5., - £141.27, .47 u 41 Lu «'43:: 5"}‘V‘,’ {44}? :HN : Jr}: .\ ”4,2" l {VOW-g 3““ #01,,“ [(29:3: 1": ‘ f;'/‘Il. ‘ .;+,, 44,4 3"". nu ‘541'1‘11; {2,4,4 4‘- 4 .g' 4.4". ~,‘ 40 . . ,an,‘ .4 ‘1]. :3 4 ”4‘: J ‘1, y qfqfl“ 4"\"".". 41,43 33 I.‘ v‘ ,. . 1 IriI’4 \ '4 ;‘ 4 $12.1, 3",; {‘1‘ . Fry-If” M444. In}: - '. ..‘ I?! ' " ' M 7 ,- a f'}\ . - ;.-’,- {fig/4, :;‘7-1 :14" _4\ 3 1;". ”as: ,u...‘ “ '\'4 w}?- , 1““ V . .f . I“? 595 - . V ' ‘ -£’ "‘33:!“ ‘ 4, . ‘5“?‘11‘35’U n 4 .1 _ '. \fi'gg? . g “31:33“? “NH-i 3‘- “3‘. v \§.t‘¢f< y: Aha," " 4. W.I_I,_;,g ‘1, 44 4p ”“43“" ‘ {wile V 4“ t, , 4:134“ ‘ 4...“ 337%? £3? I :15“ 15,-4.4, ”$3 1va ‘5‘} 7.4.554}, ‘1 1 51-4- if "C‘ ‘4\ . .1 ‘ ‘44 _ I“ .4“ 3:. ‘04; Ukififg} ijr'i, ”yrs“; 333,41; .4 l < 14.44 cc. ,4}! ”1‘“. 8 3:4. ' l 3 . 133; {“3“ ‘31:": 4‘5. {1. “$43,? «3‘4 334:3” :72}; ”$1.“. ‘ ‘dk ‘37-!" V“ a . 5144 I,“ ‘L “‘1‘ 4'35} ‘ 4 v 4 ‘ “QJIII‘ $1“ A,‘ SE' 2977‘»: .‘v ‘ 4 f-v' 4:4“: 5“ ‘ J 'h : ‘:‘“C“ 7 4‘ " 4 _ ,5 ., , . . '. 11‘3‘ Kiwififi.“ , . l‘ . g ‘3' ‘L. H ’44- 3‘ 1:15;?!“ ‘4}??? J 31;" i ‘4' £713” 21?] 1,1" .“4.‘: “Mix" 1' 34“,»: ."4 4’ ‘1‘! 5}" 4', 7 141.457,,” 4‘4"“: ‘4;- . .. #35“, . .4:- . \'\‘;L > . -. A; 4 I,“ "Fs'f‘ , 2.34:4 ijfiJ ”‘3’“ 'iféiu JEN”? :24» . 1,1,}, "’é, 'v‘“ v.43. . 4%,,” 4"". 3,235; ‘1'? 4w; ‘ '5‘" 4- r‘u‘t , 4 .' ,4 in!“ a .454“. {7“ , s "“x' I If (It? i‘ '14 l ‘ ’ ‘ 4:4 1190. .“i a}: _ , 4. ' '23:?" Mar. "WW“; 51”,;nlg‘Ul 4, 1"” ”,3, r5 '4 2/ 4:54“... .3}, 2" ‘ G ' ‘ R43?" 4. 4.1' "'1“ I ‘3 _“"“"“ “j“! l‘ 4'14“ ' ‘ - '(‘V 1‘ fl ‘4‘ . 731,, 5 ..~.\. .2120; 044.5,,“ a, m bflé‘ffi‘Ifl' ff; "(tfi 1317., 23- ‘ «"39" WW5; Vlétufiéfih “‘YU‘} “’51!“ I ‘r ’13:; ?“‘““?‘“ [Egan “44.1%.; “hi/:5» ‘1‘“ fit!“ “‘4“ “"331: ”‘35:; g“““;€{ ‘zéyfl‘fiyygfi a?” 33,594 115%: 0'51" ..P.! $;{f;u:";“ :4. N ”’34.: fife. . I‘rJ' 1/ 325'" . ‘ find 4.” ' ) filf'i, f», :. gffi‘u‘w “I“; 54. 4‘, 5,21% In; ‘3' ”5-; i453; 1‘ ., 3‘14-w‘93‘m‘ ’ “ I‘llflff (‘1' . :4 ,2 {2,7,5 V; - ' ‘L viz? , "J A!” . ‘5?N}VI’{;’1(‘SIE viz: 4",” ,‘_ ..»....4 114‘” '3 .9; " 4 t (4“. ".4“ 1‘» " 443‘. 42 ”1'4," , 4 ' I ”45°. .4‘. '1. 1H“: fl‘lr‘fi'! . 9:“; A 41,! (2;, )4?” (1424??! 5‘1. “t"‘:f‘; y '1 ”3... ‘4, (vita-1.: r .4}; .r‘q M. H'GAN STA l/llll'll/Ill/ I//II// [Hill/ill a $09 5 Ll I ‘é 89510 ww- L LIBRARY Michigan State University This is to certify that the thesis entitled THE DEVELOPMENT OF A METHOD FOR DERIVING THE CORRELATION BETWEEN FREE FALL AND SHOCK MACHINE DROP HEIGHT BASED ON EQUIVALENT VELOCITY CHANGE presented by Fanfu Li has been accepted towards fulfillment of the requirements for M.S. Packaging degree in Date November 3, 1988 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution -9. w—o'. r PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. DATE DUE DATE DUE DATE DUE J I «159 ”film My \<( " 51(3):; 2 3 If}; MSU Is An Affirmative Action/Equal Opportunity Institution ,_. _———. THE DEVELOPMENT OF A METHOD FOR DERIVING THE CORRELATION SET'EEN FREE [ALL AND SHOCK NACHINE DROP HEIGHT BASED ON EQUIVALENT VELOCITY CHANGE BY rentu Li A THESIS Submitted to NICHIGAN STATE UNIVERSITY In pertiel fulfillment of the require-ente for the degree of MASTER OF SCIENCE School of Peokeging 1988 ABSTRACT THE DEVELOPMENT OF A METHOD FOR DERIVING THE CORRELATION BETWEEN FREE FALL AND SHOCK MACHINE DROP HEIGHT BASED ON EQUIVALENT VELOCITY CHANGE BY Fanfu Li The purpose of this research is to derive the correlation between free fall and shock machine drop height based on equivalent velocity change. The velocity change of free fall drops have never been measured precisely due to the unavailability of accurate instrumentation. Therefore, a trigger device was developed for use in conjunction with a waveform analyzer in the measurement of velocity change. The drop height correlation, the descriptions of the operation and components of the device are presented. The measuring system was used to obtain the data of velocity change in free fall drops performed with drop teeter. The velocity change of shock machine drop was acquired through the usage of an shock machine system. The data were then analyzed and the correlation of drop height for the equivalent velocity change between free fall and shock machine was derived. To my parents, Uncle and hunt. ACRNO'LEDGMENTS I wish to express my sincere appreciation for the guidance and support given in this research by Dr. James W. Goff, Professor, School of Packaging, Michigan State University. I am indebted to Dr. Diana Twede, Assistant professor, School of Packaging, for arranging the necessary financial assistance during my research and serving as one of my committee members. I also extend my appreciation for the assistance offered by the other members of my committee, Dr. Paul Singh, Assistant Professor, School of Packaging, and Dr. Richard F. Gonzalez, Professor of Management at Michigan State University. A special thanks to Mr. Songnian Pan for the assistance with experimental material preparation and Ms. Wendy Aquilina for proofreading the draft. TABLE OF CONTENTS Page LIST OF FIGURES . ....... ...... ...... .......... ....... ii INTRODUCTION .... ................ ....... ...... .. ..... 1 LITERATURE REVIEW ....... ......... ....... ............ 4 RESEARCH DESIGN ............................. ........ 8 TEST INSTRUMENTATION ........................... 8 TEST MATERIAL .................................. 11 TEST PROCEDURE ................................. 14 STATISTICAL DESIGN .. ......... .... ......... ..... 15 DATA ANALYSIS AND RESULT ............................ 17 CONCLUSIONS ......................................... 22 APPENDICES OOOOOOOOOOOOOOO ......... OOOOOOOOOOOOOOOOOO 25 Appendix A. Pulse Weighing Method for Velocity Change ............................. 25 Appendix B. Trigger Device................. ..... 29 Appendix C. Shock Machine Calibration Table..... 36 Appendix D. Handling Environment................ 37 Appendix E. Testing Raw Data.................... 38 REFERENCES OOOOOOOOOOOOO... ...... 0.. ....... 00.0.00... 82 LIST OF FIGURES Figure Page 1. The complete test package ............... ............ l3 2. The total view of the shock machine system .......... 16 3. The total view of the drop tester .......... ......... 16 4. The relationship between drop height and velocity change ................... .............. 27 5. The correlation between shock machine drop height and free fall drop height ............ ........ 28 El. Operation of the trigger device ........ ............ 31 32. Top View of NESSBN quad timer .......... ........ .... 32 83. Programmable sequence ... ....... .. .................. 33 B4. Timing diagram ......... ......... . .................. 34 BS. Top view of logic circuit ............ .............. 35 ‘7 INTRODUCTION Mechanical damage is a common occurrence during distribution of packaged articles. During material handling operations, packages are often dropped, thrown, kicked and ‘ otherwise abused. They are also subjected to a variety of vehicle-induced impacts: starting, stopping, jolting, and other violent actions (1). However, it is generally agreed that, the most severe shocks likely to be encountered in shipping result from handling operation (2,3). These shocks result from dropping the package onto a floor, dock or platform. It is also known that the shocks of the largest amplitude occur when a package lands flat on a non-resilient horizontal surface (4). In order to reduce the incidence of mechanical failures of packaged articles, it is necessary to design packages to protect products from impacts, especially from flat drops since this kind of drop produce the most severe shock. In the design of protective packages, a major consideration is the physical environments which the packages will encounter. The most common way of specifying the environment is in terms of the probable height of 1 . free-fall drop (5). It is important to realize that the most relevant concept for characterizing an impact is its velocity change: since shock is a sudden change in velocity, and velocity change has been found to be an accurate way to characterize a large class of shock motions for engineering applications (6). In modern packaging laboratories, stateeof-the-art shock testing equipment has been used to simulate shocks which damage products in physical distribution. With a shock machine, however, there exists a fundamental problem: the lack of knowledge concerning the correlation between a shock machine drop height and an actual free fall drop height. Without understanding this correlation, any results obtained in shock testing are difficult to explain. Since drop height is one of the key factors that determines velocity change, it is reasonable to correlate shock machine drop height with free fall drop height based on the equivalent velocity change. Although modern shock machine has the capability to measure the velocity change it generates, free-fall velocity change has never been measured precisely, due to the fact that there was no existing instrument to perform this measurement. Therefore, a system for accurately measuring free-fall drop velocity change was developed as part of this research. 