Extrusion International 2-2023

44 Extrusion International 2/2023 BLOWN FILM EXTRUSION – FROM THE RESEARCH out by means of lamps, which are positioned behind a textile screen. During the tests, the film contour is re- corded with one image per second. The bubble geom- etry is evaluated for each test point by a tool developed at IKV using MATLAB, MathWorks, Inc., Massachusetts, USA. The symmetry axis is assumed to be orthogonal to the annular gap die. Subsequently, the image coor- dinates are transformed into metric coordinates, since a later mathematical description of the film geometry should be physically meaningful in millimeters rather than pixels. Calibration is performed by recording a ref- erence pattern of known geometry in the visible edge of the film bubble with subsequent data transforma- tion. To model the film geometry as a function of the extrusion height, Spirgatis proposes a fifth-degree polynomial [Spi04], which also turns out to be an excel- lent fitting of the measured values in this application. Picture 5 shows the principal procedure for the survey of the film geometry using the example of the bubble geometry at low melt temperature and blower power as well as high blow-up ratio and film thickness. In the the polynomial BR(h), there are six coefficients which describe the film geometry. Since the information of the die radius (h = 0 mm) and the bubble diameter at frost line height (h = 500 mm) is already contained in the coefficients iq and if, the number of coefficients can be reduced to five (K4’ to K0’) by deriving the geometry function according to the extrusion height. The result- ing function BR’(h) thus describes the expansion of the film bubble in the extrusion direction (h). As already described, in addition to the description of the elongation, the cooling behaviour in the tube forma- tion zone is relevant for the determination of the me- chanical properties. To analyse the cooling behaviour, a thermal imaging camera of the type Flir SC 305 from Flir Inc., Wilsonville, Oregon, USA, with a resolution of 320 x 240 pixels and a maximum recording rate of three im- ages per second is used. The temperatures in the image area are stored as a data matrix in a CSV file. To identify the relevant cooling process, a Python script is usedwhich stores the image coordinates with the corresponding temperature value in an array. For the transformation of the image coordinates into metric coordinates, the geometry of the tube formation zone from the thermal and industrial camera is related to each other. Analogous to the acquisition of the geometry, the description of the cooling process is subsequently carried out by means of a fourth-degree polynomial as a function of the extrusion height. Picture 6 shows the procedure for determining the cooling curve at the process point. To determine the mechanical properties in the longi- tudinal and transverse directions, a Zwick Z10 universal tensile testing machine from Zwick GmbH Co. KG, Ulm, is used. For each test point 10 specimens are tested. Fol - lowing DIN EN ISO 527-1 [NN19a], the specimen clamp- ing length is 50 mm. The crosshead speed is 200 mm/ min, reduced to 5 mm/min for the measurement of the modulus of elasticity. Due to the poor model quality for the determination of the tensile strength in Ohlen- dorf’s modelling, an improved modelling for the tensile strength is considered. After data analysis, the coefficients K5 to K0 are now available for each process point as a measure for the ex - pansion of the tube formation zone and T4 to T0 as a measure for the cooling behaviour. There now are sever- al possibilities to use these to improve the model quality. When using so-called white box models, the systembe- haviour is clearly described by physical relationships, for example by differential equations. The advantage lies in the interpretability of themodel and the high acceptance by the users. On the other hand, there is an enormous number of parameters needed to describe the physical relationships and a high numerical effort. In contrast, Blackbox models do not draw on any structured knowl - edge about the process. Instead, the modelling is com- pletely data-based, which means that with a sufficient amount of data, even high complex differential equa- tions can be represented. The disadvantage is that this model cannot be interpreted physically and no further understanding of the process can be built up. Also, ex- trapolation for a prediction outside of the captured data Factor K 4 K 3 K 2 K 1 K 0 T 3 T 2 T 1 T 0 K 4 1 -0,988 0,941 -0,834 0,651 0,044 -0,021 -0,016 0,1 K 3 1 -0,981 0,904 -0,738 -0,17 0,147 -0,101 -0,004 K 2 1 -0,967 0,838 0,333 -0,315 0,267 -0,145 K 1 1 -0,942 -0,514 0,517 -0,484 0,363 K 0 1 0,617 -0,663 0,673 -0,597 T 3 1 -0,982 0,922 -0,788 T 2 1 -0,978 0,882 T 1 1 -0,956 T 0 1 Table 4: Correlation matrix of the determined coefficients Factor level Mass temperature [°C] BUR [-] Film thickness [μm] Blower power [%] -1 200 2,4 100 15 0 215 2,8 150 25 1 230 3,2 200 35 Table 3: Factor levels