Sensitivity analysis of two-dimensional viscoelastic film casting processes using transfer functions by transient frequency response method

The sensitivity of two-dimensional (2-D) film casting processes for viscoelastic fluids is investigated using a transfer function approach based on the transient frequency response method. The transient responses of state variables to step-changed film tension have been conveniently changed into corresponding transfer functions via the Laplace transform in a tension-controlled system. The transfer function between take-up velocity and film tension plays a key role in elucidating both sensitivity and the stability of film drawing systems. Various amplitude ratios of state variables are effectively evaluated over a wide range of frequencies when an ongoing disturbance is imposed at take-up velocity. The aspect ratio (up to 1 in this study) tends to make the system less sensitive to disturbances. The effect of viscoelasticity on the sensitivity is related to stability patterns, which depend on the aspect ratio and Deborah number.