1906.
  • 4. J. Tlusty, Stability of machine tool against self-excited vibration in machining, Int. Prod. Eng Res. Conf-Proc., 465-474. 1963.
  • 5. K. Li, S. He, H. Liu, X. Mao, B. Li, B. Luo, Bayesian uncertainty quantification and propagation for prediction of milling stability lobe, Mechanical Systems and Signal Processing, 138, 2020.
  • 6. J. Tlusty, W. Zaton, F. Ismail, Stability lobes in milling, CIRP Annals, 309–313, 1983.
  • 7. E. Budak, Y. Altintas, Analytical prediction of stability lobes in milling, CIRP Annals, 357-362. 1995.
  • 8. A. Çomak, E. Budak, Eşzamanlı frezeleme operasyonlarının dinamiği ve kararlılığı, 3. Ulusal Talaşlı İmalat Sempozyumu (UTIS 2012). 4-5 Ekim 2012, Ankara, Türkiye.
  • 9. Y. Altintas, Y. Cao, Virtual design and optimization of machine tool spindles, CIRP Annals, 379–382, 2005.
  • 10. Y. Altintas, Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations and CNC Design, 2nd ed., Cambridge University Press, Cambridge, 2012.
  • 11. Z.-Q. Yao, X.-G. Liang, L. Luo, J. Hu, A chatter free calibration method for determining cutter runout and cutting force coefficients in ball-end milling, Journal of Materials Processing Technology, 1575–1587, 2013.
  • 12. E. Budak, Y. Altintaş, E.J.A. Armarego, Prediction of milling force coefficients from orthogonal cutting data, Journal of Manufacturing Science and Engineering, Transactions of the ASME, 216–224, 1996.
  • 13. K. Kiss, D. Hajdu, D. Bachrathy, G. Stepan, Operational stability prediction in milling based on impact tests, Mechanical Systems and Signal Processing, 103:327–339, 2018.
  • 14. Y. Altintaş, E. Budak, Analytical prediction of stability lobes in milling, CIRP Annals, 357–362, 1995.
  • 15. E. Budak, Y. Altintas, Analytical prediction of chatter stability in milling-part I: general formulation, ASME, 120-29, 1998.
  • 16. D. Bachrathy, G. Stepan, Improved prediction of stability lobes with extended multi frequency solution, CIRP Annals, 411–414. 2013.
  • 17. Y. Fu et al., Timely online chatter detection in end milling process, Mech Syst Signal Process, 668–688, 2016.
  • 18. T.L. Schmitz, Chatter recognition by a statistical evaluation of the synchronously sampled audio signal, Journal of Sound and Vibration, 262(3): 721–730, 2003.
  • 19. C.L. Zhang, X. Yue, Y.T. Jiang, W. Zheng, A hybrid approach of ANN and HMM for cutting chatter monitoring, Advanced Materials Research, 3225–3232, 2010.
  • 20. J.H. Navarro-Devia, Y. Chen, D.V. Dao, H. Li, Chatter detection in milling processes—a review on signal processing and condition classification, The International Journal of Advanced Manufacturing Technology, 125(9): 3943–3980, 2023.
  • 21. M.-Q. Tran, M.-K. Liu, M. Elsisi, Effective multi-sensor data fusion for chatter detection in milling process, ISA Transactions, 514–527, 2022.
  • 22. D. Chen, X. Zhang, H. Zhao, H. Ding, Development of a novel online chatter monitoring system for flexible milling process, Mechanical Systems and Signal Processing, 159, 2021.
  • 23. P. Stavropoulos, T. Souflas, C. Papaioannou, H. Bikas, D. Mourtzis, An adaptive. artificial intelligence-based chatter detection method for milling operations, The International Journal of Advanced Manufacturing Technology, 124(7): 2037–2058, 2023.
  • 24. O. Özşahin. E. Budak, H.N. Özgüvenc, Frezeleme esnasındaki tezgâh dinamiğinin belirlenmesi ve modellenmesi, 6. Ulusal Talaşlı İmalat Sempozyumu (UTİS 2015), 5-7 Kasım 2015, İstanbul, Türkiye.
  • 25. H. Li, Y.C. Shin, A comprehensive dynamic end milling simulation model, J Manuf Sci Eng., 86–95, 2005.
  • 26. C. Araujo, P. Pacheco, M. Savi, Dynamical analysis of an end milling process, 20th International Congress of Mechanical Engineering, 2009.
  • 27. N.K. Chandiramani, T. Pothala, Dynamics of 2-dof regenerative chatter during turning, Journal of Sound and Vibration, 290:448–464, 2006.
  • 28. M. Aydın, B. Kuryel, G. Oturanç, G. Gündüz, Diferansiyel denklemler ve uygulamaları, Baris Yayinlari Fakulteler Kitabevi, Ankara, 2019.

