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This is to certify that the
dissertation entitled
Measuring and Modeling the Effect of Time and

Temperature on Removal Torque and Sealing Force
of 3 Continuous Thread Closure

presented by
Supachai Pisuchpen
has been accepted towards fulfillment

of the requirements for

Ph . D . degree in Packaging

 

 

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To AVOID FINES return on or before date due.
MAY BE RECAUJED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 cJCIRC/DateDuepes-p. 15

 

MEASURING AND MODELING THE EFFECT OF TIME AND TEMPERATURE
ON REMOVAL TORQUE AND SEALING FORCE OF A CONTINUOUS
THREAD CLOSURE

By

Supachai Pisuchpen

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

School of Packaging
2002

ABSTRACT

MEASURING AND MODELING THE EFFECT OF TIME AND TEMPERATURE
ON REMOVAL TORQUE AND SEALING FORCE OF A CONTINUOUS
THREAD CLOSURE

BY

Supachai Pisuchpen

A new technique for measuring the sealing force of a container-closure
system was developed by employing a strain gage based transducer. The
sealing force is considered a direct indicator for monitoring the mechanical seal
integrity of the container-closure systems. A sealing force measuring device and
a torque meter were used to investigate the effect of environmental conditions on
the relaxation behavior of a 28-400 closure system. The responses from both
devices during storage over time were transformed to the percent (%) force
retention (FRT) and percent (%) torque retention (T RT) and used to analyze the
effect. The high temperature and relative humidity of tropical conditions showed
significant effect on the relaxation of the systems studied. It was found that the
% TRT overtime data were less consistent than the % FRT due to the nature of
torque measurement and effect of environmental conditions. The % TRT data
were higher than the % FRT indicating less relaxation of torque than of force.
Therefore, using the removal torque or % TRT may be misleading in the

interpretation of the seal integrity of the container-closure systems. The apparent

seal integrity is less when measured by force retention. Mathematical modeling
of the relaxation behavior of the systems revealed that the theoretical models
derived from spring and dashpot are not applicable. Empirical models using the
curve fitting techniques were then applied and excellent agreement with the
experimental data was found. The mathematical models developed were
extended to long-tent! prediction for 3 years; the predicted values of the % F RT

and % TRT were in the acceptable range for agreement among the models.

Copyright by
SUPACHAI PISUCHPEN
2002

ACKNOWLEDGMENTS

I would like to express my appreciation to my research guidance
committee: Dr. Hugh Lockhart, my major adviser, for his support, advice and
guidance throughout my graduate program. He is the model for students in
teaching and researching. His help in providing financial support and giving me
the opportunities to work in many projects are a major contribution to my
success. I thank Dr. Gary Burgess for his valuable advice and support. He
always comes up with thoughtful solutions for students all the time. I am grateful
to Dr. Gary Cloud for his great help and guidance in introducing me to the area of
experimental mechanics. I also thank Dr. Robert Clarke for his encouragement,
guidance, and constant greeting which is a resource of comfort during my study
in the School of Packaging.

I thank Bob HUTWItZ, a best friend, who always inspires me and supports
me. Your friendship will always be with me and my family.

I would like to acknowledge the Thai government for the scholarship and
support given throughout my study at Michigan State University.

I heartily thank my parents for their support and encouragement toward
educafion.

Finally and most importantly, my beloved wife: Wariya, a special thanks is
given to her, for her strength, support, understanding, and friendship. She is
always there with me during hard times. The appreciation is beyond words and

will never fade away.

TABLE OF CONTENTS

LIST OF TABLES ............................................................................... vii
LIST OF FIGURES ............................................................................. viii
LIST OF ABBREVIATIONS ................................................................... xii
1. INTRODUCTION ........................................................................... 1
2. LITERATURE REVIEW .................................................................. 4
3. THEORETICAL AND TECHNIQUE DEVELOPMENT ............................. 11
4. MATERIALS AND METHODS .......................................................... 39
5. RESULTS AND DISCUSSION ........................................................... 61
6. CONCLUSIONS, RECOMMENDATIONS AND FUTURE WORKS ........... 109
APPENDIX-COMPUTER PROGRAMS ................................................... 114
REFERENCES .................................................................................. 121

vi

P93!”

9» .01

LIST OF TABLES

Comparison between Experimental Sealing Force and Theoretical Sealing

Force ............................................................................................................ 1 5
Description of Container-Closure Systems ................................................... 39
Summary of Container-Closure Systems Dimensions .................................. 61
Summary of %FRT and %TRT of Container-Closure Systems ..................... 66

Empirical Models for %FRT and %TRT of Container-Closure Systems ........ 81

Predicted Values of %FRT and %TRT for Long-Term Prediction ................. 98

vii

10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.

LIST OF FIGURES

The Comparison between Removal Torque and Sealing Force ...................... 2
General Purpose Strain Gage ......................................................................... 7
Pure Elastic Response (Spring) and Pure Viscous Response (Dashpot) ....... 8
First Design of Sealing Force Measuring Device .......................................... 18
Second Design of Sealing Force Measuring Device ..................................... 20
30 of Top Panel of Tubular Shell for Second Design .................................... 21
ZD of Top Panel of Tubular Shell for Second Design ................................... 21
Temperature-Compensated Circuit (Half-Bridge) .......................................... 24
Kelvin-Voight Model ...................................................................................... 26
Force Diagram of Liner and Threaded Part of Container .............................. 27
Separate Force Diagram of Liner and Threaded Part of Container ............... 28
Liner Material in Model A (Kelvin-Voight Model) ........................................... 28
Plot of Force F as a Function of Time t ......................................................... 29
Plot of % Force Retention vs Time of Liners Tested on Instron .................... 31
Liner Material in Model B .............................................................................. 32
Comparison between Experimental and Predicted %Force Retention .......... 36
% Force Retention of Foam Liner as a Function of Time .............................. 37
Dimensions of Container-Closure System .................................................... 42
Actual Situation of Container-Closure System under Loading ...................... 43
Test Fixtures for Design Verification ............................................................. 44
Calibration Jig for Sealing Force Measuring Device ..................................... 46
Calibration Setup for Sealing Force Measuring Device ................................. 47

viii

23.

24.

25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.

38.

39.

40.

41.

Calibration Curve for Sealing Force Measuring Device ................................ 48
Setup for Verification of Temperature Compensation and Moisture
Protection ..................................................................................................... 50

Strain as Function of Standard Weight Obtained from Test Conditions ........ 51

Experimental Design for Relaxation Study .................................................... 54
Experimental Setup for Relaxation Study ..................................................... 54
Empirical Models for Relaxation Data of %FRT and %TRT .......................... 56
Force as a Function of Time obtained from Unrestrained Fixture ................. 64
Force as a Function of Time obtained from Restrained Fixture .................... 64
Plot of %F RT as a Function of Time for All Treatments ................................ 68
Plot of %TRT as a Function of Time for All Treatments ................................ 69
Plot of %FRT as a Function of Time for PE Foam Liner ............................... 71
Plot of %FRT as a Function of Time for Paper Pulp Liner ............................ 71
Plot of %TRT as a Function of Time for PE Foam Liner ............................... 72
Plot of %TRT as a Function of Time for Paper Pulp Liner ............................ 72
Comparing %FRT and %TRT of Systems at Test Conditions ....................... 76
%FRT and %TRT of Systems at Standard Conditions at the End of 15

Minutes ........................................................................................................ 78
Comparison between Experimental and Predicted %FRT of PE Foam Liner at
Refrigerated Conditions (Short-Tenn Prediction 5 Days) ............................. 83
Comparison between Experimental and Predicted %FRT of PE Foam Liner at
Standard Conditions (Short-Term Prediction 5 Days) .................................. 84

Comparison between Experimental and Predicted %FRT of PE Foam Liner at

ix

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

52.

53.

54.

Tropical Conditions (Short-Term Prediction 5 Days) .................................... 85
Comparison between Experimental and Predicted %FRT of Paper Pulp Liner
at Refrigerated Conditions (Short-Term Prediction 5 Days) ......................... 86
Comparison between Experimental and Predicted %FRT of Paper Pulp Liner
at Standard Conditions (Short-Term Prediction 5 Days) .............................. 87
Comparison between Experimental and Predicted %FRT of Paper Pulp Liner
at Tropical Conditions (Short-Term Prediction 5 Days) ................................ 88
Comparison between Experimental and Predicted %TRT of PE Foam Liner at
Refrigerated Conditions (Short-Term Prediction 5 Days) ............................. 89
Comparison between Experimental and Predicted %TRT of PE Foam Liner at
Standard Conditions (Short-Term Prediction 5 Days) .................................. 90
Comparison between Experimental and Predicted %TRT of PE Foam Liner at
Tropical Conditions (Short-Term Prediction 5 Days) .................................... 91
Comparison between Experimental and Predicted %TRT of Paper Pulp Liner
at Refrigerated Conditions (Short-Term Prediction 5 Days) ......................... 92
Comparison between Experimental and Predicted %TRT of Paper Pulp Liner
at Standard Conditions (Short-Term Prediction 5 Days) .............................. 93

Comparison between Experimental and Predicted %TRT of Paper Pulp Liner

at Tropical Conditions (Short-Term Prediction 5 Days) ................................ 94
%FRT as a Function of Logarithmic Time ..................................................... 97
%TRT as a Function of Logarithmic Time ..................................................... 97
Long-Term Prediction of %FRT Values for PE Foam Liner .......................... 99
Long-Term Prediction of %FRT Values for Paper Pulp Liner ...................... 100

55.

56.

57.

58.

59.

60.

61.

Long-Term Prediction of %TRT Values for PE Foam Liner ........................ 101
Long-Term Prediction of %TRT Values for Paper Pulp Liner ...................... 102
Comparison between Predicted %FRT and %TRT at 3 years

using Model C ............................................................................................ 105
Comparison between Predicted %FRT and %TRT at 3 years

using Model D ............................................................................................ 105
Comparison between Predicted %FRT and %TRT at 3 years

using Model E ............................................................................................ 105
Coefficient of Friction at Thread Interface determined from Sealing Force
Measuring Device and Actual System ........................................................ 106
Coefficient of Friction at Liner Interface determined from Sealing Force

Measuring Device and Actual System ........................................................ 107

xi

TIP
AT

RT

% FRT
% TRT
PE
PET
HDPE
PP

T9

LIST OF ABBREVIATIONS

Torque Inch Pounds
Application Torque
Removal Torque

Percent Force Retention
Percent Torque Retention
Polyethylene

Polyethylene Terephthalate
High-Density Polyethylene
Polypropylene

Glass Transition Temperature

xii

1 . INTRODUCTION

The seal integrity of a container-closure system is important, not only for
packaging appearance but for consumer satisfaction and safety as well. Today,
consumers expect effective packaging as well as product quality. The
expectations of container-closure systems especially for pharmaceuticals focus
on functional performance of the seal. The consumer would avoid buying
products having an improper seal. Indications of an improper seal can be shown
in detectable leakage, tampering, contamination, and ergonomic factors such as
ease of opening and closing. Therefore, finding ways to maintain and monitor
the seal integrity of the container-closure systems is necessary.

