Gary Burgess

Measurement, Analysis, and Comparison of the Parcel Shipping Shock and Drop Environment of the United States Postal Service with Commercial Carriers

The past decade has shown a great increase in the number of direct to consumer shipments of products and packages. As a result, parcel delivery companies like DHL, FedEx, UPS, and the USPS have strengthened their presence in air transport to deliver products faster and through larger distances. Using cargo planes, they route packages from various destinations to large airport hubs, where they sort millions of packages and ship them to their destinations. There is a continuous need to quantify what happens to these packages as they are handled both manually during collection and delivery and on large high-speed conveying and sortation equipment at hubs. The dynamic events during these moves can cause damage. The information collected in this study helps packaging engineers design protective packaging. This study measured and compared shock and drop events for these carriers during next-day and two-day shipping service between Michigan and California. Data are presented in terms of drop heights associated with the 90, 95, and 99th percentile of occurrence for DHL, FedEx, UPS, and USPS. Impact orientation is also discussed. The data from this study are beneficial to new test methods being developed for drop testing of single parcel shipments by ASTM.

Practical thermal resistance and ice requirement calculations for insulating packages

Several styles of insulating packages were studied, ranging in size from 0.5 to 5 cubic feet and varying in construction from the ordinary expanded polystyrene cooler to various liner-in-box arrangements with and without aluminium foil surfaces. Ice-melt tests were conducted to measure package insulating ability and the results were used to determine the thermal resistance (R-value). The R-value was then related to details connected with package construction including wall thickness, number of layers and number of foil surfaces through a simple equation so that it can be estimated for any construction. The system R-value can then be used to estimate refrigerant requirements and temperature holding times for known shipping environments. Examples are included. Copyright

The fundamental collocation method applied to the nonlinear poisson equation in two dimensions

Abstract The fundamental collocation method is adapted to the nonlinear Poisson equation in two dimensions with mixed boundary conditions of the Dirichlet and Neumann type. The technique is an iterative collocation procedure which requires a representation of the boundary of a finite region by N points and of the interior by M points. The order of the problem as determined by the dimensions of the collocation matrices is N × N for each iteration. The method also employs an adjustable parameter S which can be used to check for stability. The accuracy and efficiency are shown to be quite good on three example problems, two of which are for heat-transfer and non-Newtonian laminar flow. Suggestions for improving the method are made.

A numerical method for laterally loaded thin plates

Abstract A numerical method for dealing with laterally loaded thin plates is presented and compared to the similar but more basic numerical technique used in [1, 2]. This method considers the plate to be embedded in the infinite plane and uses point load sources external to the plate boundary to satisfy boundary conditions as in collocation. The exact solution for a constant lateral load acting over an arbitrary polygon in the infinite plane is first derived and then used to couple the effects of lateral loading to the collocation method described above. The results show that less than half the number of collocation points used in [1, 2] is needed for the same accuracy and that the computer execution time is reduced several hundred times. This method is not limited to particular plate shapes, boundary condition types or load distributions. Five examples are used to illustrate the method.

Measurement and Analysis of the United Parcel Service Ground Shipping Environment for Large and Heavy Packages

This study investigated the United Parcel Shipping environment for shipping large and heavy packages weighing up to 150 lb. The data were collected using instrumented packages that contained triaxial recorders to measure acceleration levels produced by drops and impacts during shipping and handling. The study showed that the existing test methods used to design and evaluate such packages for this type of shipping environment in accordance with ASTM (American Society for Testing and Materials) and ISTA (International Safe Transit Association) test methods do not replicate the levels of damage found in real shipments. The study recommends tests that would produce more realistic damage levels for this environment.

