Xf. Guan et al., VISCOELASTIC EFFECTS IN MODELING WEB HANDLING SYSTEMS - UNSTEADY-STATE ANALYSIS, Journal of applied mechanics, 65(1), 1998, pp. 234-241
A model to predict the tension in open spans of web handling systems d
uring transient operations has been developed. Governing equations wer
e developed by rising the White-Metzner equation to describe the mater
ial response in conjunction with mass and force balances. The governin
g equations were nondimensionalized and solved via the MacCormack pred
ictor/corrector technique. Two dimensionless parameters emerged from t
he analyses, the Deborah number, De, and the ratio of the viscous stre
ss to the steady state stress, N. The resulting model is the companion
to a previously reported model for steady-state operations (Guan et a
l., 1995). The model was used to predict the behavior of a web handlin
g system during start-up, transition between steady states, and a peri
odic disturbance. During start-up and transition, systems responded mo
re vapidly at low De. The system response during a periodic disturbanc
e was correlated to De, the frequency, and the magnitude of the distur
bance.