Study on boundary conditions considering unwinding velocity in transient unwinding equations of motion

Abstract

The unwinding behavior of thin cable has been studied in textile engineering. Recently, J.W. Lee derived transient equations of motion for an unwinding cable. Thus, this paper discusses numerical simulations of unwinding behavior as compared to experiments. The cable unwinding system is modeled using cylindrical coordinates, and Hamilton’s principle in an open system is used to represent the mass change of the cable in the control volume. In a transient equation of unwinding motion, the transient-state response is affected by twopoint boundary conditions, such as the guide-eyelet point and the lift-off point. In previous research, only the unwinding velocity at the guide-eyelet point defined the boundary. Here, a boundary condition at the lift-off point is also considered in the unwinding velocity along with the unwinding length of cable in the control volume. The results of this study show that transient equations of motion should be derived by considering angular acceleration because of time-varying angular velocity.