Illll 'clell‘wlll llll . .TQIS I3 “1293 10699£3 ' '-a‘}.t’5"'._ Q ‘ I ffl?~?.3._.~..fi (:11. A 4' "Ov-Wr-awo; cave”; t:- 999V~LQLL¢ I" This is to certify that the thesis entitled THE EFFECT OF RIBBING ON SHOCK TRANSMISSION THROUGH EXPANDED POLYSTYRENE CUSHION MATERIAL I presented by George Kuo-Hsin Chen has been accepted towards fulfillment of the requirements for MS degree in mm— t 74,2.“ / Major professor Date _ilune_l]+_1285_ 0-7639 MSU is an Affirmative Action/Equal Opportunity Institution MSU LIBRARIES » RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. 6% 31102993 THE EFFECT OF RIBBING ON SHOCK TRANSMISSION THROUGH EXPANDED POLYSTYRENE CUSHION MATERIAL BY George Kuo-Hsin Chen A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE School of Packaging 1986 ABSTRACT THE EFFECT OF RIBBING ON SHOCK TRANSMISSION THROUGH EXPANDED POLYSTYRENE CUSHION MATERIAL BY George Kuo-Hsin Chen This study evaluates the effect of ribs on shock transmission through Expanded Polystyrene (EPS). Since the shape of a cushion influences its cushioning behavior, the cushion curves developed on Flat EPS are inadequate to describe the cushioning characteristics of Ribbed EPS packages used in industry. The effects of ribs on shock transmission were examined for two different densities (1.25 pcf and 1.35 pcf) EPS cushion. The experimental results showed that at low drop heights (24 inch and lower) or under low static stress levels (0.6 psi and lower), both Ribbed EPS and Flat EPS produced similar peak acceleration levels. At greater drop heights (24 inch and higher) or under high static stress levels (1.0 psi and higher), Ribbed EPS yielded greater peak acceleration levels than Flat EPS. Therefore, when designing an EPS cushioning package for a fragile product involving high static stress levels and drop heights, the effect of EPS ribbing on shock transmission must be taken into consideration. To my wife, mother and sons ACKNOWLEDGEMENTS I would like to thank several people for their valued contributions to the completion of this study. First, Dr. Julian Lee, my major professor, for his considerable amount of time, advice, and encouragement devoted to my study. I would also like to express my appreciation to the members on my thesis committee, Dr. ~Richard K. Brandenburg and Dr. Gary J. Burgess, for their support during the research. I am also indebted to Dr. T. S. Lin, Chairman of the Board, Tatung Company for sponsoring the necessary financial assistance during my study in the School of Packaging at Michigan State University. My thanks are also conveyed to Mr. Thomas Woolaway, Vice President, Tuscarora Plastics Inc., for the donation of the test material (i.e. expanded polystyrene planks) used in this study. My sincere appreciation is also extended to Dr. Jack R. Giacin for providing me with employment during my graduate study. Finally, my gratitude and appreciation to Mr. David E. Henderson, President of International Packaging Systems Inc. and Mr. Y. M. Yang for their kind encouragement and financial support during the study. TABLE OF CONTENTS Page LIST OF TABLES vi LIST OF FIGURES vii LIST OF SYMBOLS AND ABBREVIATIONS ix INTRODUCTION 1 MATERIALS AND METHODS V 5 Test Apparatus 5 Determination of Gate Time and Equivalent Free Fall Drop Height 5 Determination of Effective Bearing Area 7 Test Specimens 10 Test Procedures ' 13 DATA ANALYSIS AND RESULTS DATA ANALYSIS 14 Determination of Shock Transmission Level (g's) 14 Generation of Cushion Curves 14 Analysis of Variance (Completely Randomized Design) 30 Pairwise Comparison of Ribbed BPS versus Flat BPS on Shock Transmission 33 RESULTS 35 DISCUSSION 38 CONCLUSIONS . 40 Conclusions 40 Recommendations 41 APPENDICES A. LIST Determination of effective bearing area for Ribbed EPS test sample Peak acceleration (g's) transmitted through BPS Data set-up for Analysis of Variance (Completely Randomized Design) of one sample set Pairwise comparison of Ribbed EPS versus Flat EPS on shock transmission of one sample set Comparison of Ribbed EPS versus Flat EPS on the final thickness of one sample set OF REFERENCES 42 46 53 54 55 56 Table 10. 11. LIST OF TABLES Gate time, impact velocity and free fall drop height. Peak acceleration transmitted through 1.25 pcf EPS at 12 in. drop height. Peak acceleration transmitted through 1.25 pcf EPS at 18 in. drop height. Peak acceleration transmitted through 1.25 pcf EPS at 24 in. drop height. Peak acceleration transmitted through 1.25 pcf EPS at 30 in. drop height. Peak acceleration transmitted through 1.25 pcf EPS at 36 in. drop height. Peak acceleration transmitted through 1.25 pcf EPS at 42 in. drop height. Peak acceleration transmitted through 1.35 pcf EPS at 36 in. drop height. Analysis of Variance (Completely Randomized Design) of one sample set (3 in. 1.25 pcf EPS at 36 in drop height). Significance level of effect of EPS shape on shock transmission (g's). Significance level of difference between Ribbed FPS and Flat EPS on shock transmission (g's). vi Page 46 47 48 49 40 51 52 31 32 34 LIST OF FIGURES Figure 1. 10. 11. Representative oscilloscope shock pulses (indicating a successive recorded on an increase in g's due to multiple drops). Configurations and samples. Configurations and samples. dimensions of Ribbed EPS test dimensions of Flat EPS test EPS rib cutting device. EPS rib cutting device in operation. Cushion curves for versus Flat EPS on EPS at 12 in. drop Cushion curves for versus Flat EPS on EPS at 12 in. drop 'drops average). Cushion curves for versus Flat EPS on EPS at 18 in. drop Cushion curves for versus Flat EPS on EPS at 18 in. drop drops average). Cushion curves for versus Flat EPS on EPS at 24 in. drop Cushion curves for versus Flat EPS on EPS at 24 in. drop drops average). the comparison of Ribbed EPS shock transmission (1.25 pcf height, first drop). the comparison of Ribbed EPS shock transmission (1.25 pcf height, second through fifth the comparison of Ribbed EPS shock transmission (1.25 pcf height, first drop). the comparison of Ribbed EPS shock transmission (1.25 pcf height, second through fifth the comparison of Ribbed EPS shock transmission (1.25 pcf height, first drop). the comparison of Ribbed EPS shock transmission (1.25 pcf height, second through fifth vfi Page 11 12 16 17 18 19 20 21 12. 