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Two novel prediction methods for milling stability analysis based on piecewise polynomial interpolations

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Abstract

Chatter has been one of the major limiting factors leading to poor productivity and surface finish. The prediction of the stable cutting zones of cutting parameters is thus vital in machining. On the basis of piecewise polynomial interpolations, two efficient and accurate methods are developed in this paper for calculating the stability lobes. Firstly, the dynamic milling process with regenerative effect is modeled by delay differential equations (DDEs) with time-periodic coefficients. The principal period of system is easily separated based on the existence of any non-zero elements of coefficient matrix, and the forced vibration phase is equally discretized into a series of subintervals. Piecewise polynomial interpolations are adopted in two contiguous subintervals to estimate all parts of the DDEs. Secondly, the state transition matrix is formed to search for the borderline of stable cutting region based on Floquet theory. Thirdly, the convergence rates of the two proposed methods are analyzed through comparison with four existing algorithms. The results validate that the two proposed approaches achieve higher convergence rate, accuracy, and efficiency than the others within the same time intervals. Finally, the operability of the two proposed methods is verified by cutting tests, which indicate that the two proposed methods are of effectiveness and practicability.

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Funding

This work was partially supported by the alliance research of Hunan province and Hengyang city through grant number (Grant No. 2018JJ4031), aid program for science and technology innovative research team in higher educational institutions of Hunan province and Hengyang science and technology guidance project grant number (Grant No. 2017KJ161), and scientific research projects of Hunan Education Department (Grant No. 18B466).

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Authors and Affiliations

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

    Anmin Liu, Bin Deng & Tuo Ye

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

    Yi Wu

Authors
  1. Anmin Liu
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  2. Yi Wu
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  3. Bin Deng
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  4. Tuo Ye
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Correspondence to Yi Wu.

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Liu, A., Wu, Y., Deng, B. et al. Two novel prediction methods for milling stability analysis based on piecewise polynomial interpolations. Int J Adv Manuf Technol 109, 2113–2132 (2020). https://doi.org/10.1007/s00170-020-05692-1

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  • DOI: https://doi.org/10.1007/s00170-020-05692-1

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