The use of plastics in container-closure systems has become the
predominant choice in packaging applications because of inherent advantages
over other materials. Plastics offer good barrier and mechanical properties,
flexibility in forming different shapes and an economical advantage. A major
drawback is that plastic material properties are highly dependent on time and
temperature. This strong time and temperature sensitivity of plastic properties is
a consequence of the viscoelastic nature of polymeric materials. This implies
that plastics exhibit combined viscous and elastic behavior. A good example of
these properties is that if a weight is suspended from a piece of plastic, the strain
.or elongation will not be constant but will increase slowly with time. In a
container-closure system, the effect of viscoelastic properties shows in the stress
relaxation behavior which is primarily suspected as a major cause of loss of seal

integrity. Numerous studies have been conducted to research this behavior by

using the removal torque as the indicator but the reliability of removal torque for
indicating loss of seal integrity has not been established. One reason is that the
characteristics of removal torque are fairly complex; variation from one measure
to another is usually large. There are other factors involved not related to the
seal integrity, such as adhesion, threads and dimensions mismatch, closure
misalignment and human factor. However, a positive aspect of the removal
torque testing is that it is inexpensive, easy and quick. This method is well
known and commonly used as the mechanical seal indicator throughout industry.
The removal torque can be precisely defined as the unscrewing moment
needed to start the various surfaces in the system sliding against friction forces

(Figure 1).

Sealing Force

Removal Torque

 

 

 

Figure 1 Comparison Between Removal Torque and Sealing Force

A previous study (Pisuchpen, 2000) explained how the seal mechanism in
the container-closure system works. Torque applied to a container-closure
system is actually translated to a sealing force which is the compression force or

axial force acting at the liner and thread interface. The radial force that is

generated from factors not related to the seal integrity is excluded from the
system. Therefore, the sealing force keeping all interfaces in contact can be
considered as a direct indicator for seal integrity of a container-closure system.
Assessing and comparing both indicators through the relaxation behavior of the
container-closure system offer a better understanding of the seal integrity of the
system. Although the sealing force seems to be an alternative indicator, there is
no easy way to measure this force directly in the system yet (Pisuchpen, 2000).
This indicates that research in this area is needed. In addition, consideration
should be given to the prediction of relaxation behavior of container-closure
systems as well since the sealing force associated with the viscoelastic
properties is a function of time. The economical way to predict this long-term
behavior of the system is by using mathematical modeling.
Objectives

One objective of this research was to develop a technique for measuring
the sealing force of container-closure system. This will provide another way to
verify and monitor the seal integrity of the system other than using the removal
torque. A second objective was to apply a technique developed by this research
to investigate the effect of time and temperature on the relaxation behavior of
container-closure systems. The final objective was to establish mathematical
models for long-term prediction of the relaxation behavior of container-closure

systems.

2. LITERATURE REVIEW

The research began with surveying literature in this area in order to gather
the information for experimental design. The concept of sealing force is certainly
not new. In 1956, Robert V. McCarthy (McCarthy, 1956) conducted research in
determining performance of plastic screw thread caps on glass bottles. He
developed a measuring device using a strain gage to determine the sealing force
of glass bottle-plastic closure systems over a short period of time (20 min.) at
room temperature. Typical relaxation curves were found by using his measuring
device. One limitation of his research is that the measuring device was not
designed to account for the relaxation behavior of the liner which is one of the
most important factors in providing the seal integrity of the system. The empirical
model for sealing force decay was also developed from various exponential
relationships; the calculated values from the model compared favorably with the
experimental data. After 1956, there is no published research conducted in the
sealing force area. One reason is that other researches followed the ASTM
D3198 test method which recommends using the removal torque as a guideline
for measurement. In 1992, Dr. Hugh E. Lockhart (Lockhart, 1992) studied the
torque loss over time for a 28 mm metal closure on plastic bottle which was
subjected to various temperatures (5°C, 23°C and 43°C) for 12 weeks. He
concluded that temperature, time and application torque all have a statistically
significant effect on the level of removal torque. However, these effects are of

little practical importance except for the torque losses at 43°C. This study

indicates that high temperature significantly increases the torque loss of the
system through the relaxation behavior. The next publication in the relaxation of
container-closure system is in 1993 by Dr. Gerald Greenway (Greenway, 1993).
He conducted a short-term study (10 days) of closure torque decay for 24 mm
HDPE closures with paper pulp liner on PET bottles. The container-closure
systems were stored at room temperature and tested for ten days. He concluded
that the removal torque decay process is a logarithmic function. It decreases
initially at a very rapid rate and continues to gradually decrease at slower and
slower rates. A plot of removal torque vs log of time shows a good linear
relationship. This study shows a typical relaxation curve obtained from using the
removal torque and the semi log can be used to describe the relaxation behavior.
The relaxation rate increases as the application toque increases. In 1999, Dr.
Ching-Sung Lai and Dr. Gerald Greenway (Lai and Greenway, 1999) published a
study on the effect of time on closure removal torque. A PP closure with vinyl
liner on a PET bottle were studied at room temperature. It was found that a plot
of removal torque vs log of time exhibits an “S” shape response. The removal
torque first starts increasing until reaching the maximum level after around 10
days storage and then changes to slowly decrease over time. They believed that
this phenomenon results from the interaction between the liner and the land area
of the container, developing an adhesion effect. They said that the adhesion
becomes stronger at the first period of storage time and then, as the storage time
increases beyond 10 days, the adhesion becomes weaker causing a reduction of

removal torque. This study is a good example of the uncertainty of using the

removal torque technique because the result suggests that the removal toque
can be easily affected by other factors which, in turn, can affect the interpretation
of the seal integrity. Adhesion is an uncontrolled factor which may or may not
occur in the system. Therefore, the increase of the removal torque does not
absolutely tell that the seal integrity is intact. In fact, the sealing force of the
system initially decreases at a rapid rate and then continues to decrease at
slower and slower rate. This is the actual relaxation behavior that could be
obtained if using the sealing force as the indicator.

After surveying the experimental stress analysis techniques that can be
applied to the research, it was found that the transducer strain gage technique is
considered as the best tool for this research. The bonded resistance strain gage
consists of a filament of very thin metallic foil mounted on plastic backing sheet
(Figure 2). The filament material has a linear relation between the electronic
resistance and the strain. The strain gage is widely used in measuring the strain
on structural members for stress analysis. In addition to the direct determination
of strain, the strain gage is employed as the sensing element for measuring load,
force, torque, displacement and other physical variables. Good examples of the
application are the electronic torque meter and the load cell of the Instron

machine.

 

 

Ill“'”/r—Foil

Grid

 

 

 

 

 

 

 

 

 

 

 

 

 

,— Terminal K

/' Backing g

 

 

 

   

 

 

 

Figure 2 General Purpose Strain Gage

From simplicity, modeling the relaxation behavior of the container-closure
system in this research is confined to the linear viscoelastic behavior, one-
dimensional situation since non-linearity adds to the complexity of the problem.
Such a linear viscoelastic behavior is sometimes a reasonable approximation for
real materials, such as polymers, metals and ceramics at high temperatures
(Dowling, 1993). The term linear refers to the mechanical response in which the
ratio of the overall stress to strain is a function of time only and is independent of
the magnitudes of the stress or strain. As a result of this situation, the stress-
strain relationship for any given value of time is a straight line. The linear
viscoelastic behavior of solid polymers can be observed under limited conditions
which are homogeneous, isotropic, amorphous under small strains and at
temperature close to or above Tg (Ferry, 1970). In spite of its limited use, the
theory of linear viscoelasticity provides a useful starting point for numerous
applications. To aid the analysis of viscoelastic response, mechanical models
using spring and dashpot are usually introduced to represent the extremes of the
mechanical response spectrum as shown in Figure 3 (Aklonis, 1972). The spring

represents a linear elastic or Hookean solid. It responds instantaneously to

reach an equilibrium strain 6 as long as the stress a is maintained constant.
Sudden removal of the stress causes in instantaneous recovery of the strain as
well. It has a constant modulus that is independent of the strain rate or the
speed of testing. Thus, the stress is a function of the strain only. In contrast to
the spring, a linear viscous or Newtonian fluid is represented by a dashpot which

is a piston moving in a cylinder of Newtonian fluid. A dashpot has no modulus

but the shear stress is proportional to the speed of testing (strain rate ;). In

other words, the strain is a linear function of time at an applied external stress.
Thus, the strain rate determines whether the deformation is elastic (spring) or
viscous (dashpot). If a constant stress 1' is suddenly applied to the dashpot, the

strain 7 increases linearly with time t as shown in Figure 3.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0' T
t t
t1 t1
6 7
t t
t1 t1
6 $
2'
«in
8 7

 

 

 

 

Figure 3 Pure Elastic Response (Spring) and Pure Viscous Response (Dashpot)

However, no real material shows either ideal elastic behavior or pure
viscous flow. Viscoelastic materials such as polymers combine the
characteristics of both elastic and viscous materials. In a polymer structure, the
spring can be viewed as the contractile polymer chains and the dashpot is
descriptive of the motion of chains caused by adjacent chains (Arridge, 1985).
The mathematical expression used to describe the experimentally determined
stress-strain response is known as the constitutive equation. Each constitutive
equation is an idealization or mathematical abstraction of a measured stress-
strain response of a real material. It is important to remember that each
constitutive equation is only a model adopted to describe the most significant and
idealized mechanical behavior of the material. It represents a simplification of
the real stress-strain behavior of the specific material. It has significant
restrictions and limitations for its general applicability. A simple constitutive
relation for the behavior of a linear viscoelastic solid can be obtained by

combining the Hookean solid (spring) and Newtonian fluid (dashpot). The

mechanical response is described by Hooke’s law( 0', = E .e) and the

da
response of a fluid to a stress is given by 0’4 = 77 67;. A possible formulation of

linear viscoelastic behavior combines these equations; thus, the total stress

supported by the parallel arrangement of the spring and dashpot is

0'=0'+0' ==E.8+77€£- 1
l S d dt ()

This makes the simplest possible assumption that the stresses related to

the strain and strain rate are additive (Rosen, 1993). The equation represents

the Kelvin-Voight model, one of the simple models for linear viscoelastic
behavior. The Kelvin-Voight model will be used as the basis model for relaxation
behavior of the container-closure system. It represents the following
characteristics of solid materials during loading. The spring and dashpot always
remain parallel. This means that the strain in each element is the same. The
total stress supported by the model is the sum of the stresses in the spring and
dashpot. From Equation (1), if the strain is set to be constant, the solution for
stress relaxation can be obtained. The viscoelastic behavior of material, in
general, may be investigated by the use of mechanical models which consist of
finite networks of springs and dashpots. Several springs and dahpots can be
arranged in many ways; the application of the Boltzmann superposition principle

which is of great use in linear viscoelasticity is recommended (Arridge, 1985).

