were

 

I/llllllllilli/lllll/llllllllli/l

31 300908 880

This is to certify that the
thesis entitled
PREDICTING SHOCK TRANSMISSION CHARACTERISTICS

FOR RIBBED EXPANDED POLYPROPYLENE CUSHIONS USING
STANDARD CUSHION CURVES FOR FLAT PLANK CUSHIONS

presented by

GARY CARLTON GRANT HEN

has been accepted towards fulfillment
of the requirements for

_M.a.__S_-__ degree in PACKAGING

'0: professor

Date MAY 21 1991

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

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University

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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

m M m 33323}; 2063

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU Is An Affirmative Action/Equal Opportunity Institution
cmmuna-DJ

 

PREDICTING SHOCK TRANSHISSION
CHARACTERISTICS FOR RIBBED EXPANDED POLYPROPYLENE CUSHIONS

USING STANDARD CUSHION CURVES FOR FLAT PLANK CUSHIONS

BY
Gary Carlton Granthen

A THESIS
Sublitted to
Michigan State university
in partial fulfillnent of the requirenents
for the degree of

MASTER OF SCIENCE

School of Packaging

1991

ABSTRACT

PREDICTING SHOCK TRANSMISSION CHARACTERISTICS
FOR RIBBED EXPANDEI POLYPROPYLENE CUSHIONS USING
STANDARD CUSHION CURVES FOR FLAT PLANK CUSHIONS
BY

GARY CARLTON GRANTHEN

This study examines seven different mathematical models
which predict the peak deceleration G in dynamic loading of
1.9 PCF ribbed expanded polypropylene cushions. Each method
is based on converting the ribbed cushion into an equivalent
plank cushion so that published.cushion curve data can be used
to determine G. ‘Three drop heights of 18", 30" and 42", three
rib angles of 5?, 15°, and 25°, three static loadings, and
three rib heights of 1.5", 2.0" and 2.5" were tested.

The results show that the Equivalent Volume method which
weighs the varying cross sectional areas of the ribbed.portion
and the plank.portion of the cushion equally, best predicts G.
This newly calculated "bearing area" based on this method can
then be used to calculate the static stress which in turn can
be used to determine the peak deceleration from the standard
cushion curves. This model is shown to rest on solid physical
grounds through an examination of the resistance to

compression using the Gas Law.

ACKNOWLEDGMENTS

I wish to thank Dr. Paul Singh and Dr. George Mase for
their support and helpful suggestions while serving on my
Graduate Committee. I also wish to thank Joseph Franklin of
ARCO CHEMICAL COMPANY for his guidance and material donation
that made this whole project possible. A very special thanks
goes to Dr. Gary Burgess for his time, patience, good humor,
and guidance while acting as my advisor and.helping me through
the difficult times. I am deeply indebted and forever

appreciative.

iii

TABLEOF CONTENTS

PAGE

LIST OF TABLES ....................................... v

LISTOF FIGURES ...................................... vi

CHAPTERI ............................................ 1

INTRODUCTION . ............... ......... ....... .... 1

CHAPTER2 ............................................ 19

HATERIALSANDHETHODS .................... . ...... 19

2.]. MATERIAL ................................. 19

2.2 DESIGN OF EXPERIMENT .......... . ....... ... 19

2.3 TESTINGAPPARATUS ........................ 27

TESTPROC-URE ....................... . .......... 27

CHAPTER3 ............................................ 33

PREDICTION METHODS USING PLANK CUSHION CURVES . . . 33

CHAPTER4 ............................................ 43

4.1 DISCUSSIONANDCONCLUSION ........... ..... .. 43

4.2 RECOMMENDATIONS FORFUTURERESEARCH ........ 47
APPENDICES

APPENDIX A: RIBBED CUSHION SURVEY .............. 49

APPENDIX B: TABLES FOR DATAANDRESULTS ........ 50

APPENDIX C: COIIPUTERPROGRAH.................... 60

mmcns .OOOOOOOO ..... OOOOOOOOOOOOOOCO ....... 0.0... 61

iv

LIST OF TABLES

TABLE PAGE
1 EXPECTED DROP HEIGHT VERSUS PACKAGE WEIGHT .. 2
2 RESULTS FOR RIBBED CUSHION SURVEY ........... l6
3 GATE TIME, IMPACT VELOCITY AND FREE FALL .... 30

DROP HEIGHT.

4 SUmARy 0F ASSOCIATED ERRORS O O O O O O O O O O O O O O O O 32

FIGURE

10

11

12

13

14

15

16

17

DAMAGE BOUNDARY CURVE

LIST OF FIGURES

CUSHION CURVES FOR ARPROo 3319 EPP BEAD ....

CUSHION BUCKLING ASSOCIATED WITH A BEARING
AREA THAT IS TOO SMALL

32 POUND PRODUCT ON A PLANK CUSHION ........

MATERIAL REMOVED FROM A PLANK CUSHION TO FORM

A CUSHION WITH A NON-UNIFORM CROSS SECTION

HOT WIRE AND RIB CUSHION CUTTING FIXTURE ...

GENERIC DIMENSIONS OF THE RIBBED CUSHIONS
EXAMINED IN THE EXPERIMENT

RIBBED

RIBBED

RIBBED

RIBBED

RIBBED

RIBBED

RIBBED

RIBBED

RIBBED

CUSHION

CUSHION

CUSHION

CUSHION

CUSHION

CUSHION

CUSHION

CUSHION

CUSHION

CONFIGURATION

CONFIGURATION

CONFIGURATION

CONFIGURATION

CONFIGURATION

CONFIGURATION

CONFIGURATION

CONFIGURATION

CONFIGURATION

8

9

PAGE

6-7

11

13

20

21

22

22

23

23

24

24

25

25

26

TESTING APPARATUS & SHOCK MONITORING EQUIPMENT 28

vi

INTRODUCTION AND LITERATURE REVIEW

Selecting the best type and amount of cushioning for a
particular packaging application depends on only three or
four variables in most instances. There are some general
procedures that may be applied so that the process of
designing a cushion for a fragile item need not be very
complicated [Hanlon, 1971]. Unfortunately, these procedures
are limited to plank type cushions which often do not offer
the most economical protection. The purpose of this research
is to extend these procedures to include designing ribbed
cushions using published data for plank cushions.

Rational cushion design requires the consideration of
many factors“ The procedure for cushion design as outlined in
MIL - HDBK - 3048 (1978) is as follows:

Part 1. Determine all pertinent elements of the
problem. These include items such as product
weight, size and shape, the expected drop
height, and product fragility.

Part 2. Determine the most economical cushioning
material for protection of the product.

Part 3. Estimate the allowance in thickness of
cushioning pads that is required to offset
creep.

Part 4. Calculate the exterior container dimensions.

Part 5. Perform impact tests to verify package design.

2
One of the considerations in Part 1 is the type of
distribution environment the package is likely to encounter
such as whether it is shipped by truck, rail, boat, air or
combinations of these and how it is handled (forklifts,
cranes etc.) Table 1 may be used to establish an expected
drop height for the package if the weight is known [ASTM

Std. D 3332 — 88].

TABLE 1. Expected drop height versus package weight.

 

 

Package weight, Type of handling Drop height,
pounds inches

0 - 20 1 man throwing 42
21 - 50 1 man carrying 36
51 - 250 2 men carrying 30
251 - 500 Forklift truck 24
501 - 1000 Forklift truck 18
1000 - Up Forklift truck 12

 

Another consideration in Part 1 is determining the
fragility of the product” The fragility of the product can.be
determined by performing drop tests on a shock machine and
constructing a damage boundary curve [ASTM STD. D 3332 - 88]
as in Figure 1.

The product is first subjected to a series of very
short, constant duration shocks from greater and greater drop
heights until it.breaks~ The critical velocity change for the
product is recorded as the area under the shock pulse which
just causes damage to the product. In theory, the product

will be able to endure shocks of any amplitude (peak

PEAK DECELERATION (G'S)

 

100 lN/SEC

 

 

DAMAGE

 

 

 

 

 

CRITICAL
VELOCITY
CHANGE

 

 

//

80 6'5 CRITICA AL DECELERA TION

VELOCITY CHANGE (IN / SEC)

 

FIGURE 1. DAMAGE BOUNDARY CURVE.

4

deceleration) as long as the velocity change for the shock is
less than this critical velocity change for the product. The
actual velocity change in any drop may be estimated from the
expected drop height in Table 1 as the sum of the impact
velocity and the rebound velocity. When the velocity change
for any other shock is greater than the critical velocity
change for the product, the product becomes sensitive to shock
amplitude [Newton 1968].

