Analysis of Calendering

A detailed analysis of the flow of molten plastic between two rotating rolls is very complex but fortunately sufficient accuracy for many purposes can be achieved by using a simple Newtonian model. The assumptions made are that 

If the clearance between the rolls is small in relation to their radius then at any section x the problem may be analysed as the flow between parallel plates at a distance h apart. The velocity profile at any section is thus made up of a drag flow component and a pressure flow component. 

For a fluid between two parallel plates, each moving at a velocity Vj, the drag flow velocity is equal to Vd- In the case of a calender with rolls of radius, R, rotating at a speed, N, the drag velocity will thus be given by InRN. 

The velocity component due to pressure flow between two parallel plates has already been determined in Section 4.2.3(b). 

Considering unit width of the calender rolls the total throughput, Q, is given by 

---

However, in the analysis of calendering this equation is found to be difficult to work with and a useful approximation is obtained by expanding (R — using the binomial series and retaining only the first two terms. This gives... 

Fig. 6.27 Comparison between experimental pressure profile for plasticized thermoplastic resin (34) and theoretical pressure profiles for n — 1 and n — 0.25 calculated by Kiparissides and Vlachopoulos (35). The theoretical curves were calculated both by finite element method and analytically by way of Gaskell type models, as discussed in this section, giving virtually identical results. [Reprinted by permission from C. Kiparissides and J. Vlachopoulos, Finite Element Analysis of Calendering, Polym. Eng. Set, 16, 712-719 (1976).]...

A 3D analysis of calendering was performed by Luther and Mewes [83] and reveals the spiral motion in the third or z-direction as shown in Figure 4.27. Although this work represents the only 3D effort to date in the open literature, it is not a trivial matter to reproduce it or use it iteratively for design purposes. Therefore, a very interesting 3D computation of calendering still remains a challenge. 

J. Vlachopoulos and C. Kiparissides, An Analysis of Thermoplastics in Calendering, paper presented at the 26th Canadian Chemical Engineering Conf., Toronto, Canada, 1976. 

ANALYSIS OF COMPOSITION OF COATINGS FORMED ON CALENDERS DURING PRODUCTION OF PVC FILM... 

The power requirement depends on the geometry of the roll, speed and gap, as well as on polymer viscosity. In spite of an initial high capital investment and a relatively long time to reach a steady-state, calendering offers an apparent advantage for the fabrication of sheets at a high rate with excellent quality. A mathematical analysis of the flow process in a calender has been developed for both Newtonian and non Newtonian liquids, including viscoelastic behavior, whereas, in simple cases an analytical solution is possible. 

Figure 1. Diels-Alder reaction of calendic acid methylester and maleic anhydride and X-ray structure analysis of the product.

Fig. 10.20 Axial location of the two planes perpendicular to the counterrotating screws, where velocity fields were calculated. Plane (I) is at the middle of the side, and plane (II) at the middle of the calender gaps. [Reprinted by permission from T. Katziguara, Y. Nagashima, Y. Nakano, and K. Funatsu, Numerical Study of Twin Screw Extruders by 3-D Flow Analysis - Development of Analysis Technique and Evaluation of Mixing Performance for Full Flight Screws, Polym. Eng. Sci., 36, 2142 (1996).]...

---