Bakalov Valery, Chernihiv National University of Technology (95 Shevchenka Str., 14027 Chernihiv, Ukraine)

Skrypnyk Sofia, Chernihiv National University of Technology (95 Shevchenka Str., 14027 Chernihiv, Ukraine)

Cherednichenko Petr, State research test center of Ukraine Armed Forces, Chernihiv, Ukraine

Ihnatenkov Alexander, Chernihiv National University of Technology (95 Shevchenka Str., 14027 Chernihiv, Ukraine)

Language: ukrainian


Relevance of the research. Polymer films are increasingly used as packaging materials in various industries. Existing methods of calculation is not possible to determine the width of the formed polymer film depending on the geometrical parameters of receiving and cooling equipment. This hinders the implementation of such equipment in the industry.

Target setting. The work is devoted to developing the mathematical model of the process of pulling a flat polymer film ploskoschilynniy between the head and the receiving-cooling roll, and the process of stretching and narrowing the width of the film on the cooling roll. The model allows to calculate the width and thickness of the films produced.

Statement of the material. An formula for calculating the axial force that stretches the polymer film, changing the current friction forces of the film receiving-cooled roll changes depending on the angle coverage of his film.

Shows the current formula for determining the force that pulls polymer film in the transverse direction.

The differential equation for determining the angle of inclination of the edge of the polymer film to receiving and cooling rolls. To find the original entrance angle polymer film on the roll, which stretches and cools it used numerical method of "fire." This method is for the above equation that states received final width of film, in which the final angle of the edge is zero, and backwards pulling the film is determined by the angle of the edge of the receiving-cooling roll. This initial angle of the edge of the polymer film should provide a falling edge of the film in the end ploskoschilynniy head that forms it. Dichotomy method to determine a given accuracy (less than 1 mm) width obtained final polymer film.

The mathematical model allows to calculate the final width of the obtained polymer film on the installation of ploskoschilynniy head, the current width of the film on the transceiver and the current cooling roll film width depending on the distance between the said roll and ploskoschilynniy head.

Conclusions. Mathematical model to determine the impact: the installation of geometric dimensions (diameter transceiver cooling roll away from him to ploskoschilynniy heads) and the coefficient of friction of plastic film and intruder-cooled roll for width obtained polymer film.

Mathematical model and calculation algorithm can be used in practice in the design ploskoschilynni heads and receiving and cooling devices that draw out the film.

Key words:

modeling, polymer film, molding, extrusion, film width, coefficient of friction, receiving and cooling roll


1. Cherednichenko, P.I., Bakalov, V.H. & Bakalov, O.V. (2009). Modeliuvannia protsesu rukhu polimeru u ploskoshchilynnii holovtsi [Modeling of process of movement of the polymer in the flat die head]. Matematychni mashyny i systemy – Mathematical Machines and Systems, no. 1, pp. 150–158 (in Ukrainian).

2. Cherednichenko, P.I., Bakalov, V.H. & Bakalov, O.V. (2009). Ploskoshchilynni holovky dlia laminuvannia materialiv. Konstruktsiia, rozrakhunok, proektuvannia [Flat die heads for laminating materials. Construction, calculation, design]. Chernihiv: Chernihiv State Technological University (in Ukrainian).

3. Shapoval, V.M. (2007). Mekhanika elongatcionnogo techeniia polimerov [Mechanics elongational flow polymers]. Moscow: Fizmatlit (in Russian).

4. Turchak, L.I. (1987). Osnovy chislennykh metodov [Basics of numerical methods]. Moscow: Gl. red. fiz.-mat. lit. (in Russian).