3 The purpose of this research is to accurately determine the correlation between free fall drop height and shock machine drop height based on the equivalent velocity change of the shock. The previous work of Goff, et, a1. (7) was used as a starting point. The following are the objectives of this research: (1) To measure and correlate the velocity change of free-fall drop height and shock machine drop height. This correlation is expected to be about 2.8. (2) To determine if cushioning inside the package affects the correlation. LITERATURE REVIEU Although much research has been done on the subject of shock testing, it was only after the presentation of Newton's theory (8) that velocity change was widely considered as one of the key elements in describing a product fragility. The purpose of this chapter is to review the historical development of this concept. In 1945, Mindlin (9) initiated the scientific approach to the Packaging Dynamics by investigating the dynamics of package cushioning. He conceptualized packages as a linear spring-mass system representing an element of the packed article which is susceptible to damage. He derived mathematical models to predict the maximum acceleration of the packaged article and the form of the acceleration-time relation. He also studied the potentially damaging effect of acceleration on the packaged article. In 1954, Kornhauser (10) proposed the damage "sensitivity" curve. Again, a mass-spring system was used to model a shock-resistant structure. When the mass-spring system is subjected to acceleration-time pulses of varying amplitude and duration, it was found that the minimum shock 4 5 values required to damage the system followed a curve. He called it the "sensitivity curve” which is defined by the velocity change and average acceleration of the shock pulse. Kornhauser began to appreciate the dependence of "damage" upon both velocity change and average acceleration. Later, in 1964, he applied the concept of the "sensitivity curve" to the study of both structure (steel, aluminum) and biological (mice, human) tolerance to shock (11). He plotted out the damage-sensitivity curves for the structure of steel, mice and the human body. The experimental data on human impact strength (supine position) showed that the criteria for damage are 20 g and 960 in/sec velocity change, both of which must be exceeded concurrently for damage to occur to a well-supported human in the supine position. In 1965, Pendered (12) further developed the concept of damage-sensitivity as a means of indicating the fragility of an item. In 1965, Newton (8) established fragility assessment theory and its test procedures, in which he introduced the concept of the Damage Boundary Curve. The concept implied that the fragility of a product could be characterized by a damage boundary, using the peak faired maximum acceleration and the velocity change of damaging shock pulse. Newton stated that damage would not occur unless both velocity change and peak faired acceleration of a shock pulse reached 6 certain values. Here, velocity change was presented as one of the key elements of the concept. In 1969 Goff and Pierce (13) presented a workable procedure to determine the damage boundary for several different items to be packaged. Damage boundary plots were developed for such products as television sets, refrigerators, alarm clocks, typewriters and several other products. It was shown that the determination of damage boundaries is both possible and practical. In 1977, ASTM (14) presented the completed procedure for the development of the damage boundary curve as in ASTM D 3332-77, "Standard Test Methods for Mechanical-Shock Fragility of Products, Using Shock Machines". The shock- pulse velocity change, in addition to shock pulse shape and shock-pulse maximum-faired acceleration, was included as one of the three parameters of the shock pulse required to determine the fragility of a product. In 1978, Cesari (15) studied the injury mechanisms of automobile side impact. Two tests were conducted in this study. The first test was carried out by allowing a car striking a stationary one with an angle of 75 degree at 40.5 kph impact speed, and the second test was conducted the same except that the impact speed was 49.7 kph. The velocity change of different parts of cars and of dummies were 7 - measured in the tests conducted. Here, the velocity change was used as the major parameter to indicate the severity of auto side impact. In 1976 Goff, Chatman, Imashimizu and Collins (7) investigated the correlation of free-fall drop height and shock machine drop height for equivalent velocity change. The velocity change of both machine drop and free-fall drop was analyzed by the pulse weighing method (Appendix A). The relationship between velocity change and drop height was represented by hand plotted curves, and no cushion was used. A correlation of 2.8 between shock machine height and free- fall height was estimated by comparing the curve slopes. As described above, the velocity change has been widely recognized as one of the basic elements in shock analysis. However, due to the previous unavailability of accurate instrumentation, the actual velocity change of free fall drop has never been measured, and thus the true correlation between shock machine height and free fall height had, until this research, remained unknown. RESEARCH DESIGN In order to achieve the goal of this study, the tests are designed to obtain accurate test data. The description of sophisticated test instrumentation used is presented in this chapter. The descriptions of test material, test procedure, and statistical design of the study are also addressed. I£§I_IN§IEEE§!IAIIQE A programmable shock machine system and a free-fall drop tester were the two major instruments employed to generate and measure the shock pulse. In addition, during the testing a special trigger device was developed to serve as an interface between the drop tester and the waveform analyzer which is part of programmable shock machine system. Descriptions of these instruments follows. (1) Programmable shock machine system An MTS 846.36 shock test system was used for these tests. The system was designed to have the capability to 8 9 perform a wide range of shock tests. It consists of three essential parts: the shock machine itself, an MTS model 466.10 waveform analyzer, and a TEXTRONIX 2213A 60 mhz oscilloscope. The test is performed by dropping the shock table onto a plastic programmer which consists of eight cylindrical plastic rods made of high strength thermoplastic material. These plastic rods are spaced to distribute the shock load evenly into the underside of the table. This plastic programmer produces half sine shock pulses with a duration of two milliseconds. This is a simulation of shocks encountered in free fall drop environments. A 3/16" thick sheet of high density felt is placed between the plastic programmer and the impacted underside of the shock table to smooth the onset of the pulses. The felt reduces the excitation of high frequency ringing or noise at the start of pulse. The microprocessor-based MTS Model 466.10 Waveform Analyzer is a device that samples an analog waveform, converts the sample values to a digital format, and determines the values of pertinent points along the waveform. It then presents the resulting data, such as change in velocity, in digital form on two multi-purpose displays. 10 The TEKTRONIX 2213A Oscilloscope is a dual-channel instrument that can be used to provide the visual feature of shock pulses. It features a bright, sharply defined trace on an 80 by 100 mm cathode ray tube (crt). Its range system supplies calibrated deflection factors from 2 mV per division to 5 V per division. The horizontal range provides calibrated sweep speeds from 0.5 sec per division to 50 ns per division. (2) Free Fall DrOp Tester The LANSMONT model PDT 56E Precision Drop Tester was also employed in these tests. This machine is designed to comply with ASTM D-775 Test Standard. It is equipped with a drop leaf pneumatic actuation system which prevents package rotation and insures repeatable results. A high velocity pneumatic system accelerates the drop leaf vertically downward at greater than the gravity. True vertical motion is obtained by means of two precision guides. The package is dropped on a 46" x 36" x 0.5" steel plate which is mounted in concrete. (3) Trigger device The waveform analyzer on the MTS shock machine system was also used to transfer the shock pulse into useful data. However, a trigger signal was required to initiate the ll analyzer an instant before impact. The MTS shock machine system uses a trigger flag and an optical sensor to generate this trigger signal.