Lagrangian modeling and analysis of the dynamics of frictional winding mechanisms

This paper investigates the dynamics of frictional-type winding mechanisms widely used in textile industry. The mechanism under study is used to wind various kinds of thread onto bobbins of cylindrical form. The system essentially consists of a motor-driven cylinder which is pressed to a cylindrical bobbin hence bringing the latter into rotation through friction between the two surfaces. A textile thread is supplied into the contact zone and winds around the bobbin. For the winding operation to proceed accurately, the winding mechanism must be free of vibrations to ensure a constant and reliable contact zone. Proposed in the paper is a comprehensive dynamic model that accounts for as many as six degrees of freedom of the mechanism. Six position variables therefore are selected for the generalized coordinates of the system and Lagrangian approach is employed to obtain six differential equations of motion of the system. The obtained equations are highly nonlinear and are solved numerically for typical values of the system’s design parameters. The proposed model and analysis allow the designer to account for all the main factors that affect mechanical and technological characteristics of the mechanism.