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A new concept of dropping damage boundary surface is proposed to evaluate the dropping damage of a critical component for a hyperbolic tangent nonlinear packaging system. A novel dynamic model is established to analyze the effect of three key coordinate parameters, i.e., the non-dimensional dropping shock velocity, the frequency parameter ratio and the defined system parameter, on dropping damage potential. An experiment, which showed good agreement, was conducted to verify the theory proposed.

SUMMARYThis paper analyses the packaging system of a product as a two-degrees-of-freedom system, one degree for the key component and the other for the main part of the product. The dropping damage boundary curve was developed based on the key component for linear and non-linear packaging systems to predict product damage as a result of drop impacts. The dynamic models of two-degrees-of-freedom dropping shock were obtained. For a linear packaging system, the dropping response of the key component was determined by the dimensionless dropping shock velocity, the frequency parameter ratio, the mass ratio and the damping parameters; for a non-linear system, the system parameter was also used. The frequency parameter ratio of the packaging system and the dimensionless dropping shock velocity were selected as the basic evaluation quantities for the dropping damage of the key component. As an example, the dropping damage boundary curves based on the key component were given for linear and tangent packaging systems. The infl uence of related parameters such as the mass ratio, the system parameter and the damping parameters on the dropping damage boundary curve was investigated. To verify the theory, experiments were designed and completed. Experiment results for both linear and tangent packaging systems were consistent with the theory suggested in this paper. These results have important value not only for the design of cushioning packaging but also for the improvement of products.

The concept of the damage boundary curve is the basic qualification in the evaluation of product fragility and in designing cushioning package systems. This paper investigates the dropping shock equations and dropping damage boundary curves for cubic and hyperbolic tangent cushioning systems based on the key component. The dropping damage boundary curves of key component are determined not only by the dropping height but also by the dimensionless fragility, damping ratio, frequency ratio, system parameter and mass ratio for this cushioning system. The results obtained in this paper and the previous paper presented by Z‐W. Wang compose the complete descriptions of product dropping damage boundary curves for linear and non‐linear packaging cushioning systems based on key component. Copyright © 2011 John Wiley & Sons, Ltd.