‘This signal consists of two short pulses with a duration of 0.15 ms separated by a time delay of from 0.417 ms to 41.7 ms. Both the trigger flag and the optical sensor are designed to be used only in the shock machine system. In order to make the waveform analyzer measure a shock pulse generated by the free-fall drop tester, it was necessary to develop a device. Therefore, as a significant part of this research, a device was developed to generate the required trigger signal (Appendix 2). T££T_MAT£BIAL The test package (Figure 1) consisted of four components: an instrumented wooden block, a piece of cushioning material placed on both the top and bottom of the block, and this assembly is packed into an outer corrugated paperboard container. (1) Instrumented wooden block A 10 pounds and 16 oz, 8 inches x 8 inches x 8 inches wooden block constructed of maple dieboard was used 12 throughout the testing. Four aluminum rods, each weighing 1 pound and 15 oz with length of 6 1/8 inches and diameter of 1 7/8 inches, were bolted into the block to simulate a heavy product which has total weight of 12 pounds and 1 oz. Four foam rods, each weighs 5/16 pound with length of 5 1/8 inches and diameter of 1 7/8 inches, were bolted in the block to simulate a light product which has total weight of 12 l/8 pounds. The block is instrumented with a KISTLER model 818 accelerometer mounted in its center to pick up the shock signals. The accelerometer has sensitivity of 10 millivolts per g. (2) Cushioning material Two types of cushioning material, Ethafoam* 220 with density of 2.2 pounds per cubic feet and Ethafoam HS 45 with density of 3.8 pounds per cubic feet, were chosen to be the media between wooden block and outer container. The cushion thickness variables were 1 inch and 2 inches. All cushion blocks used have same bearing area of 8 inches x 8 inches. (3) Outer container The containers were regular slotted containers made of zoo-pound C-flute corrugated paperboard. Due to two variables of cushion thickness, two different dimensions of * Ethafoam is a registered trade name of the Dow chemical Company for its polyethylene foam cushioning material 13 boxes were used, the inner dimensions are, 8 inches x 8 inches x 10 inches and 8 inches x 8 inches x 12 inches. /Corrugated Box Cushion ///////////////// ...................................................... ..... .“..'. ........ .......... 8x8x8in.Block a" ..... ....... ........... ...................................................... ///////////////// Figure 1. The complete test package 14 T££T_RBQ£EDQE§ The test consisted of two parts. (1) The shock machine test was designed to measure the velocity change of shock pulses produced at each -shock machine drop height. (2) The free-fall drop test was designed to measure the velocity change of shock pulse produced at each free-fall drop height. There was at least a one minute pause between each drop to allow for cushion recovery. (1) Shock machine The total view of the shock machine system is shown in figure 2. The instrumented package was placed on the shock table with a restraint fixture which does not contact the package but prevents it from falling off of the shock machine table. The machine was dropped five times at each height from 8" to 24" at increments of 1". The same cushion material was used throughout the test sequence. The shock signal that the test specimen received was measured by a accelerometer inside of wooden block. The signal was then sent to the waveform analyzer and oscilloscope via a KISTLER model 587 PIEZOTRON coupler. (2) Free-fall drop test 15 The total view of the drop tester is shown in figure 3. The package is dropped as flat as possible. Each test was replicated five times at each drop height from 20" to 50" at increments of 2”. The test procedure is similar to the shock machine test procedure except that the waveform analyzer was initiated by the trigger device developed for this research. Figure 9 shows a shock pulse generated in a 30" free-fall drop. filATIfiTIQAL_DE§I§N Two steps of statistical analysis were taken in this research. First, the correlation between drop height and velocity change of each sequence drop for both drop tester and shock machine was investigated. Second, the correlation between drop tester and shock machine drop height was derived through studying their predicted drop heights based on the same amount of velocity change at each level. MSTAT, a statistical computing program, was used to analyze the data in this research. Figure 2. The total view of the shock machine system Figure 3. The total view of the drop tester DATA ANALYSIS AND RESULTS The physical law of gravitation shows that the drop height can expressed as a function of the impact velocity: h = vZ/zg (1) Where h - the drop height v = impact velocity 9 a the gravitational constant In addition, the rebound velocity is described as a function of the impact velocity: v - e x v (2) r Where e = the value of the coefficient of restitution. The velocity change is defined as the sum of the absolute values of the impact and rebound velocities: V a v + v = (l+e)v (3) r Where V = the velocity change 17 18 It is reasonable to deduct that the drop height can be expressed as a function of velocity change. The following mathematical model is then established: h = f(V2) = av2 + bV + c (4) Where a, b, and c are the coefficients. By actually calculating with the experiment data, it was found that the coefficient a was not significant. The equation was then simplified as follow: h - f(V) - bV + c ' (5) or V f(h) = mh + n (5) where m = l/b n = 1/c The V is the average value of velocity change corresponding to each drop height. Since there are 8 simulated product configurations, 8 equations were built for both shock machine and drop tester by testing data (Appendix E). Following are the results of calculation. 19 Table 1. formulas for calculating the correlation between velocity change and drop height for shock machine and free fall drop tester configuration formula correlation probability f111 V=108.8+4.632h 0.998 0.000 m111 V=91.59+9.866h 0.999 0.000 £112 V=122.2+4.333h 0.994 0.000 m112 V=89.44+9.438h 0.999 0.000 £121 V=106.3+4.285h 0.999 0.000 m121 V=88.09+9.433h 0.999 0.000 f122 V=107.9+4.323h 0.998 0.000 m122 V=101.5+8.635h 0.999 0.000 £212 V=108.6+4.348h 0.998 0.000 m212 V-105.9+9.096h 0.999 0.000 £211 V8119.1+4.275h 0.998 0.000 m211 V8111.7+9.072h 0.995 0.000 £222 V8118.8+3.960h 0.998 0.000 m222 V=108.3+8.510h 0.999 0.000 £221 V=103.8+4.247h 0.998 0.000 m221 V=95.49+8.973h 1.000 0.000 where first figure represents the type of drop f a free fall m a shock machine second figure represents the type of product weight 1 = heavy weight 2 = light weight third figure represents the type of cushion 20 l = ethafoam 220 2 - ethafoam HS-45 forth figure represents the thickness of cushion 1:1" 2:20: Based on above equations, 6 velocity change values of 200, 220, 240, 260, 280, 300 were chosen for correlating shock machine and free fall drop heights. These two drop heights were then compared to obtain the correlation between them for each configuration Table 2. correlation of drop height between shock machine and drop tester based on equivalent velocity change. configuration formula correlation probability 111 H=2.14+0.459h 0.999 0.000 112 H33.46+0.459h 1.000 0.000 121 H-1.90+0.455h 0.999. 0.000 122 H=0.95+0.497h 0.999 0.000 212 H=0.29+0.478h 1.000 0.000 211 H=1.15+0.458h 0.999 0.000 222 H-1.23+0.465h 1.000 0.000 221 H-1.04+0.470h 0.998 0.000 21 Where H the drop height of shock machine 5‘ II the drop height of drop tester Above equations show that a strong correlation between the drop heights exists in 8 out of 8 cases, with the probability of null hypothesis 0 and the correlation coefficient close to l, regardless of the variable of cushion type, cushion thickness and product weight used in the research. Finally, a general equation is derived by comparing the expected shock machine drop height to every corresponding free fall drop height. As shown in (7) H = 1.31 + 0.474h (7) The above equation has the correlation coefficient of 0.984 and probability of null hypothesis of 0. This implies that free fall drop height can be represented by shock machine drop height with high confidence.. CONCLUSIONS The correlation between shock machine and free fall drop height for each simulated product configuration was first derived separately based on the equivalent velocity change each of them received. Then a general formula was formed to represent the correlation with consideration of effect of all configurations. It can be seen that both hypothesis 1 and hypothesis 2 were correct in this research. The research consisted of developing a device for triggering accurate measurement of free fall shock pulses. This device equipped the drop tester with a sophisticated analyzing instrument makes the tester more useful. The testing procedure developed to measure the free fall drop signal could be a valuable reference for setting industrial testing standards. During testing, it was observed that the testing data could be affected by the time between drops and the flatness of the drop. The longer the time, the smaller the value of velocity change and acceleration. The closer to a perfect flat drop, the larger the value of velocity change and do he“ 23 acceleration. When using a free fall drop tester, it is impossible to control rotational motions during the free fall; With a shock machine drop, this factor does not exist since the product can be placed flat on the shock table and remain flat through the impact. This is an advantage that a shock machine has over a free fall drop tester. It is important to realize that different shock machines may generate different velocity change at the same drop height. Therefore, a calibration table of the shock machine used is presented in appendix C. It should also be noted that since this investigation of the correlation was based on a simulated product configuration, the number of variables were limited. In order to extend the application value of this research, more work needs to be done to verify this correlation. Three possible research methods were proposed. The first is to study the effect of the product/cushion/box configuration on the shock pulse. Whether the cushion material is placed inside of the box or on the impact surface could make big differences in the testing results. The existence of the corrugated box should also be studied since corrugated board acts as a type of cushion. 