10

3. THEORETICAL AND TECHNIQUE DEVELOPMENT

The relaxation behavior in a container-closure system reflects in the decay
of sealing force over time that results from subjecting it to a constant strain. This
can be measured through the instrumentation on the actual container-closure
system. The basic concept for instrumentation is that the stress and strain are
related to each other by a fundamental relation, the modulus of elasticity, for
linearly elastic materials (Dally, 1993). The response by the instrumentation to
an applied load is normally presented in strain. Strain is a fundamental physical
quantity and stress or force (sealing force in this case) on the instrumentation is a
derived quantity. Selection of an appropriate measuring technique for a
particular application of the research is very important. Experimental stress
analysis techniques: strain gage and photoelasticity were considered for this
application. After careful consideration of complexity, physical size or shape
limitations, operating environment, cost constraints and test limitations, the
bonded resistance strain gage was finally selected to develop a sealing force
measuring device. The strain gage is not used to measure strain, but it is to give
a measurement of sealing force. In application the strain gage is called a
transducer, which is an electromechanical device converting a mechanical
change into an electrical signal. The basic concept of transducer design is a
common principle. A spring element, which simply is a piece of suitable metal
designed to deform elastically and linearly over the desired loading range, has

strain gages mounted to it. The deformation on the spring element from the

11

applied load is then converted into strain output. It only needs an accurate
calibration against the corresponding forces before use.

A sealing force measuring device using the transducer strain gage
technique constructed according to the second design in this chapter was used in
the preliminary study in order to compare the theoretical sealing force with an
experimental sealing force. The purpose of the experiment was to evaluate the
torque-friction model developed from a previous study and determine the
potential of modification of the model to describe the relaxation behavior. The
28-400 HDPE containers and PP closures with PE foam liner were used in the
preliminary study. The theoretical sealing force based on the torque-friction
model (Equations (2) and (3)) assumes that the container-closure system is a
rigid body. The torque-friction model was then developed from the equations of

equilibrium for all forces acting on the system. The values of parameters (p, Ht.
Ill. r7 and}: ) used in equations below were taken from a previous study

(Pisuchpen, 2000).

 

 

— . + 2. . — —
T "TE-r: cosfip _7r,u,r, +1”!!! (2)
cos 6.2.7”, - ,u, .p
—2.. .-—cos6i. -
T'=FL-n flfl’r’ — p +1111: (3)
cos 9.2.7”, + ,u, .p
where T, T’ = Application torque (TIP), Removal torque (TIP)
F" = Sealing force (lb)
p = Thread pitch (inch) = 0.167 (6 threads/inch)
in = Coefficient of friction at thread interface HDPE-PP = 0.17

12

p. = Coefficient of friction at liner interface HDPE-PE foam =

0.50
27 and; = Mean radius of the thread contact (inch) = 0.5131”

and liner contact = 0.4534”
0 = Contact angle between container threads and closure
threads (degree) = 42.07°

There are 2 special cases in Equations (2) and (3) involving the design of a
sealing force measuring device that should be considered.

1. p. at 0. In this case, a liner is sliding on the bottle finish, while torque is
applied to a closure. Thus, the static coefficient of friction at liner interface
should be taken into the account. A closure in this case is considered as a glued
attachment liner type, in which a liner is attached to the top panel of the closure
by glue. The liner rotates with the closure when torque is applied. A system of
HDPE-PP using PE foam liner is used as an example for this case and the

solutions of Equations (2) and (3) are:

T = 0.372512, or F; = 2.68461" (4)

T'= 0.3166}: or F“, = 3.15861“ (5)
If the application torque, T and the removal torque, T’ are 14 and 8 TIP, the
sealing forces will be 37.58 and 25.27 lb respectively.
2. u. = 0. A liner is not sliding against a bottle finish but stays at the original

position, while torque is applied to a closure. The static coefficient of friction at

the liner interface is not involved in the equations in this case. It is assumed that

13

the friction generated between the center of the top panel of the closure and of
the liner is negligible. This is a non-glued attachment liner type. The sealing
force measuring device developed in this research is based on this case. A liner
stays still on a container finish while the center of the shell is spinning against the
lubricated “bump” disk. The static coefficient of friction at liner interface with the
land area of container finish is therefore neglected. Only the coefficient of friction
at thread interface is used in the equations. Therefore, when the rest of the

parameters are substituted in Equations (2) and (3), the equations reduce to

T = 0.145817; or F; = 6.8587.T (6)
T'=0.09OE, or F; =11.11T' (7)

Again, if the application torque, T and the removal torque, T’ are 14 and 8
TIP, the sealing forces will be 96.02 and 88.88 lb respectively. Clearly, the
sealing force increases 2.5-3.5 times compared with u. at 0 case. This is due to
the mechanical advantage; torque is efficiently translated into sealing force
without loss from friction at the liner interface. Both special cases point out an
interesting issue in the relationship among torque, sealing force and the static
coefficient of friction at liner interface. Theoretically, the most effective way to
achieve the highest sealing force is by approaching II: = 0.

Equations (6) and (7) give a theoretical sealing force for a system which can
be used to compare with the results from the experiment. The equations indicate
a linear relationship between the application torque (removal torque) and the
sealing force. To investigate the accuracy of Equations (6) and (7), a

comparison between the experimental sealing force and theoretical sealing force

14

was conducted and the result is shown in Table 1. In the experiment, hand-

applied application torque (T) of 14 TIP was used on the sealing force measuring

device having PP closure and PE foam liner installed. The initial sealing force

was recorded. The immediate removal torque (T’) and the sealing force were

then measured after storage for 15 min at room temperature. The application

torque and removal torque were used to calculate the theoretical sealing force

and the results were compared with the experimental sealing force from the

sealing measuring device.

Table 1 Comparison between Experimental Sealing Force and Theoretical

Sealing Force

 

 

 

 

 

 

 

 

Sample Torque Experimental Theoretical % Difference
TIP Sealing force, lb Sealing force, lb (from experiment)
1 T= 14.0 110.0 96.0 13
T’= 9.0 61.8 100.0 62
2 T= 13.9 107.1 95.3 11
T’= 9.2 58.3 102.2 75

 

A comparison shows that Equation (6) for application torque estimates the

sealing forces close to those experimentally measured, whereas the Equation (7)

for removal torque gives a theoretical sealing force higher than the experimental

results by about 70%. The difference between theoretical and experimental

sealing force may result from the coefficient of friction at thread interface, which

has a broad range of values used in models. A previous study found that the

coefficient of friction for the container-closure systems can vary up to 35%

(Pisuchpen, 2000); this can in turn cause the variation of the calculated sealing

force. In addition, the mathematical model assumes that the container-closure

15

 

system is a rigid body; there is no deformation and change in the boundary
condition of the system. The actual system, however, is made of plastic a non-
rigid structure. It is a highly stressed system with a very complex shape and
several stress concentrations. The basic defamation is usually elastic but there
are always portions of the container-closure system that deform plastically; for
example, a liner and the thread roots which can alter the geometry of the system.
Moreover, the viscoelastic properties of the system made of plastic also add to
the complexity of the system due to the time dependence of these properties.
Therefore, the boundary condition of the system changes over time. This
contributes to a large difference between the theoretical results from the removal
torque and the experimental results.

Besides, from a work and energy concept, the torque-friction model
(Equation (2) and (3)) only describes action and reaction force and torque on the
system. It does not describe the various forms of heat and strain energy
introduced to the system by the input work done on the system. The torque-
friction model suggests that the input work ends up as friction loss but actually
portions of the input work end up as liner and thread deformation also. The “true”
relationship between the input torque and the sealing force, therefore, must take
these outputs into account.

The serious limitation of the torque-friction model developed from previous
research suggests that it is not applicable to use as a basic model for describing

the relaxation behavior of the container-closure system. It is necessary to turn to

16

other theories that can be applied in the research to explain the viscoelastic
properties of the system better.
3.1 Sealing Force Measuring Device Design

The development started with a simple design using two steel tubes
having circular thin flat plate 1/32” thick at one end. The outer tube is hollow.
One end is closed and the other end has circular thin flat plate. The inner tube
having a radius end for low friction and the other end with circular thin flat plate is
solid. A strain gage is attached at the middle of the outer tube in the axial
direction which is the location of average strain. The assembly drawing of the
design is shown in Figure 4. In use, both tubes are inserted into a plastic
closure; the (upper) plate of the outer tube has a clearance of 1/32” from the
(lower) plate of the inner tube. A liner is placed in between the lower plate and
the land area of container finish. When torque is applied on a closure, torque is
then translated into a sealing force by pushing the liner against the land area of
the container finish. The reaction force from container finish transfers to a liner,
lower plate of inner tube and radius end where inner tube and outer tube are in
contact. This radius end then will push against the outer tube end in which the
upper plate is restrained by compression of the closure top panel and the
engagement of closure threads and container threads as a result of axial tension
force on the outer tube. This axial tension force which is a sealing force will be

computed from strain measured by the strain gage.

