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This is to certify that the

thesis entitled

Compression Performance of Corrugated Fiberboard
Shipping Containers Having Fabrication Defects:
Fixed Versus Floating Platens

presented by

Mary Margaret Langlois

has been accepted towards fulfillment
of the requirements for

M. S. Packaging

degree in

 

 

 

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Major profeg
3. Paul Singh

v

Date March 13, 1989

 

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COMPRESSION PERFORMANCE OF CORRUGATED FIBERBOARD
SHIPPING CONTAINERS HAVING FABRICATION DEFECTS:
FIXED VERSUS FLOATING PLATENS

BY

Mary Margaret Langlois

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

MASTER OF SCIENCE

School of Packaging

1989

COMPRESSION PERFORMANCE OF CORRUGATED FIBERBOARD
SHIPPING CONTAINERS HAVING FABRICATION DEFECTS:
FIXED VERSUS FLOATING PLATENS

BY

Mary Margaret Langlois

The compression strength of corrugated fiberboard containers
was studied to determine the effect of using a fixed versus
floating platen. . There was a significant difference in the
compression strength and deflection values of the containers
measured using the fixed and floating platens. The floating
platen gave a compression value 3.6% higher than the fixed

platen.

Three degrees of defect, (1°, 2° and 3°) and a control were
incorporated into the boxes during fabrication to determine
the effect on compression strength. Two box sizes were
used. As the degree of defect was increased, there was a
decrease in the compression strength. The deflection
values were not significantly affected by the fabrication

defects.

to my parents ,

for their encouragement, love, and belief in me.

iii

ACKNOWLEDGEMENTS

I would like to thank my major professor, Dr. Paul Singh,

for his guidance, academic support and time. I would also
like to thank my committee members, Dr. Gary Burgess, Dr.
Diana Twede, and Dr. George Mase for their assistance and

support.
I wish to express my appreciation to Dr. John Gill ,
(Department of Animal Science) for his advice on statistical

analysis.

A special thanks goes to ARVAN Corporation for donating the

corrugated board for this research.

I would also like to thank Kris Nieman and Pat Brady,

friends, for assisting me in fabricating the boxes.

Finally, I wish to thank my family and friends for their

encouragement and faith throughout this research.

iv

TABLE OF CONTENTS

page
LIST OF TABLES .......................................... Vi
LIST OF FIGURES ......................................... ix
1.0 INTRODUCTION .................................... 1
2.0 LITERATURE REVIEW ............................... 4
2.1 Compression Strength ....................... 4

2.2 Transport Requirements and Quality
Standards .................................. 7
2.3 Corrugated Box Closures .................... 9
2.4 Box Size .................................. 10
3.0 MATERIALS AND METHODS .......................... 11
3.1 Box Specification ......................... 11
3.2 Box Construction .......................... 12
3.3 Test Methods .............................. 15
3.3.1 Moisture Content ................... 15
3.3.2 Static Compression Test ............ 16
4.0 DATA AND RESULTS ............................... 19
4.1 Compression ............................... 21
4.2 Deflection ................................ 31
5.0 CONCLUSIONS .................................... 39
5.1 Recommendations for Future Work ........... 41
6.0 APPENDICES ................................... ..42
A. Compression and Deflection Data ............ 42
B. Data on Statistical Analysis ............... 58
7.0 REFERENCES ..................................... 70

LIST OF TABLES

Table Page
1 Average Compression and Deflection Values ......... 20
2 Analysis of Variance for Compression .............. 23

3 Compression T-Test Results of Fixed versus
Floating Platen ................................... 24

4 Tuckey's Multiple Range Test of Effect of Degree
of Defect on Compression .......................... 25

5 Compression TrTest Results of 2-Way Interaction

of Box Size and Defect ............................ 27
6 Factor Anlysis of Compression ..................... 28
7 Analysis of Variance for Deflection ............... 33

8 Tuckey's Multiple Range Test of Effect of Degree

of Defect on Deflection ........................... 33
9 Deflection T-Test Results of 2-Way Interaction

Between Platen Type and Box Size .................. 34
10 Deflection T-Test Results of 2-Way Interaction

Between Box Size and Degree of Defect ............. 34
11 Factor Analysis of Deflection ..................... 36
12 Moisture Content .................................. 36

A-l Compression and Deflection Values for Box A, 0°
Defect on the Fixed Platen ........................ 42

A-2 Compression and Deflection Values for Box A, 1°
Defect on the Fixed Platen ........................ 43

A-3 Compression and Deflection Values for Box A, 2°
Defect on the Fixed Platen ........................ 44

A-4 Compression and Deflection Values for Box A, 3°
Defect on the Fixed Platen ........................ 45

A-S Compression and Deflection Values for Box A, 0°
Defect on the Floating Platen ..................... 46

A-6 Compression and Deflection values for Box A, 1°
Defect on the Floating Platen.. ........... . ........ 47

vi

Table Page

A-7 Compression and Deflection Values for Box A, 2°

Defect on the Floating Platen ..................... 48
A-8 Compression and Deflection Values for Box A, 3°
Defect on the Floating Platen ..................... 49
A-9 Compression and Deflection Values for Box B, 0°
Defect on the Fixed Platen .............. ..........50
A-lO Compression and Deflection Values for Box B, 1°
Defect on the Fixed Platen ....................... 51
A-11 Compression and Deflection Values for Box B, 2°
Defect on the Fixed Platen ....................... 52
A-12 Compression and Deflection Values for Box B, 3°
Defect on the Fixed Platen ....................... 53
A-13 Compression and Deflection Values for Box B, 0°
Defect on the Floating Platen .................... 54
A-14 Compression and Deflection Values for Box B, 1°
Defect on the Floating Platen .................... 55
A-15 Compression and Deflection Values for Box B, 2°
Defect on the Floating Platen .................... 56
A-16 Compression and Deflection Values for Box B, 3°
Defect on the Floating Platen .................... 57
B-l Description of Code Numbers ....................... 58
B-2 Compression 3-Way ANOVA Test Results .............. 59

8-3 Compression T-Test Comparing the Compression
Values of the Fixed Versus The Floating Platen....60

B-4 Tuckey's Multiple Range Test Comparing the
Compression Values by Degree of Defect ............ 61

B-5 2-Way Interaction Comparing Compression values
of Box A to B with the Same Defect and the Same

Platen ............................................ 62
B-6 Factor Analysis of Compression .................... 64
B-7 Deflection 3-Way ANOVA Results .................... 65

B—8 Tuckey's Multiple Range Test Comparing the ,
Compression Values by Degree of Defect ............ 65

vii

, Table Page

B-9 2-Way Interaction Comparing Deflection Values
of Each Platen and Each Box Size .................. 66

B-lO 2-Way Interaction Comparing Deflection Values
of Box A to B with the Same Defect and the Same
Platen ........................................... 67

8—11 Factor Analysis of Deflection .................... 69

viii

LIST OF FIGURES

Figure Page
1 Defect Introduction in a RSC during Fabrication...13

2 RSC Blank with 0°, 1°, 2° and 3° Flute Defects....14

3 Floating Platen Compression Test .................. 17
4 Cylinders used to Convert from Floating to

Fixed Platen ...................................... l7
5 Compression Tester with Conversion Cylinders

in Place .......................................... 18
6 Fixed Platen Compression Test ..................... 18
7 Compression Strength Averages for Box A ........... 29
8 Compression Strength Averages for Box B ........... 30

ix

1.0 INTRODUCTION

The compression strength of corrugated containers has been
studied at length under varying conditions. Tests have been
performed with corrugated containers conditioned to hot and
cold temperature extremes as well as high and low relative
humidities. All of previous published studies have been
performed using a fixed platen compression testing machine.
However, the effect of using a floating versus fixed platen
to evaluate the performance of corrugated containers has not

been studied.