Another drop test on a shock machine using an identical
new product is required to determine the critical shock
amplitude. The product is now subjected to a series of much
longer duration shocks with steadily increasing shock
amplitudes until it breaks. The peak deceleration which just
causes damage is recorded as the critical acceleration for the
product, also loosely called its fragility. This completes
the damage boundary picture in Figure 1.

In theory, any shock whose velocity change and peak
deceleration are such that they fall within the damage region
will cause the product to breakn As a consequence of this, if
the velocity change that.a product is expected to encounter in
a drop is less than the critical velocity change for the
product (from the damage boundary curve), then no cushioning
is needed in the package since the primary protective function
of the cushion is to limit the peak deceleration and the peak
deceleration is irrelevant in this situation. It is usually
the case however that the velocity change exceeds this value

so that a cushion is needed to keep the peak deceleration less

5
than the critical deceleration (from the damage boundary
curve).

Once the product fragility is known, there are many types
of cushioning materials which may be used in Part 2 of the
MIL-HDBK cushion design procedure. Cushions may be divided
into two categories based on structure: open cell and closed
cell foams. In general, closed cell (trapped air) foams are
stiffer and therefore produce higher G's than open cell (air
flow) foams. Closed cell foams are capable of supporting much
heavier products however. The dynamic performance for many of
these materials is published in the form of cushion curves
where the peak deceleration is plotted on the ordinate (y-
axis) against static stress on the abscissa (x-axis) as in
Figure 2. It is important to note that all published curves
are for plank type cushions (uniform thickness) only: It also
should be noted that each of the cushions curves in Figure 2
go through a minimum at some static stress. .At the low static
stress end, a high peak-G is obtained because there is
insufficient energy to compress the cushion. At the high
static stress end, a high peak-G is also obtained because the
cushions "bottoms out" in an attempt to absorbrthe excess free
fall energy [Benning, 1969]. At some static stress in between

these limits, the peak-G is lowest.

42" DROP
__i

42“ Drop. 1st Impact

Density II 1.9 PCP

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

42" One. 2-5 Impacts

J

Density-1.01m!r

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

129 12
\\ ,0.
\ / j"
'5.” x —‘ 5W / 21
§ §
:5: oo- 74 u- .g ”J /A
\¥ Aer %ur
20 fl" 2c
° 1. o J.
0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0
51.11:: Streee. eel Static Street. 906 .
36" DROP
35 ' Drop. 1st Impact Density - 1.0 POP 35" Drop. 2-5 Impacts Density - 1.9 PCF
1 2C 7‘? I 2C ' L."
IOO-i Z 1... \‘ ‘E
.. /
.. l . z
W // i” V / 7f
5 .5
E sol AB:— ‘6 .0- n/ /
1. / w
3 .___3/ / u" y///
404 r———i A r-—--l w ... fl
: 14 0.0"
20 2:: 2C 1‘!
0 0.5 1.0 1.5 2.0 2.5 3.0 o 0.5 1.0 1.5 2.0 2.5 3.0
Static 5m“. 9.6 Static Streee. oei

Figure 2.

Cushion curves for ARPRO° 3319 EPP HEAD.

:m"onop

30" 0'00. 13: 1mm:

~3-

Densutv I I 9 PCP

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

30" Drop. 25 Impacts

Demon-19 9c;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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vr
\ I ~

- or; V ‘20-
.” ac v _,. 5% se-
9 rr 9 \
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g / s h—d '
o h—Z /

‘MF— . ... 40" F—-—' d 210,.

¥— sr i,
er
0 o r
05 10 15 20 2.5 30 0.5 10 15 20 25 30
Scene Stress. as: Steve Stress. os-

18"DROP
15" Oreo. 1st Imoect Density . 1.9 PC! 15" Drop. 2-5 Imoects Density - 1 9 PCP
'20 12C

 

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.“ 00"
'0
§ 1"
inn —’,4 ————
3 ~—
1'
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w
0.,
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0 5 I O 1 S 2.0 2.5 3.0

Figure 2.

(cont'd.)

 

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1.,

 

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g

 

 

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:1"
40-1 —— g
l."
2.8”
3'
0 I
0.5 1 0 1 5 2.0 2.5 3.0

 

 

3!“ 3m ”1

8
If the cushion is designed as a simple rectangular flat
plank, the static stress (I referred.to in the cushion curves
is calculated as:

a = w / A , Equation (1)
where W is the weight of the product and .A is the bearing
area between the product and the cushion. To determine the
correct amount of cushioning required to protect the product,
the following approach is normally used in Part 2 of the MIL-
HDBK procedure:

Step 1. Determine first whether or not the product needs
a cushion. Use Table 1 to estimate the expected

drop height and calculate the maximum possible
velocity change for this height as the maximum:

AVEZJZgH. Equation (2)

If this is less than the critical velocity change
for the product from the damage boundary curve,
then the product does not need a cushion. If it
is greater than the critical velocity change,
then continue with Step 2.

Step 2. Select a particular type of cushion for the
expected drop height. The selection should be
based on economy and protective ability.

Step 3. Decide on the area A under which the product is
to be supported and calculate the static stress
a = W / A .

Step 4. Select the minimum thickness that will limit the
G-level to the fragility rating for the product
determined from the damage boundary curve. It
is recommended that the bearing area be greater
than (1.33 X thickness)2 to prevent the buckling
situation shown in Figure 3.

This procedure will now be applied to a hypothetical
situation in order to illustrate the method and to establish

‘the need for being able to handle ribbed cushions.

 

 

 

 

 

PRODUCT
/‘

 

 

 

 

 

BEARING
AREA

 

       
 

     

 

 

 

CUSHION
"Q'Q' '9'Q'Q'OZOIOLOIOIOZOZOZOIO' ' ' ' '
{9:03:93}: IMPACT SURFACE {9:03.
A x A 31010193319193:11919101910101019.

 

       

       
 
 

    
 
  
   
     
 

    

   

FIGURE 3. BUCKLING ASSOCIATED WITH A
BEARING AREA THAT IS TOO SMALL.

EXAMPLE 1:

Step 1.

Step 2.

Step 3.

Step 4.

10

A sensitive electronic product measures 8" X 8" X
6" and weighs 32 pounds. The product must be
supported under its entire base. The damage
boundary curve for the product in Figure 4 is
shown in Figure 1. Design a cushion for multiple
impacts.

From Table 1, the expected drop height is 36".
The maximum possible velocity change is

 

2J2 ... 386.4 ... 36 - 334 inches/sec , which exceeds

the critical velocity change of 100 in/sec from
the damage boundary curve. The product therefore
needs a cushion.

1.9 PCF ARPROo Expanded Polypropylene Bead was
chosen for purposes of illustration. The cushion
curves for this material are shown in Figure 2.

Since the product will be supported under its
entire base by the cushion, the bearing area is
8" X 8" = 64 in2 and the static stress a =

32 lbs / 64 in2== 0.5 psi.

From.the cushion curves in Figure 2 for a 36 inch
drop and a static stress of 0.5 psi, the
thickness of the cushion must be at least 2" in
order to keep the shock less than the fragility
limit of 80 g's from the damage boundary curve in
Figure 1. The actual shock incurred is 72 G's.
For this cushion thickness, the minimum bearing
area which will prevent buckling is (1.33 X 2")2
= 7.1 in”. Since the actual bearing area is 64
ixfi, buckling is not a problem.

In the previous example, a total of 8" X 8" X 2" = 128

ix? of cushion was required to protect the product. It is

possible to reduce this amount considerably using a ribbed

cushion as the next example shows.

EXAMPLE 2:

Step 1.

Step 2.

Suppose now you have exactly the same product as
in Example 1, but you want to reduce the amount
of material used to make the cushion to decrease
packaging costs.

Again, from Table 1, it is determined that the
product will need a cushion.

ARPROo 1.9 PCF cushioning is again chosen.

11

 

 

I
l
1'

PRODUCT

onM

/
/

F————J—
l.

8

 

l
I

 

l
l
I 32,1!
I

 

CUSHION

 

 

 

FIGURE 4. .32 POUND PRODUCT ON A PLANK CUSHION.

12
Step 3. If we temporarily relax the requirement that the
product be supported under its entire base, the
allowable bearing area may be determined from the
cushion curves.

Using a 2" thick cushion, it is possible to maintain the
same protection and.use less material by increasing the static
loading. The maximum static loading that can be used with a
2" thick plank of ARPROo 1.9 PCF Expanded Polypropylene Bead
without transmitting more than 80 G’s in a 36" drop is 1.75
psi. In order to get a static loading of 1.75 psi, the
bearing area must be reduced to 32 lbs / 1.75 psi = 18.3
ixfi. The total amount of cushioning material is now 18.3 in2
X 2 in = 36.6 in3 , a considerable reduction in the 128 in3
used in Example 1. Of course, this design is useless if we
retain the requirement.that.the product.beIsupported.under its
entire base since the bearing area of 18.3 ix? for the plank
cushion is less than the product base area of 64 in’. The
only way to maintain full base support and reduce the bearing
area is to remove some of the load bearing material from the
cushion as in Figure 5.