13. 14. 15 16. 17. 18. 19 Cushion curves for versus Flat EPS on EPS at 30 in. drop Cushion curves for versus Flat EPS on EPS at 30 in. drop drops average). Cushion curves for versus Flat EPS on EPS at 36 in. drop Cushion curves for versus Flat EPS on EPS at 36 in. drop drops average). Cushion curves for versus Flat EPS on EPS at 42 in. drop Cushion curves for versus Flat EPS on EPS at 42 in. drop drops average). Cushion curves for versus Flat EPS on EPS at 36 in. drop Cushion curves for versus Flat EPS on EPS at 36 in. drop drops average). the comparison of Ribbed EPS shock transmission (1.25 pcf height, first drop). the comparison of Ribbed EPS shock transmission (1.25 pcf height, second through fifth the comparison of Ribbed EPS shock transmission (1.25 pcf height, first drop). the comparison of Ribbed EPS shock transmission (1.25 pcf height, second through fifth the comparison of Ribbed EPS shock transmission (1.25 pcf height, first drop). the comparison of Ribbed EPS shock transmission (1.25 pcf height, second through fifth the comparison of Ribbed EPS shock transmission (1.35 pcf height, first drop). the comparison of Ribbed EPS shock transmission (1.35 pcf height, second through fifth vhi 22 23 24 25 26 27 28 29 A* ANOVA EFFDH EPS FFDH 9'5 ns pcf dx dY 3|- ** LIST OF SYMBOLS AND ABBREVIATIONS Effective bearing Area Analysis of Variance Young's Modulus of Elasticity Equivalent Free Fall Drop Height Expanded Polystyrene cushion Loading Force Free Fall Drop Height Acceleration of Gravity Shock transmission (Peak acceleration) level Drop Height Spring constant Statistically not significant Pounds per Cubic Foot Thickness of cushion Impact Velocity Total deflection of cushion Compression of slice dy of cushion Elemental thickness of cushion Static stress Strain Integration Significant at 5% level of probability Significant at 1% level of probability ix INTRODUCTION "Damage to a product occurs when it receives an excessive shock encountered during distribution and handling" (6). In order to prevent the product from damage, a cushion material must be used to buffer the impact by reducing the shock transmitted to the product. Ribbed cushions have been commonly used in industries for reasons of economy and ease of fabrication. The easiest way for a packaging engineer to determine the optimum amount of cushion material required for a fragile product is to use cushion curves. The cushion characteristics of buffering materials are described by cushion curves with peak acceleration level (g's) plotted on the ordinate and static stress level plotted on the abscissa. Cushion curves are generally developed following the procedures described in ASTM D 1596-78a, Shock Absorbing Characteristics of Packaging Cushioning Materials (1)._ It states that "The Test Method is applicable to materials exhibiting a high degree of compressibility and recovery in bulk, sheet or laminated forms used for cushioning packaged articles" (1). The ASTM Test Method D 1596-78a does not take into account the effect of shape of test specimen on shock transmision. Therefore, all cushion curves generated and reported by manufacturers are based on flat planks. Yet physical properties (compression, spring constant, and deflection) of the material are affected by the shape of the test specimen (7). It follows then that the cushion curves developed on flat planks may not be adequate for describing the ribbed cushion's behavior. In general, not much research was found to have been done on the influence of the shape of EPS (Expanded Polystyrene) on its physical properties. Yet EPS is_a widely used cushion material. Therefore, the influence of geometric shape of EPS on the cushioning characteristics is the basis for this study. In practice, an EPS cushion is molded with Ribs either on the exterior contact surface or the interior contact surface. The commonly used Rib shape is the trapezoid or the modified trapezoid. A comparison between the trapezoid Ribbed EPS which consists of 3-piece rib on a one inch thick base and the Flat EPS of the same material was performed, and the difference in shock transmission between these two samples was observed. Further, the cushioning deterioration of EPS cushion has to be considered when designing an EPS cushion package. "In normal distribution environments, a cushioned article usually encounters several shocks of varying magnitude" (3). Cushions subjected to an increasing number of loading and unloading stress cycles exhibit a decreasing hysteresis effect (7). EPS cushions produced higher shock levels as the number of successive drops increased due to cushion deterioration. Figure 1 shows that a greater shock is transmitted through the cushion with each successive drop. Therefore, it is reasonable to develop the first drop and the multiple drop cushion curves separately for the evaluation of cushioning properties of Ribbed EPS and Flat EPS cushions. The purpose of this study is to investigate the cushion curves of Ribbed EPS and Flat EPS cushions in relationship to shock transmission. The experiment of this study attempts to answer the following questions: 1) Do the cushion curves of Ribbed EPS and Flat EPS of the same material reveal any difference on shock transmission? If so, 2) How do the first drop and the multiple drops on shock transmission through Ribbed EPS differ from those of Flat EPS? FIRST DROP THROUGH FIFTH DROP III-III..- III-III.“- III-III."- Illllllllllllll Illllllllllll llllllllllllIIfllI IIIVINIHIII’II III-III..