17

fl Strain Gage
// Closure
/

 

  

 

 

 

 

 

 

 

 

 

 

Upper Plate of Outer Tube
WH/
Lower Plate of Inner Tube
K.)
. Liner
2:221:11. :F:

|.'.\~ I ,.,. 4'.
u....-,_ M... ‘ .
.:'_‘l‘.‘.'.s:'.'A ~ -" r" ’ r . :3
'."‘~i'- ~ ‘ ' .. .‘a‘.'.':i 'r'»-.~&
.h ~ “ "' .. . . .-
-' nag-wigum .. .,
.". 5 -¢ I E763.
..,n--vr ,y— .b, .-,
'-'lt"""' ' ’...~v.u~|t
".‘..';‘;'.‘.’ '.'..'. ’. - v ) ~ "-3.
' .. , ..- - u. ... n“. I I .
'. . ".'.".'..'.‘\:...I- . u a

 

 

\—
\_ \
Figure 4 First Design of Sealing Force Measuring Device
It was found that this first design shows inconsistent measuring results; a
tilting effect from improper thread engagement yielded a non-uniform sealing
force around the contact area. It did not produce a typical relaxation curve. This

is because the first design is limited by only small free headspace at the top

panel of the closure. This free headspace controls the thread engagement of the

system.

18

To solve a problem of limitation by the small headspace of closure, 3
second design was tried by assuming that dome bending near the periphery of
the dome is small and can be neglected. Hence the top panel of the closure can
be removed and this gives more space to work with. The second design consists
of a tubular shell with one closed end, a circular flat disk 0.1” thick with a “bump”
at the center and a retainer as shown in Figure 5. A circular flat disk is used as a
mechanism to transfer a reaction force from the container-closure system to a
strain gage which is installed at the center of the closed end shell where the
average strain occurs. In use, a closure without its top panel is glued into the
tubular shell and a removed top panel is glued on the flat surface side of a
“bump” disk. A liner is inserted in between the disk and the land area of
container finish. As torque is applied to the closure, the shell moving downward
is pushed by a bump on the disk at the center of the closed end shell where the
strain gage is mounted. The strain generated will be picked up by the strain
gage and the reaction force which generates the strain is the sealing force of the
container-closure system.

The next step is to estimate the thickness of the top panel of closed end
shell needed to keep it in the elastic range when loaded. Thus, the strain
generated at the center of the top panel of the tubular shell must be estimated.
The assumption is that the closed end shell in circular shape stretches only when
a force F is exerted at the center and the rim of the disk is completely restrained
(boundary condition) (Figure 6a). Figure 6b shows that the same disk is pushed

upward at the center by force F into a shape of spherical section while the base

19

is held at the original radius. Force F is applied by the “bump” disk as torque is

Aluminum Shell Alumlnum Shell
gram Gage Strain Gage Bump Disk
[— Oosure Top Panel
7
m
.w-

applied.

   
 

Liner

 
       

g— Plastlc Closure

/— Glue

   

V
W _

Closure Wlthout
‘p Pang g,
%— Retalner I
é—J ’ d x
d

I i Bump Dlsk

  

 

 

 

1 IL\

 

 

(II
III

 

 

 

 

 

 

 

 

 

 

Uner

Figure 5 Second Design of Sealing Force Measuring Device

20

Strain Gage

‘ / Shell Strain Gage
f V

R—>I

 

 

Flat Disk
(Top Panel of Shell)

 

 

 

Stretched Disk (Top Panel of Shell)
b

Figure 6 3D of Top Panel of Tubular Shell for Second Design

I Strain Gage
I

I4—R—v tr
Flat Disk, No Force

 

 

a Same Disk Under Load
a= radius of curvature

in bent configuration
c=resulting stress

b

Figure 7 2D of Top Panel of Tubular Shell for Second Design

21

Figure 7 shows in two-dimensions the top panel of shell under loading.
Because the perimeter of the disk is essentially held fixed by the shell part of the
closure, the material stretches in the radial direction which goes from length 2R

to length 2a9. Thus, strain in the radial direction produces the equation.

£=M=16—1 But sinl9=£ (3)
2R R a
a = isin‘l £_1 (9)
a

From a series expansion, sin’1x = x+x3l6+3x5l40+....

_aR R3 3R5 _R2 BR“
80 E—E z+6a3+E?+.u -1—6a2+Ea—4+... (10)

 

 

In Equation (9) “a” is large compared to R, so all higher order terms can
be dropped as a result to give Equation (11)

R2
_6a2

 

8

(11)

Equation (11) is a resulting strain based on a geometric relationship. The
next step is to get the equation based on material properties which can be

obtained from the force balance in the vertical direction.
26...... = 0, F = 0(2th I- Sim? (12)
where 21rRt = area of circular base edge

0' _ F _ F _ Fa
Therefore, - - '- 7 2 (1 3)
27rRt sml9 27:12: (R) 27m 1

 

 

a

22

Equation (13) is a resulting stress and in the elastic range, a' = Es. Then,

substitute this relation and geometry relation from Equation (11) into Equation

 

 

 

(13).
Fa _ R2
27:th —E 6a2 (14)
l
_ 7rER4t 3
Thus a— 3 F (15)

“3" gives radius of curvature of bent shape due to force F.

Equation (11) is rearranged to get “a” which is then combined with

l l
_ 7rER4t 3_ R2 5
(1’31? '5 (16)

Therefore, Equation (16) can be rearranged to get F or e in term of radius

Equafion(15)

 

R, thickness t, Young’s modulus E, and strain a or force F.

2 2

3 3 - —
F=£62 R1820r£=1—}-3 —F—3 17
3 67r ER‘ ()

Equation (17) is used to calculate the estimated strain developed in the
top panel of the aluminum shell where a strain gage is located.

Design of top panel of Mingm shell

R = radius of top panel which is fixed at 0.5 in.

Maximum applied force F = 140 lb

E of 7075-T651 aluminum alloy = 10.3x106 psi (ASM, 1990)

23

Try thickness t = 0.1”

2 2 3
a: 1(3)3 (LJ3 =0.162( 1.00 )3 =543.2,u£
6 7r ER‘ 10.3x10 x0.5x0.1

The estimated resulting strain in the top panel of the aluminum shell is

 

543.2pe which is in the elastic range of material (up to 7087pa) [ASM, 1990].
Thus, the thickness of 0.1” is fine for designing a device.

A strain gage mounted on a measuring device is connected in the form of
a half-bridge circuit. This is a common arrangement for temperature
compensation which is the use of a dummy gage, identical to the active gage
[\Nindow, 1989]. The dummy gage is bonded to a stress-free piece of aluminum
identical to the material bonding with the active gage. Both gages are placed
close to each other so that they are subjected to the same environmental

conditions. The half-bridge circuit is shown in Figure 8.

 

Uniform temperature
Active gage
on device

Dummy gage
on stress-free
aluminum

     
  

 

 

 

 

 

 

Figure 8 Temperature-Compensated Circuit (Half-Bridge)
The second design of the sealing force measuring device was used for

measuring the sealing force of container-closure systems over time under

24

different environmental conditions. Details of construction, calibration and setup
are described in the next chapter.
3.2 Theoretical Model Development

A preliminary experiment using the torque-friction model (Pisuchpen, 2000)
found that the model predicted adequately only the initial sealing force from the
application torque (Equation (2)). The sealing force predicted from the removal
torque (Equation (3)) using the torque-friction model was overestimated. In
addition, it is apparent that the equations of equilibrium for all forces acting on the
system cannot describe the time dependent behaviors. This is because the
torque-friction model does not account for viscoelastic properties of the materials.
It was assumed that the container-closure system is a rigid body in which all
parameters of the system remain constant during loading. The effects of
deformation and change in shape are neglected. In fact, the mechanical
behavior of the polymeric materials is strongly dependent on parameters such as
time, temperature and rate of loading. This suggests that the torque-friction
model is oversimplified; a more sophisticated model is necessary to study the
removal torque and sealing force over time for the container-closure systems.

There has been a reasonable amount of success in using the linear

viscoelastic behavior in modeling the polymeric materials. Of course, a
considerable amount of experimental work and data processing has been
needed to achieve this end. The theoretical model development for container-
closure systems in this research deals with certain aspects of mechanical models

using spring and dashpot for linear viscoelastic solids. Spring and dashpot

25

models are aids to visualize and develop the equations among force, deflection
and time derivatives. Such models are able to explain the stress relaxation in the
container-closure systems. The research employed an elementary model called
Kelvin-Voight model shown in Figure 9. The reason for choosing this model to
start with is that it is one of the simplest models for viscoelastic solids (Sobotka,
1984). It is composed of a spring and dashpot connected in a parallel
combination and well describes some features of creep and stress relaxation in
therrnoplastics (Ferry, 1970). The spring is considered to represent the
extension and contraction of primary bonds and angles or the entropy elasticity of
randomly kinked molecules, while the dashpot represents the time-dependent

sliding of main chains and flipping of side chains.

Figure 9 Kelvin-Voight Model

3.2.1 Modeling a Container-closure System

In modeling a system, distributed forces within a container-closure system
were evaluated. Figure 10 shows a force diagram for the liner and threaded part
of a container. In the threaded part, there are an infinite number of infinitesimal
contact forces on threads which add up to force F. From the diagram, it can be

simplified as forces distributed in a system. The applied sealing force F balances

26

with the summed forces F in which the liner arranged in series with the container
neck as shown in Figure 11a. If weights and inertia of a system are ignored, the
separate force diagrams are found in Figure 11b and 11c. These separate force
diagrams: liner and threaded part of container neck provide flexibility in modeling
the container-closure system. The liner and threaded part of container neck can
be modeled separately with respect to the material properties of each part and
then will be combined to a complete system later. The next parts will show

modeling the liner material using different configurations of spring and dashpot.

F = Applied ealing force

 

Contact Forces

 

 

 

 

 

 

Figure 10 Force Diagram of Liner and Threaded Part of Container

27

F = Applied Sealing Force

 

 

 

 

Liner in series with
container neck ll:
i F
U :3
N: i 1 C:
:2: \V/

 

 

 

 

 

Figure 11 Separate Force Diagrams of Liner and Threaded Part of Container

3.2.2 Model A for Liner Material
The simplest model: The Kelvin-Voight model was applied for modeling

the liner material as shown in Figure 12.

measuring deflection x

_ I

x
k c

F
l Reference point for

 

 

 

 

Figure 12 Liner Material in Model A (Kelvin-Voight Model)

For model A, the total force is given by

dx
F = kx +c — 13
dt ( )
where F = Compression force or sealing force
k = Spring constant

28

x = Deflection

c = Damping constant
‘5:— = Compression rate

For a liner under compression loading, there is a loading phase where the
liner is compressed at a constant rate v (known). The loading phase ends at
time”to” (also known), where the deflection is held constant at x0 = vto while the

liner material undergoes a “relaxation phase”.