During impact, the force exerted downward on the top of
the ribbed cushion by the product compresses the cushion which
in turn absorbs energy and decelerates the product. At any
instant, this force is essentially the same on every
horizontal cross section of the cushion throughout its
thickness. But, since the cross sectional area changes, the

stress on each cross section is different which causes the

cushion to deform more in thinner sections (at the feet). The

13

I

BASE OF PRODUCT CUSHION
TOP OF CUSHION THICKNESS

I

REMOVE MATERIAL

 

 

 

 

FIGURE 5. MATERIAL REMOVED FROM A PIANK CUSHION TO FORM
A CUSHION WITH A NONUNIFORM CROSS SECTION.

l4

cushion in Figure 5 therefore behaves like a smaller plank
cushion with possibly a different thickness [Burgess, 1988].
The idea behind converting a cushion with a variable cross
section into an equivalent plank cushion in terms of peak-G
performance for purposes of analysis is central to this thesis
since the primary objective is to be able to use published
cushion curve data to predict ribbed cushion performance.

Before proceeding with ribbed cushion design, the
remainder of the MIL - HDBK -304B cushion design procedure
will be discussed. The motivation behind Part 3 of the
cushion design procedure is that all cushions tend to lose
thickness and thus reduce the protection they provide when
subjected to a constant load for a period of time. This
phenomenon is known as creep. The creep rate for most
cushioning materials over time is greatest at initial loading
and declines exponentially with elapsed time thereafter.
Since theIamount.of settling'isldifficult to estimate exactly,
it must be determined by testing. If it is known from
experiment that in long term storage, a particular type of
foam settles 5 percent for example, the design thickness for
this type of cushion should be 100 / (1 - .05) = 105 %
of the thickness chosen for protection from the cushion
curves. Parts 4 and 5 of the cushion procedure are self
explanatory and for this reason will not be covered here
except to say that actual impact testing after design is
especially recommended for ribbed cushions since the mode of

defamation is much more complicated. For this reason, peak

15
therformance is expected.to be much.more approximate than for
plank cushions.

To date, not much research has been done in the area of
designing with ribbed cushions since the prediction of
deceleration levels.is.difficult~ For this reason, the survey
shown in Appendix Awwas sent to a number of foam producers and
users to evaluate the interest in these types of cushions.
The applicants were asked to rank seven reasons for using
ribbed cushions using a response of "1" as the most important
reason to "7" as the least important. Table 2 shows the
results of the survey. Reason 3 (Reducing G-levels for high
product surface area situations), received 75 percent of the
number 1 rankings while reason 5 (Better performance with less
material), received the other 25 percent of the number 1
rankings. Reason 5 also received 57 percent of the number 2
rankings and 12.5 percent of the number 3 rankings. It would
appear that reason 3 (Reducing G-Levels for high product
surface area situations), and reason 5 (Better performance

with less material), are the most popular responses.

\lmmwaI-O
eee eee

16

TABLE 2. SURVEY

FREQUENCY OF VOTES (PERCENT)

 

 

 

 

 

 

 

WMWZCZ ZOUJVDZI'JU

 

 

 

 

 

 

 

 

 

RANKING
1 2 3 4 5 6 7

1 40 33

2 12.5 40 67

3 75 12.5 20

4 43 62.5

5 25 57 12.5

6 100

7 100
REASONS

Ease of hand fabrication for short tern production runs.
Ease of soloing for long tern production runs.

Reducing G-levels for high product surface area situations.
Lower cost than plank cushions for the same perforlance.
Better perforsance with less laterial.

Colpany requires you to.

Status Quo.

17

Chen [1986] studied the effect of ribbing on the shock
transmission characteristics of expanded polystyrene cushion
material using 3 different thicknesses, 6 different drop
heights, and five different static stress levels. Side by
side comparisons for both ribbed and flat EPS were presented.
It. was observed that at lower drop heights and static
stresses, the shocks obtained from ribbed and flat EPS were
similar, at higher drop heights and static stresses however,
the cushion curves for ribbed and flat EPS differed
significantly. It was concluded that the cushion curves
developed for flat planks are inadequate to describe the
cushioning behavior of ribbed EPS under more severe
conditions.

Chen’s study outlines the basic problem of designing
ribbed cushions but does not offer a simple solution. It
would be necessary to generate an infinite number of cushion
curves to be able to predict the dynamic behavior for each
possible cushion configuration because the dynamic response of
the cushion is affected by the shape of the test specimen
[Kerstner, 1957]. Kerstner also notes that using a rib taper
of 5° to 15° also helps to reduce buckling. They [Kerstner,
1957; Pearsons and Ungar, 1961] point out that although
economy of cushioning design might dictate the reduction of
cushioning bearing area to a minimum, the designer must insure
that the load bearing area portion of the item can withstand
the resultant stress. It is the intent of this research to

simplify the design of ribbed cushions by developing a method

18
which will allow a ribbed cushion to be viewed as an
equivalent plank cushion so that the shock transmitted may be

estimated using the standard cushion curves.

MATERIALS AND METHODS

2.1 MATERIAL

The cushion material used in this research was ARPROo
3319 Expanded Polypropylene Bead with a density of 1.9 pounds
per cubic foot. The material is a low density closed cell
foam made by ARCO CHEMICAL COMPANY. Large planks were cut
into 8" X 8" X 2" squares and two squares were then glued
together with 3M 76“ High Tack Adhesive to form 8" X 8" X 4"
planks. The hot wire and fixture with interchangeable guide
plates in Figure 6 were used to cut consistent ribs into the
planks as in Figure 7.
2.2 DESIGN OF EXPERIMENT

Three different rib heights (dimension b in Figure 7) of
1.0", 1.5", and 2.0" and three different rib angles ( 6 in
Figure 7.) of 5°, 15°, and 25° for a total of 3 X 3 = 9
different cushion configurations were constructed. Figures 8
through 16 show the actual configurations that were used in
the experiment. Three different loadings and three different
drop heights of 18", 30", and 42" were chosen to simulate
”average" conditions. IEach. cushion sample ‘was randomly
assigned a loading, drop height, and rib configuration and
each data point was replicated 4 times for a total of 3 X 3 X
9 X 4 = 324 samples.

19

20

TO 12 VOLT
‘ fi/PWR SUPPLY

 

 

 

 

 

 

 

 

FIGURE 6. Hot wire and cutting fixture.

21

Depth = Width = e

 

 

_]i
«I
__II.

 

T —I

PLANK PORTION

o \< RIBBED PORTION
L -- 9 I

I-—d—-I

FIGURE 7. Generic dimensions of the ribbed
cushions examined in the experiment.

 

 

 

 

 

I'm??-

 

 

 

22

 

 

 

 

 

 

 

l-- 2.5'-"- 1.5“-

 

 

 

 

Figure 9.

 

Rib Configuration 2.

r 75"! ‘IM'
I, -I I—- 1.49"
in.
N
L
8" A.
Figure 8. Rib Configuration 1.
r1-5‘1 ‘l M-
J L 1.13"
.L a“ 4

23

I- 1.5"-| I 7 25'

_/ \_

-I I- .73"

 

r— 2.5"——I- 1.5“-

 

 

 

 

Figure 10. Rib Configuration .3.

I- ‘II‘S‘

 

 

I- I.5"-I .

T‘2""‘I‘_2"""'
I

 

 

 

 

Figure 11. Rib Configuration 4.

I. 1.5"T— 2.5" —~

24

I. 1.5%] “ [‘5'

 

 

 

 

 

 

[- 1.5”T— 2.5"—q»

 

 

 

 

-I I- 1.37”
a~ A.
Figure 12. Rib Configuration 5.
I’ I.5"-| I 7 75'
-l I— .77“
.L .- J.

 

 

Figure 1.3. Rib Configuration 6.

 

25

I' 1.5"-| “I /~15°

 

I'— 7‘1" 2"“

 

 

 

Figure 14.

I. 1.5"1

 

FYI?"

 

Rib Configuration 7.

m 25-

 

—I I— .42-

 

FTgure 15.

Rib Configuration 8.

 

.JL.

 

.IL_

 

Wa-

 

 

 

 

'- 1.531
in
(\i
,I— -II- .11"
“3.
.1— .
I? a" A.
Figure 16. Rib Configuration 9.

