# EMPIRICAL MODELS FOR PREDICTION COMPRESSION STRENGTH OF PAPERBOARD CARTON

## Authors

• Yuriy Pyr’yev Department of Printing Technologies, Faculty of Mechanical and Industrial Engineering, Warsaw University of Technology
• Edmundas Kibirkštis Department of Production Engineering, Faculty of Mechanical Engineering and Design, Kaunas University of Technology
• Laura Gegeckienė Department of Production Engineering, Faculty of Mechanical Engineering and Design, Kaunas University of Technology
• Kęstutis Vaitasius Department of Production Engineering, Faculty of Mechanical Engineering and Design, Kaunas University of Technology
• Ingrida Venytė Department of Production Engineering, Faculty of Mechanical Engineering and Design, Kaunas University of Technology

## Abstract

When designing packaging in the shape of a rectangular parallelepiped from various paperboard materials, it is important to determine their resistance to vertical compression force, which should be less than the critical compression force. This is especially relevant when the products packed in these boxes are stacked during transport or storage. The developed empirical models make it possible to more optimally / more accurately determine the critical vertical compressive strength of these packages.

The purpose of this work is to create an empirical model of the critical compressive force of a paperboard box (carton) based on the corrected formulas of the critical compressive force of the McKee corrugated cardboard box (taking into account the height) of the box and allowing to optimize of its parameters. The accuracy of the developed empirical models is presented by comparing the results of theoretical and experimental studies.

It should be noted that the determination of the critical compression force of the box is a contact problem of the non-linear theory of elasticity and plasticity for structures whose elements are made of an anisotropic material. On this basis, empirical models of three and one parameters were developed, which also estimated the values of experimental studies previously performed by other authors. One mathematical model also estimates the height of the box, which is not determined by the Mckee formula. For the experiments, we used cartons of different geometric parameters and made from different types of paperboard. During the experiment, the boxes were compressed with vertical force until the packages collapsed.

The results of the compared theoretical and experimental studies show the suitability of the proposed mathematical models for calculating the critical compressive strength of packages since the obtained MAPE error is within acceptable limits.

Taking into account the small discrepancy between the obtained experimental and theoretical research results, the proposed method for calculating the vertical critical compressive force of the rectangular parallelepiped package is suitable for use. The methodology for calculating the critical compressive strength of such packages presented in this document will be extended in the future for additional testing to verify the model with carton size and design variations.