Modeling and Experimental Methods for Dynamic Analysis of the Spaghetti Problem

Abstract

The nonlinear dynamics of a very flexible body with time-variant length encompasses several industrial applications such as high-speed automatic coiling machines and copy machines. Among others, the significant increase in the vibration that occurs when the material length is shortened with time is known as the spaghetti problem. In this paper, the modeling method and the experimental procedure for the analysis of the spaghetti problem are presented. The change in the state of the forces and displacements at the boundary with a clearance is taken into consideration by modeling the mechanical interactions resulting from the clearance. A flexible beam is modeled using the finite segment method to account for the geometric nonlinearities due to the large rotation. The contact forces at the boundary are modeled using a set of springs and dampers. The numerical results obtained using the proposed modeling method agree well with the results obtained using the experiment. The effect of the transport velocity and the clearance are demonstrated, and the cause of the significant increase in the flexible body vibration is discussed from an energy balance viewpoint.