- Peak acceleration (20 g's/div) Duration (20 ms/div) Figure 1. REPRESENTATIVE SHOCK PULSES RECORDED ON AN OSCILLOSCOPE INDICATING A SUCCESSIVE INCREASE IN g's DUE TO MULTIPLE DROPS (Photograph of a 3 in. 1.25 pcf Ribbed EPS at 36 in. free fall drop height under a static stress of 1.4 psi) MATERIALS AND METHODS TEST APPARATUS The generation of cushion curves was performed according to ASTM Test Method D 1596-78a using a Lansmont Model 23 Cushion Tester. DETERMINATION OF GATE TIME & EQUIVALENT FREE FALL DROP HEIGHT The impact velocity corresponding to a specific free fall drop height (FFDH) was determined by the time required for a trigger blade (a 0.5 in. wide metal plate firmly mounted to the back side of the platen) to pass through a photoelectric sensor located just above the impact A surface of the test specimen. The impact velocity was calculated by using Equation (1) on page 5. The gate time was measured (in milliseconds) by a GHI VS 200 Velocity Sensor. The impact velocity was used to determine the platen's equivalent free fall drop height (EFFDH) by using Equations (2) and (3) on page 5. The EFFDH is the height from which the platen is dropped to produce an impact velocity identical to the velocity that occurs from a free fall drop (2). Friction between the platen and the guide rods makes the platen velocity slightly lower than it would be in a free fall drop. Consequently, actual platen drop height is slightly greater than the free fall drop height to compensate for friction. The following equation developed by Lansmont Corp. (2) was used to calculate the impact velocity, V =-%~+0.5gt Equation (1) where: V = impact velocity d a width of trigger blade t a time readout on velocity sensor 9 acceleration of gravity Since the impact velocity in a free fall can be calculated by V =t42gh , the EFFDH is h =-—— Equation (2) Substituting Equation (1) into Equation (2), the EFFDH is (% + 0.591;)2 h = 29 Equation (3) The output shock pulse from each drop was recorded using a Kikusui COS 5020 ST Oscilloscope and a Kistler 8602A500 Accelerometer with a Kistler 5116 Piezotron Coupler. Shock pulses were also photographed using the Shackman 7000 Camera with Polaroid Type 667 film. Table 1, below, shows the gate time and impact velocity for each free fall drop height as calculated by using Equation (3). Table 1. GATE TIME, IMPACT VELOCITY & FREE FALL DROP HEIGHT GATE TIME IMPACT VELOCITY. FREE FALL DROP HEIGHT (m sec) (inch/(sec) (inch) 5.25:0.02 96.3:0.36 12:0.09 4.27:0.02 117.9i0.57 18:0.17 3.69:0.02 l36.2i0.74 24:0.26 3.30:0.02 152.3:0.91 30:0.36 3.01:0.02 166.8:1.10 36:0.49 2.7810.02 180.2i1.30 42:0.61 DETERMINATION OF EFFECTIVE BEARING AREA Configurations and dimensions of Ribbed EPS and Flat EPS test samples are shown in Figures 4 and 5 respectively. Effective bearing areas for Ribbed EPS test samples were determined by applying Hooke's Law to each crossectional SAMPLE DIMENSION (inch) EFFECTIVE BEARING AREA NUMBER H h a (sq in) 1 5 4 l 38.12 2 4 3 1 1 /4 42.57 3 3 2 1 1/2 47.19 4 2 1 1 3/4 $2.80 Figure 2. CONFIGURATIONS AND DIMENSIONS OF RIBBED EPS TEST SAMPLES H 8" 8" SAMPLE DIMENSION H BEARING AREA NUMBER (inch) (sq in) 5 5 64 6 1 4 64 7 3 64 8 2 64 Figure 3. CONFIGURATIONS AND DIMENSIONS OF FLAT EPS TEST SAMPLES 10 slice and integrating to arrive at a total force- deformation relationship that accounts for variation in crossectional area from top to bottom. Details of the determination of the effective bearing areas for Ribbed EPS test samples are described in Appendix A. TEST SPECIMENS Expanded polystyrene slabs of 2 in., 3 in., 4 in., and 5 in. thick were molded by Tuscarora Plastics Inc. The slabs were cut into 8 in. x 8 in. pieces and then randomly. packaged in corrugated boxes for shipment to the School of Packaging. In order to maintain consistency in Rib size, a hot wire cutter and a set of Ribbed aluminum guide plates mounted on a pair of wood clamps were employed to do the rib cutting. Figure' 2 shows the Rib cutting device and Figure 3 illustrates the operation. The initial thickness of a test specimen was determined by averaging the four measurements obtained from the four corners of each test specimen prior to testing. Final thicknesses of the test samples were determined in the same way with measurements conducted at least one minute after the fifth drop was completed. 11 “—'fig::::=TO TRANSFORMER HOT WIRE CUTTER p,» GUIDE PLATES \ a)“ \ \f\ WOOD CLAMP Figure 4. EPS RIB CUTTING DEVICE 12, TO TRANSFORMER 1 HOT WIRE CUTTER RIBBED EPS CUSHION GUIDE PLATES . '— isg\w$§§§&w’ \\ 944 ~\ \‘ T". A \ N WOOD CLAMP Figure 5. EPS RIB CUTTING DEVICE IN OPERATION 13 Test samples were conditioned at a temperature of 72 i 1 'F and a relative humidity of 50 i 2% for 24 hours or more prior to testing, in conformance to ASTM Test Method D 1596- 78a (1). TEST PROCEDURES This experiment was carried out in triplicate. The samples studied consisted of 1.25 pcf EPS and 1.35 pcf EPS. The 1.25 pcf EPS samples were tested at drop heights of 12 inches through 42 inches with an increment of 6 inches under each of five static stress levels (0.2, 0.6, 1.0, 1.4, and 2.0 psi). The 1.35 pcf EPS samples were investigated only at 36 inches drop height under each of five static stress levels. The static stress levels in all samples were based on effective bearing areas illustrated in Appendix A. DATA ANALYSIS AND RESULTS DATA ANALYSIS Determination of Peak Acceleration Level (gjs) The shock responses of the triplicated specimens were averaged for each of the test combinations (i.e., 6 drop heights x 5 static stress levels x 4 thicknesses) and are reported as acceleration levels (g's). Tables 2 through 7 (Appendix B) show the averaged peak acceleration levels (g's) obtained from 1.25 pcf EPS test samples at 12 in., 18 in., 24 in., 30 in., 36 in., and 42 in. drop heights. respectively. Table 8 (Appendix B) shows the averaged peak acceleration levels (g's) through 1.35 pcf EPS test samples at 36 in. drop height. Generation of Cushion Curves The first-drop peak acceleration levels obtained from both the Ribbed EPS and the Flat EPS for each test combination are plotted as cushion curves with peak acceleration level (g's) on the ordinate and static stress level on the abscissa. These cushion curves are presented in Figures 6, 8, 10, 12, 14, 16, and 18. 