27

2.3 TESTING APPARATUS

The test apparatus used was a LANSMONT MODEL 23 CUSHION
TESTER. A piezoelectric accelerometer was mounted on the
dropping head of the tester and the signal was carried by a
shielded cable to a Kistler piezotron charge amplifier and
then on to a twelve bit analog to digital card on an IBM AT
compatible 80286 computer» The software used.by this computer
to analyze the shock pulses was Test Partner from LANSMONT
CORPORATION. The shock outputs were displayed on a VGA
computer monitor (See Figure 17). ASTM D1596 - 78a was used
as a guideline for all testing. The drop tests onto the

ribbed cushion samples were conducted as follows:

TEST PROCEDURE:

1) Hook up equipment as shown in Figure 17 and allow 10
minutes for the charge amplifier to warm up.

2) Set up the computer program to monitor and analyze the
shock pulse.

3) Make sure that the guide rods are clean and have a thin
film of lubrication since air friction and friction due
to the sleeves contacting the guide rods will slow down
the dropping head. The dropping head must be raised
higher than the calculated free fall drop height.

4) Place a variety of weights on the dropping head to
alter the static loading.

5) Insert a ribbed cushion sample.
6) Raise the falling platen and drop it onto the cushion.

7) Record the peak deceleration value (the computer program
will display the shock pulse on the monitor).

8) Repeat steps 1 through 7 for all drop heights, static
loadings, and cushion configurations.

28

 

N
e

Lifting mechanism

 

 

Weights

 

Dropping head
Cushion sample
Seismic mass
Accelerometer
Charge amplifier

Central processing unit

Guide Rods

PPDNPIPIPSNN

 

 

 

 

 

 

 

 

 

TEST
PARTNER

I——4——I l I

 

 

 

 

 

 

 

 

8 I

 

 

 

 

FIGURE 8. Testing apparatus and monitoring equipment.

29

The results of the drop tests on the ribbed cushions
shown in Figures 8 through 16 are shown in Tables Bl through
B9 in Appendix B. 'The third column of each table contains the
actual peak deceleration in G's for the weight in column 2
dropped from the height in column 1 onto the configuration
referred to. The remaining 7 columns deal with prediction
methods and will be discussed in Chapter 3. Possible errors
in the raw data will be covered next.

The greatest likely source of error associated with the
technique lies in the measurement of the equivalent free fall
drop height referred to in step 3. Since the actual drop
height is less than the machine drop height due to friction,
it must be inferred from the measured impact velocity. Two
methods were used to determine the impact velocityu The first
was to use a photoelectric sensor mounted just above the
impact surface of the cushion which measures the amount of
time (gate time) it takes for a 1/2" wide trigger blade
mounted on the dropping head to pass through it. This time
value can then be substituted into the following equation:

V = d/t + .Sgt Equation (3)
suggested by LANSMONT CORPORATION, where:

V

impact velocity (in/sec)

d

width of the trigger blade = 1/2"

t = gate time (seconds)

30
The equivalent free fall drop height h corresponding to
this impact velocity must be obtained from:
h = V",/ 29. Equation (4)
TableI3 shows the gate times and impact velocities required.to

produce 18", 30", and 42" free fall drops.

TABLE 3. GATE TIME, IMPACT VELOCITY & FREE FALL DROP HEIGHT

     

GATE TIME IMPACT VELOCITY FREE FALL DROP HEIGHT
(Hilliseconds) (inches/sec) (inches)

4.27 117.9 18
3.30 152.3 30
2.78 180.2 42

 

   

 

 

 

 

 

 

 

 

Another method.used to verify the impact velocity in this
experiment was to raise the dropping head to the desired
equivalent free fall drop height, drop the head onto the
cushion, and record the shock pulse. The Test Partner
software was used.toicalculate the impact velocity as the area
under the curve up to the peak acceleration. This procedure
was repeated by adjusting the dropping head up or down until
the desired impact velocity was achieved. The two methods

gave similar results.

31

A second source for error in this experiment is the
measurement of the peak deceleration. For the accelerometer
used, the output voltage may be in error by as much as i 2%.
The coupler or charge amplifier which conditions the
accelerometer signal, may change the signal by as much as
i 5%. The analog signal may be altered an additional 5 % in
the process of passing through the signal splitter and the
analog to digital conversion card in the computer. If these
errors are additive, then the total error in measuring the
peak deceleration may be as high as i 12 %. Some other errors
include tribo-electric noise which is caused by the cable
whipping during impact, ringing noise from the test fixture
after impact and electromagnetic interference from other
pieces of electronic equipment in the building.

Finally, the material tested is rated at 1.9 pounds per
cubic foot nominal but can vary from 1.8 PCF to 2.0 PCF
depending on whether a sample is taken from the edge or the
center of the plank material [Lentz, 1990]. Table 4
summarizes all of these associated errors. Based on these
errors, the values for the actual G's reported in Tables B1
through B9 in Appendix B must be regarded as accurate to
within f 12% for drop heights which may be i 6%Idifferent than

those also reported.

32

TABLE 4. SUMMARY OF ASSOCIATED ERRORS

 

 

Drop Height:
Accelerometer:
Coupler:

Computer Hardware

6%
2%
5%
5%

 

 

CHAPTER 3

PREDICTION METHODS USING PLANK CUSHION CURVES

In this chapter, seven methods for predicting ribbed
cushion performance will be presented and evaluated. These
methods range from the very simple but crude to complex. A
side by side comparison of the actual deceleration values
obtained to the seven predicted values for each data point and
configuration are shown in Appendix B. See Figures 8 - 16 for
profiles of the actual cushion configurations used. The
following is a detailed discussion of each method (from the
simplest to most complex) and why each was considered. Since
the idea is to convert a ribbed cushion into an equivalent
plank cushion, each method will focus on producing a bearing
area and/or thickness with whidh the conventional cushions
curves can be used. The predicted G’s referred to in Tables
Bl though B9 therefore come from the cushion curves (Figure 2)
with a static loading equal to the weight divided by the

predicted bearing area.

Method 1: From Figure 7, the most obvious guess on the
equivalent bearing area is the contact area between the
product and the cushion, or "e x e" which is constant at 64
in?. This method, although over simplified, was used in the
past by packaging specialists because it was not yet well

33

34
understood how ribbing affected the overall dynamic
performance of the cushion. As shown in Tables B1 through B9,
It does appear to work fairly well but only for the medium
weights at each drop height. The trend is to overstate G for
the lower weights and underestimate it at the higher weights.
Because the ribbed cushion is much less stiff than one with a
constant bearing area of e x e, overestimation was expected.
The most.probable:reason for the underestimation at the higher
weights is that beyond the static loading of 78.5 lbs divided
by 64 in? (1.22 psi), Arproo planks show a decrease in G's
(see Figure 2) while the ribbed cushions are bottoming out.
Based on the 'Standard error' between the predicted and the

actual data, defined here to be:

SE 2 (actual G’s - predicted G’s)2
' .N Equation (5)

 

where N = 9 is the number of predictions, this method ranked

fifth in accuracy of prediction.

Method 2: This method uses the footprint of the ribbed
cushion in Figure 7 to estimate the bearing area. Since there
were two ribs throughout, each measuring d = 1.5" by e = 8"
regardless of the configuration, the bearing area using this

prediction method is constant at:

A - 2(d at e) Equation (6)

35

which equals 2*(1.5" X 8") = 24 ix? for every configuration.
This method ignores the substantial contribution of the plank
portion when the cushion is dynamically loaded at high drop
heights and high static stresses. Since the footprint area
represents the other end of the spectrum for bearing area
predictions, This method is expected to show the reverse
trend compared to Method 1. Figures Bl through B9 confirm
this. The trend now is to underestimate G for the lower
weights and overstate it at the higher weights. This method
ranked seventh in predicting the outcome of the experiment.

It is easily demonstrated by experiment that flipping the
ribbed cushion in Figure 7 upside down so that the ribs
contact the product and.the plank contacts therground.does not
change the shock G. This should be expected since the
resistance of the cushion is affected only by the change in
its thickness during compression. Based on this fact and the
complimentary trends for’Methods 1 and 2, itwwould appear that
the best choice for the bearing area would be some sort of
weighted average of the foot print and plank areas. The
remaining methods were chosen to evaluate the various ways to
weight these areas“ As the results show, it is generally true
that some sort of weighting procedure gives better results

overall, but this is not true in all cases.

36
Method 3: This method uses the average of the plank and

footprint areas. The bearing area is:

A - e(d + 9/2). Equation (7)

which is constant at: tP' * (1.5" + 8"/2) = 44 in?. This
method would appear to be a good "middle of the road"
predictor since it does take into consideration the cross
sectional change between the plank and the footprint.
However, it weighs them equally regardless of the rib height
h and the rib angle 0. It is therefore possible with this
method to get the same prediction for G for a wide variety of
rib heights and angles and also a wide variety of plank and
footprint combinations so long as the average of these two is
constant. For these reasons, this method is not sound even
though it ranked third in predicting the outcome of this

experiment.

