Longitudinal dynamics of a winding zone

The longitudinal dynamics of a moving web in a tension controlled winding zone was modeled and analyzed. The dynamics of the zone included the effects of idler roll inertia, web elasticity, package inertia and feedback control. A computer simulation program was used to solve the system of equations for the natural frequencies and transfer functions. It was found that a typical production type winding zone can have several natural frequencies in the operating range of the winder. The predicted natural frequencies were found to depend significantly on package diameter and feedback gain. As a result, resonant conditions can occur at different times during the winding cycle because the angular velocity of the spindle continually changes. Resonance can also occur with the second and third harmonics of the spindle frequency or any other rotating elements in the winding zone