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

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.