14 15 Peak acceleration levels (g's) of the second through the fifth drops obtained from both the Ribbed EPS and the Flat EPS after each test combination were averaged separately. The average values are also plotted as cushion curves and are shown in Figures 7, 9, 11, 13, 15, 17 and 19. 16 150- --RIBBED EPS, FIRST DROP TE --—FLAT EPS, FIRST DROP 3?: 3 100- w 4) (U 14 m D H 0) O 2 50+- .54 (U 0) m P o o Static Stress (psi) Figure 6. CUSHION CURVES FOR THE COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON SHOCK TRANSMISSION AT 12 in. DROP HEIGHT (1.25 pcf Expanded Polystyrene) 17 150b —— RIBBED EPS, 2nd~ 5th DROP AVERAGE a — FLAT EPS, 2nd Ms‘h DROP AVERAGE 2': 5 100b «4 4.1 a! H b d) H O O 2 50_ .54 (U 33 r o L L J g l 1 l 4 1 L 'o 0.2 0.6 1.0 1.4 2.0 Static Stress (psi) Figure 7. CUSHION CURVES FOR THE COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON SHOCK TRANSMISSION AT 12 in. DROP HEIGHT (1.25 pcf Expanded Polystyrene) 18 150l- —— RIBBED EPS, FIRST DROP ,4 FLAT EPS, FIRST DROP m . 2': a I- o 100 ‘ «'4 ‘5 \ H . \ m \'V\ '3 \\ ° \ 3 50+- 2" x "'" -— '- " '._—T- n 8 T ------ - [I . ’ -'--:- TE» " *5” O L L l 1 I 1 l 1 1 L O 0.2 0.6 1.0 1.4 2.0 Static Stress (psi) Figure 8. CUSHION CURVES FOR THE COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON SHOCK TRANSMISSION AT 18 in. DROP HEIGHT (1.25 pcf Expanded Polystyrene) 19 150- ——RIBBED EPS, 2nd~ 5‘h DROP AVERAGE A -— FLAT EPS, 2nd~ 5th DROP AVERAGE .5” r E I: 0100” 0H 4.) «U u . 0) H (D 8 4 50»- .2 CU cu . O1 0 l L l 1 l 1 l 1 1 L o 0.2 0.6 1.0 1.4 2.0 Static Stress (psi) Figure 9. CUSHION CURVES FOR THE COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON SHOCK TRANSMISSION AT 18 in. DROP HEIGHT (1.25 pcf Expanded Polystyrene) 20 150- ——RIBBED EPS , FIRST DROP TIT ""—"" FLAT EPS , FIRST DROP 2': 5 100L «4 4) “'\ a; \ 21 * ~‘ '_. \ n 0 50+- \ I / n x \~ "“"’ u 8 firs—’_. .3, o. . r—— :1 _ __ 4g, 0 l 1 l 1 l 1 L 1 1 J 0 O . 2 0 . 6 l . O 1 . 4 2 . 0 Static Stress (psi) Figure 10. CUSHION CURVES FOR THE COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON SHOCK TRANSMISSION AT 24 in. DROP HEIGHT (1.25 pcf Expanded Polystyrene) 150 50 Peak Acceleration (g's) 21 ——RIBBED EPS, 2nd~ 5‘“ DROP AVERAGE FLAT EPS, 2nd~ 5‘“ DROP AVERAGE /2 / / / / // I! / 2 // \ / \ \\ ’1' \ \ ,/ \ \ z \ \\‘ ”I n \ ~—-’ ’,,3" \\\\ ””’ 3 ,, 0.2 0.6 1.0 1.4 2.0 Static Stress (psi) Figure 11. CUSHION CURVES FOR THE COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON SHOCK TRANSMISSION AT 24 in. DROP HEIGHT (1.25 pcf Expanded Polystyrene) 22 150' —-—RIBBED EPS, FIRST DROP in . FLAT EPS, FIRST DROP .. ow ’2 v / \ /x’ 5100- .‘ / 2" u \ \ / «3 \\ \ // H / Q) i \\ \\ // '3 \ \ \K—._—-”’ N o ‘ \ ,13 O 501- \\ ”’ ” A: ——- 4". «I ~-—--—-——--———-—--"' .. g l- ‘~ -—-:j=:"""-:5 5 o I L l 1 l L l L 1 L O 0.2 0.6 1.0 1.4 2.0 Static Stress (psi) Figure 12. CUSHION CURVES FOR THE COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON SHOCK TRANSMISSION AT 30 in. DROP HEIGHT (1.25 pcf Expanded Polystyrene) 23 350'" ——RIBBED EPS, 2"°~ 5‘“ DROP AVERAGE 2" —FLAT EPS, 2nd~ 5m DROP AVERAGE / 300' / 250” N O O 1 Peak Acceleration (g's) H m o ' I 100‘ 50- 0“ l L L k l L l 1 1 L 0 0.2 0.6 1.0 1.4 2.0 Static Stress (psi) Figure 13. CUSHION CURVES FOR THE COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON SHOCK TRANSMISSION AT 30 in. DROP HEIGHT (1.25 pcf Expanded Polystyrene) 24 200+ ---RIBBED EPS, FIRST DROP //2 / — FLAT EPS, FIRST DROP / P 150- 8 C . O ”.1 u 8 O lOO~ H 0) O O . d x 8 m 50- o l 1 l 1 I 1 l 1 1 I O 0.2 0.6 1.0 1.4 2.0 Static Stress (psi) Figure 14. CUSHION CURVES FOR THE COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON SHOCK TRANSMISSION AT 36 in. DROP HEIGHT (1.25 pcf Expanded Polystyrene) 25 ,2” 2 u L --RIBBED EPS, 2nd~z5th DROP AVERAGE] I — FLAT EPS, 2nd~ 5th DROP AVERAGE // 350“ 300- l 250 200L 150% Peak Acceleration (g's) 100_ 50- 0 l 1 l J l 1 l 1 1 _JL 0 0.2 0.6 1.0 1.4 2.0 Static Stress (psi) Figure 15. CUSHION CURVES FOR THE COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON SHOCK TRANSMISSION AT 36 in. DROP HEIGHT (1.25 pcf Expanded Polystyrene) Peak Acceleration (g's) 200 150 100 50 26 ——RIBBED EPS, FIRST DROP ——FLAT EPS, FIRST DROP / l 1 l 1 l L i 1 1 L Static Stress (psi) Figure 16. CUSHION CURVES FOR THE COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON SHOCK TRANSMISSION AT 42 in. DROP HEIGHT (1.25 pcf Expanded Polystyrene) 27 --RIBBED EPS, 2nd~5th DROP AVERAGE -—-FLAT EPS, 2'“‘~5th DROP AVERAGE 2” 350- /2 300- 250" 200— 150* Peak Acceleration (g's) 100v 50- C L L l 1 l L l 4 1 I 0 0.2 0.6 1.0 1.4 2.0 Static Stress (psi) Figure 17. CUSHION CURVES FOR THE COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON SHOCK TRANSMISSION AT 42 in. DROP HEIGHT (1.25 pcf Expanded Polystyrene) 28 zool- -——RIBBED EPS, FIRST DROP L ——FLAT EPS, FIRST DROP ,2” / / A / 9 150_ / e / / 2" t: . / 9. ‘ ’ - \ 4-3 // S 100 / o E ‘ / I-l \ 8 U _ .3 / <2 \ /’ I II a 50 \\\ __._.”” “: ~‘--;—I—.:_. __i_fi-——-'-é4" b ‘M~~—____ ‘5” 0 l 1 i 1 1 1 l 1 1 l o 0.2 0.6 1.0 1.4 2.0 Static Stress (psi) Figure 18. CUSHION CURVES FOR THE COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON SHOCK TRANSMISSION AT 36 in. DROP HEIGHT (1.35 pcf Expanded Polystyrene) 29 ——RIBBED EPS, 2"“~ 5‘h DROP AVERAGE /2"2 / —— FLAT EPS, 2nd~ 5‘h DROP AVERAGE / 3501 300’ 250" N O O T Peak Acceleration (g's) H m o I I 100- 50h o l L l 1 J 1 l 1 1 l 0 0.2 0.5 1.0 1.4 2.0 Static Stress (psi) Figure 19. CUSHION CURVES FOR THE COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON SHOCK TRANSMISSION AT 36 in. DROP HEIGHT (1.35 pcf Expanded Polystyrene) 30 Analysis of Variance (Completely Randomized Design) Analysis of variance was applied to the raw data in order to explore the significance Of the effect of the EPS shape in general, and the static stress level on shock transmission. The data presented in Tables 2 through 8 (Appendix B) were analyzed in such a way that only the peak acceleration levels obtained from the Ribbed EPS and the Flat EPS samples of same density, thickness and drop height were compared. Thus a Completely Randomized Design by factorial effects where two variables (EPS shape and static stress level) were included. A representative data set-up (i.e., 1.25 pcf EPS at 36 inches drop height) for the Completely Randomized Design Analysis of Variance is shown in Appendix C, while the results of Analysis of Variance are presented in Table 9. 