. 61):
Loading ghase x =vt at O S t S t0 and x = — =v

 

dt
so F =kvt +cv (19)
Relaxation phase x =xo =vt0 at tO St 300 and x =0
so F=kx0+c(0)=/Cx0=kvt0 (20)

From the analysis above, a plot between force F and time t, can be

generated to see the theoretical behavior of a model as shown in Figure 13.

F
A

cv-I-kvto ——

 

kvt —— P

 

 

Ar t
{—Loadlng phase—«—— Relaxation phas&——+

 

 

Figure 13 Plot of Force F as a Function of Time t

29

It is apparent that the model cannot portray the relaxation behavior. The
force F drops straight down at the instant loading stops instead of coming to a
gradual drop like real curves, and then remains constant at this value. However,
It is important to transform force F to % force retention (P) in order to normalize

the unit.

 

F “i
Let P = % force retention =100 * [F _ J and the solution is:

t=0

100

c (21)
1+—
kt0

 

p:

Equation (21) indicates that % force retention is independent of
compression rate v but dependent on to. It means that high compression rate or
low compression rate does not affect % force retention as long as a system is
subjected to the same amount of time to.

After obtaining Equation (21), an experiment was performed to check the
interpretation of the equation. The liner materials (PE foam and paper pulp)
loaded at 0.1 inch/minute (in/min) were held at to of 23 seconds (sec) when
compression force of 130-150 pounds (lb) was reached. The decayed force after
loading stopped was recorded every 30 seconds (sec) for 15 minutes (min).
Relaxation curves of liner materials tested are shown in Figure 14. The
experimental data from compression of PE foam and paper pulp liner on the
Instron machine was then used as the input data to determine what the model

explains.

30

 

 

 

 

 

 

 

 

 

100*
E 90E;;;;;;ss;;;;;;;;;ssese‘
2'
3 80—
g 70“ —PE foam liner
m —.—Pa rPul liner
33 60~ pe P

50 - ‘

Time,min

 

Figure 14 Plot of % Force Retention vs Time of Liners Tested on Instron

From the curves, it was found that the PE Foam and paper pulp liner
reached steady state at force retention of 81% and 88% respectively, these

numbers substituted in Equation (21) show:

 

 

81 = 100 :> i— = 0.235 for PE foam liner
C kt
1 + — 0
kto
88 = 100 :> i- = 0.136 for paper pulp liner
1 + i. 0
ktO

Apparently, model A indicates that either cpape, < ohm, or kpaper > kfoam, or
both, in order for these numbers to turn out this way. It makes sense that kpaw>
kfoam. Thus, this model gives some insight of material properties, even though

the model is incomplete to represent the relaxation process.

31

3.2.3 Model B for Liner Material
This model is more sophisticated than the former because it has another
spring kg in series with dashpot, so the system has 2 degrees of freedom as

shown in Figure 15.

 

 

 

 

Figure 15 Liner Material in Model B

For model B, the total force is given by

F=klx +k2(x —y) (22)

and k2(x -y)=cy (23)
where F = Compression force or sealing force

k1 and k2 = Spring constant

x and y = Deflection

c = Damping constant

.7: and )3 = Compression rate
Loading phase x =vt at O S t 3 t0

32

Substituting x = vt into Equation (23) becomes

k2(vt -y) =cy

0 k2 k2
Then, y + 7y = 7‘” (24)

Equation (24) is a 1"t order linear differential equation with constant

coefficient in y(t).

The initial condition is y=0 at t = 0 and the solution is:

11'.
y(t)=vt -%v—[l-e 6] (25)

Substituting Equation (25) into (22) yields:

k2:

F =klvt +k2(vt —vt +9];V—-(1—e'c_)

’ (26)

k2:

=klvt +cv(1—e_°)

So atto, Xo =Vto
0" ‘c—
andyo=Vto—k [1‘9 ]

These are the initial conditions of the relaxation phase.
Relaxation phase x = fixed = x 0 =vt 0 at t0 S t S 00

but y will not be fixed.

Substituting x0 = vt into Equation (23) gives

k2(Vto —y)=cy

33

0 k2 k2
Then, y + ‘c—J’ = ‘6‘” 0 (27)

kzto

cv
The initial condition is y = y o =Vt 0 " 7(1 " e c ) at t = 0 (at beginning
2

of relaxation) and the solution becomes:

kzto k2:
(31/ "“‘“ ““‘
y(t)=vt0——[l—e ‘ J2 c (28)
[ell

Substituting Equation (28) into (22) yields:

kzro k2:

F=k1vt +k,(vtO—vto+§cl(1—e c )e c
2

 

 

 

(29)
12$ _’_‘_2'_
= klvtO +cv(1—e c )e 0
Let P = % force retention =100 * [Ft 7 ] the following solution is
t==0
obtained:
_k2t
1 +qe C
P - 100 *
1 +q (30)
kz’o
q = c l —e -7
where 1‘1 to [ J

Apparently, Equation (30) needs two parameters from the experimental
results: q and Iii. These two parameters are material properties in test material

C'

and can be deduced from experimental data.

34

One way to get the value of q is by assuming that the experimental data
(Figure 14) for PE foam liner and paper pulp liner reached steady state (t -+ 66)
at the force retention of 81% and 88% respectively. These numbers substituted

in Equation (30) show:

 

 

81 = 100 :> q = 0.235 for PE foam liner
1 +q
100 .
88 = 1 :> q = 0.136 for paper pulp lmer
+4

Then, substituting q into Equation (30) yields:

’62!

 

 

1 + 0.235e c
. - P = 100 *
% force retentlon of PE foam llner 1 + 0,235
$2:
1 + 0.136e ‘
. - P = 100 "'
% force retentlon of paper pulp Ilner 1 + 0.136

These equations were fitted to a curve using the experimental data (Figure

14) to get fl values. The results show that foam and paper pulp liner have 11
c c

values of 2.1 and 1.4 respectively. Although predicted curves generated in
Figure 16 follow a typical relaxation curve, the predicted curve just gradually
relaxes for a couple minutes and levels off over time. This indicates the limitation

of this model. In addition, it is important to note that the characteristics of the
predicted curve are dependent on q and £2— which are material properties, but

C

independent of compression rate v. An experimental investigation was needed

35

to check these characteristics; the % force retention is independent of
compression rate. The result can be found in the next page. The last point to be
made is that the accuracy of the prediction is based on the assumption that the
experimental data used for deducing the model parameters are obtained from

steady state. This is subjective and depends on the time frame.

 

 

 

 

 

 

 

 

 

 

I 100
g 90 -
a:
c -.
3 30- ”""'
2
3 70 Foam liner
3 ‘ -—a— Paper Pulp liner
:1 ------ Predicted PE foam liner (model B)
o 60 - Predicted paper pulp liner (model B)
50 1 ‘
0 5 10 15
Time, min

 

 

Figure 16 Comparison between Experimental and Predicted % Force Retention

One important fact follows from consideration of Models A and B. The %
force retention is independent of compression rate v but dependent on to.
Therefore, at steady state, the % force retention should depend only on how long
the loading part goes on. In other words, the results depend on how long the
system is loaded or how much it is compressed before starting the relaxation
phase. The compression rate v is excluded from the equation; nevertheless, this
result not expected because the mechanical behavior of polymeric materials is

usually strongly dependent on the loading rate or compression rate v. Derivation

36

of the solution for spring and dashpot models shows that the compression rate v
is always canceled out from the % force retention equation.

An experiment was conducted to investigate, if models A and B are
correct to tell that % force retention depends on loading time alone. The PE
foam liners were compressed on the Instron machine for the same loading time
of 23 sec at compression rates of 0.05, 0.1 and 0.15 inlmin. When they reached
the desired loading time, the loading was stopped. The liner was then allowed to

relax for 15 min, the retained force was recorded every 30 sec.

 

 

100

  
 

 

904 _::::-:==_===:=-

 

 

 

 

I:
8
E
g 80 .
a:
O
2 70 «
.2
=2 60 - - o - -0.1 inlmin, 23sec —x—-0.05 inlmin, 23 sec
—-—0.15 inlmin, 23 sec
50 .
0 5 10 15

Time, min

 

Figure 17 % Force Retention of Foam Liner as a Function of Time

The plot of experimental results in Figure 17 shows that foam liners at the
same loading time have different % force retention when they are subjected to
different compression rates v. The higher the compression rate, the greater the
force retention at steady state. This relationship seems logical because at

constant loading time t, as the compression rate v increases, the deformation x

37

will increase as well as the amount of load applied on the liner. Thus, it can be
concluded that the % force retention of the liner material depends on loading time
and compression rate.

Mechanical models using spring and dashpot for describing linear
viscoelastic behavior are useful in developing qualitative thinking. However, this
approach is inadequate to describe the relaxation behavior of container-closure
system due to the limitations described previously. More complicated spring
dashpot models can be developed to fit the actual relaxation curves but they all
have similar deficits. In addition, it might turn out that the model developed is too
complicated and impractical to use. As a result, it was decided to develop
empirical models for predicting the relaxation behavior of the container-closure
systems. Curve fitting techniques were used to fit the experimental data to the
model. The details of the techniques used and the results obtained are in

Chapters 4 and 5.

38

4.1 Materials

4. MATERIALS AND METHODS

This research focused on continuous thread closures, one of the most

widely used in the food and pharmaceutical industry. The 28-400 style: 28

millimeters (mm) in major diameter and a shallow continuous thread was

selected to test along with 2 different non—glued liner systems: PE foam and

paper pulp liner.

below.