Method 4: This method uses the area at the widest

portion of the rib. From Figure 7, this area is:

A -2 an (e a: 0) Equation (8)

The reasoning here is that the force of compression is
transmitted from the plank portion to the ribs through this
area. Separate compression tests on these ribbed cushions

show that deformation of the plank portion is greatest in the

37
regions where the ribs meet the plank. The region in between
the ribs and the outside the ribs near the edges of the plank
deform very little in comparison. This interface bearing area
may therefore be instrumental in determining the shock
transmitted. The results in Tables Bl through B9 show that
this method appears to nearly always underestimate the actual
shock by about 5 G's on the average. Simply adding 5 G’s to
the predicted result would improve the method considerably but
would be difficult to justify on physical grounds since this
approach does not and cannot take into consideration
variations in either the plank or the footprint. It is
possible with this method to get a wide range of actual G's by
varying the plank and footprint areas while keeping A = 2(e*c)
constant. In spite of this short coming, this method ranked

fourth in predicting the outcome of the experiment.

Method 5: This method weighs the cross sectional areas
equally. An estimate of the average cross sectional area can
be obtained by drawing many equally spaced horizontal lines on
the cushion as in Figure 7 and averaging the areas at these

sections,

ang-z_A_/S

N. Equation (9)

where N is the number of sections examined (lines drawn). The

true average area is obtained only in the limit as N

38
approaches infinity. Multiplying the numerator and
denominator on the right hand side of equation (9) by the

uniform spacing h between the parallel lines leads to

ang- (2 A’s) *h_ 2(Aarh)

N height Equation (10)

Since N X h is the height (total thickness) of the ribbed
cushion and since the area at any given section multiplied by
the spacing is just the volume of material contained between
two consecutive lines (one of which is at the area being
examined), in the limit as N becomes large, the true average

area approaches:

Total Cushion volume
Thickness

 

avg.4-
Equation (11)

The ribbed cushions used here are made up of trapezoidal
shapes. Figure 7 can be used to determine the total cushion
volume ‘V’Ias the sum of the contributions of the two ribs and

the plank portion,

*.be+ae2

V-2*———(C+d)
2

Equation (12)

Since the thickness is a + b, the bearing area becomes:

__ (c + d) ae2
(a-Itu *.be-+ a +1)

 

Equation (13)

39
When used along with the weight to get the static loading,
this method ranked first in predicting G. For this reason,

this method will be dealt with in more detail in chapter 4.

Method 6: This method considers the cushion to be made
of a linearly elastic material and applies Hooke’s Law'to each
variable cross section of the ribbed cushion [Faupel, 1967].
When the cushion is compressed by a force F distributed over
the topIof the cushion, this same force is transmitted through
every cross section. Since the area A changes from section to
section, the stress a = F / A. does also. From Hooke's Law,
the strain 6 (which represents the rate of change of
displacement u with respect to elevation x) is just a / E

where E is the modulus of elasticity for the material,

 

Equation (14)

The total compression of the cushion is therefore:

E0 A

Equation (15)

In the case of an equivalent plank cushion where the area is
constant at A5, the above expression yields,

11- 'Ft.
EAC

 

Equation (16)

40
Forcing the ribbed and the plank cushions to be equivalent in
producing for a given force F the same compression u,

requires that the bearing area be:

t

C 1: dx
I; —A_ Equation (17)

As with method 5, the bearing area may be approximated by
drawing N equally spaced horizontal lines on the ribbed

cushion and obtaining the area A1, A2, A3 A, at these

 

 

sections. If the spacing between lines is constant at h,
then:
A _ Nh _ N
C i . A ._h_ _1_ . _1_ . _1_ .
A1 A2 ' ' ' AN A1 A2 ' ' ' AN Equation (18)

The exact value can be obtained only by integration. Again,

referring to Figure 7, since the cushion is made up of two

parts, the rib portion and the plank portion, the integral

Equation (19)

is the sum of the separate integrals over the plank and rib

portion,
0 dx a
planl: 0 e 92

Equation (20)

41

For the two ribs,

 

I b dx
ribs I; 2[e*C + (esd -e*C) * (X/b)] E t’ (21)
qua ion

b

Libs- 2*e(c-d) 1n—

 

QQ

Equation (22)
Combining these two, the bearing area becomes:

(a +1» * e

b in £3 .
2(cg_ d) d Equation (23)

A—

 

 

53+
W

This method works well for "average" conditions and ranked
second in predicting the outcome of this experiment. This
method is suspect however because the material is unlikely to
be linear which is probably why it fails to predict G at

extreme static loadings and drop heights.

Method 7: Up to now, all of the prediction methods have
been based on converting a ribbed cushion into an equivalent
plank cushion which has the same thickness as the ribbed
cushion but has a different bearing area. This method takes
the area of the equivalent plank cushion to be the same as the
plank area of the ribbed cushion and chooses the thickness so
that the volumes of the ribbed and equivalent plank cushions

are the same. This is the compliment of the average area

42
method (Method 5). Suppose for example that a ribbed cushion
consists of a 1" thick plank portion measuring 8" X 8" with 3"
thick ribs where the total rib volume is 64 cubic inches. The
total cushion volume is therefore 8 X 8 X 1 + 64 = 128 cubic
inches. With this method, the bearing area would be 8" X 8"

= 64 in2 and the equivalent thickness would be 128 in3 / 64 in2

2 inches. Note that with Method 5, the thickness is 1" + 3"
= 4" but the equivalent bearing area is 128 in’,/ 4 in = 32
in”. This method works rather well at medium to high drop
heights and.static loadings.as expected because the plank area
is now'being accounted for, but fails to predict well at lower
drop heights and static loadings. This method ranked sixth in

predicting the outcome of the experiment.

CHAPTER 4

4.1 DISCUSSION AND CONCLUSION

Since Method 5 ranked #1 in predicting G compared to the
six other methods presented, the reasons for its performance
will be investigated here. Up to this point, we have referred
to this method as the "true average area" method since it
equally weighs each cross sectional area from bottom to top.
In essence, this method makes a plank cushion with the same
thickness out.of the same amount of material which reduces the
bearing area in the process. Keeping the thickness the same
ensures that the travel distance allotted to the decelerating
mass in coming to rest during impact remains unchanged.
Keeping the volume the same ensures that the material which
actually absorbs the energy from the impact is still there in
the same quantity. More specifically, when the air that is
trapped inside a closed cell cushion is compressed, it is the
total air yglume which determines the resistance to
compression. The proof of this is in the Gas Law: [Benning,
1969],

pV = nRT: Equation (24)
Where p is the absolute pressure of the air inside the
cells, V is the total air volume, n is the number of moles
occupying this volume, T is the absolute temperature, and R
is the universal gas constant, R = 45.61 ml - atm / mole-°R.
During the dynamic compression of a closed cell foam, the
temperature of the air trapped in the cells remains

43

44
essentially constant [Burgess, 1988]. Since the cells are
closed, the quantity of air (n moles) also remains constant.
The Gas Law therefore states that the product of the pressure
and volume remains constant at PAL ,
pV = pan Equation (25)
Where p0 = 1 atmosphere is the cell air pressure before
compression and V. = At where A is the bearing area and t
is the thickness. Equation (25) states that as the cushion is
compressed, the volume decreases and the air pressure inside
the cells increases. Since the resistance to compression is
just the air pressure multiplied by the bearing area, the
resistance therefore increases in proportion to the decrease
in volume. It can be shown [Burgess, 1988] that the cushion
curves for flat planks may be derived on the basis of this air
compression model. For these reasons, it is reasonable to
expect now that it is cushion volume which determines G and
this is the heart of Method 5. In light of these facts, we
now should view this model as the Equivalent Volume Method.
The total standard error for each method was obtained by
using all of the predicted G versus actual G data for all of
the cushion configurations (Tables B1 though B9) for the
particular method in question in Equation 5. In each case
then, N = 81. The results are shown in Table B10. The total
standard error for the Equivalent Volume Method was lowest at
4.8 G's. Total experimental measurement error on G was i 12 %
from Table 4. Also, the cushion curves are reported for a

given nominal density, which is 1.9 pounds per cubic foot for

45
Arpro" 3319. However, the density of the samples tested
varied from 1.8 PCF to 2.0 PCF which is normal according to
ARCO CHEMICAL'S Analytical Services people [Becker, 1990].
This difference in density can change the actual deceleration
values obtained by i 5 G's from the values reported in the
cushion curves. For these reasons, an analysis was carried
out to see how much of the Standard Error value of 4.8 G’s for
the Equivalent Volume Method w explained by
experimental error. For example, if the actual and predicted
G's are 25 G and 35 G respectively, then the actual G could
haye_been 25 + 12 % = 28 G and the predicted G cauld_hayg
been 35 - 5 = 30 G. The remaining discrepancy of 30 - 28 = 2
G can only be attributed to the method error. The computer
program in Appendix C, varies the actual G columns of Tables
Bl through B9 up or down by as much as i 5 G's and the
predicted.G's from the Equivalent Volume (column 5) up or down
by as much as i 12 %, whichever way reduces the discrepancy.
In line 10 of the program, the actual and the predicted G’s
for all 81 of the data points in Tables Bl through B9 are
stored in the dimensions GA and GP respectively. Lines 20
through 40 read the data into these dimensions. Lines 50
through 120 reduce the difference between the actual and
predicted G’s by the maximum amount allowed (i 12 % on actual
G, i 5 G on predicted G) and record the remaining difference
in the dimension DIFF. Lines 130 to 170 calculate the
Standard Error using Equation (5) . The reduced standard
error taking into account these errors becomes 0.09 G's.