In ASTM D642-76 (Compression Test For Shipping Containers),
the recommended procedure for testing compression strength
states that the top platen may be either fixed or swiveled
(floating) for tests where the compressive loads are applied
face to face. The standard presumes that both the fixed and
floating platens will give the same results. The TAPPI T804
standard for compression testing specifically notes that
"floating" platens are not in accordance with the standard.
The rational for this decision is that the fixed platen is
the most reproducible way of making compression tests
(Maltenfort, 1988). In general terms, it may be said that
compression testing is used to relate stacking strength of
the container (or the container and product) to the physical
distribution environment (Peleg 1985). Many people believe

that the fixed platen is not an accurate simulation of what

compressive forces a container will see. Peleg (1985)

states:

Most standard compression testing procedures of
shipping containers specify fixed platen
compression testing machines. Such machines provide
a measurement which is less realistic than a
floating-type compression testing platen. A
floating platen automatically adjusts itself
to the nonuniformly yielding containers, rather than
measuring the resistance at the strongest points in
the stack as it is compressed downwards.
The TAPPI fixed platen method does not allow a weak corner
or portion of the container to cause failure. From the box
user's point of view, if there is a weak spot, the test
method should show this, not obscure it. For the boxmaker,
on the other hand, the fixed platen method makes it easier
to qualify for a specification (Maltenfort, 1988). Although
many people agree that the floating platen is a more
realistic simulation of the compressive forces on a stack or

pallet, few people agree on which platen gives more precise

results on a single container.

The objectives of this study are as follows:

0 To compare the compression strength and
deflection of identical corrugated containers
using both the fixed and floating platens.

These results will be compared to see if there is

a significant difference between the platen types.

0 To compare the compression strength and
deflection of corrugated containers ,that have
varying degrees of defects incorporated
in during fabrication, using both the fixed and

floating platens.

0 To determine if a relationship exists between
the fixed and floating platen compression testing

methods.

0 To determine if a relationship exists between
the magnitude of fabrication defect incorporated
into the container and the subsequent compression

and deflection values obtained using both platens.

o to determine the effect of box size on compression
and deflection values using both the fixed and

floating platens.

2.0 LITERATURE REVIEW

Corrugated containers are used to package 90 to 95 % of
America's manufactured goods for the consumer (FBA, 1984).
The functions of a corrugated shipping container may be

summarized as follows:

1) Protection: The corrugated shipping container
protects the product from damage and soiling as
it moves through the transportation and handling
environment from producer to consumer.

2) Storage: It offers a convenient place and a safe
method of storing a product until it is sold.

3) Advertising: It can function as an advertising
billboard for the users product while the
container is in transit, in storage or on
display.

4) Economics: It performs above functions at a
minimal cost.

(Maltenfort, 1970)

The standardization of the corrugated shipping container is
largely governed by the railroad and motor carrier industry
of the United States. The bursting strength, basis weight,
transportation requirements, box closure and box size are
all considered when designing a corrugated box for a

product.

2.1 COMPRESSION STRENGTH

The compression strength of a corrugated container is used

I

to determine how well the container will perform throughout
transportation and storage. The higher the compression
strength, the higher the stacking height possible. During
transportation and storage it is common practice to stack
pallet loads to efficiently utilize storage space. In the
ASTM standard D 4169-82 (1981), Performance Testing of
Shipping Containers and Systems , the ability of a package
to withstand the compressive loads that occur during vehicle
transport or warehousing can be estimated using a formula
that takes into account a combined assurance level factor,

the weight of the product and the height of the stack.

Peterson and Fox (1980), reported on a theory to demonstrate
how boxes fail in compression. The compression failure
morphology of the liners was studied, to develop an
understanding of what may be done to increase compression
strength. Failure is consistently seen in regions of the
panel subjected to compressive loads 'as a result of the
critical combination of stresses acting there at a much
lower level than would be required to cause a box failure
due to tension. After a physical examination of linerboard
cross sections, that had failed under compressive loads, it
was revealed that on occasion the board delaminated as if
it were made of many layers and that the bonds between the
layers ruptured when loaded. Other samples were seen to
have fibers buckle or delaminate and then buckle. It was

concluded that interfiber bond strength and fiber stiffness

are the most important variables related to linerboard

compressive strength.

Two basic approaches are possible in constructing a
mathematical prediction model of corrugated container
stacking strength: (1) One correlates the properties of the
material, e.g., paperboard facings and corrugating medium,
to the stacking strength of the fabricated container. (2)
One views the container as a basic structure, e.g., single
degree of freedom system with inherent viscoelastic
properties (Peleg 1985). Each of these approaches have been
investigated. By far, the most common estimation of
compression strength is a well known empirical formula
adapted by McKee et a1. (1963). The final simplified
version of this formula relates the ultimate compressive
strength of a RSC container to the board caliper, container
perimeter and edgewise compressive strength of the

corrugated paperboard (Peleg 1985).
P = 5.87*Pm*(h*Z)1/2 (2-1)
where P = maximal top to bottom compressive force
Pm= edgewise compressive strength of board
h = board caliper

z = container perimeter

It is important to state that this formula is only valid for

corrugated containers of a RSC type at ambient temperatures
of 72°F and 50% RH. Kellicut and Landt (1951) investigated
the influence of humidity upon static load tests of
corrugated containers. They related the compressive
strength of moist packages to dry packages by the

relationship:
P = P0 * 10-3-01x (2-2)

where P = compression strength

Po= compression strength at 0 moisture
content

X = moisture content of corrugated
material

Hanlon (1984), states that for long term storage, it is
ideal, to use one-forth of the compressive strength of a
corrugated box as a safe load. He also states that a more
accurate method would be to calculate the fatigue factor for
the length of time the material is expected to remain in
storage. It is also important to factor in the affects of

humidity and the stacking pattern.

2.2 TRANSPORT REQUIREMENTS AND QUALITY STANDARDS

In 1914, when the use of corrugated boxes for shipping began
to grow, material standards became necessary. To ensure
and control material against the transportation hazards of

shipping, the freight carriers established rules,

regulations and specifications for corrugated containers
(Morris 1978). Various methods for defining the quality of
corrugated board were developed. These include Mullen burst
test, puncture test, short column crush test and flat crush

test.

In 1917, rule 41 and rule 222 were established by the
railroad and truck industry. As initially adopted, the
quality level of the combined board in containers producing
satisfactory performance was characterized by the then
available test procedures. These procedures were used by
papermakers to evaluate the quality of paper based on
weight, caliper and mullen strength (Morris 1978). It was
basically assumed that if all of the above factors remained
constant, the containers would perform satisfactorily.
Although these attributes were convenient for use in
establishing a grade structure, they were and are
indirectly related to corrugated container fabrication
efficiency and performance (Morris 1978). This fact has
been the center for debates over changing the testing
methods for evaluating corrugated container shipping

performance by including an edge crush test (ECT).

Various researchers like Scott (1988), Morris Jr. (1978)
and King(1975) all agree that the currently required
shipping performance measures of basis weight, caliper and

mullen burst test should be accompanied by a short column

edge crush test (ECT) if not entirely replaced by it.
Currently the Uniform Freight Classification rule 41 (UFC,
1988) and the National Motor Freight Classification item
rule 222 (NMFC, 1988) do not require any compressive
strength values. Most companies already require a ECT in
their specifications for corrugated containers. In Europe,
the ECT is fully accepted as a criterion of corrugated
container performance (Jonson,1985). This does not presume
that the mullen and puncture tests are not useful as quality
standards for corrugated material. The general bursting
strength is dependent on the type, proportion, preparation,
and amount of fibers present in the sheet and to their
formation, internal sizing and to some extent surface
treatment (Maltenfort 1979). The puncture test is useful in
measuring puncture resistance and board stiffness. All
three of the tests described above effect the overall

performance of a RSC in the distribution environment.

