Prediction of unwinding behaviors and problems of cables from inner-winding spool dispensers

• Published in: Nonlinear dynamics Vol. 67; no. 3; pp. 1791 - 1809
• Main Authors: Lee, Jae-Wook, Kim, Kun-Woo, Kim, Hyung-Ryul, Yoo, Wan-Suk
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2012; Springer Nature B.V
• Subjects: Automotive Engineering; Balloons; Cables; Centrifugal force; Classical Mechanics; Control; Coriolis force; Dispensers; Dynamical Systems; Engineering; Equations of motion; Finite difference method; Mathematical analysis; Mathematical models; Mechanical Engineering; Nonlinear differential equations; Nonlinear dynamics; Nonlinear equations; Numerical methods; Open systems; Original Paper; Partial differential equations; Predictions; Spools; Tangling; Time integration; Vibration; Winding; Newmark time integration; Unwinding dynamics; Modified finite difference methods; Behaviors of unwinding cables; Extended Hamilton principle
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-011-0106-3

Wire-guided control technologies are widely used to increase the targeting accuracy of advanced military weapons through the use of unwinding dispensers to guarantee that unwinding occurs without any problems, such as tangling or cutting. In this study, the transient behaviors of cables unwinding from inner-winding cylindrical spool dispensers are investigated. The cable is withdrawn from the spool dispenser at a constant velocity through a fixed point located along the axis of the spool dispenser. And when the cable is flown out of the dispenser, because several dynamic forces such as inertial forces, Coriolis forces, centrifugal forces, tensile forces, and fluid-resistance forces act on the cables, the cables exhibit highly nonlinear and complex unwinding behaviors which are called as unwinding balloons. For predicting these complex unwinding motions, the governing equations of motion for cables unwinding from a cylindrical spool dispenser of the inner-winding type are derived using the extended Hamilton’s principles for an open system in which mass can be transported at each boundary. Modified finite difference methods are used to discretize the spatial variables of the derived nonlinear partial differential equations. The time responses of the unwinding cables are calculated using Newmark time integration methods. Finally, in order to present numerical examples, an inner-winding spool dispenser that can be unwound up to a length of 50 km is designed by using simple geometrical relationships. The behaviors during unwinding from the designed inner spool dispenser are presented and modifications of the spool dispenser for avoiding unwinding problems are proposed by using the suggested numerical methods.