IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i12p2629-d1167005.html
   My bibliography  Save this article

A Hybrid Full-Discretization Method of Multiple Interpolation Polynomials and Precise Integration for Milling Stability Prediction

Author

Listed:
  • Xuefeng Yang

    (College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)

  • Wenan Yang

    (College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)

  • Youpeng You

    (College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)

Abstract

As milling chatter can lead to poor machining quality and limit the efficiency of productivity, it is of great significance to learn about milling chatter stability and research the effective and fast prediction of milling stability. In this study, a hybrid full-discretization method of multiple interpolation polynomials and precise integration (HFDM) is proposed for milling stability prediction. Firstly, the third-order Newton interpolation polynomial, third-order Hermite interpolation polynomial and linear interpolation are applied to approximate the state term, delay term and periodic coefficient matrix, respectively. Meanwhile, the matrix exponentials can be calculated based on the precise integration algorithm, which can improve computational accuracy and efficiency. The numerical simulation results indicate that the proposed method can not only effectively generate a stability lobe diagram (SLD) but also obtain better prediction accuracy and computation efficiency. A milling experiment is offered to demonstrate the feasibility of the method.

Suggested Citation

  • Xuefeng Yang & Wenan Yang & Youpeng You, 2023. "A Hybrid Full-Discretization Method of Multiple Interpolation Polynomials and Precise Integration for Milling Stability Prediction," Mathematics, MDPI, vol. 11(12), pages 1-23, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2629-:d:1167005
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/12/2629/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/12/2629/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ozoegwu, Chigbogu Godwin, 2016. "High order vector numerical integration schemes applied in state space milling stability analysis," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1025-1040.
    2. Yang Zhang & Kenan Liu & Wuyun Zhao & Wei Zhang & Fei Dai, 2020. "Stability Analysis for Milling Process with Variable Pitch and Variable Helix Tools by High-Order Full-Discretization Methods," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-14, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chong Tian & Taiyong Wang & Ying Tian, 2024. "The Prediction of Stability in the Time-Delayed Milling Process of Spiral Bevel Gears Based on an Improved Full-Discretization Method," Mathematics, MDPI, vol. 12(13), pages 1-9, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2629-:d:1167005. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.