31 Table 9. ANALYSIS OF VARIANCE (COMPLETELY RANDOMIZED DESIGN) OF ONE SAMPLE SET (3 inch 1.25 pcf EPS AT 36 inch DROP HEIGHT) SOURCE DF TOTAL 29 TREATMENT 9 SHAPE 1 S. STRESS 4 SHAPE x o-4 ERROR 20 SS DF MS F FIRST DROP SS MS F 18217.0 18099.0 381.6 381.6 64.9** 17345.8 4336.5 735.0** 371.5 92.9 15.7** 118.0 5.9 Sum of square Degree Of freedom Mean of square F test value 2nd--5th DROP AVERAGE SS MS F 68763.4 68502.0 3967.7 3967.5 303.6** 63213.9 15803.5 1209.1** 1320.7 330.2 25.3** 216.3 13.1 32 The significance levels for the effect of EPS shape on peak acceleration level (g's) at each test combination are listed in Table 10. Table 10. SIGNIFICANCE LEVEL OF EFFECT OF EPS SHAPE ON SHOCK TRANSMISSION (g's) OVERALL DROP HEIGHT (inch) THICKNESS 1.25 pcf EPS 1.35 pcf EPS (inch) 12 18 24 30 36 42 36 FIRST DROP ns ns ** ** ** ** 4 2 2nd--5th DROP AVERAGE ** 4* 1* *4 *4 *1 ns FIRST DROP ns ns ns ** ** ** t 3 2nd--5th DROP AVERAGE ns ns ** ** ** ** ** FIRST DROP ** ** ** ** n5 ** n5 4 2nd--5th DROP AVERAGE ns * ** ** ** ** * FIRST DROP * ** ** ** ns * * 5 2nd--5th DROP AVERAGE ** ** ns ** ** ** * *, ** Significant at 5% and 1% level Of probability respectively ns Not significant 33 Pairwise Comparison of Ribbed EPS versus Flat EPS on Shock Transmissibn In order to investigate the existence'and significance Of the difference between Ribbed EPS and Flat EPS on shock transmission , a Pairwise Comparison was performed. Peak acceleration levels Obtained from Ribbed EPS and Flat EPS samples at each test combination were compared. Appendix D illustrates a Pairwise Comparison of Ribbed EPS versus Flat EPS on shock transmission for one sample set (i.e., 3 inch thick 1.25 pcf EPS at 36 inch drop height). Table 11 presents the significance levels for the differences between Ribbed EPS and Flat EPS on shock transmission at each test combination. A comparison of Ribbed EPS versus Flat EPS on the final thicknesses of tested samples was conducted. A representative comparison of Ribbed EPS versus Flat EPS on the final thickness Of one sample set (i.e., 1.25 pcf EPS at 24 inch drop height) is shown in Appendix E. 34 Table 11. SIGNIFICANCE LEVEL OF DIFFERENCE BETWEEN RIBBED EPS AND FLAT EPS ON SHOCK TRANSMISSION (g'S) FIRST DROP 2th--5th DROP AVERAGE OVERALL 1.35 1.35 1.25 pcf EPS pcf 1.25 pcf EPS pcf THICKNESS EPS EPS (inch) DROP HEIGHT (inch) DROP HEIGHT (inch) 12 18 24 3O 36 42 36 12 18 24 3O 36 42 36 | 0.2 psi ns ns ns ns ** ns + ns ns ns ns ns * ns 0.6 psi ns ns ns * * ** ++ + ns ** ** ** ** + 2 1.0 psi * + ns * * ** + ns ns ns ** ** * ns 1.4 psi ns * * ** ** ** ++ + ** * ** ** * ++ 2.0 psi ns ** ** ** ** ** ** 4* ** ** *1 ** ** ns 0.2 psi * ns ns * ns * ns ns ns ** ns ns * ns 0.6 psi + ns ns ** + ns ns ++ ++ * ** ** ** ++ 3 1.0 psi + + ns ** * * + ++ ns ns ** ** ** ++ 1.4 psi ns * ns ** * ** ++' ns ns + ** ** ** ns 2.0 psi ns ns ns * ** ** ns ns ++ * ** ** ** ** 0.2 psi ++ ++ ** * ns ns ** ns ns ns ns ns ** + 0.6 psi + + ns ns ns ns ns ++ ++ ns ns ns ns ns 4 1.0 psi ns ns ns ns ns ns ns ++ + * ** ** ** + 1.4 psi ns ns ns * ns * ns ns ns ** ** ** ** + 2.0 psi 115 ns ** *3! n5 * ns ns ** ** ** ** ** ** 0.2 psi ns ns * * ns ns ns + ns + ns ns ns ns 026 psi ns + ns ns ++ ++ ns ns + ns ns ns ns + 5 1.0 psi ns ns ns ns ns ns ns ns * ns ** ** ** ns 1.4 psi ns ns + ns ns * ++ ns ns * ** ** ** ns I 2.0 psi ms + + * n5 ** ** n5 n5 ** ** ** ** ** *, ** Ribbed EPS yielded higher g's over Flat EPS at 5% and 1% level of probability respectively +, ++ -Flat EPS yielded higher g's over Ribbed EPS at 5% and 1% level of probability respectively ns Not significant 35 RESULTS This study intended to explore the effect of the geometric shape of EPS on shock transmission. This section presents the results Of the study. The results are described in the order of the two questions that lead to this investigation (see page 3). With regard to the difference between Ribbed EPS and Flat EPS on shock transmission the following was observed. At low drop heights (i.e., between 12 and 24 inches) the peak acceleration levels obtained from Ribbed EPS and Flat EPS showed no significant difference, while peak accelerations differed significantly at greater drop heights (i.e., between 30 and 42 inches) in such a way that Ribbed EPS produced higher peak acceleration levels. Further, it appeared that Ribbed EPS yielded greater peak accelerations under high static stress levels (i.e., 1.4 psi and higher) than did Flat EPS. Focussing on the difference between first drop and multiple drops on shock transmission the following Observations were made. Both Ribbed EPS and Flat EPS exhibited progressive increases in peak acceleration levels due to multiple drops. Each sequential drop caused an additional permanent 36 deformation to the test specimen, making the spring constant (k) of the test specimen greater and the deflection (8st) of the cushion smaller. The peak acceleration level Gm can be expressed as follows (5); _ +211}. _ 2h Gm — W or Gm — {8—1:- where: Gm = peak acceleration = drop height = spring constant W = weight of product or loading force Ost = static deflection of test specimen The results of the comparison of Ribbed EPS versus Flat EPS on the final thickness showed that the difference between Ribbed EPS and Flat EPS final thicknesses at 12 in., 18 in. and 24 in. drop heights was not significant, while at at 30 in., 36 in. and 42 in. drop heights Ribbed EPS samples exhibited greater