Mathematical Modeling of Calendering

A comprehensive mathematical model of the calendering process should consist of a coupled hydrodynamic and roll structural analysis, heat transfer in the deforming polymer 

According to Marshall (2), it can be assumed that the increase in width is virtually limited to the entrance zone up to where the peak pressure is obtained. The actual how in the nip area is further complicated because the gap clearance varies axially as a result of built-in roll-crowns, hydrodynamic hexing, and bending of the rolls. All these factors should bring about a how distribution in the nip area that results in 

Most models proposed in the literature are based on Gaskell s (4) model, which was discussed in detail in Section 6.4. This is a one-dimensional, rather restrictive model. Recall that to use the model, we must know the location X1 where the sheet detaches from one of the rolls (Xi is uniquely related to X2, the upstream location where the rolls come in contact with the polymer). This is tantamount to an a priori knowledge of the exiting sheet thickness, 2H1. The latter, however, for a given flow rate, Q, depends on the exiting sheet width W  

however, is not the only limitation of the Gaskell model. As discussed in Section 6.4, this model fails to predict the experimentally observed flow patterns in the inlet region because it neglects the effect of the incoming melt stream on the flow in the bank, as well as the non-Newtonian and viscoelastic effects. Consequently, the model does not satisfactorily predict the observed pressure profiles, as shown by Bergen and Scott (6), Unkriier (3), and others. 

Following Gaskell s work, a great deal of effort was invested by numerous researchers in the field to improve on his model. Most of this effort, however, basically concentrated on solving the Gaskell model with more realistic, constitutive equations and attempts to account for nonisothermal effects. In the original Gaskell model, a purely viscous (nonelastic and time-independent) fluid model is assumed, with specific 

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The application of interval mathematics for tolerance calculations using a statistical model to describe calendering is described. It represents a logical expansion of known methods for the use of such models and might be relevant for quality control and for cost efficient running of equipment. 8 refs. 

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