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Stability analysis in turning with variable spindle speed based on the reconstructed semi-discretization method

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Abstract

Chatter is a harmful phenomenon in metal cutting process. The turning process with variable spindle speed is an effective means for chatter suppression. In this paper, the reconstructed semi-discretization method (RSDM) is used to analyze the stability in turning process with variable spindle speed which is constructed as the dynamic model of delay differential equations with varying delay term (VDDE). Firstly, the dynamic model in turning with variable spindle speed is established. Secondly, stability analysis of VDDE based on the RSDM is introduced. For the turning process with variable spindle speed, the RSDM has been proved to be more calculation speed without reducing calculation accuracy than the well-accepted semi-discretization method (SDM) via an example of single degree of freedom turning. Finally, three types of chatter, period-one, flip, and secondary Hopf bifurcations are discussed in detail based on the RSDM. The proposed method is a good alternative method to the stability analysis in turning with variable spindle speed.

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Data availability

All data are available selectively from the corresponding author upon reasonable request.

Abbreviations

Ω(t):

Spindle speed

w :

Radial cutting depth

h(t) :

Dynamic chip thickness

m x :

Modal mass

k x :

Modal stiffness

c x :

Modal damping

F x, F y :

Cutting forces respectively in x and y direction

K f :

Cutting constant in the feed direction

w n :

Natural angular frequency.

ζ:

Modal damping rate

τ(t):

Time delay

RVA :

The ratios of modulation amplitude and

RVF :

The ratios of modulation frequency

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Acknowledgements

The corresponding author would like to thank Professor Tamás Insperger, Budapest University of Technology and Economics, who provides help for the research.

Code availability

All code can be provided selectively from the corresponding author upon reasonable request.

Funding

This study is supported, respectively, by the “Excellent Doctoral Program of Weifang University,” “Research start-up funds of Weifang University.”

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Authors and Affiliations

  1. School of Mechatronics and Vehicle Engineering, Weifang University, Weifang, 261061, China

    Xinfeng Dong

  2. College of Energy and Mechanical Engineering, Shanghai University of Electric Power, Shanghai, 200090, China

    Xinhang Shen & Zhifang Fu

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  1. Xinfeng Dong
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  2. Xinhang Shen
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  3. Zhifang Fu
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The first author completed the main work, and the second author completed the auxiliary work.

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Correspondence to Xinfeng Dong.

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Dong, X., Shen, X. & Fu, Z. Stability analysis in turning with variable spindle speed based on the reconstructed semi-discretization method. Int J Adv Manuf Technol 117, 3393–3403 (2021). https://doi.org/10.1007/s00170-021-07869-8

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