24 The second area for future research is in the effect of cushion fatigue since cushion material could be permanently deformed after certain a number of drops. Third, the type of impact surface on the free fall drop tester should also be studied since steel surfaces rarely exist in any distribution environment. Perhaps the surface should be designed to match the expected surfaces such as wood or cement. Based on this research, it can be seen that there does exist a correlation between shock machine drop height and free fall drop height. Once the correlation is defined, the estimated free fall drop height (Appendix D) in a distribution environment can be converted to shock machine drop height. However, this research addressed only the correlation of velocity change, since velocity change has been found to correlate with actual damage. APPENDICES APPENDIX A PULSE WEIGHING METHOD FOR VELOCITY CHANGE This method can be used to estimate the velocity change of shock pulse since velocity change is represented by the area under shock pulse. The shock pulse from oscilloscope screen is first photocopied to a known density piece of paper, and then the paper is cut into the size of the shock pulse whose weight will be determined. By dividing the weight by the sheet density of the paper, we obtained the shock pulse area which can be converted into velocity change. The formula for calculation is as follow: V = (C x W x M x D)/(UA xSD) Where V i The velocity change of shock pulse (in/sec) C 8 Conversion factor (386.4 in/sec/gram) W The weight of shock pulse shape paper (gram) M = Magnitude per unit division (g’s) D = Duration per unit division (sec) UA = the unit area of paper (in2) SD = The sheet density of paper (gram/inz) 25 26 In 1976 Goff used this method to measure the area under the shock pulse in order to study the correlation between shock machine drop height and free fall drop height. He intended to compare the drop heights based on the equivalent velocity change that bare shock table generated with that induced by a drop tester on a bare surface. It was found that the shock pulse obtained was difficult to be analyzed. The cushion was then placed on the table to smooth out pulse. The relationship between velocity change and drop height was represented by the curve (Figure 4). The coefficient of 2.8 between shock machine drop height and free-fall drop height was obtained by analyzing the curve slopes as shown in figure 5. Velocity Change (In/sec) Aoo woo .oo 2:: Baboon 8 can 19035... >< Tswana o: 9.50: moo Too no: ‘ A drop height and velocity change Figure 4. The relationship between can :22: 23.. O in 5. 95.83 x d 5. 9.582: D m 5., 2582: Free Fall Drop Height (in.) 28 Shock Machine Drop Height vs Free Fall Drop Height (to product the same velocity change) 60 55- 45 I I 40 35- I I 30 1 25 20 ‘firl 15 ' I 1 o elllnlrlilLLLJLLi 0 2 4 6 81012141618 Shock Machine Drop Height (in.) . O 1/2 in. Ethafoam Figure 5. The correlation between shock machine . drop height and free fall drop height x 1 in. Ethafoam El 2 in. Ethafoam APPENDIX E Trigger Device The operation of the trigger device is described by a system block diagram, as shown in Figure Bl. The basic component in this device is an integrated circuit of type NESS8N quad timer. Figure 82 is the top view of this circuit. This timing circuit is capable of producing accurate time delays. The delay time is determined by the resistor and capacitor network, and can be calculated by the following equation: T = 1.1 x R x C Where T = delay time (second) R = resistance (ohm) C = capacitance (farad) Figure B3 shows the programmable sequence of the device. The NESS8N is configured as four timers, T1,-T2, T3, T4. The delay time of T1 timer range, from 0.33 seconds to 0.55 seconds, is determined by a potentiometer R1 and a capacitor C1. This delay time is the time required for a package to free fall from 20" to 50". Each of the T3 and T4 timer is designed to produce a pulse with a duration of 0.15 ms. These two pulses are separated by a time delay range from 0.385 ms to 38.5 ms generated by RZ-Cz. Figure B4 is the timing diagram. In addition, a logic circuit of type 29 3O SN54LS32N with logic function of "OR" is used in conjunction with the IC to finalize the output signal, so that for every high-to-low signal, the trigger device generates a pair of pulses. Figure BS is the top view of this logic circuit. 31 ooa>un uuwmqus 0:H mo coaunuuco “an unawwm ozc rum... :6”... unoao.haamauoz I sz coco zaaeauoz a dam ll C . m n \im .22; no.0 >m H 00> 32 output .1 : } _1_6_ output timing _2_. : : 1_5timin9 A l l D trigger _3_ . . 1_4tri996f ' ... _ .J L. _. ..., control A. E reset V005- lg ground trigger _5_" " _: :— - _fltrigger . . l l - - timing 1 B : : C JQtImIng OUtpUt _8_ I I EDI-”pl“ l J Figure BZ. Top Viw. of NESSBN Quad Timer mucusuum uanmEEmuwoum .mm unamam a a some ".0 u.on.o 5:" "inert: H... CxSHE 5.4.,“in .5331 ms Hi . 52... I «Hi a one F H F ..I .011 .o ~oil _olfi. a. l 59.. 59:0 # N ...—d- b v... .mlpl. a... 2 n. ._. c. IA «83 u p e o 4 I e I J ... 3 s on... .3 TIL emu — = Is on... I. . M a _. ... a ... a .z ... HY ...KK“ fi I 34 )t ---—> t .0.” WI 91: V...“ 0 z----------- VbA 9t Va’i‘ """flo. 9t VGA z—----- I I I I I" I, I. '1 '2 at Vow"N z------—--- D.=0.33 —0.55 See 2.5—5.0 V Z 150 mi 0385— 38.5ms Figure B4. Timing Diagram 35 uaauuao uuwoa we aufi> doe..mm ouomfim 20 >N mu (N >— up 5 0 m v a N 0 Op .... N... 9. xm (m an >V (V on (p P 3. 00> APPENDIX C SHOCK MACHINE CALIBRATION VALUES 2 ms Half-Sine Programmers (Bare Table) Drop Height V G (in) (in/sec) (9’s) 4 83 186 5 94 212 6 102 238 7 110 256 8 117 274 9 123 291 10 130 307 11 135 320 12 141 334 13 147 349 14 153 359 15 157 371 16 165 385 17 170 394 18 174 402 19 180 412 20 184 422 21 190 436 22 194 445 23 200 453 24 204 465 APPENDIX D HANDLING ENVIRONMENT The most common way of specifying the handling environment is in terms of free-fall drops. Ostrem's (2) study on the common carrier environment found that the drop height is generally related to the product's weight or size. It is noticed that as the package becomes larger, the expected drop height decreases, due to the fact that the more cumbersome a package becomes the less likely it is to be dropped from a great height. A reference chart was then generated to reflect typical drop heights for products of various weight. Typical Drop Height Package Weight Greatest Dimension Drop Height (pounds) (inches) (inches) 0-20 48 42 20-50 36 36 50-100 48 24 100-150 60 21 150-200 60 18 200+ 72 12 APPENDIX E (H: Drop Height. V: Velocity Change. C: Acceleration Level. D: Shock Duration. X: Displacement) 1. Test Data in Free Fall Drop Table 1. Aluminum weight with 1" thick ethafoam 220 (natural frequency - 45 Hz) 0.41 0.39 0.39 0.38 0.41 0.32 0.35 0.35 0.35 0.35 0.35 0.35 0.35 H V G D [in] [in/sec] [9's] {ms} 20 193.7 67.3 11.63 197.6 70.7 11.4 200.4 73.2 11.71 201.6 74.3 11.78 200.0 73.8 11.77- Average 198.66 71.9 11.77 22 208.1 76.7 11.67 209.4 77.9 11.51 211.5 79.1 11.48 211.2 79.6 11.82 209.9 76.6 11.59 Average 210.12 77.98 11.59 24 219.9 85.7 11.44 215.3 80.4 12.01 218.6 84.6 11.75 217.4 82.1 11.94 218.1 83.3 12.05 Average 217.86 83.22 11.84 26 226.6 85 12.13 224.6 85.0 12.13 226.6 83.1 12.44 224.3 84.0 12.28 38 0.35 Average 28 Average 30 Average 32 Average 34 Average 36 Average 38 Average 40 226.6 226.14 237.8 238.6 238.2 238.7 239.8 238.62 249.8 248 248.8 245.0 249.0 248.12 260.9 260.7 260.9 259.1 258.6 260.04 270.6 271.4 271.2 270.2 271.8 271.04 276.9 278.2 280.9 278.7 278.5 278.64 287.6 288 288 288.5 289 288.22 297.1 295.4 39 82.9 84.14 93.9 94.8 95.1 95.9 97.4 95.42 104.4 100.9 99.5 99.6 98.5 100.56 108 107.5 109.9 109.1 107.7 108.44 115.7 117.3 117.3 117.3 116.9 116.9 123.1 124 124.4 124 123 123.7 131.3 133.4 132.5 133.3 132.5 132.6 142.6 138.3 12.67 12.33 12.09 12.13 12.17 11.98 12.01 12.08 11.82 11.9 11.98 11.86 12.05 11.92 11.78 11.71 11.63 11.4 11.59 11.62 11.4 11.4 11.4 11.24 11.28 11.34 . 11.05 11.24 11.17 10.9 11.17 11.106 10.59 10.82 10.78 10.67 10.71 10.71 10.59 10.55 00000 C 00000 0 00000 0 00000 0 00000 O O 0. 0. 