2.3 CORRUGATED BOX CLOSURES

 

The type of box closure may have a significant effect on the
performance of the container. Sheehan (1988) states that
when different types of closure materials are to be
compared, the physical properties of these materials are
significantly different and the performance of the closures
on-the-box must be determined for a comparison. A recent
study conducted by Sheehan at the 3M Packaging Methods

Center evaluated the compression values of empty RSC's

10

sealed with one of two closures: i) a 2 inch wide pressure
sensitive tape and ii) beads of hot melt adhesive. From
these tests, it was concluded that the compression strength
of the corrugated container is affected by'the closure. The
taped boxes averaged a higher compression strength (by 6%)
than the boxes closed with the hot melt adhesive (Sheehan,
1988). He also observed that the boxes with adhesive
closures consistently had slightly higher deformations at

failure than taped boxes.

2.4 Box Size

The relationship of the dimensions of a container to its
compression strength is linear. As the perimeter of the box
is increased, the compression strength increases.
Maltenfort (1988), states that in the top to bottom
compression testing of a container, the depth is only
slightly negatively correlated to compression strength.
What this says is that by increasing the depth alone, the
compression strength of the container will slightly

decrease.

11

3.0 MATERIALS AND METHODS

The test samples used for this study were constructed of
single wall C-flute corrugated board and were of an R.S.C.
(regular slotted container) type. Two box sizes were used
to determine if there was a relationship between the box
size and the effect of the degree of defect on the
subsequent compression strength. Fabrication defects of 1°,
2° and 3° were incorporated into the box blank. The 1°
defect was thought to be a minor defect that could go
unnoticed. The 3° defect was thought to be a more
noticeable defect on close sight of the box blank. It was
thought that any degree of defect greater than 3° would be
immediately noticed and not allowed to continue through

further fabrication.

3.1 Box Specification
Type = C-flute, double faced corrugated
Medium = C-flute
Dimensions
Box A 10" x 8" x 6" (L x W x D)
Box B 12" x 10" x 8"
Burst strength - 200 lb.
Minimum combined weight of facings = 68 lbs./1000 sq.ft.
Board components include two 42 lb./1000 sq.ft. liners,
26 1b./1000 sq. ft. medium and a regular starch

adhesive.

12

The boxes were sealed with a paper tape.

3.2 Box Construction

The boxes were manually constructed using a creasing and
cutting rule. A fabrication defect was introduced into the
manufacturing of the box by feeding the corrugated sheet
through the creasing and cutting rules at an angle (Figure
1). The box blank was then creased and slotted. The box
blank (Figure 2) was then folded and taped at the joint, top
and bottom. This technique causes the flutes in the set-up
box to be inclined instead of being vertical to the edge.
This fabrication defect also causes one corner of the box
not to match a perfect square. Four degrees of defects were

introduced into the box.

0 0° no defect (control)
0 1° fabrication defect
0 2° fabrication defect

0 3° fabrication defect

Two sizes of boxes were tested, A = 10"x8"x6" and B = 12" x
10"x8". For each degree of defect and each box size, 30
replicant boxes were fabricated at the School of Packaging

(Package Development Lab).

13

FIGURE 1

Defect Introduction in a RSC During Fabrication

 

q __.____._________._'__.______________,__H__ _____H__
___ —‘ A
GREASE
Flute
Direction
GREASE

 

 

wooden
Block

RSC Blank with 1°,2° & 3° Flute Defect

14
'FIGURE 2

 

 

 

 

 

 

 

 

 

 

 

 

Flute
Direction

b---
a’

 

 

 

 

 

 

 

 

 

RSC Blank (Normal Flute Direction)

 

l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RSC Container

 

 

 

 

 

 

 

 

 

15

3.3 TEST METHODS

3.3.1 Moisture Content

Method: The ASTM D644-82, Moisture Content of Paper and
Paperboard by Ovendrying, (1984) method was followed with
the exception that an airtight weighing container was not
used to transfer the specimen from the vacuum oven to the
balance. The room in which the balance and oven are located
is set at standard conditions of 72°F and 50% RH, which is
the same conditions the samples were pre-conditioned in.
The initial weight was recorded and the specimens were
placed in a vacuum oven for 6 hours at 90°F. The oven used
was a Vacuum Oven Model No. 5831 manufactured by National
Appliance Company. The scale used was an Analytical Balance
Model AE160 manufactured by Mettler Company. After 6 hours,
the vacuum oven was flushed with nitrogen and the specimens
were immediately transferred to a glass desiccator filled
with anhydrous Calcium Sulphate and allowed to cool to room
temperature for 1 hour. The specimens were then weighed to
determine dry weight. The moisture content on a percent dry

basis was then determined by using the following formula:
Percent Moisture = [(W1 - W2)/W2]* 100 (3-1)

where W1 = original weight of moist specimen

W2 = weight of specimen after vacuum oven
drying

16

3.3.2 Static Compression Test
Materials: 240 RSC's conditioned and tested at 72°F and
50%RH.
Apparatus: A Lansmont Model 76-5K compression tester with a
capacity of 6000 pounds was used to perform the compression
tests. The compression tester was used with both the fixed
and floating platens. The attached floating platen (Figure
3) was unable to move when the 4 steel cylinders (Figure 4)
were in place, thus simulating a fixed platen as shown in
Figures 5 and 6.
Method: All tests were done in accordance to ASTM D642-84,
Compression Test for Shipping Containers (1984). A 50 pound
preload was applied to ensure a definite contact between the
specimen and the platens. The peak compressive force and
corresponding deflection were recorded for each sample
tested. A total of 240 boxes were tested as follows:

15 A size, 15 B size at 0° defect (control)

15 A size, 15 B size at 1° defect

15 A size, 15 B size at 2° defect

15 A size, 15 B size at 3° defect

total = 120 boxes tested on the fixed platen.

15 A size, 15 B size at 0° defect (control)
15 A size, 15 B size at 1° defect
15 A size, 15 B size at 2° defect
15 A size, 15 B size at 3° defect

total = 120 boxes tested on the floating platen.

Figure 3 Floating Platen Compression Test

 

Figure 4 Cylinders used to Convert from Floating to Fixed Platen

 

19

4.0 RESULTS AND DISCUSSION

Two hundred and forty corrugated shipping containers were
fabricated and tested to determine if there was a
significant difference in compression strength and
deflection using the fixed versus floating platen. All

tests were conducted at 72°F and 50% RH.

The average compression and deflection values for each group

of boxes are summarized in Table 1. Corrugated board is a

highly variable material. The fabrication process of
containers from this material further increases the
variances. Thus the compression and deflection results

collected in this research had a large standard deviation
and variance. This variation in data obscures any trends
that may be seen by just looking at the raw data. For this
reason statistical analysis must be performed on the data to
see if there are significant differences occurring. A 3-way
between subjects analysis of variance (ANOVAL. test for
significance was performed at 90% confidence or better on
the compression and deflection results for all tests. The

three independent variable were:

0 Platen type (2 types)
fixed
floating

0 Box size (2 types)
A 10"x8"x6"
B 12"x10"x8"

20

TABLE leverage Compression and Deflection Values.

 

 

Compression
Platen Box Defect Str.(lbs.) Defl.(in.)
FIXED A 0° 695.33 .60
1° 726.47 .66
2° 689.60 .71
3° 686.80 .69
FLOATING A 0° 686.47 .72
1° 677.73 .68
2° 638.13 .76
3° 663.60 .65
FIXED B 0° 774.67 .78
1° 798.00 .85
2° 778.07 .75
3° 649.93 .65
FLOATING B 0° 728.40 .77
1° 782.80 .79
2° 777.67 .67

3° 642.47 .73

 

21

0 Type of Fabrication defect (4 types)

0° (control)

10

20

30
The dependent variables were compression and deflection.
The main purpose of these tests were to determine if there
were significant differences in the compression and
deflection values obtained from the fixed versus floating
platens. The effect of the degree of fabrication defect and

the box size on the compression and deflection values were

also analyzed.

4.1 Compression Strength

The most important test for the performance of a corrugated
container is the compression test. A high compression
strength allows the container to be stacked to efficiently
utilize storage space. An estimation or an actual test of
compression strength is used to determine the safe stacking
height of the container. External factors such as
temperature, relative humidity, time in storage and the
stacking pattern will all affect the actual compression
strength of a container. Several empirical formulas take
into account these external factors. The basis of this
study was centered on the test method used to estimate the
compression strength. The fundamental objective of the
compression test is to reflect the quality of the box being
tested under conditions as closely simulating use as

possible (Maltenfort, 1988). The ASTM standards state that

 

22

either the fixed or floating platen may be used when
compression testing. This statement suggests that there is
not a significant difference in the values obtained by the

two methods.

