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Derivation of equations of motion of an unwinding cable considering transient-state tensile force in time-varying unwinding velocity

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Abstract

Unwinding dynamics refers to the study of nonlinear behaviour, tension profile, entangling, and fracturing in the process of unwinding a fibre from a package through the guide eyelet at a specific unwinding speed, to analyse the failure and nonlinear behaviours of unwinding. Although previous studies have dealt with transients, they have been limited to the transient process of a balloon with changes in boundary and tension only under a constant unwinding speed. In this study, the analysis method of an unwinding system at a time-varying unwinding speed was studied to analyse various unwinding conditions. The transient-state tension equation was derived by considering the effects of speed and acceleration at the time-varying unwinding speed. Then, the equation of motion derived in this study was verified through a comparison with the previous study.

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Acknowledgements

This research was supported by Korea Institute of Industrial Technology (KITECH) and by National Research Foundation of Korea (No. 2018R1D1A1A09083567).

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Authors and Affiliations

  1. Daegyeong Regional Division, Korea Institute of Industrial Technology, Daegu, South Korea

    Jin-Seok Jang, Kun-Woo Kim, Ji-Heon Kang, Young-Jae Cho & Jae-Wook Lee

  2. NVH Development Team 2, Hyundai Motor Company, Hwaseong, Korea

    Hyun-Gyu Park

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  1. Jin-Seok Jang
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  2. Kun-Woo Kim
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Correspondence to Jae-Wook Lee.

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Jang, JS., Kim, KW., Kang, JH. et al. Derivation of equations of motion of an unwinding cable considering transient-state tensile force in time-varying unwinding velocity. Nonlinear Dyn 100, 3199–3214 (2020). https://doi.org/10.1007/s11071-020-05683-7

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