Dynamics of Package Cushioning 



By RAYMOND D. MINDLIN 



Introduction 



MECHANICAL damage is a common occurrence in the transportation 

 of packaged articles. The causes of failures are generally inadequate 

 protective cushioning, lack of ruggedness of the outer packing container, 

 or occasional abnormal weakness of the packaged article. The first of these 

 difficulties is the subject of this paper. 



One of the major influences in reducing the incidence of mechanical failures 

 of packaged articles in recent years has been the use of the drop test. The 

 drop test is performed simply by raising the package to a specified height and 

 dropping it to the floor. The package and its contents are then examined 

 for damage. This is a go-no-go test and requires a large number of samples 

 before a reliable estimate of quality can be made. An adequate number of 

 tests is prohibitive when the article packaged is costly. In such cases it is 

 important, and in any case it is useful, to supplement the drop test data with 

 measurements and calculations. It is also possible to evolve rational pro- 

 cedures for designing packages, as described in the present paper, so that 

 a particular product will survive a drop test at any specified height, with a 

 known factor of safety and with a minimum amount of space assigned for 

 cushioning. The drop test then becomes only a check instead of playing an 

 integral role in a cut and try design procedure. 



Assuming that the outer container is adequate, the survival of a packaged 

 article in a drop test still depends upon a large number of factors descriptive 

 of the mechanical properties of both the cushioning medium and the pack- 

 aged item. However, the more important properties can be grouped so 

 that they may be replaced by knowledge of only the following factors: 



(1) The magnitude of the maximum acceleration that the cushioning 

 permits the packaged item to reach. 



(2) The form of the acceleration-time relation. 



(3) The strengths, natural frequencies of vibration and damping of the 

 structural elements of the packaged article. 



Part I of this paper is concerned primarily with methods for predicting 

 maximum acceleration of the packaged article with emphasis on non-linear 

 cushioning. Part II deals primarily with the prediction of the form of the 

 acceleration-time relation. Part HI deals with the effect of acceleration on 



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