The main effects of the ANOVA test show that there are
significant differences between the two platen types, the
two box types and between the four defect types (Table 2).
Since there were not any 2-way or 3—way interactions
occurring with the two platen types a simple t-test for
significance was conducted. A 2 or 3-way interaction means
that the variables act together to affect the subsequent
compression strength values. Tuckey's multiple range test
was used to test for significant differences in the
compression values based on the degree of fabrication
defect. Tuckey's test allows pairwise comparisons of means

derived from an ANOVA test.

The results of the t-test show that there is a significant
difference between the fixed and floating platen values
(Table 3). The results of the Tuckey's test show that the
1° and 3° boxes were significantly different from all of the
other boxes and that the 0° and 2° boxes were significantly
different from the 1° and 3° boxes (Table 4). The results
of the ANOVA test also predict that there was a 2-way
interaction occurring between the box size and the degree of

defect (Table 2). Based on these results, t-tests were then

eva=¥%
. A L.

23

TABLE 2: Analysis of Variance for Compression.

 

 

Mean Sig.
Source of Variation DF Square of F
Main Effects 5 96142.311 .000
PLATEN TYPE 1 36927.204 .000
BOX SIZE 1 202478.504 .000
DEFECT TYPE 3 80435.282 .000
2-Way Interactions 7 25480.552 .000
PLATEN, BOX 1 3352.538 .266
PLATEN, DEFECT 3 649.582 .868
BOX, DEFECT 3 57687.526 .000
3-Way Interactions 3 5355.315 .117
PLATEN, BOX, DEFECT 3 5355.315 .117
Explained 15 45009.424 .000
Residual 224 2695.010

MSE

 

sig.
sig.
sig.

not sig.
not sig.
sig.

not sig.

 

24

TABLE 3: Compression T-Test Results of Fixed Versus Floating

 

 

Platen.

Group# Platen Average
1 FIXED 724.86

2 FLOATING 699.66

 

X1 ‘ X2

 

 

 

 

(n1) (n2)

(:i_x12 ‘ (25X1)2/n1 ) + (:£322 ‘ (2:32)2/n2 ) (hi +Ik:

(D1 + n2 - 2 )

where N = total # subjects = 240
n1= # subjects in group 1 = 120
n2= # subjects in group 2 = 120

df= degrees of freedom (n1 - n2 - 2) = 238

critical t value

1.970 at 95% confidence

t = 2.70 -> 1.970 significant

25

TABLE 4: Tuckey's Multiple Range Test of Effect of Degree of

Defect on Compression.

 

Compression
Combined Avg.

Significantly

 

Defect (Original Order) (Ranked Order) Different From
0° 721.22 1° 747.03 0°, 2° + 3°

1° 747.03 0° 721.22 1° + 3°

2° 720.87 2° 720.87 1° + 3°

3° 660.70 3° 660.70 0°, 1° + 2°

 

MSE = 2695.01
Degrees Freedom = 224
60 observations in each mean

alpha = .05

26

conducted to identify which interactions were occurring
(Table 5). In comparing the compressive values of box A to
B, with the same degree of defect and the fixed platen, it
was found that the values of the 0°, 1° and 2° boxes were
significantly different (Table 5). In comparing the
compression values of box A to B, with the same degree of
defect and the floating platen, it was found that the values

of the 1° and 2° boxes were significantly different.

A factorial analysis was performed on the compression
averages to see if there was a linear or curvature trend in
the data. Since there was not a 3-way interaction
occurring, the linear and quadratic equations were broken
down only by box size (Table 6). There were both
significant linear and curvature trends in the data
collected from the B size box. The reason both of these
trends were seen is that there were not enough data sets to
show which trend was more significant. There was no linear

or curvature trend in the data for the A size box (Table 6).

The results of this study show that there is a
statistically significant difference in the compression
values of the fixed and floating platens. The floating
platen compression averages, for each degree of defect and
box size were generally all less than the fixed platen
compression averages (Figure 7 and 8). The floating platen,

overall mean of means, gave a compression strength reading

 

27

TABLE 5: Compression T—Test Results of 2-Way Interaction of
Box Size and Degree of Defect.

 

 

95%
Platen Box Defect TB confidence
FIXED A o0 4.18 sig.
FIXED B O0
FIXED A l° 3.77 sigo
FIXED B 1° '
FIXED A 20 4.67 sig.
FIXED B 2°
FIXED A 3° 1.94 not sig.
FIXED B 3°
FLOATING A O° 2.21 not sig.
FLOATING B O°
FLOATING A 1° 5.54 sig.
FLOATING B 1°
FLOATIAG A 20 7.36 sig.
FLOATING B 2°
FLOATING A 3° 1.11 not sig.
FLOATING B 3°

 

Fvfivrzm

28

TABLE 6: Factor Analysis of Compression.

 

 

Platen Box Defect F-Linear F-Quadratic
FIXED A 0°
FLOATING A 0°
FIXED A 1°
FLOATING A 1° .304 not .0036 not
FIXED A 2° sig. 819.
FLOATING A 2°
FIXED A 3°
FLOATING A 3°
FIXED B 0°
FLOATING B 0°
FIXED B 1°
FLOATING B 1° 60.07 sig. 80.97 sig.
FIXED B 2°
FLOATING B 2°
FIXED B 3°
FLOATING B 3°

-. \‘ e zi-S‘T"

m

g:

 

* at 95% confidence level.

Compression Strength (lbs.)

850

§

29

Figure 7: Compression Strength
Averages for BoxA (i 1 0‘)

 

 

Aflxed platen Ifloating platen

p-

l i l

 

 

0 1 2 3
Degree of Defect

:- fl
.
_ ‘

30

Figure 8: Compression Strength
Averages for Box B (:1: 1 0')

 

§

Aflxed platen Ifloating platen

a: .. 3 ° 3
08080
lllll
1 I

i

 

Compression Strength (lbs.)
8.
o
l
I

' 0|
8
I

 

 

 

l l 4 l
450 O 1 2 3

Degree of Defect

31

3.6% lower than the fixed platen. As the degree of defect
was increased , from 0° to 3°, for both box sizes and platen
types , the general trend in compression values decreased
(Table 1). This decreasing trend was expected since the
greater the degree of fabrication defect, the more severe is
the incline angle at which the flutes are compressed. For
optimum performance, the flutes should be perpendicular to
the bottom edge of the box. The Tuckey's test on the
average compression values showed that in most cases the
increased degree of defect significantly changed the
compression strength. The largest defect incorporated ,
the 3° defect, lowered the compression strength by 12%. For
the same platen and the same degree of defect it was
expected that the larger B box compression values should be
greater than the A box values because the perimeter was
larger. This was true in all cases except in the 3° defect
case and the 0° defect on the floating platen. This
significant difference may be explained by the highly
variable properties of the material itself and the
fabrication process. These results provide supportive
evidence for the theory that the fixed and floating platen
compression tests give significantly different results. A
more realistic compression value that shows fabrication

defects is obtained with the floating platen.

4.2 Deflection

The deflection of a corrugated container is the other

I

32

results of a compression test. As the container is
compressed, the box panels bulge or bow out of the way
which reduces the depth of the box. This reduction is known
as the deflection (Maltenfort, 1988). ' This value is
critical when determining the proper head space needed
between the product and the corrugated container for optimum
strength. If the critical deflection is reached, the
product inside the container will become load bearing. The
outcome of the compression test is used to estimate this
headspace value. The deflection number recorded by the
compression tester is only significant to 1/100th of an
inch. Although this value meets all packaging requirements,
it does not show significant differences among the boxes

compared.

