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Enhanced dynamic modeling of chatter incorporating nonlinear Hertzian contact

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Abstract

Chatter during milling significantly hampers machining productivity, surface quality, and machine accuracy. This study introduces an analytical framework to enhance milling through the development of a Single Degree of Freedom model. The model integrates regenerative theory and Hertzian contact, incorporating factors such as cutting tool-workpiece interaction, tool geometry, and material properties. Solving a nonlinear delayed differential equation with quadratic and cubic terms, the model yields a stability criterion using the multiple scales approach. This criterion generates a Stability Lobes Diagram to predict chatter occurrence, distinguishing between stable and unstable cutting zones. Numerical verification via the Runge–Kutta method validates the model’s efficacy. These results underscore the crucial role of natural frequency and damping ratio in ensuring milling stability.

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The authors own all the material, and/or no permissions are required. The figures attached in the manuscript are all referenced below, and the included tables and results. Where the results generated by MATLAB software.

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Acknowledgements

Throughout this research, the authors would like to thank the mentors, co-authors and colleagues for their collaborative efforts, insightful discussions, and dedication to advancing this study. This research would not have been possible without the contributions and support of the individuals and entities mentioned above. We would like to express our sincere thanks to Mr. Mohamed BEY of the Centre de Développement des Technologies Avancées—CDTA—(Algiers, Algeria) for his invaluable assistance, comments, and recommendations, which allowed us to significantly improve the paper’s quality.

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Unfortunately, No funding has been received for this research.

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Authors and Affiliations

  1. University of Science and Technology Houari Boumediene, Faculty of Process and Mecanical Engineering, Bab Ezzouar, BP 32, 16111, Algiers, Algeria

    Ferhat Sehla & Faiza Boumediene

  2. Laboratory of MMESA FSTE, Department of Physics, Moulay Ismail University, Meknes, Morocco

    Amine Bichri & Mohammed Touzani

  3. Center for the Development of Advanced Technologies (CDTA), City August 20, 1956, Baba Hassen, Algiers, Algeria

    Ferhat Sehla

Authors
  1. Ferhat Sehla
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  2. Amine Bichri
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  3. Faiza Boumediene
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  4. Mohammed Touzani
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Contributions

Sahla Ferhat: Conceptualization: Initiated the idea of applying Hertzian contact theory to milling processes, setting the direction for the research. Methodology: Developed and integrated the SDOF model, Hertzian contact theory, and regenerative theories into a comprehensive framework. Software: Applied the multiple-scale technique and utilized the Runge–Kutta method for analytical and numerical validations. Writing – Original Draft: Drafted the manuscript, particularly focusing on the theoretical aspects, methodology, and results. Amine Bichri: Conceptualization: Contributed to the conceptualization of applying Hertzian contact theory to predict stability in milling processes. Methodology: Worked collaboratively on the development and integration of the SDOF model with a focus on theoretical aspects. Software: Assisted in numerical validations using the Runge–Kutta method. Review & Editing: Provided critical feedback and contributed to refining the manuscript. Faiza Boumediene and Mohammed Touzani: Provided invaluable assistance, comments, and recommendations during various stages of the research, contributing significantly to the improvement of the paper’s overall quality. All authors have read and approved the final manuscript.

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Correspondence to Ferhat Sehla.

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Sehla, F., Bichri, A., Boumediene, F. et al. Enhanced dynamic modeling of chatter incorporating nonlinear Hertzian contact. Int. J. Dynam. Control (2024). https://doi.org/10.1007/s40435-024-01433-4

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