Experimental Study on Vibration Transmissibility of Pre-loaded XPE and PE Packaging Cushioning Material

Most of the shipped products are sensitive against shock and vibration events during the distribution. Various cushioning materials are usually used to prevent the product damages. During the design process the protective packaging system is developed by the engineers based on the cushion and vibration transmissibility features (ie. cushion curve) of the material used. However, after the assembly of the packaged-product, these are stored for various long periods in warehouse. During this time the products pre-load the cushioning material and its parameters can be changed. The main goal of this study is to evaluate the vibration transmissibility of PE and XPE cushioning material at varied storage (preloaded) time and static load conditions. Four different kinds of duration (1 hour, 10 hours, 100 hours and 1000 hours) were used for the pre-loading period at three different static loads (3.488 kPa, 4.651 kPa, and 6.976 kPa), and then at 0.5 oct/min sine sweep vibration the peak frequencies of response and vibration transmissibility, and damping ratio were determined. The results show that the effect of pre-loading is minimal by PE material, but can influence the resonance frequencies by XPE cushioning material. The findings of this study help the packaging engineers to understand better the mechanism of these cushioning materials and to design suitable protective packaging systems.


INTRODUCTION
Vibration and shock may cause significant product damage during shipping of packaged products. Packaging systems are designed and developed to reduce and avoid these hazards. One of the primary hazards is the resonance, which has the potential to damage the product or the critical elements of the product due to the repetitive application of impacts. Therefore, the complete understanding of the shipping environment and the response of the cushioning material to this environment is required.
In general, the cushioning material in any packaging system gives a necessary isolation between the packaged item and the container. This can be modelled as a critical element attached to the product by a spring and a damper (Figure 1a and 1b). This protection element in the packaging system is known as a package cushion and usually is applied using plastic foams [1,2]. The usual packaging material is for cushioning a kind of lightweight, inexpensive material and holds a high strength-to-weight ratio and stiffness-to-weight ratio that has favourable cushioning characteristics and vibration transmissibility. These materials usually are plastic foam and paper packaging and have been widely applied in secondary (master) and tertiary (transportation) packaging to protect products such as medical or electronic devices and instruments, or fragile products, etc. [3][4][5]. Foams are also applied by other industries; these materials have significant effect on the ride comfort in the vehicle seats [6][7][8][9]. After the packing process, the packaged-product is usually stored for a while before it will be shipped to the temporary or final destination. During this storage the mechanical properties of the cushion material can be influenced due to the static load of the product.
Previous research on PE materials cushioning characteristics focused mainly on the shock absorption properties [10], compression stress properties [11], and determining stress-energy based cushion curves [11][12][13][14]. Ref 14 and ref 15 also observed the temperature effect on the vibration transmissibility properties.Two research studied vibration transmissibility for packaging cushion using sine sweep, but not for PE foams, instead it used experimental paperboard materials [3,16].The mechanical properties of cushion material were evaluated in both static and impact loading conditions by several authors [17][18][19]. The resonance behavior of cushioning materials was studied and mathematical models were developed by Parker and Batt [20,21].
However, the authors of this paper could not find any published laboratory cushioning research that measures and analyzes the vibration transmissibility and damping ratios of PE or XPE for packaging cushion with various pre-loading conditions. Therefore, this paper presents new measured and analyzed data that can help packaging engineers to gain a better understanding of the characteristics of these materials and for designing appropriate protective packaging for sensitive goods.
The final goal of this study is to present the effect of pre-compression or pre-loading on cushioning features of foams to the critical frequency bands and damping ratios of PE and XPE cushion materials beside real circumstances as preloading. This paper also analyzes the effect of the pre-compression period and gives relevant information for varied static loads along them. This new data can be a useful technical support for packaging engineers in packaging design.
In the remainder of the paper first an overview of the materials and test methods are presented (Section 2), then the details of pre-compression of the samples are shown, as well as the applied testing equipment and static loads. Methods for determination of vibration transmissibility and estimation of damping ratios are also presented in this section. In Section 3 the results are provided and compared with the result of previous studies. This section also discusses the implications of the result in the package design process. Section 4 provides concluding remarks and future directions of the study.