amount of permanent deformation. Further, it was noticed that 5 inch thick Ribbed EPS samples fell apart after the fifth drop at 24 inch drop height, while at 30 inch or larger drop height, Ribbed EPS samples cracked severely after the third drop and fell apart completely after the fourth drop. 37 Finally, 1.35 pcf EPS yielded lower peak acceleration levels than 1.25 pcf EPS at 36 inch drop height and under high static stress levels (i.e., 1.4 psi and greater), while under low static stress levels (i.e., 1.0 psi and lower) 1.35 pcf PS produced greater peak accelerations than did 1.25 pcf EPS. DISCUSSION The purpose Of this study was to investigate the influence of the geometric shape of EPS cushion on shock transmission. Both Ribbed EPS and Flat EPS samples of four different thicknesses were tested at six different drop heights under each of five static stress levels. The results showed the following: 1) differences between Ribbed EPS and Flat EPS on peak acceleration levels exist, and they appear to depend on drop height and static stress level; 2) differences between first drop and multiple drops on peak acceleration levels are greater for Ribbed EPS than for Flat EPS. The differences between Ribbed EPS and Flat EPS on shock transmission in general indicate that Ribbed EPS suffers a higher degree of permanent deformation under the same conditions than does Flat EPS. This finding implies that Flat EPS cushion curves can not be applied to Ribbed EPS cushion curves at drop heights Of 30 inches and higher and/ or under static stress levels of 1.4 psi and higher. With regard to the results of first drop and multiple drops on shock transmission, greater increases in peak 38 39 accelerations for multiple drops were found for Ribbed EPS as compared to that of Flat EPS. Thus, although Ribbed EPS and Flat EPS Show the same tendency to produce higher peak acceleration levels due to multiple drops, Ribbed EPS cushions appear to suffer a higher degree Of permanent deformation. CONCLUSIONS AND RECOMMENDATIONS CONCLUSIONS Cushion curves for Ribbed EPS and Flat EPS were constructed in this study. The results revealed differences between Ribbed EPS and Flat EPS on shock transmission depending on drop height and static stress level. It was Observed that at smaller drop heights and lower static stress levels the peak acceleration levels Obtained from Ribbed EPS and Flat EPS were similar. However, at larger drop heights or under high static stress levels, the cushion curves for Ribbed EPS and Flat EPS differed significantly. Therefore, it can be concluded that cushion curves developed on planks are inadequate to describe the cushioning behavior of Ribbed EPS under certain conditions. This implies that the effect of ribs of EPS cushion must be taken into account as a factor in peak acceleration when designing a cushion package for a fragile article. Especially drop height, static stress level, and density of the Ribbed EPS cushion should be considered. 40 41 RECOMMENDATIONS It is important to determine the effective bearing area properly when designing a Ribbed EPS cushion package. This is because changes in static stress levels depend on changes in effective bearing area (given that the loading force is maintained constant). Further, it is shown that static stress levels influence peak acceleration levels greatly. With regard to density a denser EPS is recommended when designing a Ribbed EPS cushion package. This is because at larger drop heights (36 inches and higher) and/or under higher static stress levels (1.4 psi and higher) denser Ribbed EPS cushions suffer less permanent deformation from each drop, as shown by their lower peak acceleration levels. IMPLICATIONS OF THIS STUDY The main implications Of this study are Of practical value: knowledge of effect of Ribbing on shock transmission through Expanded Polystyrene cushion allows for more economical designing of Ribbed EPS cushion package with regard to time and material. APPENDICES APPENDIX A DETERMINATION OF EFFECTIVE BEARING AREA FOR RIBBED EPS TEST SAMPLE Assume that the spring constant, k, for EPS is linear in all cases. Consider a cushion with a variable crossection as shown below; Load EPS cushion ‘ 6 E: f 1‘3 Y At any section of Y Hooke's Law applies so that F -_d_x. O-A EE-E dY where: t = Thickness of cushion o- = Static stress F 8 Loading force A* = Effective bearing area E = Young's modulus Of elasticity e = Strain dy = Elemental thickness dx = Compression of slice dy of cushion . F dx Since A — 135' dx =-£;dy Equation (1) EA 42 43 Appendix A (Continued) Integrating both sides of Equation (1) l" t" dx = J[ -—-dy o o'EA The total deflection X of this cushion is t x =1 91- Equation (2) E o A 'E Equation (2) can be written as F ='_7?——-X Equation (4) 91 o (A If the crossectional area is constant, then Equation (3) reduces to F =%X. Denoting by A* the effective bearing area defined to be the area which gives the simple force/ deformation relation for a constant crossection, g; = BAA = E . X _t T— Equation (4) 91 o A Therefore, the effective bearing area (A*) is t . A* = Equation (5) Ex 0 A, In this study, the effective bearing area for a 2 inch thick Ribbed EPS sample was determined using Equation (5) figure below: and the 44 Appendix A (Continued) Ribbed EPS test Specimen 8" The entire cushion specimen consists of two portions, the base and the three ribs, so that the integral in Equation (5) must be split into two parts: [tax- -1: % +I2fi¥y where: My) - 3 x at-fi-Jl) o 64 16 -y 1 1 2dy 1 =—— d + — 64L Y 6 19-y -_1_ 1 - 2 =-l- (Ln7 Ln8) 64 “1-1 .2. ’64 6ms 45 Appendix A (Continued) The effective bearing area from Equation (5) is 2 t . A* =T_= m= 52.80 (sq 1n) dy ° J[ ‘A Note that A* is between the maximum area (64 inz) and the minimum area (42 in?) as expected. The effective bearing areas for 3, 4, and 5 inch thick Ribbed EPS test samples were determined in the same way and the results are: Overall thickness Effective of Ribbed EPS bearing area (inch) (sq in) 3 47.19 4 42.57 5 38.12 APPENDIX B Table 2. PEAK ACCELERATION TRANSMITTED THROUGH 1.25 pcf EXPANDED POLYSTYRENE AT 12 inch DROP HEIGHT PEAK ACCELERATION (g's) STATIC DROP STRESS 2 inch 3 inch 4 inch 5 inch (psi) No. FLAT RIBBED FLAT RIBBED FLAT RIBBED FLAT RIBBED 1 96 98 94 100 93 76 90 85 2 96 102 95 103 93 97 92 83 0.2 3 98 101 97 98 94 92 94 86 4 100 104 98 102 95 94 96 87 5 103 101 100 102 97 98 97 82 2-5 AVE 99 102 97 101 95 95 95 85 1 46 43 44 38 43 36 42 38 2 49 48 40 40 44 39 43 38 0.6 3 51 48 50 41 45 39 44 40 4 52 50 47 42 47 41 46 39 5 52 51 46 43 48 42 47 39 2-5 AVE 51 49 47 42 46 40 45 39 1 33 28 '28 25 28 25 26 27 2 37 32 30 29 31 28 29 27 1.0 3 41 38 32 31 32 29 30 28 4 42 41 34 32 33 29 30 28 5 44 44 35 32 33 30 30 28 2-5 AVE 41 39 33 31 32 29 30 28 1 24 25 20 20 20 20 19 20 2 29 32 24 25 21 22 22 20 1.4 3 34 37 25 27 23 24 23 20 4 36 42 27 28 25 25 24 21 5 38 45 28 30 26 25 24 21 2-5 AVE 34 39 26 28 24 24 23 21 1 20 24 16 17 16 14 15 14 2 30 36 22 23 18 18 17 16 2.0 3 35 44 26 27 21 20 19 17 4 39 48 28 30 22 23 20 19 S 41 51 29 32 23 26 21 20 2-5 AVE 36 45 26 28 21 22 19 18 46 47 Appendix B (Continued) Table 3. PEAK ACCELERATION TRANSMITTED THROUGH 1.25 pcf EXPANDED POLYSTYRENE AT 18 inch DROP HEIGHT PEAK ACCELERATION (g ' s) STATIC DROP ‘ STRESS 2 inch 3 inch 4 inch 5 inch (psi) No. FLAT RIBBED FLAT RIBBED FLAT RIBBED FLAT RIBBED 1 108 104 104 105 102 92 100 90 2 109 114 105 104 102 93 100 93 0.2 3 110 111 105 105 103 100 99 97 4 112 118 107 107 104 98 100 91 5 113 110 108 107 105 99 101 97 2-5 AVE 110 113 106 106 104 98 100 94 1 51 48 46 41 46 39 45 41 2 56 53 49 45 48 41 48 41 0.6 3 61 57 51 48 50 43 47 44 4 64 60 52 49 50 44 49 44 5 65 66 52 49 51 44 50 43 2-5 AVE 61 59 51 48 50 43 49 43 1 37 32 31 28 31 28 29 28 2 46 47 35 33 32 29 22 29 1.0 3 53 55 40 36 34 32 34 29 4 58 60 44 40 34 33 35 29 5 60 63 46 44 36 34 36 30 2-5 AVE 54 56 41 38 34 32 35 29 1 28 33 23 25 21 22 21 18 2 42 50 29 30 25 26 23 22 1.4 - 3. 52 62 34 35 27 28 25 ‘ 26 4 57 68 38 40 30 30 27 28 5 61 72 40 44 31 30 28 31 2-5 AVE 53 63 35 37 28 29 26 27 1 30 38 21 21 18 17 17 14 2 51 71 32 34 25 28 21 20 2.0 3 65 86 39 43 29 34 25 26 4 72 98 43 49 31 40 26 30 5 79 106 45 54 32 43 27 32 2-5 AVE 70 90 40 45 29 36 25 27 48 Appendix B (Continued) Table 4. PEAK ACCELERATION TRANSMITTED THROUGH 1.25 pCf EXPANDED POLYSTYRENE AT 24 inch DROP HEIGHT PEAK ACCELERATION (g ' s) STATIC DROP STRESS 2 inch 3 inch 4 inch 5 inch (psi) No. FLAT RIBBED FLAT RIBBED FLAT RIBBED FLAT RIBBED 1 112 108 105 104 101 98 100 97 2 110 116 101 108 100 113 125 98 0.2 3 112 118 102 112 105 105 125 99 4 114 122 105 113 106 121 120 101 5 113 117 110 119 107 122 120 103 2-5 AVE 112 118 105 113 105 115 123 100 1 55 51 44 43 42 43 41 42 2 56 62 47 50 45 46 47 44 0.6 3 62 74 51 53 48 47 47 44 4 66 78 54 55 49 49 49 46 5 69 83 55 58 49 50 48 44 2-5 AVE 63 74 52 54 48 48 48 45 l 42 43 33 32 31 29 31 29 2 59 64 43 41 36 34 34 31 1.0 3 71 75 48 47 40 37 35 33 4 79 85 52 51 43 40 38 34 5 85 91 54 56 44 41 39 38 2-5 AVE 74 79 49 49 41 38 37 34 1 35 44 27 29 24 25 23 18 2 66 73 38 42 32 30 27 29 1.4 3 81 92 49 52 35 36 31 37 4 91 108 55 60 39 41 33 42 5 99 119 59 65 41 44 34 47 2-5 AVE 84 98 50 55 37 38 31 39 1 48 65 29 32 22 24 20 20 2 90 121 49 54 32 43 27 34 2.0 3 118 153 61 69 40 55 31 47 4 134 176 69 78 45 62 34 53 5 144 192 73 85 46 69 36 59 2-5 AVE 122 161 63 71 41 57 32 48 49 Appendix B (Continued) Table 5. PEAK ACCELERATION TRANSMITTED THROUGH 1.25 pCf EXPANDED POLYSTYRENE AT 30 inch DROP HEIGHT PEAK ACCELERATION (g's) STATIC DROP STRESS 2 inch 3 inch 4 inch 5 inch (psi) No. FLAT RIBBED FLAT RIBBED FLAT RIBBED FLAT RIBBED 107 115 101 113 99 109 92 102 117 123 112 114 114 114 93 108 123 126 117 118 108 120 98 107 120 130 112 121 104 113 99 111 129 140 114 112 107 118 99 111 2-5 AVE 122 130 114 121 108 116 97 109 O N (”DUMP 1 56 63 47 48 42 43 40 38 2 75 91 56 59 49 48 43 39 0.6 3 87 107 62 66 52 52 47 44 4 95 118 66 71 55 54 49 48 5 99 126 68 75 57 58 49 54 2-5 AVE 89 111 63 68 53 53 47 46 1 56 66 37 41 30 32 27 26 2 92 113 54 64 40 46 34 40 1.0 3 111 142 62 78 47 54 39 48 4 123 154 67 88 50 60 41 56 5 132 173 70 96 52 65 42 60 2-5 AVE 114 146 63 81 47 56 39 51 1 67 78‘ 37 45 28 32 25 25 2 126 154 59 76 42 54 33 43 1.4 3 160 198 72 100 51 68 40 55 4 181 229 80 114 56 79 42 63 5 197 251 88 125 59 87 45 72 2-5 AVE 166 208 75 104 52 72 40 58 1 96 120 47 57 30 34 23 39 2 190 244 87 112 51 70 35 57 2.0 3 239 326 109 146 62 92 39 73 4 273 365 124 169 70 108 49 82 5 294 416 136 191 73 119 53 89 2-5 AVE 249 338 114 155 64 97 44 75 50 Appendix B (Continued) Table 6. PEAK ACCELERATION TRANSMITTED THROUGH 1.25 pcf EXPANDED POLYSTYRENE AT 36 inch DROP HEIGHT PEAK ACCELERATION (g ' s) STATIC DROP STRESS 2 inch 3 inch 4 inch 5 inch (psi) No. FLAT RIBBED FLAT RIBBED FLAT RIBBED FLAT RIBBED 1 127 154 106 120 108 105 104 100 2 142 130 119 126 114 110 110 112 0.2 3 150 139 127 131 119 117 112 114 4 153 139 122 136 117 103 110 110 5 157 145 127 136 118 104 109 112 2-5 AVE 151 138 124 132 117 109 110 112 1 67 75 55 51 48 45 40 35 2 93 119 67 69 55 55 49 43 0.6 3 109 144 74 83 61 62 55 56 4 118 158 78 91 64 66 57 61 5 127 170 82 96 66 70 58 65 2-5 AVE 112 148 75 85 62 63 55 56 1 70 89 47 48 36 36 30 29 2 129 165 72 86 50 56 40 49 1.0 3 162 214 88 108 58 71 47 61 4 182 240 95 120 62 85 51 70 5 197 259 102 128 67 90 54 79 2-5 AVE 167 220 89 110 59 76 48 65 1 97 134 49 62 35 38 28 32 2 196 241 89 115 57 74 44 60 1.4 3 248 309 114 145 68 96 52 78 4 280 356 128 168 73 111 58 81 5 303 391 140 190 79 123 61 91 2-5 AVE 257 324 118 155 69 101 54 78 1 125 185 70 81 46 51 38 38 2 304 397 138 170 76 103 58 78 2.0 3 395 495 180 ‘186 98 140 70 104 4 450 561 216 274 117 160 79 118 5 489 602 244 306 136 180 87 152 2-5 AVE 410 514 194 234 107 146 73 113 51 Appendix B (Continued) Table 7. PEAK ACCELERATION TRANSMITTED THROUGH 1.25 pCf EXPANDED POLYSTYRENE AT 42 inch DROP HEIGHT PEAK ACCELERATION (g's) STATIC DROP STRESS 2 inch 3 inch 4 inch 5 inch (psi No. FLAT RIBBED