0. .36 .35 .35 .35 .35 .35 .35 .35 .33 .34 .34 .34 .34 .34 .34 .33 .34 34 .34 .34 .33 .34 .34 .33 .34 .34 32 .33 .33 .33 32 .32 .32 .32 32 32 32 .32 .31 .31 Average 42 Average 44 Average 46 Average 48 Average 50 Average 296.6 297.1 295.5 296.34 304.6 304.3 304 303.8 301.7 303.18 310.8 311.1 312.1 312.8 313.8 312.12 322.1 321.8 321.6 323.3 321.8 322.12 325.7 327.4 329.8 330 330.3 328.64 336.3 334.9 333.1 334.5 337.7 335.3 40 143 141.9 139 140.96 151.9 147.7 148.9 149.7 145 148.64 152.3 154.7 158.2 157.9 158.2 156.26 172.1 167.6 168.5 169.5 171.1 169.76 174.6 178.9 179.3 182.4 178.1 178.66 190.6 182.8 179.3 182.8 188.7 184.84 10.51 10.47 10.59 10.52 10.4 10.32 10.32 10.36 10.28 10.34 10.09 10.13 10.13 10.2 10.05 10.12 9.86 10.05 9.94 10.01 9.74 9.92 9.67 9.63 9.63 9.78 9.67 9.67 9.28 9.74 9.78 9.7 9.43 9.58 00000 0 00000 0 00000 0 00000 0 00000 O 000 O .31 .31 .31 .31 .31 .31 .31 .30 .30 .30 .30 .31‘ .31 .32 .31 .31 .31 31 .31 .31 .31 .31 .31 .31 .30 31 .31 .31 .31 .31 .30 .30 .28 Table 2. Aluminum weight with 2" thick ethafoam 220 (natural frequency = 38 Hz) Average 22 Average 24 Average 26 Average 28 Average 30 199.1 201.7 203.0 202.3 201.8 201.58 211.0 212.6 214.0 215.5 214.0 213.43 223.3 223.9 222.8 224.9 223.9 223.76 235.2 234.3 235.4 236.6 236.0 235.5 246.4 245.4 245.9 244.1 246.9 245.74 254.4 255.6 256.6 258.7 255.2 62.72 65.3 65.9 65.4 65.6 65.6 65.56 68.2 68.0 67.1 66.6 67.7 67.52 71.3 70.3 70.5 70.1 69.3 70.3 72.8 71.7 71.3 71.3 71.7 71.76 74.9 74.7 74.7 74.9 74.0 15.44 15.29 15.17 15.1 15.17 15.48 0.37 0.38 0.37 0.39 0.38 0.37 0.38 0.39 0.39 0.39 0.38 0.38 0.38 0.38 0.38 0.38 0.40 0.37 0.42 0.40 0.39 0.37 0.37 0.36 0.39 Average 32 Average 34 Average 36 Average 38 Average 40 Average 42 Average 44 256.1 263.3 266.2 264.5 256.3 263.8 264.62 271.5 272.4 273.3 273.4 272.2 272.56 278.6 281.1 282.9 282.2 280.6 281.08 286.9 286.7 285.9 288.5 290.3 '287.66 295.1 294.8 295.3 296.8 298.4 296.08 303.1 299,4 303.7 305.2 304.8 303.24 311.7 312.6 311.6 310.4 42 74.64 76.3 77.56 77.1 77.3 76.2 76.88 78.7 77.5 78.7 79.4 78.4 78.54 80.7 82.9 82.2 82.0 82.9 82.14 84.2 84.2 82.9 84.5 84.3 84.3 87.6 84.5 85.7 86.4 86.4 86.12 90.3 87.7 89.9 90.1 90.0 89.6 92.6 92.6 92.5 92.7 15.24 15.63 15.48 15.60 15.44 15.43 15.52 15.41 15.83 15.79 15.63 15.75 15.69 15.79 15.36 15.4 15.56 15.44 15.51 15.44 15.6 15.75 15.44 15.53 15.53 15.52 15.67 15.75 15.71 15.75 15.68 15.4 15.71 15.63 15.67 15.71 15.62 15.52 15.56 15.67 15.63 0.38 0.37 0.38 0.37 0.37 0.37 0.38 0.38 0.38 0.38 0.37 0.36 0.37 0.37 0.38 0.37 0.37 0.38 0.36 0.37 0.36 0.38 0.39 0.37 0.37 0.36 0.36 0.37 0.38 0.37 0.36 0.36 0.36 0.38 Average 46 Average 48 Average 50 Average Table 3. Aluminum weight with 1" thick ethafoam HS-45 (natural frequency = 58 Hz) 312.5 311.76 317.4 319.0 317.7 318.5 319.7 318.46 322.8 326.9 325.8 324.1 324.7 324.86 333.5 337.3 336.0 336.7 333.1 335.32 43 92.7 92.62 95.7 94.8 95.0 93.8 93.8 94.62 96.1 97.3 97.3 96.9 97.3 96.98 100.5 102.2 102.1 103.1 102.5 102.08 15.63 15.6 15.48 15.33 15.13 15.63 15.75 15.56 15.48 15.63 15.56 15.56 15.60 15.57 15.63 15.44 15.48 15.29 15.4 15.45 0.37 0.38 0.38 0.37 0.38 0.39 0.38 0.39 0.39 0.39 0.38 0.38 0.38 0.39 0.37 Average 22 185.1 187.8 189.5 190.5 191.4 188.86 198.8 197.5 197.6 196.8 198.3 92.7 88.6 88.6 89.9 91.0 8.87 9.09 9.26 9.67 9.51 9.79 Average 24 Average 26 Average 28 Average 30 Average 32 Average 34 Average 36 197.8 208.1 209.7 211.0 210.2 209.5 209.7 216.6 218.5 220.7 221.0 220.3 218.82 226.5 226.3 225.5 227.5 229.1 226.98 234.4 238.2 236.1 236.1 239.3 236.8 243.5 247.8 247.0 243.7 242.5 244.2 252.8 252.0 256.8 256.9 256.8 255.06 261.1 259.4 260.2 259.4 44 90.16 93.7 95.9 97.1 93.9 93.9 95.48 99.8 98.6 99.2 102.6 99.7 99.98 103.3 104.4 106.3 106.8 104.1 105 105.5 109.0 109.1 111.3 110.2 109.2 114.4 115.7 114.6 114.6 117.8 115.42 121.7 123.9 122.8 124.1 119.5 122.4 126.3 127.4 127.7 125.4 9.67 9.63 9.67 10.05 10.05 9.74 9.7 9.59 9.97 9.94 10.09 9.86 10.17 10.28 10.32 10.09 10.28 10.2 10.28 10.05 10.28 10.17 9.86 10.13 10.4 10.90 10.20 '10.44 10.01 10.39 10.09 9.55 10.01 10.01 10.01 9.93 9.47 10.24 10.20 10.01 0.27 0.27 0.29 0.29 0.31 0.31 0.30 0.29 0.29 0.30 0.31 0.31 0.32 0.30 0.29 0.31 0.29 0.29 0.30 0.32 0.30 0.28 0.30 0.30 0.31 0.30 0.29 0.28 0.28 0.28 0.28 0.30 0.30 0.30 0.29 Average 38 Average 40 Average 42 Average 44 Average 46 Average 48 Average 50 262.7 260.56 271.2 268.1 266.8 258.0 271.6 267.14 278.1 282.5 273.0 281.8 281.4 279.36 287.2 290.2 288.5 290.4 290.1 289.28 294.3 297.0 295.4 292.5 293.7 294.58 303.0 305.7 306.3 299.6 302.4 303.4 309.7 310.3 314.1 310.7 312.6 311.48 315.5 310.4 45 125.4 126.44 132.4 129.5 127.4 130.2 131.2 130.12 137.1 146.2 132.7 142.8 142.7 140.3 140.6 150.9 149.7 148.8 148.24 148.24 153.8 159.2 157.2 158.5 150.0 155.14 161.7 163.0 169.6 164.2 161.4 164.04 173.0 169.9 173.3 175.3 164.1 171.12 179.3 173.1 10.13 101.01 9.32 9.95 9.90 9.94 9.94 9.64 9.74 9.55 9.44 9.63 9.40 9.54 9.59 9.40 9.51 9.47 9.34 9.48 9.09 9.01 9.29 9.13 9.28 9.12 8.86 9.20 9.20 8.93 9.09 9.06 8.90 8.93 9.05 8.86 9.16 8.89 8.86 8.82 0.27 0.30 0.30 0.27 0.27 0.28 0.27 0.30' 0.35 0.26 0.28 0.26 0.27 0.28 0.29 0.27 0.26 0.29 0.29 0.30 0.28 0.29 0.25 0.27 0.30 0.28 0.27 0.28 0.27 0.27 0.28 Average 316.2 321.0 319.3 316.48 46 177.0 174.6 173.9 175.7 8.97 9.01 8.78 8.89 0.26 0.26 0.26 Table 4. Aluminum weight with 2’ thick ethafoam HS-45 (natural frequency = 55 Hz) Average 22 Average 24 Average 26 Average 28 183.6 185.8 189.4 190.8 191.5 192.3 188.9 198.3 201.6 201.5 211.0 199.7 202.42 208.9 208.4 211.2 211.0 212.3 210.36 220.6 219.9 221.2 221.0 223.2 221.18 230.7 231.1 229.4 82.0 82.6 82.0 11.48 11.78 11.78 11.78 11.82 11.67 11.77 11.71 11.82 12.21 0.27 0.26 0.31 0.30 0.31 0.30 0.30 0.31 0.28 0.33 0.29 0.30 0.30 0.30 0.29 0.30 0.29 0.30 0.29 0.29 0.29 0.30 0.31 Average 30 Average 32 Average 34 Average 36 Average 38 Average 40 Average 42 228.6 227.7 229.5 236.1 239.7 239.0 241.2 240.8 239.36 249.2 248.6 247.8 248.9 250.7 249 259.0 257.5 255.7 256.6 256.1 256.98 261.8 265.7 , 265.8 267.4 266.3 265.4 271.2 273.7 274.5 276.4 277.6 274.7 283.5 282.7 280.8 282.2 281.9 282.22 292.0 47 80.9 80.3 81.56 82.6 83.8 82.0 83.2 83.8 83.08 86.1 87.3 86.1 87.3 86.7 86.7 89.6 88.5 85.0 88.5 87.9 87.9 89.6 90.2 91.4 90.8 90.8 90.56 92.0 92.0 93.2 93.6 93.7 92.9 96.7 96.7 94.9 95.5 95.5 95.86 98.4 12.32 12.44 12.1 12.09 12.4 12.25 12.40 12.28 12.28 12.71 12.55 12.67 12.44 12.67 12.61 12.63 12.71 12.90 12.63 12.75 12.72 12.71 12.86 12.96 12.94 12.90 12.87 13.13 13.09 12.90 13.21 13.17 13.1 13.13 13.17 13.17 13.21 13.09 13.15 13.25 Average 44 Average 46 Average 48 Average 50 Average Table 5. Aluminum weight with 2" thick ethafoam 220 (natural frequency = 49) 291.8 292.0 289.6 286.1 290.3 296.7 299.2 299.9 299.3 293.9 297.8 303.1 303.6 303.2 306.8 308.4 305.02 312.0 314.1 311.4 309.0 314.2 312.14 322.7 323.2 322.1 323.3 318.8 322.02 48 99.0 99.0 97.9 95.5 97.96 100.2 100.8 102.0 100.8 97.9 100.34 102.0 103.1 102.5 102.5 103.1 102.64 106.5 108.4 106.1 103.7 106.1 106.16 110.7 109.6 109.6 110.2 107.8 109.58 13.25 13.36 13.40 13.59 13.37 13.13 13.13 13.32 13.40 13.86 13.42 13.44 13.32 13.25 13.44 13.52 13.39 13.44 13.32 13.36 13.71 13.32 13.44 13.32 13.40 13.40 13.44 13.4 0.32 0.33 0.33 0.32 0.31 0.32 0.31 0.34 0.35 0.32 0.31 0.30 0.32 0.39 0.34 0.33 Average 22 Average 24 Average 26 Average 28 Average 30 Average 32 Average 191.2 190.8 190.6 187.8 190.5 201.9 203.5 204.5 203.4 203.5 203.36 211.0 212.9 214.5 215.0 213.6 213.4 224.0 223.6 220.6 218.9 219.2 221.26 231.1 233.7 234.9 233.2 231.0 232.78 237.4 239.1 242.1 242.8 243.4 240.96 251.6 249.6 249.2 247.9 244.8 248.62 49 76.2 75.1 75.1 73.8 75.52 79.5 79.3 78.6 77.4 77.1 78.38 79.4 80.4 81.8 80.9 79.3 80.36 84.0 82.0 78.2 78.1 78.1 80.08 86.3 86.7 85.5 84.4 79.7 84.52 84.0 84.4 85.5 87.5 87.9 85.86 91.1 87.9 87.7 87.9 85.5 88.02 10.47 10.55 10.59 11.17 10.58 10.51 10.74 10.74 11.07 10.94 10.77 11.13 11.01 11.05 11.17 11.28 11.13 11.9 11.36 11.63 11.82 11.71 11.68 11.51 11.40 11.77 11.78 11.94 ' 11.67 12.13 11.90 11.82 11.94 12.01 11.96 12.01 12.28 12.36 12.63 12.32 12.32 0.31 0.33 0.32 0.34 0.31 0.32 0.32 0.33 0.33 0.34 0.32 0.32 0.32 0.33 0.32 0.33 0.33 0.34 0.34 0.32 0.31 0.30 0.32 0.33 0.33 0.32 0.32 0.31 0.33 0.30 0.32 0.32 0.33 0.33 34 Average 36 Average 38 Average 40 Average 42 Average 44 Average 46 257.0 259.0 261.4 261.7 254.9 258.8 258.3 262.8 264.8 268.0 260.8 262.94 272.9 277.3 278.2 271.0 269.3 273.74 282.0 284.6 286.6 286.4 283.6 284.64 295.1 297.1 294.2 296.3 290.8 294.7 297.9 300.5 303.4 300.8 303.6 301.24 308.6 307.1 307.7 310.9 310.1 50 91.4 91.3 91.1 90.2 85.5 89.9 88.6 89.1 88.9 91.4 87.6 89.12 92.0 92.6 93.7 90.3 90.3 91.92 94.9 95.8 102.7 94.9 92.6 96.18 94.6 96.1 100.0 102.2 98.1 98.2 103.1 104.3 104.9 104.3 105.2 104.36 108.7 108.1 107.7 106.6 108.3 12.32 12.21 12.36 12.55 12.98 12.48 12.67 12.59 12.67 12.75 12.94 12.72 12.86 12.81 13.09 13.09 12.98 12.98 13.17 13.05 13.36 13.21 13.4 13.24 13.40 13.44 13.13 13.55 13.58 13.42 13.67 13.59 13.52 13.67 13.82 13.65 13.75 13.98 13.94 13.75 13.98 .31 .30 .30 .30 .32 00000 0.32 0.30 0.31 0.31 0.30 0.32 0.31 0.31 0.30 0.33 0.32 0.32 0.31 0.31 0.29 0.29 0.31 0.30 0.31 0.40 0.32 0.31 0.31 0.31 0.30 0.29 0.30 0.29 0.30 0.30 0.31 0.31 0.29 0.30 Average 48 Average 50 Average Table 6. Aluminum wieght with 1” thick ethafoam 220 (natural frequency = 52) 308.88 316.9 313.8 315.5 316.3 317.0 315.9 321.2 322.7 319.0 321.1 318.1 320.4 51 107.88 113.7 112.5 112.1 112.2 110.2 112.14 114.8 114.8 112.5 112.5 114.8 113.88 13.88 13.94 14.06 14.09 13.94 13.79 13.96 14.06 14.13 14.25 13.86 14.25 14.11 0 .30 .29 .31 .30 .30 .30 