Kesme Kuvvetine Bağlı Olarak Parmak Freze Hareket Denklemlerinin Sayısal Analizi

Year 2024, , 14 - 22, 30.04.2024
https://doi.org/10.52795/mateca.1436817

Abstract

Frezeleme işleminin doğası gereği kesme işleminde oluşan yükler kesintili ve periyodiktir ve bu yükleri altında çalışan kesici takımda oluşan titreşimler kaçınılmazdır. Ancak uygun olmayan kesme şartları altında sisteme etki eden yükler çoğu zaman sönümlenemez ve kararsız durum olarak ifade edilen tırlamaya neden olur. Tırlama kontrol edilemeyen bir titreşim türüdür. Yüzey kalitesi, takım ömrü ve takım tezgahı bileşenleri üzerinde olumsuz etkilere sahiptir. Bu problemin ortadan kaldırılması veya engellenmesi için doğru kesme parametrelerinin belirlenmesi gereklidir. Bu çalışmada, kesme kuvvetleri altında çalışan kesici takımın kararlığının izlenmesi, tırlama frekanslarının tahmini ve kararlı kesme şartlarının belirlenmesi için bir yöntem sunulmuştur. Sunulan yöntemde parmak freze, ankastre kiriş olarak sönümlü iki serbestlik dereceli sistem olarak modellenmiştir. Matematiksel modelin çözümünde sonlu fark denklemleri kullanılmış ve sistemin cevap fonksiyonları hesaplanmıştır. Sisteme etki eden kesme kuvvetlerinin sürekli zaman fonksiyonları deneysel ölçüm verileri kullanılarak Fourier yaklaştırması yöntemi ile Fx ve Fy kuvvet bileşenleri için sırasıyla %94.76 ve %93.81 doğruluk oranları ile elde edilmiştir. Deneylerde iş parçası olarak AISI 4140 ıslah çeliği ve kesici takım olarak 9.5 mm çapında 38° derece helis açısına sahip AlCrN kaplamalı Tungsten karbür (WC) parmak freze kullanılmıştır. Kesme parametreleri olarak iş mili hızı 3350 dev/dk, diş başı ilerleme 0.04 mm/diş ve eksenel kesme derinliği 0.5 mm şeklinde seçilmiştir. Sistemin cevap fonksiyonları bilgisayar ortamında Python programlama dili aracılığı ile gerçekleştirilmiş sonuçlar zaman alanında grafiksel olarak verilmiştir. Çalışma, sunulan yöntem ile anlık takım izlemesi, tırlama frekanslarının belirlenmesi, akıllı teknikler ile kararlı kesme aralıklarının tayin edilmesi, yüzey pürüzlülüğü, boyutsal hatalar ve takım ömrünün iyileştirilmesi gibi endüstriyel uygulamaların geliştirilmesine referans teşkil eder.