Table 2 Description of Container-Closure Systems

A description of the container-closure systems tested follows

 

 

 

 

 

Component Finish size-style Material Description
mm
Closure 28-400 PP closure/ PE Fine rib closure,
foam liner white color, non-
glued, made by
Owen-Illinois
28-400 PP closure/Paper Fine rib closure,
Pulp with Saran white color, non-
film coated glued, made by
Owen-Illinois
Container 28-400 HDPE White color, 60 ml

 

 

 

volume, square
shape, made by
Owen-Brockway
Plastics &
Closures

 

4.2 Equipment

- Self temperature compensated bonded resistance strain gages:

Measurement Group CEA-13-125-UN-120

- Direct-reading strain indicators: Measurement Group P-3500

- Flat-bed plotters: Linseis L-6012 and L-6512

 

- Data logger: Omega OM-500

- Manual electronic torque tester: Secure Pak

- Manual spring torque tester: Secure Pak

- Environmental chambers: EGC and Lab-line Instruments

- Universal testing machine: Instron Model 4201

- Mitutoyo digital caliper

- Mitutoyo dial caliper gage

- Bridgeport comparator
4.3 Methods

In this research, the stress relaxation study was conducted differently from
the conventional technique because it was almost impossible to measure a
predetermined initial strain on the actual container-closure system. The stress
relaxation measurement in the actual container-closure system was studied by
initiating strain of the system to a predetermined application torque or
compression force using the torque meter or Instron machine. The deformation
of the system was then held constant for a specific time, while a force over time
was being recorded.
4.3.1 Cross-Sectional Measurement of the Container-Closure System
Five replicates of the container-closure systems: PE foam liner and paper

pulp liner were measured for the dimensions. The measurement of T, E and I of
the containers were made using a digital caliper and dial caliper gage. Next, a
closure was applied on the container with the prescribed application torque of

14.521: 0.5 TIP using the electronic torque tester. A container-closure system was

40

then placed upside down into a prepared box of 3x3x1.25 inches (the inside
surface of the box was covered with pressure sensitive tape). The clear casting
resin and polyester catalyst were thoroughly mixed and poured into the sample
and prepared box. This step was performed in the hood. The box was cured in
the hood until the casting was completely dry, after which the casting was
removed from the box. Finally, the casting was cross-sectioned using a band
saw and polished to make a smooth clear surface. The measurements of the
angles or and 9 were made using an optical comparator. For the container, the T
dimension is the major diameter of the container finish including the threads.
The E dimension of the container is the minor outside diameter of the container
finish excluding the threads. The diameter at the smallest opening inside the
finish is the I dimension. The angle a is the incline angle made by the spiral of
the thread in relation to the horizontal plane measured at the mean diameter of.
the thread interface. Likewise, the T dimension of the closure is the major inside
diameter measured from one side panel to the opposite side panel and the E
dimension of the closure is the minor diameter measured between threads.
Finally, the angle 0 is the contact angle between the closure threads and the
container threads measured along the vertical axis. The illustrations of these

parameters are shown in Figures 18.

41

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 18 Dimensions of Container-Closure System

4.3.2 Sealing Force Measuring Device Fabrication Technique

The configuration of the measuring device arose from the need to
measure axial force within the small space constraint of the actual container—
closure system. Strain gages were utilized to produce sufficient sensitivity and
accurate measurement of force over time. Strain gages and supplies used in the
fabrication were obtained from Measurements Group Inc, Raleigh, NC. The
bonding area of the measuring device made of 7075-T651 aluminum alloy was
abraded and cleaned by water-based cleaner (MCA and MN5A) to give it the
proper chemical affinity for the adhesive. The epoxy adhesive (AE-15) was then
used to bond the strain gage at the center of the closed end aluminum shell.
After the adhesive was completely cured, a three-conductor cable (326-DFV)
with vinyl insulation was soldered on the terminals of the strain gage. Butyl
rubber sealant (M-Coat F) was used to cover the strain gages in order to provide
moisture protection in which the damp environmental conditions to be tested.
After finishing the active gage on the measuring device, a dummy gage prepared
using the same procedure was bonded on a stress-free 7075-T651 aluminum

alloy disk to provide bridge completion and temperature compensation.

42

4.3.3 ’ Test Method for Sealing Force Measuring Device Design Verification

The objectives of this test were to verify a “restrained” design system,
which is used in the second design of the sealing force measuring device, and to
propose a simple technique to study relaxation of a system on a basic testing
instrument e.g. Instron. The actual situation of container-closure system after
torque applied to the system can be viewed as in Figure 19 in which shaded
areas are locations on a closure, liner and container where the relaxation is likely

to be highest.

 

 

 

s g) - Shaded area

3 g = Possibly highest
/ ' ' R stress relaxation area

 

 

Figure 19 Actual Situation of Container-Closure System Under Loading

43

Compression Force from Compression Force from
Instron Instron

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

HR

- Shaded area
- Possibly highest
stress relaxation area

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

' I
Is— Fme Floating Container ___v_____l \ J

Unrestrained Test Fixture Restrained Test Fixture

 

Figure 20 Test Fixtures for Design Verification

An unrestrained test fixture was developed according to the distribution of
stress analysis (Figure 19) in order to simulate the actual situation when the
container-closure system is under loading. Both test fixtures have the same rigid
support to hold test container-closure system above the ground. But the
difference is that the closure is mounted directly on an unrestrained test fixture,
whereas the restrained test fixture requires a closure without top panel glued into
the shell as shown in Figure 20. The restrained design assumes that the dome
bending near the periphery of the dome is negligible. This design concept using
a closure without its top panel is necessary for a sealing force measuring device.
This is because it offers more headspace which makes a proper thread

engagement and eliminates a titling effect. On the other hand, to gain more

44

headspace in the unstrained design, the height of the land area of test container
must be cut to have enough space for inserting a plunger. Both test fixture
designs shown in Figure 20 were tested at standard conditions on 28 mm PP
closure with PE foam liner and HDPE container. In testing, the test container
was screwed into the closure mounted on the test fixture to the same depth as
the actual system applied by application torque of 14 TIP. This condition will
make the threads in contact in the test fixture as close as in the actual container-
closure system. The Instron machine was set at crosshead speed of 0.1 inlmin
and set to stop loading when the compression force of 130 lb was reached. This
value is the maximum value of force which corresponded to 14 torque-inch-
pounds (TIP) application torque from a preliminary study. The crosshead speed
was set to achieve the same loading time as manual application torque. The
deflection was maintained constant and in the mean time, the compression force
over time was recorded every minute for 15 min. Five replicates were carried out
in both fixtures. The comparison was then made by constructing the relaxation
curves from both fixtures.
4.3.4 Test Method for Sealing Force Measuring Device Calibration

The sealing force measuring device was calibrated against a weight
calibrated 1 kN load cell (Instron model 2518-806, Canton, MA) by applying loads
ranging from 10 to 150 lb using Instron machine model 4201 at test speed of 0.2
inlmin. A jig shown in Figure 21 made of steel was used to facilitate this process
and a calibration setup is shown in Figure 22. The measuring device was placed

up side down into the countersink of the jig while the Instron machine was

45

applying a compression force through a “bump” disk (Figure 22). The strain
readings obtained from a direct-reading strain indicator were plotted against each
load and the linear regression was used to fit a plot. The slope of a fit line was
used as a calibration factor (us/lb) for converting strain reading to sealing force.
A dummy gage was used for temperature compensation during calibration at

standard conditions (73°F, 50% RH).

 

/
Countersink \ ,,,,,,

 

 

 

 

 

Figure 21 Calibration Jig for Sealing Force Measuring Device

46

Compression Force from Instron

Compression Platen

 

 

 

 

   

"Bump" Disk

Measuring Device

La / /r Jig
\/

\v Compression Platen

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/

/////////////////

 

 

 

Figure 22 Calibration Setup for Sealing Force Measuring Device

The calibration result was plotted along with a fit line from linear
regression as shown in Figure 23. The reason to use a direct calibration instead
of shunt calibration is that the effects of a number of absolute error sources are
eliminated. Calibration against a known traceable force produces readout

directly related to the cause.

47

 

 

 

 

 

 

2500
2000 — y = 13.419x - 2.3256
,5 R2 = 0.9998
.5. 1500 .
2
2
E
5‘ 1000 .
9
m 500 + Experimental data
Linear (Experimental data)
0

O 20 4O 60 80 1 00 1 20 140 160
Force, lb

 

 

 

Figure 23 Calibration Curve for Sealing Force Measuring Device

Figure 23 shows the linear relationship between the applied force and
strain with the coefficient of determination of 99.98% which indicates that the
measuring device is nearly perfectly elastic over the service strain range.
Besides, the results show that the calibration factor is 13.4 pellb. This shows that
the ability of the measuring device to detect changes in strain from the applied

force is adequate for measuring the relaxation in the system studied.

48

4.3.5 Test Method for Temperature Compensation and Moisture Protection

Verification

Since the change in resistance of the strain gage associated with strain is
very small, it is necessary to consider the effect of temperature and moisture on
the measuring device for two reasons. First, temperature is a major cause of non-
strain induced resistance changes. Second, moisture acts to place a resistance
path in parallel with the strain gage, thereby producing a change in resistance
equivalent to strain. Theoretically, calibration with a known force should be
carried out in a similar environment in which the device will be used. However, in
practice it is very difficult to completely follow because there are many limitations
of the instruments used in calibration. Temperature compensation of the
measuring device is accomplished by using half-bridge configuration in which an
identical gage to the active gage is mounted on an unstressed piece of the same
type of material used in the measuring device. Adequate temperature
compensation is an absolute necessity for accurate measurement of strains from
a strain gage bonded on the measuring device. In addition, this verification also
tested the effectiveness of moisture protection for the strain gage which will be
subjected to very high humidity environments. For this research as described
previously, the measuring device was intended for use at three environmental
conditions: standard conditions (73.4:t2°F, 5012% RH), refrigerated conditions
(41i4°F, 85i5% RH) and tropical conditions (104i4°F, 85i5% RH). The simplest
approach to verify the effectiveness of temperature compensation and moisture

protection of the measuring device is to perform a small calibration check.

49

A

Dead Weight

 

 

 

 

 

 

 

 

 

 

 

Measuring Device

 

 

 

 

 

 

 

L12 if
Q

/ Jig

 

 

 

 

 

 

 

 

 

 

 

Figure 24 Setup for Verification of Temperature Compensation and Moisture
Protection
This was done by using a jig and setup as shown in Figure 24 to support
dead weight in the vertical position during loading. The verification method is
quite similar to the calibration of the measuring device except a series of 9
different standard weights ranging from 1 to 25 lb was used for providing an

increasing load for constructing a relationship between strains and the applied

50

loads under each test condition. The test conditions generated from the
environmental chambers were 73.4i2°F, 50i2% RH, 41i4°F, 85i5% RH and
104i4°F, 85i5% RH. Finally, the applied load and strain relationships
established from each test condition were then compared in a plot. The protection
was considered effective if the results of the test conditions have no significant

difference among them.