Therefore, all of the difference between actual and predicted

46

actual and predicted G's cam explained by measurement error
except for 0.09 G's which must be associated with the method.

Based on this result and the simplicity of the method,
the Equivalent Volume Method should be regarded as the "method
of choice" when trying to determine the bearing area for a
cushion design even though it is not a perfect model. It is
fairly simple to use and should give engineers a useful tool
to help cut down the amount of time needed for a ribbed

cushion design.

4.2 RECOMMENDATIONS FOR FUTURE RESEARCH

The amount of deflection that the cushion experiences
during impact may help to explain why the predicted results
were not very close to correct for the extremes of static
loading and drop height. A similar experiment may be
performed that would include a high speed video camera that
could observe the amount of deformation in the ‘various
components (plank and rib portions) of the cushion. It is
most probable that in light static loading and low drop
heights, the ribbed portion of the cushion was absorbing most
of the shock. Therefore, the method was overestimating the
contribution of the plank portion of the cushion to the total
bearing area. In contrast, for higher static loading and
greater drop heights, the plank portion of the cushion was
absorbing more of the shock and therefore the method was
underestimating the contribution of the plank portion. A high
speed video camera could capture these events and allow for
closer scrutiny that in turn could help improve the model.

Also, due to the size constraint of the cushion tester
used, only cushions up to 8" x 8" could be tested. The rib
angle of the cushion could therefore only be a maximum of 25
degrees when the plank thickness was 1.5" and the number of
ribs was 2. Consequently, the cushion configurations were
relatively similar in shape. This may account for the good
performance of the model. A cushion tester with a larger
dropping surface area could allow for the study of many ribs

47

48
and larger rib angles to see if the method works just as well

with more variance of the cushion parameters.

JKIPIPIEDIE)]E)K IL

RIBBED CUSHION SURVEY

APPENDIX A: RIBBED CUSHION SURVEY

Dear Packaging Specialist:

I as a graduate student at Michigan State University in the school of Packaging and I as working on a
thesis involving ribbed cushions. I would appreciate it very such if you would take a couple of
sinutes of you tise to fill out this survey and return if to me at your convenience. Thank you very
such for your tile.

Sincerely,

Mr.

Gary C. Granthen
I. Your Job Title

A) Packaging Engineer
B) Packaging Supplier
C) Other (Please specify)

II. Main Duties Performed.

A) Designing packages for your company.
B) Designing and/or selling packages to other companies.
C) Other (Please specify).

III. Do you design and/or use ribbed cushions? (Closed cell)

A) Yes
B) No

IV. If your answer to III is yes, place in order of
importance the following reasons why you use them (1 =
most important reason).

Ease of hand fabrication for short ters production runs.
Ease of solding for long ters production runs.

Reducing G-levels for a high product surface area scenario.
Lower cost than plank cushion for the sase perforsance.
Better perforsance with less saterial.

__ Cospany requires you to.
Rawsmm.

Other (Please specify).

 

V. If your answer to III. is no, please state why not in the
space below.

 

 

49

APPENDIX B
TABLES B1 THROUGH BIO

5O

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

APPENDIX B. TABLES E31 — 810

TABLE BI. ACTUAL AN0 PREDICTED PEAK DECELERATION VALUES FOR CONFIGURATION 1 (IN 0'5).
DROP WEICHT ACTUAL 1 2 3 4 5 5 7

HEIGHT (POUNDS) 0’3
18" 41.4 25.5 40.2 18.3 29.6 20.3 32.9 28.0 41.8
18' 72.3 21.0 25.2 11.9 18.8 14.7 20.5 18.2 27.0
18" 103.3 19.0 19.1 23.5 15.7 9.9 16.7 15.0 20.8
30" 4 1.4 33.5 42.8 24.0 33. 1 26.3 35.8 32.0 45.4
30" 72. 3 29.3 30.0 20.0 24.7 19. 9 28.5 23.8 32.8
30" 103.3 28.5 25.0 39.7 20.4 23.2 21.8 20.0 28.9
42" 41.4 42.8 48.8 29.3 37.5 30.2 40.8 36.0 53.0
42" 72.3 37.5 33.5 30. 1 29.5 29.0 30.3 29.2 39.3
42" 103.3 39.0 29.6 76.2 29.0 40.4 29.0 29.0 37.1
STANDARD ERROR (G’S) 7.3 31.6 5.9 7.8 5.6 5.6 8.0

BEARING AREA PREDICTION METHOD NUMBER AREA (IN 2 )

1. PLANK AREA - o2 64.0

2. FOOTPRINT AREA - 20. 24.0

3. AVERAGE 01" PLANK AND FOOTPRINT AREAS - 0(d + 0/2) 44.0

4. TOP OF RIB AREA - 200 26.1

5. 1'RUEAVERAGEAREA-04[(c+a)+b+(c+d)]/(a+b) 49,3

6. HOOKE'S LAW AREA - (0 + b) a 0 / [(0/0) + b/2 o (c - d) In(c/d)] 41,4

7. EQUIVALENT THICKNESS AREA - 02 .- T - (c + d) 4 b . (./54) + a 54.0

51

APPENDIX B (cont,d.)

TABLE 82. ACTUAL AND PREDICTED PEAK DECELERATION VALUES FOR CONFIGURATION 2 (IN G'S).

 

 

 

DROP WEIGHT ACTUAL 1 2 3 4 5 5 7
HEICHT (poms) G'S
18" 44.9 27.0 37.8 17.6 27.5 23.6 31.5 28.0 39.2
16" 78.5 21.8 23.4 10.3 16.0 15.5 19.7 16.2 25.0
18" 112.3 20.0 16.1 44.3 14.6 11.7 16.3 15.0 19.7

 

 

 

 

 

30' 44.9 33.5 40.2 22.9 31. 7 28.9 34. 7 32.0 42. 6
30' 78.5 29.0 28.8 20.6 23.5 21.2 25. 7 23.8 31.4
30" 112.3 28.5 23.8 62.7 19.9 20.1 21.0 20.0 27.7
42' 44.9 41.0 46.0 29. 1 35. 6 32.3 39.4 36.0 49.9
42" 78.5 35.5 32.2 32.2 29.2 29.0 29.9 29.2 37. 6

 

 

 

 

 

STANDARD ERROR (G'S)

 

 

 

 

 

 

 

 

 

BEARINC AREA PREDICTION METHOD NUMBER AREA (IN 2 )
1. PLANK AREA - 4 2 64.0
2. FOOTPRINT AREA - 2:10 24.0
3. AVERAGE OF PLANK AND FOOTPRINT AREAS - 6(d + 6/2) 44.0
4. TOP OF RIB AREA - 24c 30.4
5. TRUEAVERAGEAREA=O¢[(B+O)+b+(c+d)]/(a+b) 51,4
6. HOOKE'S LAW AREA - (0 + b) 4 e / [(0/6) + b/2 4 (c - d) In(c/d)] 44.9
7. EOUIvALENT THICKNESS AREA - 4 2 .- T - (c + a) 4 b 4 (4/64) 4 a 64.0

52

APPENDIX B (cont,d.)