Supporting Institution

Gazi Üniversitesi Bilimsel Araştırma Projeleri Birimi

Project Number

BAP-FYL-2021-7274

Thanks

Bu çalışma Gazi Üniversitesi Bilimsel Araştırma Projeleri tarafından desteklenmiştir (Proje no: BAP-FYL-2021-7274)

References

  • 1. R. Bellman, J. Casti, Differential quadrature and long-term integration, Journal of Mathematical Analysis and Applications, 34(2):235-238, 1971.
  • 2. L. Zhu, C. Liu, Recent progress of chatter prediction. detection and suppression in milling, Mechanical Systems and Signal Processing, 143, 2020.
  • 3. F.W. Taylor, On the Art of Cutting Metals, American society of mechanical engineers, California, 1906.
  • 4. J. Tlusty, Stability of machine tool against self-excited vibration in machining, Int. Prod. Eng Res. Conf-Proc., 465-474. 1963.
  • 5. K. Li, S. He, H. Liu, X. Mao, B. Li, B. Luo, Bayesian uncertainty quantification and propagation for prediction of milling stability lobe, Mechanical Systems and Signal Processing, 138, 2020.
  • 6. J. Tlusty, W. Zaton, F. Ismail, Stability lobes in milling, CIRP Annals, 309–313, 1983.
  • 7. E. Budak, Y. Altintas, Analytical prediction of stability lobes in milling, CIRP Annals, 357-362. 1995.
  • 8. A. Çomak, E. Budak, Eşzamanlı frezeleme operasyonlarının dinamiği ve kararlılığı, 3. Ulusal Talaşlı İmalat Sempozyumu (UTIS 2012). 4-5 Ekim 2012, Ankara, Türkiye.
  • 9. Y. Altintas, Y. Cao, Virtual design and optimization of machine tool spindles, CIRP Annals, 379–382, 2005.
  • 10. Y. Altintas, Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations and CNC Design, 2nd ed., Cambridge University Press, Cambridge, 2012.
  • 11. Z.-Q. Yao, X.-G. Liang, L. Luo, J. Hu, A chatter free calibration method for determining cutter runout and cutting force coefficients in ball-end milling, Journal of Materials Processing Technology, 1575–1587, 2013.
  • 12. E. Budak, Y. Altintaş, E.J.A. Armarego, Prediction of milling force coefficients from orthogonal cutting data, Journal of Manufacturing Science and Engineering, Transactions of the ASME, 216–224, 1996.
  • 13. K. Kiss, D. Hajdu, D. Bachrathy, G. Stepan, Operational stability prediction in milling based on impact tests, Mechanical Systems and Signal Processing, 103:327–339, 2018.
  • 14. Y. Altintaş, E. Budak, Analytical prediction of stability lobes in milling, CIRP Annals, 357–362, 1995.
  • 15. E. Budak, Y. Altintas, Analytical prediction of chatter stability in milling-part I: general formulation, ASME, 120-29, 1998.
  • 16. D. Bachrathy, G. Stepan, Improved prediction of stability lobes with extended multi frequency solution, CIRP Annals, 411–414. 2013.
  • 17. Y. Fu et al., Timely online chatter detection in end milling process, Mech Syst Signal Process, 668–688, 2016.
  • 18. T.L. Schmitz, Chatter recognition by a statistical evaluation of the synchronously sampled audio signal, Journal of Sound and Vibration, 262(3): 721–730, 2003.
  • 19. C.L. Zhang, X. Yue, Y.T. Jiang, W. Zheng, A hybrid approach of ANN and HMM for cutting chatter monitoring, Advanced Materials Research, 3225–3232, 2010.
  • 20. J.H. Navarro-Devia, Y. Chen, D.V. Dao, H. Li, Chatter detection in milling processes—a review on signal processing and condition classification, The International Journal of Advanced Manufacturing Technology, 125(9): 3943–3980, 2023.
  • 21. M.-Q. Tran, M.-K. Liu, M. Elsisi, Effective multi-sensor data fusion for chatter detection in milling process, ISA Transactions, 514–527, 2022.
  • 22. D. Chen, X. Zhang, H. Zhao, H. Ding, Development of a novel online chatter monitoring system for flexible milling process, Mechanical Systems and Signal Processing, 159, 2021.
  • 23. P. Stavropoulos, T. Souflas, C. Papaioannou, H. Bikas, D. Mourtzis, An adaptive. artificial intelligence-based chatter detection method for milling operations, The International Journal of Advanced Manufacturing Technology, 124(7): 2037–2058, 2023.
  • 24. O. Özşahin. E. Budak, H.N. Özgüvenc, Frezeleme esnasındaki tezgâh dinamiğinin belirlenmesi ve modellenmesi, 6. Ulusal Talaşlı İmalat Sempozyumu (UTİS 2015), 5-7 Kasım 2015, İstanbul, Türkiye.
  • 25. H. Li, Y.C. Shin, A comprehensive dynamic end milling simulation model, J Manuf Sci Eng., 86–95, 2005.
  • 26. C. Araujo, P. Pacheco, M. Savi, Dynamical analysis of an end milling process, 20th International Congress of Mechanical Engineering, 2009.
  • 27. N.K. Chandiramani, T. Pothala, Dynamics of 2-dof regenerative chatter during turning, Journal of Sound and Vibration, 290:448–464, 2006.
  • 28. M. Aydın, B. Kuryel, G. Oturanç, G. Gündüz, Diferansiyel denklemler ve uygulamaları, Baris Yayinlari Fakulteler Kitabevi, Ankara, 2019.
There are 28 citations in total.