The results of the ANOVA test suggest that there were 2-
way interactions between the platen type and box size and
between the box size and the degree of defect (Table 7). A
2-way interaction means that the two variables act together
to affect the deflection value obtained. Based on these
results, t-tests were then conducted to identify which
interactions were occurring (Tables 9 and 10). Tuckey's
multiple range test was used to test for significant
differences in the deflection values based on the degree of

fabrication defect (Table 8).

The results of the Tuckey's test show that the 0°, 1° and 2°

.M:‘ ‘i
J - —->

’I‘ ML...
In
A

33

. TABLE 7: Analysis of Variance for Deflection.

 

 

 

Mean Sig.
Source of Variation DF Square of F
Main Effects 5 .080 .000
PLATEN TYPE 1 .007 .286
BOX SIZE 1 .260 .000
DEFECT TYPE 3 .044 .000
2-Way Interactions 7 .056 .000
PLATEN, BOX 1 .058 .002 sig.
PLATEN, DEFECT 3 .017 .040 not sig.
BOX, DEFECT 3 .094 .000 sig.
3-Way Interactions 3 .054 .000
PLATEN, BOX, DEFECT 3 .054 .000 sig.
Explained 15 .063 .000
Residual 224 .00616
MSE

 

TABLE 8: Tuckey's Multiple Range Test of Effect of Degree of
Defect on Deflection.

 

Deflection
Combined Avg. Significantly
Defect (Original Order) (Ramked Order) Different From

 

0° 0.72 1° 0.75 3°
1° 0.75 0° 0.72 3°
2° 0.72 2° 0.72 3°
3° 0.68 3° 0.68 0°, 1° + 2°

 

MSE = .00616
Degrees Freedom = 224
60 observations in each mean

alpha = .05

34

TABLE 9: Deflection T-Test Results of 2—Way Interaction
Between Platen Type and Box Size.

 

 

95%
Platen Box Defect TB confidence
FIXED 0°-3°
versus 2.66 sig.
FLOATING A 0°-3°
FIXED B 0°-3° . ”I
versus 1.40 not 819. =‘
FLOATING B 0°-3°

 

TABLE 10: Deflection T-Test Results of 2-Way Interaction
Between the Box Size and Degree of Defect.

 

 

95%
Platen Box Defect TB confidence
FIXED A O° 6.27 sig.
FIXED B O°
FIXED A 10 6.62 sig.
FIXED B 1°
FIXED A 2° 1.39 not sig.
FIXED B 2°
FIXED A 3° 1.39 not sig.
FIXED B 3°
FLOATING A O° 1.74 not sig.
FLOATING B O°
FLOATING A 10 - 3.83 sig.
FLOATING B 1°
FLOATING A 20 3.14 'sig.
FLOATING B 2°
FLOATING A 3° 2.79 sig.
FLOATING B 3°

 

35

box values were significantly different from the 3° box and
the 3° box values were significantly different from the 0°,
1° and 2° box values (Table 8). The average deflection
value for box A using the fixed platen, was determined to be
significantly different than the deflection value on the
floating platen (table 9). The average deflection value for
box B, using the fixed platen, was determined to not be
significantly different than the deflection value on the
floating platen (Table 9). In comparing the deflection
values of box A to B, with the same defect on the fixed
platen, it was found that the values of the 0° and 1° boxes
were significantly different (Table 10). In comparing the
deflection values of box A to B, with the same defect on the
floating platen, it was found that the values of the 1°, 2°,
and 3° boxes were all significantly different (Table 10).
One explanation for the differences in these results is the

high variability of the corrugated material.

The ANOVA test results also suggest that there is a 3-way
interaction occurring between the box type, the platen type
and the degree of fabrication defect. What this means is
that the three variables contribute together to affect the
deflection value obtained. A factorial analysis was
performed on the deflection averages to see if there was a
linear or curvature trend in the data (Table 11). Since
there was a 3-way interaction occurring, the linear and

quadratic equations were broken down by box type and platen

 

36

TABLE 11: Factor Analysis Of Deflection.

 

Platen Box Defect F-Linear

F-Quadratic

 

FIXED A 0°
FIXED A 10 12.49 sig.
FIXED A 2°
FIXED A 3°
FIXED B 0°
FIXED B 1° 29.28 sig.
FIXED B 2°
FIXED B 3°
FLOATING A 0°
FLOATING A 1° 2.06 not
FLOATING A 20 sig.
FLOATING A 3°
FLOATING B 0°
FLOATING B 10 7.02 sig.
FLOATING B 2°
FLOATING B 3°

4.0 sig.
18.06 sig.
3.06 sig.
1.0 not

31g.

 

* at 95% confidence level

TABLE 12: Moisture Content.

 

Sample # WI (91118.) W2 (91113.)

% Moisture

 

1 10.2731 9.5949

2 10.0652 9.4214

Avg.

7.069%
6.834%
= 6.95%

 

r (q! til.”

37

type (Table 11). The calculations showed that there was a
significant linear relationship in the fixed and floating
platen-size A box and in the fixed platen-size B box. The
quadratic equations showed that there was a significant
curvature trend in the fixed and floating platen-size A box
and in the fixed platen size B box (Table 11). This trend
implies that as the degree of defect is increased a

decreasing trend is seen in the data.

The results of this study also show that there is a
significant difference in deflection values for the A size
box on the fixed and floating platens. The floating platen
results, on the average for box A, gave a reading of 5.5%
higher than the fixed platen. The deflection results for
the larger B size box were not found to be significantly
different on the two platens. This may be explained by
suggesting that the deflection of the larger B size box is
not affected by using either platen. This may also be
explained by the fact that even though the deflection
reading is measured to 1/100th of an inch, which meets all
packaging requirements, it does not show significant
differences among the boxes compared (as described above).
Tuckey's test shows that the 0°, 1° and 2° deflection values
were all significantly different from the 3° defect, but not
significantly different from each other. This shows that ,
in general, the deflection of the boxes is not greatly

affected by incorporating a fabrication defect. Both linear

38

and curvature trends were Observed for both box sizes and
platen types. The reason both trends were seen is that
there were not enough data sets to determine which trend

was actually significant.

 

39

5.0 CONCLUSIONS

The results of this study are:

There was a significant difference in the compression
strength values of identical corrugated containers
using the fixed and floating platens. There was a
significant difference in deflection values for the

smaller A size box using the two platens.

The varying degrees of defect incorporated during
fabrication had a significant effect on the
compression values of the boxes. The deflection
values were not greatly affected by incorporating a

defect into the boxes.

The fixed platen gave an average compression value

3.4% higher than the floating platen.

As the degree of fabrication defect was increased, the
compression strength of the containers decreased using

both platen methods.

The larger (B size) boxes had higher compression
strength and deflection values than the smaller (A)
boxes. There was no interaction between the box size

and the platen type.

”if L’

40

Based on the results of this study, it can be concluded that
the ASTM standard for compression testing Of shipping
containers, which states that either a fixed or floating
platen may be used, should recommend that the results from
the tWO’ tests will be different. This study shows that the
fixed platen gives significantly higher results.
Maltenfort (1988), states that it is safe to say that what
ever the condition of stress application in real life, the
one condition which is certain never to occur, except by
some freak coincidence, is the one simulated by the TAPPI
(fixed platen) version, where the load is applied in such a
manner that the weakest portion, if there is one, cannot
fail first. From the box makers point of view, using the
fixed platen makes it easier for a box to pass
specification. The box user, on the other hand, believes
that if a box has a weak point, the test should show this,
not obscure it. Box users should state in their corrugated
container specifications that the floating platen should be

used to achieve a realistic compression strength.

 

41

5.1 RECOMMENDATION FOR FUTURE WORK

The major recommendation of this research is that the
floating platen compression test be used to estimate the
performance of corrugated containers. A similar study is
suggested using a larger number of boxes to account for
variation in fabricated corrugated as well as additional box
sizes. A similar study that looks into other fabrication
defects such as nonuniform slotting and misaligned joints
would be of interest to the packaging industry. It is also
recommended that a similar study be conducted using a wider
range in the degree of defect fabricated into the container
to determine whether a linear or curvature trend is actually

occurring.