TABLE 83. ACTUAL AND PREDICTED PEAK DECELE’MTION VALUES FOR CONFIGURATION 3 (IN G'S).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DROP WEIGHT ACTUAL 1 2 3 4 5 5 7
HEIGHT (mums) 6'5
16" 48. 1 26.0 35.6 17.0 25.9 27. 1 30.6 28.0 37.0
16' 64.1 20.0 22.1 9.6 17.4 17.6 19.3 16.2 23.5
16' 120.2 19.0 17.5 66.9 13.7 14.5 16.0 15.0 16.6
30" 46.1 34.5 36.3 22.0 30.5 31.4 33.9 32.0 40.3
30' 84.1 28.0 27.6 21.6 22.6 23.3 25.3 23.6 30.2
30’ 120.2 26.5 22.6 91.5 19.6 19.9 20.7 20.0 26.5
42- 46.1 40.5 43.6 29.0 34.2 35.2 36.5 36.0 47.3
42' 64. 1 35.3 31.3 36.2 29.0 29. 1 29.7 29.2 36.2
42" 120.2 37.6 29.1 151.2 29.2 29.0 29.0 29.0 35.5
STANDARD ERROR (0’5) 4.9 31.0 5.9 5.5 4.7 4.7 4.6
BEARING AREA PREDICTION METHOD NUMBER AREA (IN 2 )
1. PLANK AREA - 43 64.0
2. FOOTPRINT AREA - 200 24.0
3. AVERAGE OF PLANK AND FOOTPRINT AREAS - 0(d + 0/2) 44.0
4. TOP OF RIB AREA - 206 35.1
5. TRUEAWRAGEAREA-cc[(c+a)+b+(c+d)]/(a+b) 53.2
6. HOOKE'S LAW AREA - (a + b) v 0 / [(0/0) + 0/2 0 (c - d) In(c/d)] 48.1
7. EDUIvALENT THICKNESS AREA - 4 2 .- T - (c + d) 4 b 4 (4/64) 4» a 64.0

53

APPENDIX B (cont,d.)

TABLE 84. ACTUAL AND PREDICTED PEAK DECEERATION VALUES FOR CONFIGURATION 4 (IN G 'S).

 

 

 

 

 

 

 

 

 

 

 

 

 

DROP WEIGHT ACTUAL 1 2 3 4 5 5 7

HEIGHT (461m; 05

18" 37.6 25.5 43. I 19.4 32. 1 22. 7 33.0 26.0 45.3
16" 65.6 17.3 27.3 13.7 20.0 16.2 20.5 18.2 29.7
18" 94.2 18.0 20.3 12.6 16.5 10.6 16.7 15.0 22.6
30" 37.6 32.0 46.0 25.4 35.1 26.3 35.6 32.0 49.5
30' 65.8 28.0 31.5 19.8 26.0 20.8 26.5 23.6 35.0
30- 94.2 26.0 26.3 27.3 21.2 20.4 21.6 20.0 30.6
42" 37.6 36.5 52. 1 29. 7 40.0 31. 7 40.9 36.0 57.3
42" 65.6 35.5 35.4 29.2 30.0 29.0 30.3 29.2 42.5
42' 94.2 37.0 30.1 51.0 29.0 31.3 29.0 29.0 39.3
STANDARD ERROR (G'S)

 

 

 

 

 

 

 

 

 

 

  

 

BEARING ARE PREDICTION METHOD NUMBER

PLANKAREA-Oz

FOOTPRINTARE-Zdo

AVERAGE OFPLANK AND FDOTPRINT ARES - 0(d + 0/2)
TOPOFRIBARE-2oc
TRUEAVERAGEAREA-oo[(o+a)+b+(c+d)]/(a+b)
HOOKE’S LAW ARE - (0 + b) o 0 / [(0/0) + b/2 o (c - d) In(c/d)]
EDUIVALDVTMCKNESSAREA-4’;T-(c+6)464(4/64)+6

g
o

N999?!“

ARE (IN 2)

64.0
24.0
44.0
26.8
45.4
37.7
64.0

 

54

APPENDIX 8 (cont, d.)

TABLE 85. ACTUAL AND PREDICTED PEAK DECRERATION VALUES FOR CONFIGURATION 5 (IN G'S).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DROP WEIGHT ACTUAL 1 2 3 4 5 6 7
HEIGHT m} 6'5
18' 42.4 36.8 39.5 18.1 28.9 27.3 31.4 28.1 41.3
18" 74.5 19.0 24.5 11.3 18.5 17.8 19.6 18.1 26.5
18' 106.2 18.0 18.7 29.3 15.4 14.6 16.3 15.0 20.6
30' 42. 4 32.5 42. 0 23. 7 32. 7 3 1.5 34.5 32. 0 44. 9
30' 74.5 27.0 29.6 20.2 24.3 23.3 25.6 23.8 32.7
30' 1 06.2 30.0 24. 6 46.0 20.2 19.9 20. 9 20.0 29. 1
42' 42. 4 36.5 47.9 29.2 36.9 35.3 39.2 36. 1 52. 6
42" 74.5 35.0 33.0 30.6 29.3 29. 1 29.8 29.2 39.5
42' 106.2 39.0 29.4 87. 1 29.0 29.0 29.0 29.0 37.9
STANDARD ERROR (G'S) 6.6 31.3 5.8 6.3 5.3 5.3 7.8
BEARING ARE PREDICTION METHOD NUMBER AREA (IN 2 )
1. PLANK AREA - 43 64.0
FOO'IPRINT ARE - 264 24.0
AVERAGE 01' PLANK AND F'OOTPRINT AREAS - 4(6 + 4/2) 44.0
TOP 01' R16 AREA - 24: 32.5
TRUEAVE'AGEARE-OOKO+O)+b+(c+d)]/(c+b) 48.3
HOOKE'S LAW ARE - (a + b) o O / [(0/0) + 6/2 a (c - d) In(c/d)] 42.5
EDUIVALENT THICKNESS AREA - 4’.- T - (c + d) 4 b 4 (4/64) 4 a 64.0

N999?!“

 

55

APPENDIX 8 (cont, d. )

TABLE 86. ACTUAL AND PREDICTE PEAK DECELERATION VALUES FOR CONFIGURATION 6 (IN G'S).

 

 

 

 

 

 

 

 

 

   
 

 

 

 

DROP WEIGHT ACTUAL 1 2 3 4 5 5 7

HEIGHT (m; 6'5

18" 46.8 28.5 36.6 17.2 26.5 31.7 30.4 26.0 38.0
16' 62.0 20.8 22.6 9.7 17.6 19.8 19.2 16.2 24.2
18" 117.2 16.5 17.7 59.5 14.1 16.3 16.0 15.0 19.2
30' 46.6 32.3 39.0 22.3 31.0 34.6 33.6 32.0 41.4
30" 82.0 25.5 26.2 21.3 22.9 25.6 25.1 23.8 30.8
30" 1 17.2 26.5 23.2 60.2 19.8 21.0 20.6 20.0 27.3
42- 46.8 37.0 44.6 29.0 34.7 39.5 36.3 36.0 46.6
42" 62.0 33.5 31.6 34.4 29. 1 29.9 29.6 29.2 37. 1
42" 1 17.2 38.0 29.1 136.9 29. 1 29.0 29.0 29.0 36.4
STANDARD ERROR (G'S)

    

 

 

 

 

 

 

 

 

BEARING AREA PREDICTION METHOD NUMBER AREA (IN 2 )
1. PLANK AREA - 42 64.0
2. FOOTPRINT AREA - 264 24.0
3. AVERAGE 01' PLANK AND FOOTPRINT AREAS - 0(d + 4/2) 44.0
4. TOP OF RIB AREA - 244: 26.1
5. TRUEAVERAGEARE-Ooao-I-a)+04(c+d)]/(a+b) 51.5
6. HOOKE'S LAW ARE - (a 4- b) o O / [(0/0) + b/2 o (c - d) In(c/d)] 46.8
7. EOUIVALENT THICKNESS AREA - 4’.- T - (c 4 a) 4 b 4 (4/64) 4 0 64.0

 

56

APPENDIX B (cont,d.)

TABLE 87. ACTUAL AND PREICTED PEAK DECRERATION VALUE FOR CONFIGURATION 7 (IN G'S).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DROP WEIGHT ACTUAL 1 2 3 4 5 6 7
HEIGHT (POMS) 6'3
18' 34.8 26.5 45.5 20.5 34.3 25.3 32.4 28.0 48.2
18" 61.0 19.0 29.2 14.8 21.2 17.1 20.2 18.2 32.0
18' 87.0 17.5 21.5 9. 7 17.1 13.3 16.6 15.0 24.5
30' 34.8 33.0 48.8 26.5 3 7.0 30.1 35.4 32.0 53. 1
30' 61.0 25.0 32.9 19.9 27. 1 22.2 26.2 23.8 37. 1
30' 87.0 26.3 27.4 22.8 22.1 19.8 21.3 20.0 32.5
42' 34.8 36.3 54.9 30.3 42.2 33. 7 40.3 36.0 61.0
42' 6 1. O 34.0 3 7. 1 29. 0 30. 7 29. O 30. 1 29.2 45.4
42' 87.0 38.5 30.9 39.2 29.0 29.3 29.0 29.0 41.5
STANDARD ERROR (G'S) 11.6 29.3 5.2 4.7 4.6 4.8 15.0
BEARING ARE PREDICTION METHOD NUMBER ARE (IN 2 )
1. PLANK AREA - 01 64.0
2. FOOTPRINT AREA - 264 24.0
3. AVERAGE OF PLANK AND F'OO‘IPRINT AREAS - 0(d + 4/2) 44.0
4. TOP OF RIB AREA - 244.- 27.5
5. TRUEAVmAGEARE-04K04-O)+b+(c+d)]/(0+b) 41.2
6. HOOKE'S LAW ARE - (0 + b) o 0 / [(0/0) + b/2 c (c - d) In(c/d)] 34.8
7. EDUIVALENT THICKNESS AREA - 4’.- T - (c + d) 4 b 4 (0/64) 4 0 64.0

57

APPENDIX 8 ( cont, d. )

TABLE 88. ACTUAL AND PREDICTH) PEK DECELERATION VALUES FDR CONFIGURATION 8 (IN G'S).