Rotational fluid flow using a least squares collocation technique

Abstract A potential theory approach for incompressible viscous flow which leads to the biharmonic equation is first developed. A numerical least squares collocation technique using fundamental singular solutions of the biharmonic equation is then applied to a rotational flow problem with moving boundaries that produce discontinuous boundary conditions associated with the biharmonic. It is shown that the least squares technique smoothes out local disturbances in boundary data of the type which are likely to present difficulties to the more commonly used boundary element method. A compact computer program for the method and the results for the problem of a rectangular channel with one moving boundary are included along with an experimental verification of the results using the thin plate bending analogy.

Some Thermodynamic Observations on the Mechanical Properties of Cushions

T he shock transmission properties of most commercially available cushions are published in the form of cushion curves [1] which relate the peak deceleration of an object dropped on the cushion to the object’s weight, the drop height, the impact area, and the cushion thickness. Because of the many types of cushions available and the parameters which determine their behavior, the number of cushion curves required for a thorough account of the subject is immense. It is natural therefore to try to reduce the data base to descriptive equations either by curve fitting or by solving the dynamics problem using a model of the cushion. The latter approach has been the focus of considerable research [2-7]. The earliest manageable model which appears to account for the quasistatic behavior of low density foams under compression is that of an elastic network of interconnected membranes partially trapping air under isothermal conditions [2]. An experimental study of the effects of foam parameters not considered in this basic model, in particular the open cell fraction, on the static compression properties of cushions indicates that the contribution of the air component in the model to the overall compression strength is substantial [3]. When modified to account for what is assumed to be the adiabatic compression of the air trapped in low-density closed-cell foams for use in predicting dynamic

A Laplace transform-based fundamental collocation method for two-dimensional transient heat flow

The fundamental collocation method (FCM) is extended to handle two dimensional transient heat conduction problems in solids. The method is applied in the Laplace transform domain, after which an inversion technique is used to retrieve the time-domain solution. Examples are used to illustrate the method and a technique for evaluating accuracy is discussed. The performance was found to be very good. The method is capable of handling regions of arbitrary shapes, subjected to constant temperature initial conditions and mixed type, time-independent boundary conditions. Due to its inherent advantages over the domain-oriented techniques like the finite element and, finite difference methods, the Laplace transform-based FCM approach presented here may be regarded as a simpler method for solving a wide variety of time-dependent problems in heat conduction and related fields.

An analytical contour integration method for handling body forces in elasticity

Abstract In the boundary element and superposition methods for two-dimensional elasticity problems, the presence of body forces requires the integration of the basic point load solution against the body force field over a specified area. For polynomial body forces, x m y n , these area integrals may be transformed into contour integrals which have closed form analytic representations when the area is a polygon. This paper shows that commonly used numerical integration techniques developed for area integrals are unsuitable for handling body forces using the above named methods. Not only are these techniques inaccurate but expensive in terms of execution time in comparison to the analytical algorithm developed here. A computer program and four example problems are included.

Migration of antioxidants from polylactic acid films: A parameter estimation approach and an overview of the current mass transfer models

Migration studies of chemicals from contact materials have been widely conducted due to their importance in determining the safety and shelf life of a food product in their packages. The US Food and Drug Administration (FDA) and the European Food Safety Authority (EFSA) require this safety assessment for food contact materials. So, migration experiments are theoretically designed and experimentally conducted to obtain data that can be used to assess the kinetics of chemical release. In this work, a parameter estimation approach was used to review and to determine the mass transfer partition and diffusion coefficients governing the migration process of eight antioxidants from poly(lactic acid), PLA, based films into water/ethanol solutions at temperatures between 20 and 50°C. Scaled sensitivity coefficients were calculated to assess simultaneously estimation of a number of mass transfer parameters. An optimal experimental design approach was performed to show the importance of properly designing a migration experiment. Additional parameters also provide better insights on migration of the antioxidants. For example, the partition coefficients could be better estimated using data from the early part of the experiment instead at the end. Experiments could be conducted for shorter periods of time saving time and resources. Diffusion coefficients of the eight antioxidants from PLA films were between 0.2 and 19×10-14m2/s at ~40°C. The use of parameter estimation approach provided additional and useful insights about the migration of antioxidants from PLA films.