 

 

APPENDIX A

42

COMPRESSION TESTING

TABLE A-l: Compression and Deflection Values for Box A 0°
Defect on the Fixed Platen.

 

Compression Deflection

 

 

 

Platen Box Defect Replication Str.(lbs.) (in.)
FIXED A 0° 1 630.00 0.50
2 654.00 0.57

3 750.00 0.69

4 679.00 0.62

5 621.00 0.60

6 706.00 0.38

7 729.00 0.57

8 748.00 0.61

9 695.00 0.62

10 662.00 0.65

11 704.00 0.60

12 677.00 0.62

13 733.00 0.59

14 707.00 0.65

15 735.00 0.68

AVERAGE 695.33 0.60

STD.DEV. 39.52 0.07
VARIANCE 1561.956 0.005

CODES

 

Platen: fixed or floating

Box: A = 10"x8"x6"
B = 12"x10"x8"
Defect: 0° no defect
1.

3o

43

TABLE A-2: Compression and Deflection Values for Box A 0°
Defect on the Fixed Platen.

 

 

Compression Defl.

Platen Box Defect Replication Str.(lbs.) (in.)
FIXED A 1° 1 718.00 0.59
2 712.00 0.66

3 707.00 0.65

4 801.00 0.67

5 698.00 p 0.72

6 739.00 0.60

7 735.00 0.65

8 700.00 0.64

9 771.00 0.63

10 774.00 0.69

11 689.00 0.60

12 706.00 0.71

13 669.00 0.62

14 754.00 0.71

15 724.00 0.74

AVERAGE 726.47 0.66

STD.DEV. 34.73 0.05

VARIANCE 1205.849 0.002

 

 

44

TABLE A-3: Compression and Deflection Values for Box A 2°
Defect on the Fixed Platen.

 

Compression Deflection

 

Platen Box Defect Replication Str.(lbs.) (in.)
FIXED A 2° 1 712.00 0.74
2 715.00 0.74

3 639.00 0.69

4 716.00 0.77

5 722.00 0.69

6 642.00 0.69

7 654.00 0.69

8 680.00 0.77

9 730.00 0.70

10 683.00 0.65

11 597.00 0.58

12 722.00 0.74

13 729.00 0.71

14 729.00 0.77

15 674.00 0.69

AVERAGE 689.60 0.71

STD.DEV. 39.77 0.05

VARIANCE 1581.840 0.002

45

TABLE A-4: Compression and Deflection Values for Box A 3°
Defect on the Fixed Platen.

 

Compression Deflection

 

Platen Box Defect Replication Str.(lbs.) (in.)
FIXED A 3° 1 721.00 0.71
2 768.00 0.71

3 713.00 0.66

4 660.00 0.71

5 732.00 0.67

6 653.00 0.67

7 600.00 0.44

8 716.00 0.75

9 703.00 0.70

10 686.00 0.69

11 635.00 0.53

12 703.00 0.74

13 633.00 0.74

14 688.00 0.79

15 691.00 0.77

AVERAGE 686.80 0.69

STD.DEV. 42.32 0.09

VARIANCE 1790.827 0.008

 

46

TABLE A-5: Compression and Deflection Values for Box A 0°
Defect on the Floating Platen.

 

Compression Deflection

 

Platen Box Defect Replication Str.(lbs.) (in.)
FLOATING A 0° 1 628.00 0.71
2 621.00 0.76

3 759.00 0.83

4 648.00 0.63

5 713.00 0.70

6 654.00 0.78

7 694.00 0.73

8 642.00 0.60

9 756.00 0.77

10 751.00 0.67

11 769.00 0.79

12 628.00 0.73

13 651.00 0.73

14 698.00 0.68

15 685.00 0.73

AVERAGE 686.47 0.72

STD.DEV. 50.90 0.06
VARIANCE 2590.649 0.003

 

47

TABLE A-6: Compression and Deflection Values for Box A 1°
Defect on the Floating Platen.

 

 

Compression Deflection

Platen Box Defect Replication Str.(lbs.) (in.)
FLOATING A 1° 1 606.00 0.56
2 700.00 0.66

3 695.00 0.69

4 707.00 0.58

5 682.00 0.72

6 663.00 0.60

7 686.00 0.76

8 735.00 0.78

9 633.00 0.60

10 685.00 0.72

11 713.00 0.71

12 624.00 0.77

13 698.00 0.68

14 709.00 0.59

15 630.00 0.72

AVERAGE 677.73 0.68

STD.DEV. 36.73 0.07

VARIANCE 1348.729 0.005

 

48

TABLE A-7: Compression and Deflection Values for Box A 2°
Defect on the Floating Platen.

 

Compression Deflection

 

Platen Box Defect Replication Str.(lbs.) (in.)
FLOATING A 2° 1 660.00 0.76
2 632.00 0.77

3 535.00 0.68

4 556.00 0.71

5 636.00 0.77

6 592.00 0.72

7 662.00 0.87

8 689.00 0.81

9 709.00 0.82

10 597.00 0.77

11 645.00 0.71

12 619.00 0.75

13 597.00 0.70

14 754.00 0.81

15 689.00 0.74

AVERAGE 638.13 0.76

STD.DEV. 56.58 0.05

VARIANCE 3201.316 0.003

 

49

TABLE A-8: Compression and Deflection Values for Box A 3°
Defect on the Floating Platen.

 

Compression Deflection

 

Platen Box Defect Replication Str.(lbs.) (in.)
FLOATING A 3° 1 666.00 0.72
2 694.00 ‘ 0.57

3 674.00 0.63

4 727.00 0.67

5 653.00 0.72

6 639.00 0.57

7 647.00 0.56

8 671.00 0.67

9 704.00 0.77

10 653.00 0.53

11 653.00 0.67

12 618.00 0.61

13 644.00 0.66

14 716.00 0.71

15 595.00 0.67

AVERAGE 663.60 0.65

STD.DEV. 34.52 0.07

VARIANCE 1191.840 0.004

 

50

TABLE A-9: Compression and Deflection Values for Box B 0°
Defect on the Fixed Platen.

 

Compression Deflection

 

Platen Box Defect Replication Str.(lbs.) (in.)
FIXED B 0° 1 724.00 0.75
2 700.00 0.73

3 798.00 0.82

4 824.00 0.77

5 832.00 0.85

6 713.00 0.72

7 757.00 0.79

8 665.00 0.71

9 844.00 0.84

10 745.00 0.80

11 788.00 0.75

12 826.00 0.78

13 821.00 0.77

14 776.00 0.73

15 807.00 0.95

AVERAGE 774.67 0.78

STD.DEV. 53.07 0.06
VARIANCE 2816.222 0.004

 

51

TABLE A-lO: Compression and Deflection Values for Box B 1°
Defect on the Fixed Platen.

 

Compression Deflection

 

Platen Box Defect Replication Str.(lbs.) (in.)
FIXED B 1° 1 789.00 0.66
2 803.00 0.83

3 754.00 0.85

4 747.00 0.69

5 756.00 0.64

6 724.00 0.74

7 827.00 0.95

8 835.00 0.89

9 788.00 1.01

10 821.00 0.85

11 882.00 0.97

12 797.00 0.83

13 801.00 0.96

14 804.00 0.91

15 842.00 0.94

AVERAGE 798.00 0.85

STD.DEV. 39.80 0.11
VARIANCE 1584.000 0.013

 

52

TABLE A-ll: Compression and Deflection Values for Box B 2°
Defect on the Fixed Platen.

 

Compression Deflection

 

Platen Box Defect Replication Str.(lbs.) (in.)
FIXED B 2° 1 677.00 ' 0.61
2 766.00 0.73

3 812.00 0.80

4 660.00 0.75

5 772.00 0.86

6 686.00 0.68

7 847.00 0.74

8 804.00 0.75

9 783.00 0.59

10 803.00 0.69

11 786.00 0.76

12 774.00 0.72

13 777.00 0.86

14 842.00 0.86

15 882.00 0.85

AVERAGE 778.07 0.75

STD.DEV. 60.56 0.08

VARIANCE 3666.996 0.007

 

53

TABLE A-12: Compression and Deflection Values for Box B 3°
Defect on the Fixed Platen.

