Multi-Objective Optimal Design of Dropping Shock of Series Cushioning Packaging System

Abstract

The product bears the shock load during the circulation process. The cushioning materials need to absorb the energy generated during the shock to prevent damage to the product. The cushion packaging system generally consists of products, cushioning materials, and an outside packaging carton. Therefore, it is necessary to study the factors affecting the cushion performance of the system. This paper adopts a BP neural network to develop a more precise constitutive relationship. Based on the trained constitutive network model, the dynamic equation of the system is established, and the Runge-Kutta algorithm is utilized to resolve it. The multi-objective optimization (MOP) model of the series cushioning system is established for the first time. The model considers more factors, such as the stability of the cushioning material and whether to use local cushioning. The factors affecting the performance of the cushioning system are deeply studied, and a variety of evolutionary algorithms (PESA2, SPEA2, MOPSO, MOEA/D, and NSGA-II) are utilized to solve the multi-objective optimization problem. The performances of the solution sets obtained by the evolutionary algorithms are studied based on several performance indicators. The results show that these solution sets have good convergence, and the all-around performance of NSGA-II ranks first. Finally, comparing the knee point of the non-dominated solution set calculated by NSGA-II with the parameters in the literature, it is found that the former has better defense performance and less material consumption, which can be used for future product design. Therefore, the evolutionary algorithm can favorably resolve the multi-objective optimization of the series cushioning packaging system under the dropping shock.

Research on the Design Method of Cushioning Packaging for Products with Unbalanced Mass

“…For the materials with larger damping coefficients, we observe that the acceleration response tends to decrease more significantly, especially near the eccentricity. This is consistent with the findings of Xue et al [15] in 2022, who also find that the damping properties of the damping material have a significant effect on the vibration response.…”

“…y 1 , y 2 , y 3 , and y 4 in Equations ( 11)-( 14) represent the y-axis displacement, y-axis velocity, z-axis rotation angle, and z-axis angular velocity of the motion parameters, respectively. The mass-balanced and vibration response of the mass-unbalanced product are solved using Equation (15). The vibration response diagrams are shown in Figure 2a,b.…”

“…He discussed the effects of axial force position and the number of spring-mass systems on the system's natural frequency under axial force. Yang et al [15] established the dynamic equation of the system based on BP neural network and solved it using Runge-Kutta algorithm. A multi-objective optimization model for series buffering systems and an examination of factors impacting system performance was developed.…”

Exploring factors affecting the conversion of the coefficient of restitution to equivalent free fall drop height

“…When developing a new product‐package system 30 and simulating it in the laboratory, it is essential to know the equivalent free fall drop height. Investigating how COR influences packaging design is relatively unfamiliar to packaging practitioners.…”