 

 

600
Calibration Factor for Standard Conditions
= 13.30 us , r2 = 0.9998

500 9 Calibration Factor for Refrigerated
Conditions = 13.43 us, r2 = 0.9990

 
   
  
  

.E 400 - Calibration Factor for Tropical

% Conditions = 13.4909 , r2 = 0.9971

2

.2 300 «

E

.E’

E

0") 200 +Standard conditions
100 + Refrigerated conditions

+Tropica| conditions

 

 

 

T

0 10 20 30 40 50
Standard Weight, lb

 

 

 

Figure 25 Strain as a Function of Standard Weight obtained from
Test Conditions
Plots shown in Figure 25 indicate that the best fit of relationship between
strain and standard weight would be linear for all test conditions. There is no
significant difference among the three calibration factors for all test conditions. A

comparison of the results among three test conditions indicates that the sealing

51

force measuring device can be used effectively for studying a relaxation all three
conditions: standard, refrigerated, and tropical.
4.3.6 Test Method for Relaxation Study

The experimental design in Figure 26 and its procedure were established
after several preliminary studies with the container-closure systems to be tested.
Three different storage environments: (1) standard conditions (73.4:2 °F, 50:t2%
RH), (2) refrigerated conditions (411:4 °F, 85i5% RH) and (3) tropical conditions
(104:4 °F, 85i5% RH) were selected for studying the relaxation of the systems.
These test conditions were set in accordance with ASTM D 4332 Standard
Practice for Conditioning. The experiment, which had a total of 6 treatments, ran
for 10 replicates of each test condition of each container-closure system (PE
foam and paper pulp). A test closure was prepared by removing the top panel of
the closure from its body. Then, the closure without top panel was dotted using
solder gun to increase surface area and friction before gluing in the aluminum
shell by epoxy adhesive (Selleys Chemical Company, Australia), whereas a top
panel of closure was glued on a “bump” disk. The closure will be replaced with a
new closure every time when starting the experiment. The experimental setup is
shown in Figure 27. The plastic container with a measuring device mounted on
the top was inserted in holder to protect from shape distortion. Next, it was kept
in the environmental chamber for 15 min to eliminate errors from the effect of
instantaneous temperature change on the strain gage. The measuring device
was then clamped in an electronic torque tester and pre-applied slowly on the

container until the nose of “bump” disk just touched the inside top panel of

52

aluminum shell. The application torque of 14.51: 0.5 TIP was manually applied
on the system at test conditions with the loading time of 5 sec. The electronic
torque tester was used for measuring the application torque at standard
conditions; for the other two test conditions, the spring torque tester was
employed. This is because the electronic torque tester was not designed for use
at high humidity environment. After applying the application torque, the signal
response generated by unbalancing of the half bridge was indicated on the
display of strain indicator. The signal response was also recorded by the data
logger and plotter every 30 sec for the first hour and every hour for 5 days. At
the end of day-5, the container-closure system with a measuring device mounted
on the top was taken from the environmental chamber to measure the removal
torque by using the electronic torque tester. In addition to the sealing force
measuring test set, six sets of the actual container-closure system were also
stored at the same environments. The closures were slowly applied on the
containers until the liners just touched the land area of containers. This ensured
proper placement to provide the consistent results and deformation of all
container-closure systems. The application torque and loading time similar to the
measuring device were then manually applied. The actual container-closure
systems were taken in a set of five replicates from the test environments to
measure the removal torque after the first 15 min storage and then every day
until reaching five-day storage. The data of sealing force during storage time

from the measuring device and removal torque during storage time from the

53

actual container-closure systems were used to calculate the % force retention

(FRT) and % torque retention (T RT) respectively.

 

 

Experimental Design

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

Container-Closure PP closure-PE foam PP closure-Paper pulp
Systems liner-HDPE container liner-HDPE container
9 v t 0
Standard Tropical Standard Tropical
733‘ conditions Refrigerated conditions conditions Refriggrated conditions
“with” 73'4F' 4:?" 8'52"ng 1°45 73'4F' 4$lgn8533RsH 104E
50%RH ' ° 85%RH 50%RH ' 85%RH
i _J __f v v i
Sealing Sealing Sealing Sealing Sealing Sealing
~> force over l-D force oven + force over w force over Lu force over fl force over
Responses time time time time time time
Removal Removal Removal Removal Removal Removal
+ torque Lu torque a torque + torque w torque fl torque
over time over time over time over time over time over tlme
Figure 26 Experimental Design for Relaxation Study
P: Power Input
_ Ham! S- Signal Output

 

 

 

 

 

 

 

 

 

 

 

"— Stress-Free

  
   

 

 

Aluminum

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 27 Experimental Setup for Relaxation Study

54

4.3.7 Data Analysis

The collected data were generally organized into 2 categories: (1) the
sealing force over time data and (2) the removal torque overtime data. Both
categories contained data of 6 treatments from 2 factors studied: (1) the
container-closure systems and (2) the environmental conditions. The data of two
categories were normalized to the % force retention (FRT) and % torque

retention (T RT) using the following equations:

 

%FRT = w (31)
Fr'
%TRT = RT'AXTIOO (32)
where Ft = Sealing force at time t, lb
F, = Initial sealing force, lb
RT, = Removal torque at time t, TIP
AT = Application torque, TIP

The % FRT and TRT data were used as the input data for developing the
empirical models for each treatment. Generally, many physical processes such
as the relaxation follow an exponential decay rule. Several models and
algorithms from the simplest exponential function to the rational fraction that have
this characteristic were brought in to examine the fit of the experimental data of
the % FRT and % TRT. The maximum error calculated from the predicted and
experimental data was one of the criteria for selecting the best fit model along

with practicality and easy to use. After examining, It was found that there are

55

three models that can properly represent the relaxation characteristic of the test

container-closure systems (Figure 28).

 

Empirical models

l i l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model C Model D Model E
= a + __ = k . mx + C = + k l x
y (1 +k.x”) y y y " x,
Algorithm 1 l
Seaching for k and p Algonthm Algorithm
. Sum Squares Errors Sum Squares Errors
With the smallest (SSE) (SSE)
error of prediction

 

 

 

 

 

 

 

 

 

Figure 28 Empirical Models for Relaxation Data of % F RT and % TRT

Model C

Model C derived from the general form of the exponential function can be

b
expressed as y = a + W (33)
_ 100 —yn
where a —y,, -—pr—
b = 100 —a

x and y = Time (min) and % FRT or % TRT
x" and yn = last data point of time (min) and % FRT or % TRT
k and p = Coefficients of the equation
The concept of this model is that the model is forced to fit through the first

data point: (0, 100%) and the last data point at 5 days: (7200, yn). The condition

56

on fitting through the first and last data point will ensure that the predicted
relaxation curve willfollow the experimental relaxation curve as close as
possible. This is expected to give a good prediction of the % FRT and % TRT
after the five-day experiment. The coefficient k and p in the equation are
determined from developing a computer program in BASIC to search for the
coefficients that provide the minimum error of prediction. This approach is
basically searching for the coefficients (k and p) that offer the best fit. This was
done by arbitrarily trying some range of number for k and p first and then the
range for these two coefficients is narrow down until finding the optimum number
for k and p. This is only possible done by using the computer. In computer
program, after choosing the range of number, the number in that range is
changed in small step and the error between the predicted data and experimental
data is calculated for every number in that range. The reason for choosing this
algorithm over the sum square error is that it gives a better fit solution for a non-
linear form. The adequacy of the fit can be determined from the max error
obtained from calculating the difference between the experimental data and
predicted data.

Model D

A previous investigation found that the characteristics of the relaxation
curves are non-linear and a simple exponential model (y = a + b .e "‘ "‘ ) is

incomplete to describe the behavior. The semi-log model (model D) was then
selected to model the behavior since its simple form holds the decay

characteristics. The model can be expressed mathematically as:

57

y = k. lnx + c (34)
where x and y = Time (min) and % FRT or % TRT
k and c = Coefficients of the equation
The curve-fitting criterion of this model is that the sum of the squares of
the errors (SSE) be minimized. Then, the derivative of the SSE equation with
respect to each coefficient is set the result to zero. This is the customary
approach to minimize the error between the calculated value and actual value

and it returns the resulting equations for finding the coefficients as follows:

n.2(lnxi.y,.) —Zlnx,.2y,
: i=1 i=1 i=1
11.nZ(1nJlt,.)2 —(:lnx,)2
i=l i=1

 

k (35)

ZanOHL-V —Zlnx,.Z(1nx,.y,.)
:: i=1 i=1 5:] i=1

n.:(lnx,)Z —(:lnx,.)2

 

and C (36)

Note that n = number of experimental data points from i=1 to n
After the coefficients are established, one frequently wishes to know how
well the predicted line fits the experimental data. The measure of the best-fit is

the correlation coefficient r and the equation is:
n.2(lnx,.y,) — Zlnx,.2y,
i: i=1 i=1
n l n n n ”2
{@0an «zlnxfllnzy: 4292]}
i=1 i=l i=1 i=1

r ::

 

(37)

58

M2995

Model E is actually a special case of the semi-log model D in which the
model is forced to fit through the last data point (men). The reason to force fit the
last data point is that the model is aimed to predict long term response. It is
better to extrapolate the predicted results by focusing on the latest information.
In addition, the last data point is least sensitive to the experimental errors made

in the beginning of the experiment. The model relaxes logarithmically with time

y =y. +k-1“[;x—] (38)

where x and y = Time (min) and % FRT or % TRT

and is given by

xn and yn = Last data point of time (min) and % FRT or % TRT
k = Coefficient of the equation
The sum of the squares of the errors (SSE) algorithm was used to derive

the coefficient k which can be shown the resulting equation as follows:

= 1210 -y,.).lz.[2:: ]] (39)
Elli)

The adequacy of the fit is measured by using the correlation coefficient r in

 

 

 

the following equation:

59

 

20’: -yic)2
_ i=1

 

r=1

I 20» -;7)2

(40)

 

Note that yic = predicted y from the model and 33 is the average of y from

experimental data.