Experimental materials
Two types of PEs and one type of XPE closed-cell foams were used for this study.

Method for pre-loading
Before each test, the test samples were pre-compressed for 1, 10, 100 and 1000 hours with different static loads at 20 temperature and this temperature condition was maintained during the entire measurement process. The static loads were 3.488 kPa, 4.651 kPa, and 6.976 kPa by weighted concrete mass blocks. The blocks were placed to the top of the foam and then a fixture was clamped to hold the static load in the required centered position. The same static load was maintained during the vibration test.

Method for vibration transmissiblity
The theory of vibration transmissibility for cushioning material of packages is generally described as the ratio of the force transmitted to the force applied at different static loads [22]. Transmissibility is a non-dimension ratio of output to input vibration of the packaged product. Figure 4 shows the test system of this measurement containing a TIRA TV59355AIT electrodynamic vibration tester, a VR 9500 vibration testing controller and an acquisition system with a software VibrationView for the processing of the measurement. During the measurements one acceleration sensor controlled the excitation input at the platform of the vibration head expander, and another sensor was attached to the mass block to measure the response acceleration.
The details of the vibration test setup for all measurements was sine sweep at 0.5 oct/min with an amplitude of 0.5g (zero-to-peak). The frequency range was 3 to 300 Hz by fitting to the most common test standards for transportation simulation of goods, because the most common and relative high amplitude vibration can be found at this frequency band.
The measured acceleration data were analyzed and presented in the form of vibration transmissibility and frequency curve. Then, after the series of tests, the vibration transmissibility and frequency curves at different static loads were evaluated. The numerical results for resonance frequency bands, and their values, are naturally reported for this study.

Method for estimation of damping ratio
The transmissibility value (T r ) for a linear spring-mass system with single degree of freedom system with viscous damping may be calculated from the following equation using Fourier transform of equation of motion [23].
When T r >> 1 the damping ratio can be estimated from Equation (2) [24] As a summary of this section, the evaluation of the effects of pre-compression on vibration transmissibility is the following.
1. Preparation of samples and mass blocks (size, weight, number) 2. Pre-compression of samples (static load, time) 3. Assembly of test measurement system (fixture, static stress) 4. Parameter setting for vibration measurement (frequency band; sweep rate; amplitude; frequency range; 5. Calculation and analysis of measured result (applied equations; units).

Experimental results
On the pre-compressed cushion materials according to the test method defined in Section 2, the sine sweep tests were performed. Frequency ranges and vibration transmissibilities were measured from vibration tests directly. Vibration transmissibility and frequency curves of the tested cushion materials are shown in Figure 5-7. The curves with different pre-loading duration of PE 25 at static loads 3,488 kPa, 4,651 kPa and 6.976 kPa can be see in Figure 5. Figure 6 and 7 provide the same for PE30 and for XPE materials.
The damping ratios were calculated from the experimental data by Equation (2) and Equation (3). Both experimental and calculated values can be seen in Table 1 to Table 3. Each table separately provides the experimental results of PE25, PE 30 and XPE cushion materials at different temperatures and at different static loads such as 3.488 kPa, 4.651 kPa, and 6.976 kPa.

Findings from the Experimental Results
By comparing and analyzing the experimental results of vibration transmissibility and frequency curves of the pre-loaded PE25, PE30 and XPE cushion materials at different static loads the following observations may be discussed. f) The average value of transmissibility was influenced by the duration of the pre-loading only by XPE. The deviation from the average was under 5% of all other materials. The values are summarized in Table  2.

CONCLUSIONS
Polyethylene is a widely used material for protective packaging in distribution. This paper provides important properties of cross-linked and non-cross-linked polyethylene foam relevant to their application after different storage time and offers advice on the cushioning design of packaging through the measured resonant frequencies and the calculated damping ratios. The results show that PE25 and PE30 are less influenced by the duration of pre-loading compared to XPE. Over 86 Hz for non-cross-linked PE and over 126 Hz for crosslinked PE the frequency is in the attenuation zone at all investigated static loads and duration. The results of this paper provide new information on cushion materials for PE and XPE foams for packaging engineers, which can help obtain optimal packaging solutions that give suitable protection to the products and can reduce the packaging mass used in practice.