FLAT RIBBED FLAT RIBBED FLAT RIBBED 1 126 132 111 126 107 116 105 105 2 130 148 115 131 110 138 110 108 0.2 3 139 115 119 146 113 146 110 109 4 141 162 120 147 113 128 113 112 5 145 173 124 151 117 123 114 107 2-5 AVE 139 160 119 144 113 134 112 109 1 66 75 51 53 48 45 46 35 2 93 114 54 70 55 54 50 45 0.6 3 110 138 74 84 61 61 54 57 4 125 151 '79 93 65 67 58 64 5 134 162 84 97 66 70 58 73 2-5 AVE 115 141 73 86 62 63 55 60 1 69 93 44 51 35 37 31 31 2 129 166 66 88 48 56 40 55 1.0 3 169 215 83 110 56 75 47 69 4 200 243 97 126 62 87 50 82 5 222 264 115 138 65 95 54 89 2-5 AVE 180 222 90 116 58 78 48 74 1 87 125 47 60 33 41 28 36 2 184 245 87 115 56 79 43 69 1.4 3 249 311 112 149 68 103 51 89 4 293 364 134 175 73 119 56 101 5 320 398 154 197 81 133 61 109 2-5 AVE 262 330 122 159 69 109 53 92 1 142 189 65 81 39 59 29 41 2 303 370 138 164 77 123 52 86 2.0 3 384 460 183 222 100 164 68 115 4 437 518 209 259 116 199 76 142 5 480 560 230 291 122 232 81 158 2-5 AVE 401 477 190 312 104 180 69 125 52 Appendix B (Continued) Table 8. PEAK ACCELERATION TRANSMITTED THROUGH 1.35 pcf EXPANDED POLYSTYRENE AT 36 inch DROP HEIGHT PEAK ACCELERATION (g's) STATIC DROP STRESS 2 inch 3 inch 4 inch 5 inch (psi) No. FLAT RIBBED FLAT RIBBED FLAT RIBBED FLAT RIBBED 1 147 134 143 146 139 151 137 129 2 166 195 153 161 141 148 138 132 0.2 3 173 173 160 169 146 137 139 152 4 181 169 160 166 145 131 138 162 5 181 163 155 168 141 130 139 162 2-5 AVE 175 175 157 166 143 137 139 152 1 72 63 63 55 58 53 50 51 2 96 91 71 63 63 62 58 52 0.6 3 111 108 80 69 69 62 61 52 4 122 118 86 74 72 65 64 53 5 130 128 89 78 74 68 65 55 2-5 AVE 114 111 81 71 69 64 62 53 1 70 63 47 42 41 38 36 33 2 119 110 69 60 51 47 45 38 1.0 3 152 144 84 76 60 54 49 46 4 169 171 91 87 66 60 51 51 5 181 187 97 96 69 63 54 57 2-5 AVE 155 153 85 80 62 56 50 48 1 88 72 46 40 36 32 31 25 2 176 145 79 74 53 47 40 40 1.4 3 235 198 100 98 67 62 46 52 4 269 233 111 117 75 74 50 61 5 290 262 120 131 80 83 55 68 2-5 AVE 243 209 102 105 69 66 48 55 1 131 185 60 62 36 40 28 32 2 281 312 123 136 68 87 46 60 2.0 3 380 408 163 186 88 120 58 78 4 435 465 190 220 102 135 65 88 5 468 505 210 243 113 149 68 99 2-5 AVE 391 422 171 196 93 123 59 81 APPENDIX C DATA SET-UP FOR ANALYSIS OF VARIANCE (COMPLETELY RANDOMIZED DESIGN) OF ONE SAMPLE SET (1.25 pcf EPS) DROP HEIGHT = 36 inch OVERALL THICKNESS OF EPS = 3 inch EPS STATIC PEAK ACCELERATION (g's) STRESS SHAPE (psi) FIRST DROP 2nd—-5th DROP AVERAGE TOTAL TOTAL 0.2 106 112 101 319 124 121 127 372 0.6 55 55 54 164 77 74 76 227 FLAT 1.0 47 ‘ 47 46 140 90 89 88 267 1.4 47 49 53 149 118 119 117 354 2.0 70 71 68 209 193 196 195 584 0.2 124 119 117 360 140 126 130 396 0.6 51 50 51 152 86 85 85 256 RIBBED 1.0 49 48 48 145 110 110 109 329 1.4 62 63 62 187 153 162‘ 151 466 2.0 81 83 80 244 232 240 230 702 53 APPENDIX PAIRWISE COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON SHOCK TRANSMISSION (g's) OF ONE SAMPLE SET (1.25 pcf EPS) DROP HEIGHT = 36 inch STATIC STRESS (Psi) OVERALL THICKNESS OF EPS = 3 inch FIRST DROP RIBBED FLAT DIFF. 124 106 18 119 112 7 117 101 16 _ 41 d 13.67 t=—= =4.04 ns Sd 3.38 51 55 -4 50 55 -5 51 54 -3 _ -12 d -4 t --——-- =-6.9O + Sd 0.58 ' 49 47 2 48 47 1 48 46 2 _ 5 d 1.67 t =-——-= = 5.50 * Sd 0.33 62 47 15 63 49 14 62 53 9 _ 38 d 12.67 t --——---——-—-= 6.81 * Sd 1.86 81 70 11 83 71 12 80 68 12 _ 35 d 11.67 t = =——— = 35.35 ** Sd 0.33 54 2nd--5th DROP AVERAGE RIBBED FLAT DIFF. 140 124 16 126 121 5 130 127 3 _ 24 d 8 t =—= 1.98 ns Sd 4.4 86 77 9 85 74 ll 85 76 9 _ 29 d 9.67 t =— =-—= 14.22 ** Sd 0.67 110 90 20 110 89 21 109 88 21 _ 62 d 20.67 t =—=——= 62.63 ** Sd 0.33 153 118 35 162 119 43 151 117 __;4_ _ 112 d 37.33 t =——-= a 13.10 ** Sd 2.85 232 193 39 240 196 44 230 195 35 _ 118 d 39.33 t =— = = 15.13 ** Sd 2.60 APPENDIX E COMPARISON OF RIBBED EPS VERSUS FLAT EPS ON THE FINAL THICKNESS OF ONE SAMPLE SET (1.25 pcf EPS AT 24 inch DROP HEIGHT) STATIC STRESS (P81) 0.2 NHHO OhOO) (101.6 mm) STATIC FINAL THICKNESS (mm) STRESS (psi) RIBBED FLAT DIFF. 0.2 72.25 73.20 -0.95 0.6 65.77 66.50 -0.73 1.0 62.80 63.93 -1.13 1.4 60.35 60.50 -0.15 2.0 60.17 58 10 2.07 -0.89 3 -0.178 t =-—=———=-0.304 ns Sd 0.586 t .10(4) = 2.132 t .05(4) = INITIAL THICKNESS=2 in. (50.8 mm) FINAL THICKNESS (mm) RIBBED FLAT DIFF. 47.40 47.90 -o.50 42.60 43.20 -O.60 40.20 41.20 -l.00 39.30 39.40 -o.10 38.10 37 80 -0.30 -1.90 H -0.380 Sd 0.222 INITIAL THICKNESS=4 in. 55 INITIAL THICKNESS=3 in. (76.2 mm) FINAL THICKNESS (mm) RIBBED FLAT DIFF. 97.80 ’ 99.20 -1.40 91.15 91.10 -0.05 87.20 88.50 -1.30 83.60 83.13 -0.47 81.05 81.10 -0.05 -2.33 a -0.460 t=—=——=-1.246 ns Sd 0.374 INITIAL THICKNESS=5 in. (127.0 mm) FINAL THICKNESS (mm) RIBBED FLAT DIFF. 122.90 124.80 -1.90 116.00 116.53 -0.53 111.80 109.73 2.07 109.75 106.67 3.08 104.00 102.87 1.13 3.85 3 -0.777 t =-—-= =-0.869 ns Sd 0.894 3.182 t .01(4) = 5.841 LIST OF REFERENCES LIST OF REFERENCES Anonymous American Society For Testing And Materials D 1596-78a. 1984. "Test Method for Shock Absorbing Characteristics of Package Cushioning Materials." Anonymous Manual number MM-340. "Instruction Manual for the Lansmont Model 23 Cushion Test System Opus I" 1984. Lansmont Corporation, Pacific Grove, California. Brandenburg, R. K. and Lee, J. L., 1985. "Fundamentals Of Packaging Dynamics," MTS Systems Corporation, Minneapolis, Minnesota. 1 : 1-2. Brandenburg, R. K. and Lee, J. L., 1985. "Fundamentals Of Packaging Dynamics," MTS Systems Corporation, Minneapolis, Minnesota. 2 : 3-12. Brandenburg, R. K. and Lee, J. L., 1985. "Fundamentals Of Packaging Dynamics," MTS Systems Corporation, Minneapolis, Minnesota. 6 : 73-95. Goff, J. W. and Twede, 0., 1983. "Shake and Break Laboratory Adventures in Package Dynamics," Michigan State University, School of Packaging, East Lansing, Michigan. Timoshenko, S. and Young, D. H., 1962. "Elements of Strength of Materials," 0. Van Nostrand Company Inc., Princeton, New Jersey. 11 : 294-339. 56 HICHI 9N S TE UNIV, LIBRQRIES 1111/11/11 1111/ Ill/1W 111111111111H! 31293106993813