Details

Primary Language Turkish
Subjects Optimization Techniques in Mechanical Engineering, Numerical Modelling and Mechanical Characterisation, Manufacturing Processes and Technologies (Excl. Textiles)
Journal Section Research Articles
Authors

Bayram Sercan Bayram 0000-0002-9092-6274

İhsan Korkut 0000-0002-5001-4449

Project Number BAP-FYL-2021-7274
Early Pub Date April 30, 2024
Publication Date April 30, 2024
Submission Date February 14, 2024
Acceptance Date March 21, 2024
Published in Issue Year 2024

Cite

APA Bayram, B. S., & Korkut, İ. (2024). Kesme Kuvvetine Bağlı Olarak Parmak Freze Hareket Denklemlerinin Sayısal Analizi. İmalat Teknolojileri Ve Uygulamaları, 5(1), 14-22. https://doi.org/10.52795/mateca.1436817
AMA Bayram BS, Korkut İ. Kesme Kuvvetine Bağlı Olarak Parmak Freze Hareket Denklemlerinin Sayısal Analizi. MATECA. April 2024;5(1):14-22. doi:10.52795/mateca.1436817
Chicago Bayram, Bayram Sercan, and İhsan Korkut. “Kesme Kuvvetine Bağlı Olarak Parmak Freze Hareket Denklemlerinin Sayısal Analizi”. İmalat Teknolojileri Ve Uygulamaları 5, no. 1 (April 2024): 14-22. https://doi.org/10.52795/mateca.1436817.
EndNote Bayram BS, Korkut İ (April 1, 2024) Kesme Kuvvetine Bağlı Olarak Parmak Freze Hareket Denklemlerinin Sayısal Analizi. İmalat Teknolojileri ve Uygulamaları 5 1 14–22.
IEEE B. S. Bayram and İ. Korkut, “Kesme Kuvvetine Bağlı Olarak Parmak Freze Hareket Denklemlerinin Sayısal Analizi”, MATECA, vol. 5, no. 1, pp. 14–22, 2024, doi: 10.52795/mateca.1436817.
ISNAD Bayram, Bayram Sercan - Korkut, İhsan. “Kesme Kuvvetine Bağlı Olarak Parmak Freze Hareket Denklemlerinin Sayısal Analizi”. İmalat Teknolojileri ve Uygulamaları 5/1 (April 2024), 14-22. https://doi.org/10.52795/mateca.1436817.
JAMA Bayram BS, Korkut İ. Kesme Kuvvetine Bağlı Olarak Parmak Freze Hareket Denklemlerinin Sayısal Analizi. MATECA. 2024;5:14–22.
MLA Bayram, Bayram Sercan and İhsan Korkut. “Kesme Kuvvetine Bağlı Olarak Parmak Freze Hareket Denklemlerinin Sayısal Analizi”. İmalat Teknolojileri Ve Uygulamaları, vol. 5, no. 1, 2024, pp. 14-22, doi:10.52795/mateca.1436817.
Vancouver Bayram BS, Korkut İ. Kesme Kuvvetine Bağlı Olarak Parmak Freze Hareket Denklemlerinin Sayısal Analizi. MATECA. 2024;5(1):14-22.