Calendering roll separating forces

Calendering problem with a Newtonian viscosity polymer. A calender system with R = 10 cm, w = 100 cm, h0 = 0.1 mm operates at a speed of U =40 cm/s and produces a sheet thickeness In = 0.0218 cm. The viscosity of the material is given as 1000 Pa-s. Estimate the maximum pressure developed in the material, the power required to operate the system, the roll separating force and the adiabatic temperature rise within the material. 

A calendering system (R of 0.17 m. Ho of 0.006 m, roll speed of 0.1 m/s) processes a material whose viscosity is 1 X 10 N s/m. For this system, find the sheet thickness, maximum pressure, and roll-separating force. 

Figure 6.22 depicts schematically the flow configuration. Two identical rolls of radii R rotate in opposite directions with frequency of rotation N. The minimum gap between the rolls is 2H0. We assume that the polymer is uniformly distributed laterally over the roll width W. At a certain axial (upstream) location x = X2 (X2 < 0), the rolls come into contact with the polymeric melt, and start biting onto it. At a certain axial (downstream) location x A), the polymeric melt detaches itself from one of the rolls. Pressure, which is assumed to be atmospheric at X2, rises with x and reaches a maximum upstream of the minimum gap location (recall the foregoing discussion on the pressure profile between non-parallel plates), then drops back to atmospheric pressure at X. The pressure thus generated between the rolls creates significant separating forces on the rolls. The location of points A i and X2 depends on roll radius, gap clearance, and the total volume of polymer on the rolls in roll mills or the volumetric flow rate in calenders. 

Calendering of Polymers The Newtonian Haskell Model A 0.2-m-diameter, 1-m-wide, equal-sized-roll calender operates at a speed of 50 cm/s. At a gap separation of 0.02 cm, it produces a 0.022-cm-thick film. Assuming a Newtonian viscosity of 104 poise, calculate in the last nip (a) the maximum pressure (b) the separating force and (c) estimate the mean temperature rise. 

Separating Force between Rolls in an Experimental Calender A cellulose acetate-based polymeric compound is calendered on a laboratory inverted, L-shaped calender with 16-in-wide rolls of 8 in diameter. The minimum gap between the rolls is 15 mil. The sheet width is 15 in. Calculate the separation force and the maximum pressure between a pair of rolls as a function of exiting film thickness, assuming that film thickness equals the gap separation at the point of detachment. Both rolls turn at 10 rpm. The polymer at the calendered temperature of 90°C follows a Power Law model with m = 3 x 106 dyne.s"/cm2 and n = 0.5. [Data based partly on J. S. Chong, Calendering Thermoplastic Materials, J. Appl. Polym. Sci., 12, 191-212 (1968).]... 

The calendering operation is essentially a process involving laminar flow with heat transfer in a roll system. Typical design outputs include desired roll dimensions, roll speeds, separation of rolls, temperature profiles in the processed material, roll-suspension force, and required power. 

Of importance to the mechanical design of the calendering system and to the prediction of the film thickness uniformity is the force separating the two rolls, F. This is computed by integrating the pressure over the area of interest on the surface of the roll... 

Ultimately, equations are obtained for various process parameters, such as Pniaxj maximum pressure Z, the power F, force separating rolls and Q, the volumetric calendering rate). These are given in the following equations ... 

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