# Control of Physical Processes in an Extrusion Line Polymer Sleeves Production
## 2 Materials and Methods
### Deformation Process  
In the manufacture of polypropylene sleeves, the main technological operations are to blow, draw, and cooling of the sleeve blank [16]. The influence of technological parameters  
Figure 8: Diagram of an angular angle head: 1—adjustable head jaws; 2—mandrel; 3—holder; 4—channel for air supply for sleeve inflation.  
on the quality of the process is necessary. The tubular extrusion rod, leaving under low pressure, at a certain velocity, Vex, is subjected to air cooling through channel 4 (Figure 8), and it is stretched along the length by pulling rolls, inflated across the width by air supplied to the inside of the sleeve. Therefore, the sleeve must have the maximum deformation capacity, which is achieved by using a melt with a lower melt flow rate.  
The deformation process occurs between the die and solidification line, and the cooling continues until the film is compressed by the pulling rollers [29]. Thus, up to the crystallization line, there is:  
1. [noitemsep]
2. Swelling (increase in thickness) of the extrudate relative to the size of the annular gap of the die;
3. Stretching and/or blowing of the tubular blank;
4. Cooling of the melt;
5. Crystallization (to crystallize polymers).  
Elastic swelling of the extrudate occurs as a result of the highly elastic deformation accumulated in the polymer melt. The highly elastic deformation of the melt is formed when it passes through the head-forming channels, and its value is greater the higher the shear stress [30].  
Stretching and inflation of the sleeves lead to a thinning of the workpiece and orientation of the chains in the film (hardening) [31]. Stretch can be quantified by the stretch ratio \(\mathrm{e}_{v}\):  
\[\mathrm{e}_{v}=\frac{V_{fil}}{V_{ex}} \tag{1}\]  
where \(V_{fil}\)--film velocity after the pulling rolls equal to the linear velocity of rotation of the pulling rolls.  
\(V_{ex}\)--extrude exit velocity.  
Accordingly, the degree of inflation \(\mathrm{e}_{inf}\) is determined as follows:  
\[\mathrm{e}_{inf}=\frac{D_{sl}}{d_{g}} \tag{2}\]  
where \(D_{sl}\)--swollen sleeve diameter.  
\(d_{g}\)--is the diameter of the sleeve emerging from the head annular gap.  
Film thickness \(d_{fil}\) can be calculated by the formula:  
\[d_{fil}=\frac{d_{ex}}{\left(\mathrm{e}_{inf}\cdot\mathrm{e}_{v}\right)} \tag{3}\]  
where \(d_{ex}\)--extrudate thickness (neglecting melt swelling, we can assume \(d_{ex}=d_{g}\) (\(d_{g}\) is a head annular gap thickness)).  
The total amount of deformation of the extrusion tubular billet is estimated as:  
\[\mathrm{e}_{overall}=\frac{d_{ex}}{d_{fil}}=\mathrm{e}_{inf}\cdot\mathrm{e}_{v} \tag{4}\]  
Having previously calculated the productivity of the extruder \(Q=0.68D^{2.5}\) (\(D\)--is the diameter of the screw) [31], you can calculate the velocity \(V_{ex}\):  
\[V_{ex}=\frac{Q}{\left(\rho d_{ex}d_{g}\right)} \tag{5}\]  
where \(d_{ex}\cdot d_{g}\)--cross-sectional area of tubular billet--melt.  
\(\rho\) is melt density.  
In practice, we often have values of \(\mathrm{e}_{inf}\) from 2.5 to 3.5 and \(\mathrm{e}_{v}\) from 1.5 to 3.0.  
Large values of \(\mathrm{e}_{inf}\) and \(\mathrm{e}_{v}\) lead to a decrease in the stability of the sleeve dimensions, a noticeable manifestation of the defects in the design of the equipment and uniformity of cooling. With an increase in e\({}_{inf}\) and e\({}_{v}\), the orientation of macromolecules increases, which leads to an increase in the mechanical characteristics of the product. By changing the ratio e\({}_{inf}\)/e\({}_{v}\), it is possible to obtain films with an oriented, equal strength or given strength in the longitudinal and transverse directions.