00000 0.30 0.30 0.30 0.31 0.32 0.33 Average 22 Average 24 196.6 196.6 198.9 202.5 202.9 199.5 207.9 210.9 211.1 212.5 214.1 211.3 224.0 225.4 225.4 224.7 225.2 95.38 102.0 103.2 102.0 102.0 102.0 9.67 9.59 9.55 9.70 9.7 9.78 0.29 0.28 0.30 0.28 0.28 0.27 0.27 0.27 0.27 0.30 Average 26 Average 28 Average 30 Average 32 Average 34 Average 36 Average 38 224.94 228.1 232.0 230.4 233.8 234.5 231.76 241.8 239.5 237.7 237.7 236.0 238.54 245.6 248.9 249.9 249.9 246.5 248.16 252.1 254.2 255.8 259.5 257.4 255.8 260.1 262.8 262.6 262.9 268.2 263.32 275.7 272.3 273.2 276.4 278.0 275.12 282.5 281.7 283.8 52 102.24 102.0 105.1 102.7 106.2 105.0 104.2 109.0 103.9 102.8 104.3 103.0 104.6 108.7 112.1 113.2 113.2 110.2 109.74 111.3 113.2 115.6 118.2 116.3 114.92 118.4 120.7 121.5 120.7 124.3 121.12 130.1 128.8 128.9 131.2 132.4 130.28 136.8 136.8 137.2 9.97 9.82 9.97 9.82 9.97 9.91 9.94 10.05 10.17 10.24 10.28 10.14 10.13 10.17 10.09 9.94 10.13 10.09 10.32 10.28 10.13 12.05 10.09 10.17 10.09 10.01 10.05 9.97 10.05 10.03 9.74 9.90 9.94 9.82 9.86 9.85 9.63 9.82 9.82 0.30 0.25 0.29 0.28 0.28 0.28 0.29 0.28 0.29 0.31 0.31 0.30 0.31 0.29 0.29 0.29 0.30 0.30 0.32 0.30 0.29 0.29 0.32 0.30 0.31 0.30 0.31 0.30 0.30 0.30 0.29 0.30 0.30 0.29 0.29 0.29 0.29 0.29 0.29 Average 40 Average 42 Average 44 Average 46 Average 48 Average 50 Average 285.6 287.2 284.16 290.3 291.6 291.6 295.3 296.6 293.08 301.2 298.8 298.4 298.6 299.0 299.2 306.3 310.2 310.0 308.2 305.2 308.0 314.4 314.3 316.9 318.3 318.2 316.42 323.1 321.9 322.6 319.8 320.9 321.66 327.9 333.7 329.2 326.3 327.7 329.0 53 138.3 139.5 137.54 143.0 143.0 144.0 146.5 148.4 144.98 152.3 151.2 151.2 150.0 150.0 150.94 155.9 160.5 159.4 158.9 157.3 158.4 164.1 164.4 168.3 168.8 169.6 167.04 172.0 172.3 172.3 171.6 170.7 171.78 175.8 183.7 179.3 179.1 177.7 179.12 9.67 9.70 9.73 9.63 9.74 9.67 9.59 9.59 9.64 9.36 9.43 9.43 9.43 9.55 9.37 9.24 9.28 9.24 9.24 9.28 9.25 9.13 9.16 9.16 9.13 9.13 9.14 8.97 8.97 8.93 8.97 9.01 8.97 8.86 8.93 8.86 8.86 8.86 8.87 0.29 0.29 0.28 0.28 0.28 0.28 0.29 0.29 0.29 0.29 0.29 0.28 0.28 0.28 0.28 0.29 0.29 0.28 0.27 0.28 0.28 0.28 0.30 0.27 0.72 0.27 0.28 0.28 0.27 0.27 0.27 0.27 0.28 54 Table 7. Foam weight with 2" thick ethafoam HS-45 (natural frequency = 57 Hz) H V G D X [In] tin/sec] [9's] [ms] [In] 20 195.0 92.6 8.78 0.26 195.3 93.6 8.74 0.25 191.5 89.1 8.93 0.27 194.1 91.4 8.86 0.27 195.1 91.4 8.90 0.27 Average 194.2 91.62 8.84 0.26 22 200.8 92.3 9.20 0.29 204.4 95.7 8.97 0.27 206.0 95.7 9.01 0.25 205.0 93.7 9.09 0.27 204.1 94.5 9.16 0.27 Average 204.06 94.38 9.09 0.27 24 208.7 95.8 9.28 0.30 210.3 97.1 9.28 0.29 212.1 97.3 9.28 0.29 212.5 98.0 9.24 0.29 213.7 97.3 9.20 0.29 Average 211.46 97.1 9.26 0.29 26 220.0 102.0 9.20 0.29 224.8 103.1 9.05 0.25 224.1 102.0 9.28 0.27 221.7 100.6 9.40 0.28 224.9 101.7 9.28 0.26 Average 223.1 101.88 9.24 0.27 28 227.0 102.8 9.59 0.30 232.8 103.9 9.40 0.28 231.8 104.0 9.40 0.27 232.7 104.3 9.40 0.26 229.1 102.0 9.63 0.29 Average 230.28 103.4 9.48 0.29 30 239.2 106.5 9.47 0.27 Average 32 Average 34 Average 36 Average 38 Average 40 Average 42 Average 238.4 238.7 241.4 242.7 240.08 248.7 248.8 248.3 249.6 249.4 248.96 257.3 258.7 258.4 256.7 256.4 257.5 260.3 261.0 262.6 264.1 262.7 262.14 267.7 264.8 269.0 272.4 272.7 269.32 275.5 276.4 278.1 279.1 279.6 277.74 286.8 285.5 284.0 285.2 281.9 284.68 55 105.6 105.0 105.0 104.3 105.26 106.6 107.8 106.6 107.5 107.5 107.2 110.2 111.3 110.9 109.0 109.0 100.08 111.0 109.7 111.3 111.3 111.3 110.92 113.7 110.2 112.1 113.7 111.3 112.2 114.4 113.7 116.0 116.0 116.0 115.22 120.3 118.1 114.8 118.4 114.4 115.94 9.59 9.74 9.67 9.7 9.63 9.82 9.82 9.86 9.94 10.05 9.9 9.97 10.01 9.97 10.05 10.05 10.01 10.20 10.28 10.28 10.17 10.13 10.21 10.40 10.63 10.44 10.32 10.40 10.44 10.59 10.51 10.51 10.47 10.47 10.51 10.42 10.51 10.74 10.59 10.86 10.62 0.29 0.29 0.26 0.26 0.27 0.27 0.28 0.27 0.28 0.26 0.26 0.26 0.28 0.29 0.27 0.29 0.30 0.30 0.28 0.28 0.30 0.32 0.30 0.28 0.28 0.31 0.30 0.31 0.30 0.30 0.30 0.27 0.28 0.29 0.30 0.32 44 Average 46 Average 48 Average 50 Average Table 8. Foam weight with 1" thick ehtafoam HS-45 (natural frequency = 71 Hz) 293.1 293.2 290.7 291.7 291.4 292.02 297.2 299.9 299.8 301.9 299.8 299.72 304.9 307.4 308.8 309.0 309.0 307.82 313.4 315.4 315.6 315.5 314.5 314.88 56 118.4 118.1 118.1 116.9 116.7 117.64 119.5 120.3 120.7 119.5 118.4 119.68 122.6 124.1 120.7 121.9 122.6 122.38 125.4 126.1 126.6 123.9 125.1 125.42 10.67 10.67 10.71 10.90 10.97 10.784 10.86 10.82 10.82 10.74 10.86 10.82 11.05 10.94 10.90 11.05 10.94 10.98 10.97 11.01 11.01 11.13 11.01 11.03 0.28 0.27 0.28 0.29 0.30 0.28 0.30 0.29 0.29 0.27 0.29 0.30 0.29 0.27 0.28 0.28 0.30 0.28 0.29 0.28 0.29 Average 181.9 183.0 183.1 183.1 185.1 182.84 114.64 22 Average 24 Average 26 Average 28 Average 30 Average 32 Average 34 188.1 197.2 195.9 193.5 186.9 192.32 203.3 207.9 209.1 209.9 208.8 207.8 211.2 214.7 219.3 219.3 218.1 216.52 222.6 223.8 227.9 228.2 224.2 25.34 232.4 231.7 231.0 232.9 233.5 232.3 241.3 241.6 241.4 242.1 241.3 241.54 248.5 251.9 253.5 252.5 252.1 57 111.3 114.8 115.9 113.4 106.1 116.08 120.1 122.6 119.6 118.9 118.4 119.92 116.6 119.5 123.0 122.5 120.7 120.46 122.3 121.9 125.4 124.8 121.9 123.26 127.7 123.6 123.6 126.0 127.4 125.66 132.4 127.7 130.7 131.8 131.2 130.76 135.3 135.3 138.0 137.5 135.3 7.51 6.97 7.32 7.47 7.93 7.44 7.35 7.16 7.39 7.39 7.51 7.97 7.78 7.55 7.62 7.70 7.53 7.97 7.97 7.74 7.82 8.13 8.01 8.13 8.13 8.05 8.13 8.09 8.09 8.28 8.16 8.16 8.20 8.18 8.20 8.13 8.09 8.13 8.32 0.27 0.23 0.25 0.27 0.28 0.26 0.23 0.22 0.23 0.24 0.24 0.27 0.26 0.23 0.23 0.24 0.25 0.27 0.26 0.23 0.23 0.26 0.25 0.25 0.25 0.26 0.25 0.26 0.25 0.25 0.24 0.25 0.26 0.26 0.26 0.24 0.24 0.25 0.25 Average 36 Average 38 Average 40 Average 42 Average 44 Average 46 Average 48 251.66 254.1 258.9 261.3 260.7 261.5 259.3 266.1 265.4 268.8 268.3 269.6 267.74 276.2 275.2 274.0 273.2 275.7 274.86 282.8 283.2 280.5 280.0 282.2 281.74 290.9 288.6 289.2 288.1 289.0 289.16 293.4 299.2 297.9 298.1 297.0 297.12 303.4 305.9 306.1 304.0 58 136.32 136.5 141.8 142.8 141.6 141.2 140.78 144.1 143.6 145.3 145.9 143.0 144.38 148.5 148.2 148.0 145.9 147.7 147.66 153.5 154.7 153.4 154.7 153.2 153.9 158.8 158.6 158.2 158.2 158.8 158.52 161.7 168.8 167.0 167.0 166.1 166.12 179.9 174.6 172.3 171.7 8.28 8.16 8.13 8.25 8.28 8.22 8.24 8.24 8.16 8.20 8.32 8.23 8.32 8.28 8.24 8.39 8.39 8.32 8.36 8.36 8.28 8.28 8.28 8.31 8.39 8.28 8.39 8.36 8.36 8.36 8.39 8.20 8.43 8.32 8.39 8.35 8.28 8.39 8.28 8.39 0.28 0.26 0.25 0.25 0.24 0.25 0.27 0.25 0.26 0.24 0.24 0.25 0.26 0.26 0.25 0.25 0.24 0.25 0.27 0.26 0.25 0.25 0.25 0.26 0.27 0.26 0.26 0.27 0.25 0.25 0.25 0.26 0.25 0.26 0.25 0.26 Average 50 Average 306.2 305.12 314.5 314.1 316.6 313.6 315.5 314.86 59 177.1 173.82 179.9 183.5 179.3 182.8 182.4 181.58 2. Test Data in Shock Machine Drop Table 1. Aluminum weight with 1" thick ethafoam 220 (natural frequency = 45 Hz) 0.26 0.26 0.25 0.26 0.25 0.26 0.25 Average 10 Average 11 Average 12 178.7 179.2 179.2 179.4 179.9 179.28 195.1 195.6 195.8 196.1 196.2 195.76 200.6 200.5 199.6 195.5 198.2 198.88 208.5 Average 13 Average 14 Average 15 Average 16 Average 17 Average 18 Average 19 207.3 207.8 209.6 210.0 208.64 218.3 219.1 221.8 221.9 220.78 231.7 231.6 230.1 229.3 230.2 230.58 238.1 239.8 238.9 238.1 238.72 246.8 249.9 251.6 252.2 252.6 250.62 260.0 260.8 261.4 262.8 262.6 261.52 268.6 270.2 270.6 271.7 271.4 270.54 278.8 60 83.2 82.6 84.4 85.0 83.8 89.6 90.9 90.2 91.4 90.58 97.3 97.3 94.3 94.3 94.3 95.38 101.2 102.5 100.8 100.2 101.22 107.8 109.3 110.1 110.2 110.2 109.52 116.7 117.0 117.2 119.2 118.9 117.8 123.0 125.0 125.4 126.0 126.1 125.1 131.2 11.05 11.9 11.05 10.97 11.05 10.9 10.94 11.05 10.94 10.95 10.78 10.78 10.90 10.94 11.01 10.90 10.78 10.57 10.82 10.86 10.80 10.59 10.63 10.63 10.63 10.59 10.61 10.44 10.44 10.36 10.32 10.32 10.38 10.28 10.17 10.17 10.17 10.17 10.18 9.97 0.23 0.23 0.23 0.23 0.25 0.25 0.26 0.25 0.26- 0.26 0.26 0.26 0.27 0.28 0.28 0.28 0.28 0.29 0.30 0.30 0.30 0.29 0.30 0.30 0.33 0.31 0.31 0.30 0.31 0.32 0.31 0.31 0.31 0.31 0.32 Average 20 Average 21 Average 22 Average 23 Average 24 Average Table 2. Aluminum weight with 2" thick ehtafoam 220 (natural frequency a 45 Hz) 281.2 280.9 281.3 281.9 280.82 289.6 290.1 290.0 290.7 291.2 290.32 297.5 299.0 299.4 300.0 299.7 299.12 306.6 307.7 307.9 308.5 308.5 307.84 314.7 315.9 316.8 318.1 318.0 316.7 323.3 325.5 325.7 326.3 326.5 325.25 61 134.2 134.3 134.8 135.9 134.08 142.2 141.8 141.3 143.7 143.0 142.5 148.8 150.3 150.0 151.2 151.2 150.3 158.6 160.5 160.4 161.1 161.4 160.4 168.8 168.5 171.1 172.3 172.0 170.54 178.1 181.6 181.6 182.8 184.0 181.62 10.01 9.97 9.94 9.85 9.97 9.63 9.74 9.67 9.63 9.70 9.67 9.63 9.55 9.51 9.51 9.51 9.54 9.36 9.28 9.32 9.28 9.24 9.30 9.09 9.20 9.09 9.05 9.09 9.10 8.90 8.93 8.90 8.90 8.78 8.88 0.32 0.32 0.32 0.32 0.33 0.33 0.33 0.33 0.33 0.34 0.34 0.34 0.34 0.34 0.34 Average 9 Average 10 Average 11 Average 12 Average 13 Average 153.9 160.1 162.1 163.4 163.2 160.54 172.7 172.7 172.8 173.4 173.5 173.02 182.4 183.4 183.5 184.1 184.1 183.5 192.8 193.4 193.8 194.1 194.1 193.64 202.0 203.5 204.4 204.2 204.6 203.74 212.4 212.4 213.4 213.9 214.0 213.22 55.94 58.9 58.6 58.4 58.6 57.7 58.2 60.8 60.9 60.8 60.8 60.9 60.84 63.6 63.6 63.6 