 

Compression Deflection

 

Platen Box Defect Replication Str.(lbs.) (in.)
FIXED B 30 1 647.00 0773*
2 698.00 0.74

3 621.00 0.60

4 695.00 0.62

5 574.00 0.58

6 630.00 0.66

7 615.00 0.62

8 689.00 0.81

9 633.00 0.55

10 613.00 0.57

11 691.00 0.79

12 644.00 0.67

13 739.00 0.66

14 689.00 0.71

15 571.00 0.51

AVERAGE 649.93 0.65

STD.DEV. 47.02 0.09

VARIANCE 2210.596 0.007

 

54

TABLE A-13: Compression and Deflection Values for Box B 0°
Defect on the Floating Platen.

 

Compression Deflection

 

Platen Box Defect Replication Str.(lbs.) (in.)
FLOATING B 0° 1 712.00 0.87
2 721.00 0.83

3 700.00 0.88

4 653.00 0.64

5 804.00 0.77

6 659.00 0.69

7 785.00 0.71

8 791.00 0.73

9 713.00 0.73

10 710.00 0.67

11 785.00 0.88

12 806.00 0.81

13 642.00 0.78

14 706.00 0.74

15 739.00 0.79

AVERAGE 728.40 0.77

STD.DEV. 53.13 0.07
VARIANCE 2823.307 0.005

 

55

TABLE A-14: Compression and Deflection Values for Box B 1°
Defect on the Floating Platen.

 

 

Compression Deflection

Platen Box Defect Replication Str.(lbs.) (in.)
FLOATING B 1° 1 760.00 0.86
2 812.00 0.89

3 798.00 0.94

4 763.00 0.82

5 771.00 0.71

6 816.00 0.82

7 698.00 0.58

8 863.00 0.85

9 838.00 0.82

10 850.00 0.77

11 744.00 0.77

12 741.00 0.73

13 785.00 0.83

14 788.00 0.74

15 715.00 0.69

AVERAGE 782.80 0.79

STD.DEV. 46.41 0.09
VARIANCE 2153.627 0.008

 

 

56

TABLE A-15: Compression and Deflection Values for Box B 2°
Defect on the Floating Platen.

 

Compression Deflection

 

Platen Box Defect Replication Str.(lbs.) (in.)
FLOATING B 2° 1 721.00 0.65
2 801.00 0.71

3 763.00 0.77

4 805.00 0.73

5 863.00 0.63

6 654.00 0.49

7 798.00 0.72

8 812.00 0.70

9 804.00 0.68

10 821.00 0.66

11 803.00 0.75

12 750.00 0.55

13 795.00 0.76

14 730.00 0.50

15 745.00 0.72

AVERAGE 777.67 0.67

STD.DEV. 49.33 0.09

VARIANCE 2433.556 0.008

 

57

TABLE A-16: Compression and Deflection Values for Box B 3°
Defect on the Floating Platen.

 

Compression Deflection

 

Platen Box Defect Replication Str.(lbs.) (in.)
FLOATING B 3° 1 642.00 0.71
2 485.00 0.76

3 481.00 0.73

4 647.00 0.84

5 710.00 0.80

6 692.00 0.74

7 654.00 0.72

8 615.00 0.78

9 612.00 0.72

10 857.00 0.90

11 562.00 0.57

12 642.00 0.63

13 621.00 0.76

14 716.00 0.70

15 701.00 0.61

AVERAGE 642.47 0.73

STD.DEV. 90.00 0.08

VARIANCE 8100.782 0.007

 

APPENDIX B

58

STATISTICAL ANALYSIS

The following code #‘s represent which average compression
or deflection value is used in the statistical formulas
used.

TABLE B-l: Description of Code Numbers.

 

 

 

Code # Platen Box Defect
l FIXED A 0°
2 FIXED A 1°
3 FIXED A 2°
4 FIXED A 3°
5 FIXED B 0°
6 FIXED B 1°
7 FIXED B 2°
8 FIXED B 3°
9 FLOATING A 0°
10 FLOATING A 1°
11 FLOATING A 2°
12 FLOATING A 3°
13 FLOATING B 0°
14 FLOATING B 1°
15 FLOATING B 2°
16 FLOATING B 3°

 

SYMBOLS USED:
P1 = fixed platen

P2 = floating platen

3
m

n
ll

mean square error
Bl = bOX A
B2 = 130)! B

Yx = average of 15 replications for
that code no.

EL = all box defects

TABLE B-2:

59

Compression 3-Way ANOVA Test Results.

 

Main Effects

 

PLATEN
BOX
DEFECT

2-way inter.

 

PLATEN-BOX
PLATEN-DEFECT
BOX-DEFECT

3-way inter.

 

PLATEN-BOX-
DEFECT
Explained
Residual

Total

 

Sum of Mean Sig.
Squares DF Square F of F
480711.554 5 96142.311 35.674 .000
36927.204 1 36927.204 13.702 .000
202478.504 1 202478.504 75.131 .000
241305.846 1 80435.282 29.846 .000
178363.862 7 25480.552 9.455 .000
3352.538 1 3352.538 1.244 .266
1948.746 3 649.582 .241 .868
173062.579 3 57687.562 21.405 .000
16065.946 3 5355.315 1.987 .117
16065.946 3 5355.315 1.987 .117
675141.363 15 45009.424 16.701 .000
603682.133 224 2695.010
1278823.496 239 5350.726

 

60

TABLE B-3: Compression T-Test Comparing the Compression
Values of the Fixed Versus the Floating Platen.

 

 

 

 

 

 

 

 

 

 

 

 

 

Group # Platen Compression Avg.
1 FIXED 724.33
2 FLOATING 699.66
X1 - 322
t =
LX12 __(§1)2/n1 ) +L§22 -£&)2/na n1 + n2
(in + n2 - 2) (n1 n2)
where X1 = any score from group 1
X} = mean of group 1
n1 = # of subjects in group 1
X2 = any score from group 2
X3 = mean of group 2
n2 = # of subjects in group 2
N = total # of subjects
724.86 - 699.66
t:
(63594247 - 869832) + (59442797 - 839592) 240
120 I20
(120)(120)
(240 - 2)
25.20
t = = 2.70

 

 

(543894.59) + (700182.99)
(.01666667)

 

238

critical t value at 95% confidence = 1.970

t = 2.70 >= 1.970 significant

61

TABLE B-4: Tuckey's Multiple Range Test Comparing the
Compression Values by Degree of Defect.

 

Compression
Combined Avg.

Defect (Original Order) (Ranked Order)

Significantly
Different From

 

 

0° 721.22 747.03 0°, 2° + 3°
1° 747.03 721.22 1° + 3°

2° 720.87 720.87 1° + 3°

3° 660.70 660.70 0°, 1° + 2°
MSE 2695.01

Degrees Of Freedom

= 224

60 observations in each mean

at alpha

.05

62

TABLE B-5: 2-Way Interaction Comparing Compression Values
of Box A to B with the Same Defect and the Same

 

 

 

Platen.
Compression

Platen Box Defect Avg. Ts
FIXED A 0° 695.33
FIXED B 0° 774.67 4.18 sig.
FIXED A 1° 726.47
FIXED B 1° 798.00 3.77 sig.
FIXED A 2° 689.60
FIXED B 2° 778.07 4.67 sig.
FIXED A 3° 686.80
FIXED B 3° 649.93 1.94 not sig.
FLOATING A 0° 686.47
FLOATING B 0° 728.40 2.21 not sig.
FLOATING A 1° 677.73
FLOATING B 1° 782.80 5.54 sig.
FLOATING A 2° 638.13
FLOATING B 2° 777.67 7.36 Sig.
FLOATING A 3° 663.60 .
FLOATING B 3° 642.47 1.11 not 319.

