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A correction method for milling stability analysis based on local truncation error

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Abstract

The appearance of chatter vibration can severely affect the product quality and machining productivity. Hence, prediction of chatter stability is becoming increasingly significant to achieve stable milling operations. Based on local truncation error, this study develops a correction Milne-Simpson method (CMM) for chatter stability analysis by using two linear multistep methods. The dynamic model of milling operations embracing the self-excited vibration is represented by delay differential equations (DDEs). With the period of milling system being carved up into two different subintervals, two kinds of linear multistep methods are combined together by using local truncation error to estimate the state terms. Subsequently, two benchmark dynamic models and two typical discretization methods are employed to demonstrate the characteristics of CMM. The convergence rates and stability boundaries are analyzed in detail, and the contrastive results show that the CMM exhibits better prediction accuracy and provides more satisfactory calculation speed than the others under the same discrete parameters. Finally, for the purpose of verifying the validity and operability of CMM, modal impact experiment and actual cutting tests are performed on a CNC machine tool (EMV650). It is apparent that the predicted stability lobes show better coincidence with experimental results, which indicates that the CMM is of practicability and feasibility.

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Funding

This work was partially supported by the National Natural Science Foundation of China (Grant No. 51775277), the alliance research of Hunan province and Hengyang city through grant number (Grant No. 2018JJ4031), the Key Scientific Research Fund of Hunan Provincial Education Department of China (Grant No. 18B466), and the Scientific Research Program of Hengyang (Grant No. 2019yj011174).

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Authors and Affiliations

  1. College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Yi Wu, Youpeng You & Weifang Chen

  2. Research Institute of Automobile Parts Technology, Hunan Institute of Technology, Hengyang, 421001, China

    Anmin Liu, Bin Deng & Tuo Ye

Authors
  1. Yi Wu
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  2. Youpeng You
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  3. Anmin Liu
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  4. Bin Deng
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  5. Tuo Ye
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  6. Weifang Chen
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Contributions

Yi Wu: methodology, formal analysis, writing-original draft. Youpeng You: conceptualization, investigation, writing-review, and editing. Anmin Liu: experiments, data curation. Bin Deng: experiments, data analysis. Tuo Ye: language modification. Weifang Chen: conceptualization, writing-review, and editing.

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Correspondence to Youpeng You.

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Wu, Y., You, Y., Liu, A. et al. A correction method for milling stability analysis based on local truncation error. Int J Adv Manuf Technol 115, 2873–2887 (2021). https://doi.org/10.1007/s00170-021-07262-5

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  • DOI: https://doi.org/10.1007/s00170-021-07262-5

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