Transverse stretching

We want to learn how to quantize the radiation field. As a first step, consider a continuous elastic system. Any classical continuous elastic system in one dimension can be treated by a normal-mode analysis. Consider an elastic string of length a [m], tied at both ends to some fixed objects, with density per unit length p [kg m ], and tension, or Hooke s law force constant kH [N m-1]. The transverse displacements of the string along the x axis can be described by a transverse stretch y(x, t) at any point x along the string and at a time t. One can describe the y(x, t) as a Fourier sine series in x ... 

The web, now moving at a line speed proportional to the stretch imparted by the MDO unit, enters the TDO unit. The TDO unit has a large enclosed oven that uniformly heats the sheet for the transverse stretch. The transverse stretch is accomplished by the use of film clips (Figure 11.3). These clips are attached to a chain-drive system on each side of the web. Each chain-clip assembly clamps the web upon entering the oven and stretches (tenters) the sheet because of the increasing width between the chains along the machine direction (Figure 11.4). On exit of the TDO unit, the web has now been oriented in both the machine... 

During the stretching of tubular films, as discussed in the previous section, longitudinal and transverse stretching are usually carried out simultaneously. This is also possible in flat-film stretching by means of a tenter frame. 

As noted earlier in sections 2 and 3, LCPs are different from typical random coil polymers, in that the orientation that is produced in the die does not relax quickly. For this reason, the transverse stretch from internal air pressure and the longitudinal stretch from the take-up speed enhance the orientation from the die, and do so within a relatively short distance from the die lips. Typical blown film conditions would be 2 to 1 blow-up ratio, with the bubble reaching full diameter within a height equal to one to two times the die diameter. Typical LCP film thickness is 12 to 75 micrometers (0.0005 to 0.003 in.). 

When the molten tube expands, it stretches the film in the transverse direction. A measure of this transverse stretching of the bubble is the blow-up ratio (BUR) ... 

Heaters will soften the tube and the tube is inflated with air. The initial filling of the tube with air requires good timing by the operator. As air is pumped into the expanding tube, the operator pulls the tube away faster than the top nip supplies cast tube. Once the inflated bubble reaches the bottom of the stretch tower, a second nip closes. This second nip seals the air in the tube. The second nip runs at a speed greater than the first and provides the machine direction orientation. The amount of air pumped into the tube before the second nip closes is one of the primary factors in the transverse direction stretch ratio. Other process variables that contribute to the transverse stretch ratio are the web temperature and machine direction stretch ratio. Pressure in the tube may be increased by narrowing the frame used to collapse the bubble. 

Example No. Width/Thickness of Extruded Film, cm/mm Latent Solvent /wt% Film Temperature at Machine Direction Stretch, °C Fast Roll Speed /Slow Roll Speed /MD Stretch Ratio, cm/min Preheating Air Temperature at Transverse Stretch, °C Width/ Thickness of the Oriented Film, cm/mm Temperature/ Duel Time iu DryiugZone, C/sec... 

The total transverse elongation of the element W due to Oj is the combined transverse stretching of fibers and matrix ... 

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