 

 

 

 

 

 

 

 

 

 

 

DROP WEIGHT ACTUAL 1 2 3 4 5 5 7
HEIGHT (POM) G 'S
18" 40.8 28.5 40. 6 18.5 29.9 30.8 30.9 28. 0 42. 7
18' 71.6 20.0 25.4 12.1 18.9 19.3 19.4 18.1 27.7
18' 102.2 18.5 19.2 21.8 15.8 16.1 16.1 15.0 21.4
30" 40.8 33. 0 43.2 24.2 33.4 34.0 34.2 32.0 46. 7
30' 71. 6 28.0 30.2 20.0 24.8 25.3 25.4 23.8 33. 7
30' 102.2 26.3 25. 1 3 7. 7 20.4 20. 7 20.8 20.0 30. 1
42" 40.8 3 7.5 49.2 29.3 37.8 38. 6 38.8 36.0 54. 6
42' 71. 6 34.0 33. 7 29.9 29.5 29. 7 29. 7 29.2 41. 1
42' 102.2 39.0 29.6 72.6 29.0 29.0 29.0 29.0 39.2
Lr=_—B==L———W-é====5==%==7
STANDARD ERROR (G'S) 7.5 30.2 4. 4 4. 4 4. 4 4.4 9. 7

 

 

 

 

 

 

 

 

 

 

BEARING ARE PREDICTION METHOD NUMBER AREA (IN 3 )
I. PLANK AREA - 41 64.0
2. FOOTPRINT ARE I 260 24.0
3. AVEAGE OF PLANK AND FOOTPRINT ARES I 0(d + 0/2) 44.0
4. TOP OF RIB AREA .4 200 34.7
6. TRUEAVERAGEARE-0c[(0+0)+b+(c+d)]/(0+b) 45.7
6. HOOKE’S LAW ARE - (0 4- b) c 0 / [(0/0) 4- 0/2 c (c - d) In(c/d)] 40.9
7. EOUIVALENT THICKNESS AREA - 4’.- T - (c 4 d) 4 14 4 (0/64) 4 0 64.0

58

APPENDIX 8 (cont, d. )

TABLE 89. ACTUAL AND PRmICTEJ PEAK DECELERATION VALUES FOR CONFIGURATION 9 (IN G'S).

 

 

 

 

 

 

 

 

 

 

 

 

 

  

DROP WEIGHT ACTUAL 1 2 3 4 5 5 7

HEIGHT (m1 6'3

18" 46.4 29.0 36.8 17.3 26.7 35.6 30.2 28.0 38.3
18' 81.2 21.5 22.6 9.6 17.7 22.0 19.1 18.2 24.5
16' 115.6 20.0 17.8 55.1 14.3 17.5 15.9 15.0 19.4
30" 46.4 36.0 39.3 22.4 31.1 36.1 33.7 32.0 41.6
30" 61.2 28.5 28.3 21.1 23.1 27.7 25.1 23.6 31.1
30' 1 15.6 27.5 23.3 75.0 19.8 22.8 20.6 20.0 27. 7
42' 46.4 39.5 44.9 29.0 34.9 43.6 38. 1 36.0 49. 1
42' 81.2 36.0 31.6 33.8 29.1 31.2 29.6 29.2 37.6
42- 1 15.8 39.0 29. 1 130.1 29. I 29. 1 29.0 29.0 36.8
STANDARD ERROR (G 'S)

 

 

 

 

 

 

 

 

  

 

BERING ARE PREDICTION METHOD NUMBER

-.
0

599.4141»

PLANKARE-03
F'OOTI’RINTARE-ch
AVEAGEOFPLANKAND FOOTPRINTARES-«d-I-O/Z)
TDPOFRIBARE-20c
WEAVWGEMEA-04[(0+a)+b+(040)1/(04-0)
HOOKE'S MW ARE - (0 + b) v 0 / {(0/0) + b/2 4 (c - d) In(c/d)]
EOUNALEVTTHIGKNESSARE-OZ:T-(c+d)vbo(0/64)+0

ARE (IN’)

64.0
24.0
44.0
42. 7
50.6
46.4
64.0

 

59

APPENDIX B (cont.d.)

TABLE 810. TOTAL STANDARD ERROR FOR ECH METHOD (IN G’S).

PREDICTION METHOD 1! 1

BERING ARE PREDICTION METHOD NUMBER

PLANKARE-03

FOOTPRINTARE-Zd.

AVEAGEOFPLANKAND FOOTPRINTARES-0(0+0/2)
TOPOFRIBAfl'A-2oc
TRUEAVWGEAREA-04K04-a)+b+(c+d)]/(a+b)
HOOKE'SLAW ARE - (0 + b) 0 0/[(0/0) + 0/2 l11(0 - d) In(c/d)]
EOUNALEVTTI-IICKNESSARE-0237-(c+0)004(0/64)+0

%
0

Nuns-$41»

APPENDIX C
COMPUTER PROGRAM

05
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
RUN

60

APPENDIX C

COMPUTER PROGRAM TO REMOVE EXPERIMENTAL ERROR

REM: ACTUAL G’S, PREDICTED G’S, AND DIFFERENCE
DIM GA(81), GP(81), DIFF(81)
FOR I=1 TO 81

READ GA(I), GP(I)

NEXT I

FOR I=1 TO 81
DIFF(I)=ABS(GA(I)-GP(I))
TOL=.12*GA(I) + 5

IF DIFF(I)>TOL THEN 110
DIFF(I) = 0

GOTO 120
DIFF(I)=DIFF(I)-TOL

NEXT I

SUM=0

FOR I=1 TO 81

SUM = SUM + DIFF(I)‘2

NEXT I

STDERR=SQR(SUM/81)

PRINT "STDERR = G’S"
PRINT STDERR

END

STDERR = .09 G’S

LI ST OF REFERENCES

10.

11.

12.

13.

61

LIST OF REFERENCES

American Society for Testing and Materials, "Standard
Test Method for Shock Absorbing Characteristics of
Package Cushioning Materials", ASTM Method D 1596 - 78a,
(Reapproved, 1983).

American Society for Testing and.Materials, "Mechanical-
Shock Fragility Of Products Using Shock Machines", ASTM
Method D 3332 - 88.

Becker, W. P. , Arco Chemical Analytical Service Engineer,
personal communication, November, 1990.

Benning, C. J., "Plastic Foams; The Physics and
Chemistry of Product Performance and Process Technology. "
Volume II. "Structure Properties and Applications",
New York, Wiley-Interscience, 1969.

Burgess, G. J., "Some Thermodynamic Observations on the
Mechanical Properties of Cushions", Journal Of Cellular
Plastics, January 1988.

Chen, G. K., "The Effect.of'Ribbing on Shock Transmission
Through Expanded PolyStyrene Cushion.Material", Michigan
State University, 1986.

Faupel, J. H., "Engineering Design", John Wiley and.Sons,
New York, 1967.

Hanlon, J. F., "Handbook of Package Engineering", McGraw
Hill, 1971.

Kerstner, O. 8., "General Principals of Package Design",
NAI-57-187, Northrop Aircraft, Inc. , Hawthorne, Ca, 1957.

Lentz, A. M. , Arco Chemical Engineering Foams Technician,
personal communication, October, 1990.

Military Standardization Handbook, Mil-HDBK-304B,
"Packaging Cushion Design", United States Department of
Defense, 1978. '

Newton, E., "Fragility Assessment Theory and Test
Procedure", Monterey Research Laboratory, Inc.,
Monterey, California, 1968.

Pearsons, K. S., and Ungar, E. E., "Development of
Packaging Material with Constant Restoring Force", WADD
TR 60-573, U. S. Air Force, Wright-Patterson AFB,

Ohio, 1961.

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