TRANSLATING WEBS WITH ROLLER MISALIGNMENT PART I: MODEL AND EQUILIBRIUM

摘要

The literature on thin,narrowaxially moving materials isdiverse and mature. However, few investigators have studied thebehavior of thin,widetranslating continua. This paper and asequel evaluate the effect of out-of-plane, roller misalignment onthe equilibrium and dynamic behavior of wide, axially moving,paper and textile webs. In this paper, a fully nonlinear shell theorythat incorporates transverse shear strains is developed andused to determine the equilibrium deformation caused by rollermisalignment. This model allows for consideration of large, possiblyintentional, roller misalignment. The equations of equilibriumare reduced by assuming the web is deformed into a righthelicoid. The resulting nonlinear, ordinary, differential equationsare solved both numerically and analytically, employing perturbation.It is found that the longitudinal, membrane stressincreases with the magnitude of roller misalignment. However,in a web with free longitudinal edges, the lateral, membranestress iscompressiveforanyroller misalignment. The translationspeed acts, by way of centrifugal tensioning, to increase the lateral,membrane stress. Example results highlight other importantconclusions concerning the equilibrium response of webs to outof-plane roller misalignment.