63.6 63.6 63.6 66.6 66.9 66.9 66.8 67.1 66.86 69.6 69.6 69.6 70.3 70.3 69.88 0.23 0.25 0.26 0.26 0.26 0.26 14 Average 15 Average 16 Average 17 Average 18 Average 19 Average 20 222.6 223.0 223.6 223.8 224.2 223.24 231.0 231.6 232.5 232.8 232.3 232.04 241.5 241.7 242.2 242.2 242.3 241.94 251.0 251.8 251.4 251.8 252.2 251.64 259.9 260.7 260.7 261.8 261.1 260.84 268.1 269.8 271.4 270.6 271.3 270.24 277.2 278.2 279.3 279.4 279.2 63 72.7 72.7 73.1 73.1 73.1 72.94 75.4 75.0 75.4 75.4 75.1 75.26 78.8 78.7 78.5 78.5 78.7 78.6 82.0 81.3 81.3 81.3 82.0 81.58 84.8 84.8 83.6 84.8 83.6 84.32 87.2 87.9 88.3 88.0 88.3 87.99 90.4 90.7 91.8 91.7 91.6 13.48 13.44 13.44 13.44 13.51 13.46 13.44 13.55 13.55 13.59 13.71 13.57 13.63 13.67 13.71 13.75 13.79 13.71 13.75 13.82 13.98 13.94 13.90 13.88 13.90 13.94 13.94 13.98 14.02 13.96 13.86 13.90 13.94 13.94 13.94 13.92 13.90 13.98 13.94 13.98 14.02 0.27 0.27 0.27 0.28 0.28 0.29 0.29 0.29 0.29 0.29 0.29 0.31 0.31 0.31 0.31 0.31 0.32 0.33 0.33 0.32 0.33 0.34 0.34 0.34 0.34 0.34 0.34 0.36 0.36 0.36 0.36 0.36 0.36 0.37 0.37 0.37 0.38 0.37 Average 21 Average 22 Average 23 Average 24 Average 278.66 285.1 286.6 287.8 288.3 289.5 287.46 294.8 295.9 296.5 297.2 297.8 296.4 303.5 303.9 305.2 307.0 304.8 304.88 310.8 312.5 313.0 312.7 313.4 312.48 64 91.24 93.9 94.2 95.2 95.4 95.4 94.82 97.4 97.7 97.7 98.6 98.9 98.06 99.0 101.5 100.2 101.4 99.6 100.34 103.7 104.9 104.9 104.3 104.6 104.48 13.96 14.02 14.06 13.98 13.97 13.98 14.0 14.06 14.06 14.13 14.02 13.98 14.05 14.44 14.25 14.40 14.48 14.29 14.34 14.25 14.29 14.25 14.36 14.25 14.28 0.38 0.38 0.39 0.39 0.39 0.40 0.41 0.41 0.40 0.41 0.41 0.42 0.42 0.43 0.43 0.43 0.43 0.44 0.44 0.44 0.44 0.44 0.44 Table 3. Aluminum weight with 1" thick ethafoam HS_45 (natural frequency - 65) 156.9 160.4 162.8 158.2 Average 9 Average 10 Average 11 Average 12 Average 13 Average 14 Average 15 155.7 158.8 - 169.5 169.7 170.1 170.7 170.5 170.1 180.4 181.8 183.0 181.3 182.0 181.7 192.1 192.2 192.6 193.4 194.3 192.92 200.3 202.6 203.1 203.2 203.4 202.5 212.2 212.2 212.3 212.5 214.8 212.78 220.9 220.9 222.7 222.4 220.3 221.44 228.0 228.7 65 74.1 85.4 84.4 84.0 84.4 84.7 84.2 84.3 88.8 88.6 87.9 87.1 86.9 87.9 91.7 91.6 91.0 90.2 90.2 90.9 94.2 94.2 94.8 93.9 93.7 94.2 98.4 98.9 98.5 99.2 100.3 99.96 104.3 103.6 103.1 104.3 100.8 103.2 105.9 106.6 8.38 8.55 8.59 8.63 8.63 8.59 8.60 8.82 8.82 8.86 8.90 8.90 8.85 8.86 9.01 9.05 8.97 9.01 8.98 9.05 9.09 9.09 9.13 9.20 9.11 9.16 9.20 9.20 9.20 9.36 9.25 9.43 9.36 0.14 0.14 0.14 0.14 0.14 0.15 0.15 0.16 0.16 0.16 0.16 0.17 0.17 0.17 0.17 0.17 0.18 0.18 0.19 0.18 0.19 0.18 0.20 0.20 0.20 0.20 0.20 0.20 0.21 0.21 0.21 0.21 0.21 0.22 0.22 Average 16 Average 17 Average 18 Average 19 Average 20 Average 21 Average 229.2 231.3 232.6 229.96 239.9 240.9 241.4 242.3 243.4 241.58 247.3 250.9 250.8 250.8 252.0 250.34 258.5 260.8 258.6 258.6 261.7 259.64 266.7 267.9 270.2 269.7 271.4 269.14 276.0 279.9 279.4 278.7 277.2 278.24 286.4 287.9 286.4 286.7 287.9 287.06 66 107.1 109.3 109.0 105.9 111.3 114.6 114.6 114.7 115.6 115.0 119.0 121.4 120.7 120.7 120.7 120.0 126.1 127.7 124.2 125.8 128.5 126.5 131.2 133.7 133.9 134.6 135.2 133.7 138.3 140.6 141.5 140.6 138.4 140.0 146.2 148.8 145.0 148.1 148.4 147.3 9.32 9.32 9.36 9.34 9.43 9.32 9.28 9.40 9.32 9.35 9.36 9.32 9.28 9.32 9.32 93.3 9.28 9.28 9.40 9.32 9.36 9.33 9.20 9.16 9.20 9.16 9.20 9.18 9.20 9.13 9.16 9.13 9.28 9.18 9.09 9.09 9.20 9.09 9.09 9.11 0.22 0.23 0.23 0.24 0.24 0.24 0.24 0.24 0.24 0.25 0.25 0.25 0.25 0.25 0.26 0.26 0.26 0.26 0.26 0.26 0.27 0.27 0.27 0.27 0.27 0.27 0.28 0.28 0.28 0.28 0.28 0.29 0.29 0.29 0.29 0.29 22 Average 23 Average 24 Average Table 4. 291.9 293.8 297.3 295.5 297.3 295.16 300.6 301.5 303.4 303.2 304.3 302.6 308.2 308.9 309.0 310.5 308.7 309.06 67 151.7 152.8 155.9 154.0 154.4 153.8 158.1 160.1 157.8 162.5 162.9 160.3 168.1 165.7 166.1 168.3 167.4 167.1 9.05 9.01 9.01 9.01 9.01 9.02 9.01 8.86 9.05 8.86 8.90 8.90 8.78 8.82 8.86 8.82 8.90 8.84 0.30 0.29 0.30 0.30 0.30 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.32 0.31 Aluminum weight with 2" thick ethafoam HS-45 (natural frequency = 53 Hz) Average 9 Average 10 166.1 166.9 165.0 166.2 166.9 166.22 176.1 176.6 177.4 177.3 177.0 176.88 185.7 71.74 75.6 75.6 75.6 75.6 75.6 75.6 78.6 9.36 9.55 9.47 9.51 9.51 9.55 9.52 9.55 Average 11 Average 12 Average 13 Average 14 Average 15 Average 187.6 187.7 188.0 187.6 187.32 195.4 196.4 197.0 197.2 197.0 196.6 204.6 205.7 205.2 205.9 207.0 205.68 212.2 216.2 215.7 216.4 216.4 215.38 222.7 223.1 223.1 223.6 225.4 223.58 228.9 233.9 234.2 234.3 234.9 233.4 68 78.5 78.5 77.9 77.9 78.28 80.3 80.3 80.3 80.3 79.7 80.18 82.0 82.0 81.4 81.4 81.7 81.7 82.7 83.8 83.5 83.2 83.2 83.28 85.0 85.5 85.0 85.0 85.4 85.2 86.8 87.9 88.2 87.9 87.9 87.74 9.74 9.74 9.78 9.78 9.85 9.97 9.94 10.01 10.05 9.96 10.20 10.20 10.32 10.32 10.32 10.27 10.40 10.55 10.55 10.59 10.63 10.54 10.74 10.78 10.82 10.86 10.86 10.81 10.90 10.90 11.01 11.09 11.13 11.25 0.15 0.16 0.16 0.16 0.16 0.17 0.17 0.17 0.17 0.17 0.17 0.18 0.18 0.18 0.18 0.20 0.20 0.21 0.20 0.20 0.20 0.21 0.22 0.22 0.22 0.24 0.22 0.23 0.23 0.23 0.24 0.24 0.24 16 Average 17 Average 18 Average 19 Average 20 Average 21 Average 22 240.4 242.2 242.9 244.1 244.9 242.9 249.0 250.5 250.9 251.5 251.7 250.72 257.8 259.3 259.6 260.0 260.5 359.44 264.7 266.2 265.7 267.1 267.0 266.14 272.4 273.5 274.4 274.1 274.3 273.74 280.8 282.1 283.1 283.5 283.0 282.5 288.2 289.7 291.1 293.0 293.2 69 89.6 91.1 90.8 91.3 91.7 90.76 93.2 93.7 93.7 93.7 93.7 93.6 96.7 97.3 97.3 97.9 97.9 97.42 100.0 99.0 99.6 100.3 99.6 99.7 102.0 102.7 102.7 102.7 102.5 102.5 105.3 106.5 105.8 106.3 106.3 106.04 108.3 109.3 108.3 110.2 110.2 11.17 11.17 11.21 11.21 11.24 11.25 11.28 11.28 11.28 11.32 11.32 11.30 11.36 11.36 11.36 11.36 11.40 11.38 11.36 11.48 11.36 11.40 11.36 11.39 11.51 11.55 11.59 11.59 11.59 11.57 11.59 11.55 11.59 11.59 11.59 11.58 11.59 11.59 11.75 11.67 11.67 0.25 0.25 0.25 0.25 0.25 0.26 0.26 0.26 0.26 0.26 0.27 0 27 0.28 0.28 0.28 0.28 0.29 0.29 0.29 0.29 0.30 0.30 0.30 0.30 0.30 0.32 0.32 0.32 0.32 0.32 0.33 0.33 0.33 0.33 0.33 Average 291.04 109.26 11.65 0.33 23 297.3 112.5 11.63 0.34 299.3 113.2 11.67 0.34 300.0 113.4 11.67 0.34 299.0 112.5 11.71 0.34 299.0 112.5 11.71 0.34 Average 298.92 112.82 11.68 0.34 24 303.3 114.8 11.71 0.35 304.4 114.8 11.71 0.35 304.1 114.8 11.67 0.35 304.4 114.8 11.71 0.35 304.4 115.0 11.75 0.36 Average 304.12 114.82 11.71 0.35 Table 5. Foam weight with 2" thick ethafoam 220 (natural frequency = 55 Hz) H V G D X [in] [in/sec} [9'8] [108] [In] 8 171.1 75.3 8.82 0.12 172.2 74.4 8.97 0.12 172.9 74.4 9.13 0.12 174.5 74.7 9.24 0.12 175.9 73.8 9.36 0.13 Average 173.32 74.5 9.11 0.12 9 189.9 72.0 10.31 0.15 188.2 72.1 10.32 0.15 189.4 72.1 10.44 0.16 188.8 72.1 10.40 0.15 187.7 71.5 10.40 0.15 Average 188.8 71.96 10.37 0.15 10 193.8 78.5 9.78 0.19 193.5 77.3 9.90 0.15 196.4 76.7 10.09 0.20 197.9 76.2 10.20 0.16 70 Average 11 Average 12 Average 13 Average 14 Average 15 Average 16 Average 17 197.6 195.84 225.9 207.6 208.7 206,4 208.4 207.4 216.2 216.7 217.1 217.2 216.8 216.8 224.8 226.3 227.3 226.0 228.1 226.5 234.4 235.5 235.3 232.5 231.8 233.9 240.6 241.0 242.7 240.6 242.1 241.32 247.2 249.0 252.4 250.8 254.9 250.86 260.1 267.0 71 75.6 76.86 77.9 77.9 77.9 76.2 76.8 77.34 78.7 78.7 79.1 78.5 78.5 79.1 80.9 80.9 80.7 80.4 80.9 80.76 82.1 82.9 82.0 82.0 81.4 82.0 84.4 84.5 83.8 84.2 84.1 84.2 87.3 87.3 88.1 87.6 87.9 87.52 89.5 91.5 10.24 10.04 10.47 10.71 10.71 10.74 10.78 10.68 10.86 10.90 10.97 11.05 11.05 10.97 11.09 11.17 11.32 11.28 11.32 11.24 11.44 11.40 11.51 11.32 11.40 11.41 11.55 11.63 11.71 11.59 11.69 11.63 11.55 11.71 11.78 11.82 11.90 11.75 12.01 12.25 0.17 0.18 0.18 0.18 0.18 0.19 0.19 0.19 0.20 0.20 0.21 0.21 0.21 0.22 0.21 0.23 0.22 0.23 0.32 0.23 0.24 0.24 0.24 0.23 0.23 0.23 0.25 0.26 0.26 0.26 0.27 0.26 0.28 0.28 Average 18 Average 19 Average 20 Average 21 Average 22 Average 23 Average 263.6 264.0 262.0 263.4 267.2 271.4 270.1 270.1 270.2 269.8 278.0 280.2 279.9 279.6 281.7 279.9 289.5 290.1 290.2 293.4 288.4 290.32 294.9 294.8 299.6 299.6 300.4 297.9 303.6 307.4 305.6 306.6 307.6 306.04 314.1 310.7 313.4 311.4 312.3 312.38 72 90.2 91.1 90.0 90.46 93.2 93.5 93.6 93.7 92.6 92.32 96.4 96.1 96.8 97.6 97.4 96.86 100.8 100.8 100.6 100.8 100.3 100.66 101.4 103 1 103.9 104.3 104.3 103.4 105.6 106.6 106.9 106.6 107.8 106.7 110.0 108.0 109.4 110.2 109.0 109.3 12.13 12.05 12.05 12.09 11.98 12.09 12.09 11.98 12.17 12.06 12.17 12.17 12.13 12.3 12.13 12.15 12.25 12.32 12.36 12.36 12.28 12.26 12.28 12.17 12.36 12.40 12.43 12.33 12.32 12.28 12.36 12.32 12.36 12.33 12.40 12.48 12.44 12.36 12.36 12.41 0.28 0.28 0.28 0.28 0.29 0.30 0.29 0.30 0.30 0.31 0.31 0.31 0.31 0.32 0.31 0.32 0.33 0.32 0.33 0.32 0.32 0.34 0.33 0.34 0.34 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.36 0.36 0.36 0.34 0.36 0.36 24 317.1 112.9 12.25 0.36 321.5 112.8 12.40 0.37 323.4 113.2 12.44 0.37 322.9 113.6 12.52 0.38 321.9 113.2 12.48 0.38 Average 321.36 113.14 12.42 0.37 Table 6. Foam weight with 1" thick ethafoam 220 (natural frequency = 62 Hz) H V G D x [in] [in/sec} [9'8] {ms} [in] 8 164.9 85.5 7.78 0.11 172.2 85.0 8.24 0.12 174.4 82.6 8.43 0.13 176.4 85.0 8.51 0.13 178.4 84.4 8.59 0.13 Average 173.26 85.1 8.31 0.12 9 189.0 90.8 8.66 0.13 187.4 89.7 8.74 0.14 188.4 90.0 8.74 0.15 190.5 91.1 8.78 0.15 189.0 89.1 8.86 0.14 Average 188.86 90.32 8.76 0.14 10 200.4 96.7 8.86 0.16 202.3 97.9 8.93 0.16 201.9 96.1 8.97 0.16 202.7 97.3 8.93 0.16 202.4 96.1 8.97 0.16 Average 201.94 96.8 8.93 0.16 11 213.8 102.5 8.97 0.17 214.9 102.5 9.05 0.17 215.6 103.7 9.05 0.17 216.0 103.7 9.05 0.17 216.4 103.7 9.09 0.17 Average 215.34 103.22 9.04 0.17 12 224.9 107.2 9.05 0.18 226.7 108.4 9.05 0.19 73 Average 13 Average 14 Average 15 Average 16 Average 17 Average 18 Average 225.8 227.1 227.0 226.3 235.4 237.2 235.8 236.5 237.7 236.52 244.2 244.2 244.8 243.6 244.1 244.18 253.8 255.2 254.9 251.6 251.9 253.48 256.9 259.6 258.4 256.4 253.8 257.02 261.9 263.3 263.3 262.9 263.6 262.9 270.9 273.4 273.1 273.9 274.5 273.16 74 106.1 108.4 107.2 107.46 113.1 114.3 111.9 111.9 114.3 113.1 118.1 116.3 117.8 116.6 117.2 117.2 124.6 123.6 123.6 120.9 120.0. 