 

The following formula is used:

 

 

Y1 " Y5
T5 =
J2* M33 / 15
Significance: 1% = 3.279
5% = 2.764
sample calculation:
774.67 - 695.33 79.34

 

 

 

= = 4.18 not

TB: .
J2* 2695.01/15 329.33 sig.

 

63

Factor Analvsis: Compare all compression test averages for
each box type to see if there is a linear and/or curvature

trend.

The following formulas are used:

ELIE],
QL = { ‘3[(Y1 + Y97/2] ' [(Yz + Yio)/2] +
[(Y3 + Y117/2] + [Y4 + Y12)/Z]}
FL = QL2 /[(20)(MSE)/3O]
QQ = { [(Yi + Y9)/2] ' [(Yz + Yio)/2] ‘

[(Ys + Y11)/2] + [(Y4 + Y12)/2]}

FQ = QQZ/[(4)(MSE)/3O]

EL I B2

same equations only with box size B

where QL = equation for straight line
00 = equation for curved line

FL Factorial equation for straight line

FQ = Factorial equation for curved line

6.75

Significance: 1%

5% 3.89

 

64

 

 

TABLE B-6: Factor Analysis of Compression.

Compression
Platen Box Defect Avg. QL FL
FIXED A 0° 695.33
FLOATING A 0° 686.47
FIXED A 1° 726.47
FLOATING A 1° 677.73 -86.33 .304 not
FIXED A 2° 689.60 sig-
FLOATING A 2° 638.13
FIXED A 3° 686.80
FLOATING A 3° 663.60
FIXED B 0° 774.67
FLOATING B 0° 728.40
FIXED B 1° 798.00
FLOATING B l° 782.80 -266.63 60.07 sig.
FIXED B 2° 778.07
FLOATING B 2° 777.67
FIXED B 3° 649.93
FLOATING B 3° 642.47

QQ F0

FIXED A 0° 695.33
FLOATING A 0° 686.47
FIXED A 1° 726.47
FLOATING A 1° 677.73 1.13 .0036 not
FIXED A 2° 689.60 519-
FLOATING A 2° 638.13
FIXED A 3° 686.80
FLOATING A 3° 663.60
FIXED B 0° 774.67
FLOATING B 0° 728.40
FIXED B 1° 798.00
FLOATING B 1° 782.80 -170.57 80.97 Sig.
FIXED B 2° 778.07
FLOATING B 2° 777.67
FIXED B 3° 649.93
FLOATING B 3° 642.47

 

 

sample calculation:

QL = {-3[(695.33 + 686.47)/2]

[(689.60 + 638.13)/2] + 3[(686.80 + 663.60)/2]}

-86.33

[(726.47 + 677.73)/2] +

(-86.33)2 /[(20)(2695.01)/30]

.304

65

TABLE B-7: Deflection 3-Way ANOVA Results.

 

 

 

 

 

Sum of Mean Sig.

Squares DF Square F of F
Main Effects .398 5 .080 12.917 .000
PLATEN .007 l .007 1.143 .286
BOX .260 l .260 42.219 .000
DEFECT .131 3 .044 6.074 .000
2-way inter. .391 7 .056 9.061 .000
PLATEN-BOX .058 1 .056 9.462 .002
PLATEN-DEFECT .052 3 .058 2.807 .040
BOX-DEFECT .281 3 .094 15.180 .000
3-way inter. .161 3 .054 8.700 .000
PLATEN-BOX- .161 3 .054 8.700 .000
DEFECT
Explained .949 15 .063 10.274 .000
Residual 1.380 224 .00616
Total 2.329 239 .010

 

TABLE B-8: Tuckey's Multiple Range Test Comparing the
Compression Values by Degree of Defect.

 

 

Compression

Combined Avg. Significantly
Defect (Original Order) (Ranked Order) Different From
0° 0.72 0.75 3°
1° 0.75 0.72 3°
2° 0.72 0.72 3°
3° 0.68 0.68 0°

 

MSE = .00616
Degrees of Freedom = 224
60 observations in each mean

at alpha = .05

 

66

TABLE B-9: 2-Way Interaction Comparing Deflection Values of
Each Platen and Each Box Size.

 

 

Avg. combined

Platen Box Defect Deflection Avg. TB
FIXED A 0° .60
FIXED A 1° .66
FIXED A 2° .71 .665
FIXED A 3° .69

2.66 sig.
FLOATING A 0° .72 '
FLOATING A 1° .68
FLOATING A 2° .76 .703
FLOATING A 3° .65
FIXED B 0° .78
FIXED B 1° .85
FIXED B 2° .75 .755
FIXED B 3° .65

1.40 not
FLOATING B 0° .77 si9~
FLOATING B 1° .79
FLOATING B 2° .67 .74
FLOATING B 3° .73

 

The formulas used are the same as in the compression
analysis of the same type.

where MSE = .00616
Significance: 1% = 2.838
5% = 2.258

 

67

TABLE B-lO: 2—Way Interaction Comparing Deflection Values of
Box A to B with the Same Defect and the Same

 

 

 

Platen.
Deflection

Platen Box Defect Avg. TB
FIXED A 0° .60
FIXED B 0° .78 .27 sig.
FIXED A 1° .66 g
FIXED B 1° .85 .62 sig.
FIXED A 2° .71 .
FIXED B 2° .75 .39 not 819.
FIXED A 3° .69 .
FIXED B 3° .65 .39 not 819.
FLOATING A 0° .72 .
FLOATING B 0° .77 .74 not 819.
FLOATING A 1° .68 .
FLOATING B 1° .79 .83 $19.
FLOATING A 2° .76 .
FLOATING B 2° .67 .14 $19.
FLOATING A 3° .65 .
FLOATING B 3° .73 .79 $19.

 

The formulas used are the same as in the compression

analysis of this type.

where MSE

Significance:

3.279

2.764

68

Factor Anlaysis: Compare all deflection averages for each
box type and platen type to see if there is a linear and/or

curvature trend. (3-way interaction)

The following formulas are used:

EL I PIBI

QL={"3Y1-Y2+Y3+Y4}

FL = QLz/[(20)(MSE)/15]
QQ = { Y1 — Y2 - Y3 + Y4 }
FQ = QQZ/[(4)(MSE)/15]

EL I P132

same equations only with box size B
EL I P2Bl

same equations as EL I P181 only with the floating

platen
EL I P232 etc.
where QL = equation for straight line
QQ = equation for curved line

FL = Factorial equation for straight line

Pa = Factorial equation for curved line
Significance: 1% = 6.75
5% = 3.89

69

TABLE B-ll: Factor Analysis Of Deflection.

 

 

 

Deflection
Platen Defect Avg. QL FL
FIXED A 0° .60
FIXED A 1° .66 .
FIXED A 2° .71 .32 12.49 Sig.
FIXED A 3° .69
FIXED B 0° .78
FIXED B 1° .85 .
FIXED B 2° .75 -.49 29.28 819.
FIXED B 3° .65
FLOATING A 0° .72
FLOATING A 1° .68
FLOATING A 2° .76 —.13 2.06 not
FLOATING A 3° .65 $19.
FLOATING B 0° .77
FLOATING B 1° .79 .
FLOATING B 2° .67 -.24 7.02 319.
FLOATING B 3° .73

QQ FQ

FIXED A 0° .60
FIXED A 1° .66 .
FIXED A 2° .71 -.08 4.0 819.
FIXED A 3° .69
FIXED B 0° .78
FIXED B 1° .85 _
FIXED B 2° .75 -.17 18.06 319-
FIXED B 3° .65
FLOATING A 0° .72
FLOATING A 1° .68 _
FLOATING A 2° .76 —.07 3.06 819.
FLOATING A 3° .65
FLOATING B 0° .77
FLOATING B 1° .79
FLOATING B 2° .67 .04 1.0 not
FLOATING B 3° .73 Sig.

 

sample calculation:

QL { -3(.60) - (.66) + (.71) + 3(.69)} = .32

FL (.32)2/[(20)(.00616)/15] = 12.49

L I ST OF REFERENCES

7 . 0 REFERENCES

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70

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71

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