Extrusion International 2-2023

43 Extrusion International 2/2023 of determination and the percentage devia- tion from the real data of the model, which were collected on a blown film line of Kuhne GmbH, Sankt Augustin. Clearly, the model does not have sufficient quality for calculating the tensile strength. Furthermore, no sufficient transferability to other machines is guaranteed. Derivation of development potentials In the following chapter, possible deficits of Ohlendorf’s approach will be identified. Subsequently, an approach to increase mod- el quality is presented and evaluated. As explained earli - er, the mechanical properties are decisively determined in the tube formation zone. To describe the geometric deformation of any given volume of melt, Ohlendorf uses the dimensionless numbers il, iq, if, and id, each of which relates a geometric quantity at the outlet of the extrusion die and the state at the frost line, at which the mechanical properties are defined. Picture 3 illustrates that the listed key figures can have the same value with different characteristics of the film geometry. Reasons for different bubble geometries are different settings of the double-lip cooling ring or different lip de- signs. In addition changing process and environmental conditions, such as temperature or air flows in the pro- duction building, might change the film geometry un- der otherwise identical production conditions. This leads to the necessity to introduce further parameters which characterise the elongation across the bubble geometry. A similar situation is found when considering cooling behaviour, which is described by the dimensionless num- bers it and iv, fromwhich the exact cooling behaviour of the film in the tube formation zone cannot be inferred. Using only those two parameters in a linear regression model, at most a quadratic relationship between melt temperature and path length can be described. Picture 4 shows a representative cooling curve in the tube for- mation zone. The temperature does not decrease qua- dratically in the extrusion direction in accordance with the decreasing cooling capacity, but with a non-linear relationship (e.g. exponential decay). This circumstance is not considered in the work of Ohlendorf. The process model must therefore be extended by further parameters so that an infinitesimal change in the film geometry can be assigned to an infinitesimal temperature gradient at any point in time. Therefore, new trials were conducted and significantly more data was collected on the behaviour of the film in the tube formation zone. Investigations on the extension of the process model by digital process variables The aim of these new investigations is to increase the model quality. This is made possible by continuously re - cording the film geometry and the cooling behaviour of the tube formation zone. The collected data should enable a data-driven modelling of the process to pre- dict the mechanical properties, especially the tensile strength. This is based on the idea that if the elonga- tion and the cooling behaviour in the tube formation zone are recorded, all the information for modelling is already available and the dimensionless numbers ac - cording to Ohlendorf no longer need to be used. A centrally composed 2k experimental design (see Table 3) is carried out to perform the experiments, which systematically varies the control variables of mass temperature, inflation ratio, film thickness and blower power. The material used is an LDPE (type 2102NOW, Sabic, Riyadh, Saudi Arabia). From the resulting film ge- ometry and the cooling process, additional parameters are derived to supplement the process model. For the detection of the geometry of the tube forma- tion zone, an optical detection or measuring system is necessary. In [Spi04] the use of a camera is proposed for this purpose. The geometry data is then derived from the generated photo material by (automatic) contour recognition. For this purpose, a camera of the model Basler ace 2 Basic of the company Basler AG, Ahrens- burg, which offers the possibility of recording high-reso- lution images with 3840 x 2748 pixels (10.7 MP), is used. It is placed on a tripod at a defined height and defined distance from the tube formation zone. Furthermore, a suitable lightning of the tube formation zone is carried Direction E-module Tensile strength Shrinkage r 2 [-] a [%] r 2 [-] a [%] r2 [-] a [%] Longitudinal 0,82 3,20 0,77 7,04 0,91 2,39 Cross 0,82 5,72 0,5 6,68 0,96 7,01 Table 1: Coefficient of determination and percentage deviation, LD 150 AC, IKV [Ohl04] Table 2: Coefficient of determination and percentage deviation, LD 150 AC, Kuhne GmbH [Ohl04] Direction E-module Tensile strength Shrinkage r 2 [-] a [%] r 2 [-] a [%] r2 [-] a [%] Longitudinal 0,12 14,61 - - 0,55 19,73 Cross 0,27 26,81 - - 0,85 18,73 Picture 3: Same geometrical parameters with different bubble geometry