122.54 124.6 125.9 124.6 120.8 116.2 122.42 123.3 124.4 125.2 122.9 125.5 124.3 130.4 133.6 133.7 133.9 134.7 133.26 9.16 9.09 9.16 9.102 9.13 9.13 9.20 9.20 9.13 9.16 9.09 9.32 9.24 9.24 9.20 9.22 9.16 9.16 9.16 9.32 9.32 9.22 9.24 9.36 9.36 9.43 9.55 '9.39 9.47 9.51 9.43 9.51 9.43 9.47 9.40 9.24 9.28 9.28 9.32 9.304 0.18 0.18 0.19 0.18 0.20 0.20 0.19 0.20 0.20 0.21 0.21 0.21 0.21 0.21 0.22 0.23 0.22 0.23 0.23 0.23 0.23 0.24 0.24 0.24 0.24 0.24 0.25 0.25 0.25 0.25 0.26 0.25 0.26 0.27 0.27 0.26 0.27 0.27 19 Average 20 Average 21 Average 22 Average 23 Average 24 Average 282.3 283.4 283.6 283.9 284.2 283.48 291.1 291.6 293.5 292.9 292.5 292.32 300.0 301.7 301.9 302.5 303.2 301.86 310.0 312.8 310.4 308.7 310.7 310.52 316.5 318.1 319.1 319.9 320.2 318.76 326.3 328.2 329.1 328.4 329.5 327.7 75 140.6 141.9 142.1 142.8 142.8 142.04 147.5 147.9 149.0 149.1 147.5 148.2 155.7 156.9 157.0 157.3 157.3 156.84 162.9 163.8 162.0 156.1 160.7 161.1 166.3 166.7 169.0 170.2 171.1 168.66 176.1 178.4 179.3 179.6 180.8 178.84 9.24 9.24 9.20 9.20 9.05 9.01 8.90 8.93 8.90 8.97 8.78 8.78 8.82 8.86 8.82 8.812 8.78 8.86 8.86 8.93 8.90 8.87 8.70 8.82 8.70 8.63 8.78 8.73 8.63 8.63 8.59 8.59 8.55 8.60 0.27 0.27 0.27 0.27 0.27 0.28 0.28 0.28 0.28 0.28 0.29 0.29 0.29 0.29 0.29 0.29 0.30 0.30 0.30 0.30 0.31 0.30 0.31 0.31 0.31 0.31 0.31 0.32 0.32 0.32 0.32 0.32 0.32 Table 7. Foam weight with 2" thick ethafoam HS-45 76 (natural frequency = 96 Hz) H V G D X [in] [in/sec} [9’8] {ms} [in] 8 167.5 138.6 5.21 0.10 170.7 126.8 5.47 0.10 172.0 124.5 5.58 0.10 172.6 123.7 5.66 0.10 174.0 124.5 5.70 0.11 Average 171.36 127.6 5.48 0.10 9 183.1 127.1 5.85 0.12 183.1 127.5 5.97 0.12 184.7 127.7 6.05 0.13 184.3 126.0 6.01 0.12 184.1 123.6 6.12 0.12 Average 183.86 126.58 6.00 0.12 10 192.1 129.5 6.12 0.12 190.2 128.3 6.12 0.12 193.1 128.9 6.20 0.13 192.1 127.1 6.32 0.13 192.5 126.0 6.39 0.13 Average 192.0 127.96 6.23 0.13 11 200.5 130.5 6.47 0.13 201.9 128.9 6.47 0.13 203.4 128.3 6.66 0.14 204.0 128.0 6.78 0.14 202.4 126.6 6.78 0.14 Average 202.44 128.46 6.63 0.14 12 212.3 130.7 6.85 0.15 213.0 130.1 6.89 0.15 212.5 128.9 6.93 0.15 213.8 128.3 6.97 0.15 212.7 127.7 6.97 0.15 Average 212.86 129.14 6.92 0.15 13 220.9 132.1 7.01 0.15 220.4 130.5 7.09 0.15 219.1 129.1 7.09 0.15 218.9 128.9 7.09 0.15 221.0 128.9 7.12 0.16 Average 220.06 129.9 7.08 14 Average 15 Average 16 Average 17 Average 18 Average 19 Average 20 229.2 230.0 229.4 230.5 229.0 229.62 235.7 236.3 238.4 239.1 238.4 237.58 244.7 247.3 246.9 247.6 246.2 246.54 253.5 254.9 255.2 255.4 255.6 254.92 261.9 262.8 262.4 261.9 263.8 262.56 269.3 272.3 272.4 271.4 272.0 271.48 277.5 278.5 279.4 279.6 77 133.6 132.4 131.2 130.7 130.1 131.6 131.7 132.7 130.5 130.4 129.5 130.96 133.0 132.7 131.5 130.1 130.4 131.54 132.4 132.2 132.6 132.7 132.6 132.46 135.5 134.9 133.3 130.8 131.2 133.14 135.5 135.9 134.8 133.4 132.4 134.4 135.5 133 9 135.6 135.1 7.20 7.24 7.28 7.35 7.35 7.35 7.32 7.43 7.66 7.70 7.70 7.56 7.74 7.78 7.78 7.89 7.86 7.93 7.89 7.89 7.89 7.93 7.906 7.97 8.01 8.05 8.24 8.36 8.13 8.32 8.36 8.43 8.39 8.47 8.39 8.55 8.47 8.51 8.55 0.16 0.17 0.16 0.16 0.16 0.17 0.17 0.18 0.18 0.18 0.18 0.19 0.18 ,0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.20 0.20 0.20 0.20 0.21 0.20 0.21 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.23 0.23 Average 21 Average 22 Average 23 Average 24 Average 279.2 278.84 284.5 286.1 287.5 288.5 288.2 286.96 293.0 295.0 295.0 295.6 295.1 294.74 301.0 303.1 302.2 303.3 304.6 302.84 305.9 309.3 308.8 309.7 307.6 308.26 78 134.3 134.88 136.1 136.6 137.0 136.8 136.8 136.66 139.0 140.0 139.6 138.9 138.7 139.24 141.0 141.8 141.1 141.6 141.8 141.48 141.8 144.1 143.3 141.8 141.1 142.42 8.53 8.63 8.63 8.70 8.74 8.74 8.69 8.74 8.82 8.78 8.82 8.82 8.80 8.86 8.90 8.93 8.90 8.93 8.90 8.93 8.97 9.01 9.05 9.05 0.25 0.26 0.26 0.26 0.26 0.26 0.26 0.27 0.27 0.27 0.27 0.27 Table 8. Foam weight with 1" thick ehtafoam HS-45 (natural frequency a 91 Hz) [in/sec] 160.4 164.6 166.7 164.7 168.0 [g's] 149.7 134.2 128.9 123.6 123.0 Average 9 Average 10 Average 11 Average 12 Average 13 Average 14 Average 15 164.88 177.2 176.9 178.2 176.7 177.2 177.24 186.9 187.4 187.5 187.1 188.8 187.54 196.8 197.3 195.2 186.5 190.1 193.18 201.4 203.1 203 0 203.3 204.1 202.98 213.3 214.4 214.2 213.1 213.5 213.7 221.6 222.1 224.7 224.9 224.6 223.58 230.3 229.2 228.8 226.7 79 133.5 126.6 123.0 121.3 119.2 120.0 122.0 121.9 120.7 120.7 120.6 120.7 120.9 125.4 124.2 122.2 118.4 107.2 119.5 116.0 120.1 120.1 120.1 120.5 119.4 127.1 127.1 126.6 124.8 126.0 126.3 131.2 130.7 131.8 131.8 130.7 131.2 132.9 129.5 128.3 123.0 6.05 6.12 6.20 6.24 6.28 6.14 6.39 6.43 6.43 6.43 6.51 6.44 6.58 6.82 7.01 7.09 7.39 6.98 7.09 7.01 7.01 7.05 7.09 7.05 7.05 7.05 .7.12 7.12 7.12 7.92 7.12 7.12 7.20 7.32 7.47 7.25 7.51 7.78 7.82 7.93 0.10 0.10 0.10 0.10 0.10 0.11 0.11 0.11 0.11 0.11 0.11 0.12 0.12 0.12 0.12 0.13 0.15 0.15 0.15 0.15 0.15 0.15 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.17 0.17 0.17 0.17 0.18 0.18 0.18 0.19 Average 16 Average 17 Average 18 Average 19 Average 20 Average 21 Average 22 228.7 228.74 236.8 238.4 239.5 240.9 240.9 239.3 246.5 247.8 248.6 248.5 248.4 247.96 254.2 256.1 256.2 256.9 257.1 256.1 263.1 265.3 265.1 264.7 266.5 264.94 272.6 274.6 276.8 276.3 278.1 275.68 281.8 284.7 284.7 285.1 283.8 284.02 292.0 295.0 80 127.1 128.2 134.8 136.5 135.9 137.1 137.7 136.4 141.2 142.4 143.6 143.0 142.4 142.5 147.1 148.2 147.7 148.2 148.2 147.9 152.6 154.8 153.7 152.9 155.0 153.8 158.0 160.5 161.3 161.2 162.9 160.8 163.9 166.6 167.7 169.0 166.4 166.7 173.0 177.8 0.19 0.18 0.20 0.20 0.20 0.20 0.20 0.20 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.22 0.22 0.22 0.22 0.22 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.24 0.24 0.24 0.24 0.24 0.24 0.25 0.25 0.24 0.24 0.25 0.25 Average 23 Average 24 Average 294.2 295.2 296.1 294.46 299.1 302.1 301.7 302.3 301.6 301.36 308.1 310.0 311.1 311.0 311.5 310.3 81 175.8 176.7 177.8 176.2 180.5 184.0 182.3 182.8 181.5 182.2 188.7 191.0 192.2 191.0 191.0 190.8 7.59 7.59 7.59 7.59 7.51 7.59 7.59 7.59 7.57 7.51 7.51 7.51 7.51 7.51 7.51 0.25 0.25 0.25 0.25 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.27 0.27 0.27 0.27 LIST OF REFERENCES 7. REFERENCES Brandenburg, R. K: and Lee, J. J.L; "Fundamentals of Packaging Dynamics". School of Packaging, Michigan State University. 1985. Ostrem, F. E: "Survey of Cargo-Handling Shock and vibration Environment". Shock & Vibration Bulletin 37, Part 7, Jan. 1968. Franklin, P. E: and Hatae, M. T: "Packaging Design". Chapter 41, Vol.3, Shock and Vibration Handbook, McGraw-Hill, 1961. Garmell, L. W: and Gretz, J. L; "Report on Effect of Drop Test Orientation on Impact Accelerations". Physical Test Laboratory, Texfoam Division, B. F. Goodrich Sponge Products Divisionof B. F. Goodrich Co; Shelton, Conn: 1955. Goff, J. W: and Chatman, R: "The Correlation of Shock With Free-Fall Drop Height". Technical Report No. 24. Multi-Sponsor Research Program, School of Packaging, Michigan State University, August 1976. Vigness, I: "The Fundamental Nature of Shock and Vibration". Electrical Manufacturing’s New Basic Science and Engineering Series. 1959. Goff, J. W, Chatman, R: Iwahimizu, H: and Collins, K; "Shock Machine and Free Fall Drop Correlation". Unpublished 8. 9. data. School of Packaging, Michigan State University Newton, R. E: "Fragility Assessment Theory and Test Procedure”. Monterey Research Laboratory, Montery, California. 1968 Mindlin, R. D; "Dynamics of Package Cushioning". Bell System Journal, Vol. 24, Oct 1945. 10. Kornhauser, M: "Prediction and Evaluation of Sensitivity to Transient Accelerations". Journal of Applied Mechanics, Vol. 21, No. 4, P. 371-380. 1954. 11. Kornhauser, M: "Inertia loading". Structural Effects of 82 12. 13. 14. 15. 83 of Impact. P 95-120. 1965. Pendered, J. W: "The Shock Spectrum". Univ. College, London. Dept. of Mechanical Engineering , Rept. 65/10, Dec. 1965. Goff, J. W and Pierce, S. R: "A Procedure for Determining Damage Boundaries". Shock & Vibration Bulletin 40, Part 6, Dec 1969. "Standard Test Methods for Mechanical Shock fragility of Products Using Shock Machine". ASTM D3332-77. Cesari, D; Ramet, M; and Herry, D: "Injury Mechanisms in Side Impact". Proc Stapp Car Crash Conf 22nd. Univ of Mich. Ann Arbor. Oct 24-26 1978. "‘liliiiiiillliiil“