Unwinding motion of cable by taking into consideration effect of bending on cable

Abstract

One of the most important factors influencing the performance of wire-guided missiles is the ability to exchange information through a connected cable. Some of the problems that occur during the process of unwinding the cable from the spool package are tangling of the cable because of low tensile force at the guide-eyelet point and cutting of the cable because of high tensile force. Therefore, it is important to analyze the transient motion of the unwinding cable withdrawn from the spool package, while considering the effect of flexural rigidity on the cable. The unwinding system is defined with cylindrical coordinates, and Hamilton׳s principle in an open system is introduced to represent the mass change of the cable in the control volume. Using Hamilton׳s principle, which takes into consideration the Lagrangian, virtual work, and virtual momentum transport, the unwinding equation with high non-linearity can be derived using boundary conditions. Further, by assuming inextensibility, the tensile force can be derived for the spatial variable. To solve the unwinding equation numerically, Newmark implicit integration is utilized with the central finite-difference approximation for spatial variables. The motions of the cable can be ascertained on the basis of various initial tensile forces by considering the constant unwinding velocity at the guide-eyelet point in air and water. It can be concluded from these motions that fluid resistance is the dominant force on the cable when it is unwound in the water, and, in contrast, centrifugal force is dominant in the air. Further, it can be observed that the initial tensile force required when the cable is unwound in water is greater than that required in air, to avoid unwinding problems such as tangling and cutting of the cable.