Application of parabolic blending for the estimation of thickness distribution in thermoformed products

Abstract

The Parabolic Blending (PB) technique has been widely used in various research fields, such as rotor noise prediction, over the last few decades. However, in the literature, PB is not utilised for the thickness prediction of thermoformed products. In this study, Polystyrene (PS) sheets of various thicknesses were thermoformed using a lab-scale thermoforming machine. Firstly, thickness distributions in thermoformed PS products were obtained by the experimental method. Then, PB was used to estimate the thickness distribution of conical semi-finished thermoformed parts. The obtained results were then compared with the ones obtained experimentally. A comparison reveals that the use of PB provides more accurate thickness values than the experimental results. As a result, PB can be utilised for the prediction of thickness distribution in thermoformed products which have been formed by the same mould.

Software Development for the Use of Generalized Parabolic Blending in Data Prediction Processes

“…)/16 ) (Table 2). This value means that the program produced a more accurate result in this study than in the previous study [16]. The mean percent error with the GPB was calculated as 4.2133.…”

“…This dataset was created as a result of measuring the thickness distribution of a 3mm thick high impact polystyrene product after thermoforming using a mold (Column 2 in Table 2). In a study by Ekşi and Üstünel [16], PB was used to estimate the thickness distribution of the thermoformed plate. With the coded program, correct estimation was performed with a 4.3866 percent error value.…”

“…This process can be expressed as optimizing the PB process depending on the r and s values that change independently of the t value. In order to compare the results obtained in the optimization of the PB with the results of the previous research [16], the same dataset and pattern were used in this study.…”

“…Afterwards, the results of the error calculations performed using the software were examined. In C(t), the value of y is calculated based on the calculated x value for any value of t. Then, the error value is calculated by comparing this data with the dataset( [16], Table 3 Column 2-4) regarding the thickness distribution of the thermoformed material. In this study, after this step, the case where the r and s parameters are 0.5 will be called the default PB (instead of OVR elements).…”

“…In the reference study, this error value was calculated as 4.386 for the default r-s values used for PB [16]. In this study, the aim is to obtain a lower error rate by changing C(t) and by changing the r-s values of PB.…”