All proposed models in this section were used to fit with the test data (6
treatments) and the fit results can be found in Chapter 5. The empirical models
developed in this chapter were planned to be incorporated with the torque-friction
model (Pisuchpen, 2000) derived from the force diagram. The integration of
these models was expected to improve the accuracy and usefulness of the
torque-friction model. The results of integration of the models are also shown in

Chapter 5.

60

5. RESULTS AND DISCUSSION

5.1 Cross-Sectional Measurement of the Container-Closure Systems.

A summary of cross-sectional measurement results is shown below.

Table 3 Summary of Container-Closure Systems Dimensions

 

 

 

 

 

 

 

 

 

Parameter 28 mm Container-Closure System
HDPE Container-PP Closure- HDPE Container-PP Closure-
Foam Liner Paper Pulp Coated Liner
Closure Container Closure Container
T, in 1 .0895 1 .0745 1.0895 1 .0745
E, in 1 .0050 0.9777 1.0050 0.9777
l , in - 0.8360 - 0.8360
p, in 0.167 0.167 0.167 0.167
a, degree 2.96 2.96 2.96 2.96
'5’ in - 0.5131 - 0.5131
r. ’ in - 0.4534 - 0.4534
0, degree 42.07 41.12

 

 

Note: Dimensions are the average of maximum value and the value measured at

90° away from this.

The results in Table 3 were compared with voluntary standards of closure

and container design developed by the Closure Manufacturers Association and

Plastic Bottle Institute. It was found that the dimensions of samples fall within the

range of the standard recommended. Thus, it is confident to conclude that the

closures used in this research are compatible with the containers. It is necessary

for this research area to start with the dimensions measurement because the

ability of the closure to be retained on a container by threads that engage

corresponding threads of the container depends on the compatibility of

61

 

dimensions. The use of incompatible container-closure system will adversely
affect the closure performance in providing seal integrity. The buttress thread
profiles “M” Style and “P” Style were obtained from containers and closures
respectively. The only difference between both profiles is that the “P” Style has a
full nose radius instead of a modified buttress nose profile. The results also
show that the closure threads made contact with the container threads with the
contact angle around 40 degrees. This is fairly typical contact angle value
obtained from plastic systems. In theory, a closure thread profile shows the
greatest holding power when three conditions are satisfied. Firstly, the shape of
container threads and closure thread must match each other as closely as
possible. Secondly, the engagement of threads made on two adjacent threads of
the container finish must fully contact. Lastly, both container and closure threads
must have pressure angles approaching the horizontal. However, in practice,
this consideration of optimum holding power is rarely achieved because of
variations in mold, design and dimensions, and the material used in
manufacturing. The results found from this part were used in modeling and

verifying the container-closure systems models.

62

5.2 Verification of the Design of Sealing Force Measuring Device.

There are two designs proposed in Chapter 3: unrestrained design and
restrained design. The restrained design was used as a basis for developing the
sealing force measuring device. The analysis using a force diagram indicated
that both designs have the distributed stresses all around the test unit from
loading similar to the actual container-closure system. The restrained design
was chosen over the unrestrained design because it is easier and has fewer
preparation steps when implemented in the measuring device. In addition, in
practice, using the restrained design is less likely to produce a tilting problem and
the problem of non-uniform distribution of forces. Test fixtures were developed to
verify both designs conducted on the Instron machine at standard conditions for
the relaxation test. The compression force was applied on the container-closure
system mounted on the test fixture with the loading time of 5 sec until reaching
130 lb force (the maximum force obtained from an application torque of 14 TIP).
The average and range of force over time obtained from each design during

relaxation phase were plotted as shown in Figures 29 and 30.

63

135
130
125
120
115

105
100

Force, lb

95~

90
85
80
75

110 ~

 

   
  
 

 

 

«130.5 lb 100%
" (100%FRT)
: « 90%
l.
P -80% fig
_ g a
83 lb - 700/ “
_ (63.6%FRT) °
F - 60%

 

 

0123456789101112131415

Time, min

Figure 29 Force as a Function of Time obtained from Unrestrained Fixture

135

 

130
125
120
115
110
105
100
95
90
85
80

Force, lb

   
   

 

75

F128 lb
(100%FRT)

 

.100%
. 90%

E

.2

E

- 80% 3

at

8

80.25 lb '5

(62.7% FRT) ' 70% :5
- 60%

 

0123456789101112131415

Time, min

Figure 30 Force as a Function of Time obtained from Restrained Fixture

64

In general, both designs provide typical relaxation curves with only small
variations of force over time. The applied force rapidly dropped as soon as
loading force stopped and then continued to gradually drop down until stopping
the test at 15 min. For the unrestrained design, the initial applied force of 130.5
lb or 100% force retention (% FRT) relaxed to 83.0 lb or 63.6 % FRT as much.
Likewise at the end of the test, the applied force of 80.25 lb or 62.7% FRT was
retained in the system when using the restrained design. It can be concluded
that there is no difference between the designs in the results of the relaxation
study. The results support the use of the restrained design in developing the
measuring device. The only restriction of using the unrestrained fixture is that
the height of the land area of test container is needed to be precisely out before
screwing into the closure mounted on the fixture. This is done in order to obtain
the similar condition of the thread engagement when the actual system was
applied by application torque of 14 TIP. The test fixtures are inexpensive to
fabricate and require only a basic testing instrument (e.g. Instron) for applying the
prescribed compression force. This offers the simplest technique for a direct
study of the force relaxation in the container-closure systems.

5.3 Relaxation of Container-Closure Systems

It is important to note that the relaxation of the container-closure systems
was investigated by initiating strain of a system to a prescribed application torque
(14.5 d: 0.5 TIP). The system was subjected to constant strain at test conditions
and the decay of sealing force during storage was observed over time. The

sealing force over time data was analyzed in % FRT and compared to the % TRT

65

from the actual systems. The analysis was based on the theory that the removal

torque is proportional to the sealing force. Therefore, the removal torque relaxes

in proportional to the sealing force. In other words, the % FRT must be the same

as the % TRT. The experimental results are summarized in Table 4.

Table 4 Summary of % FRT and % TRT of Container-Closure Systems

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time Parameters Test Conditions
Refrigerated Standard Tropical

PE Paper PE Paper PE Paper

Foam Pulp Foam Pu_lp Foam Pulp

0 AT, TIP 14.8 14.6 14.5 14.5 14.7 14.5
(0.4) (0.4) (0.4) (0.3) (0.4) (0.4)

Sealing force, 92.3 94.8 96.9 97.6 97.8 94.9

lb (9.8) (12.4) (10.9) (13.1) (7.9) (9.7)

15 min % FRT 58.3 55.6 61.5 56.0 55.5 49.2
(2.7) (2.8) (1.0) (1.6) (2.0) (1.8)

% TRT 65.0 72.6 63.3 67.6 60.2 63.6

(4.0) (4.4) (3.9) (3.7) (3.8) (5.6)

% TRT/% FRT 1.21 1.31 1.05 1.21 1.14 1.29

1 day % FRT 45.9 42.3 47.5 43.8 43.1 35.4
(1.6) (2.2) (1.9) (1.4) (2.2) (2.2)

(1440 min) % TRT 61.9 71.0 53.7 59.0 42.2 38.3
(2.2) (4.8) (4.0) (2.8) (5.5) (3.2)

% TRT/% FRT 1.43 1.68 1.22 1.35 1.04 1.08

2 days % FRT 44.4 41.1 45.8 42.3 41.6 33.3
(1.6) (2.1) (1.9) (1.5) (2.1) (2.2)

(2880 min) % TRT 61.0 67.9 51.8 55.6 38.2 37.8
(3.7) (3.1) (3.4) (2.7) (3.5) (4.7)

% TRT/% FRT 1.47 1.65 1.21 1.31 0.97 1.14

3 days % FRT 43.6 40.2 44.9 41.4 40.9 31.9
(1.5) (2.0) (1.8) (1.5) (2.2) (2.2)

(4320 min) % TRT 60.3 59.8 49.5 55.2 36.9 35.9
(4.4) (3.5) (3.2) (4.0) (2.3) (3.9)

% TRT/% FRT 1.48 1.49 1.18 1.33 0.96 1.13

4 days % FRT 43.0 39.6 44.2 40.8 40.3 31.0
(1.5) (2.0) (1.8) (1.5) (2.3) (2.2)

(5760 min) % TRT 58.0 58.0 50.1 53.3 35.9 34.9
(3.4) (5.3) (3.6) (2.3) (3.7) (2.5)

% TRT/% FRT 1.44 1.47 1.21 1.31 0.95 1.13

5 days % FRT 42.6 39.0 43.8 40.4 39.9 30.2
(1.5) (2.1) (1.8) (1.5) (2.4) (2.3)

(7200 min) % TRT 56.2 58.2 49.3 50.7 34.3 35.2
(3.3) (4.6) (4.3) (3.5) (3.0) (2.9)

% TRT/% FRT 1.41 1.49 1.21 1.26 0.92 1.16

 

 

 

Note: Average (Sd) from 10 runs

66

Table 4 shows that a sealing force of 92 to 98 lb is obtained from the
application torque of 14.5 i 0.5 TIP. Overall the % TRT is higher than the %
FRT. The system of PE foam liner at tropical conditions shows that the % TRT is
slightly lower than the % F RT from 1 day relaxation until the end at 5 days.

The results of the relaxation study are presented graphically in Figure 31
and 32, where the % FRT and % TRT of container-closure systems stored at
refrigerated, standard and tropical conditions are plotted against time. The
relaxation profile curves using the % FRT and % TRT as the indicator appear to
follow the typical relaxation behavior. For the % FRT in Figure 31, the sealing
force of the systems drops rapidly from 100% to around 80% as soon as loading
stopped and then the rate of drop diminishes continually. Although a similar
relaxation profile is found when using the % TRT as the indicator, large variation
of % TRT overtime is noticed. This indicates that the results from the % TRT are
less consistent than the % FRT. This is because the relaxation study using the
removal torque measurement is required to change the system studied over a
period of time. After the removal torque is measured, the container-closure
system is no longer use. Deviation of the removal torque from one measure to
another is usually fairly large causing large variation of the results.

The relaxation data from the five-day experiment shows that on day 5 the
system of PE foam liner at standard conditions has the highest % FRT at 43.8%
and the system of paper pulp liner at tropical conditions has the lowest % FRT at
30.2%. For the % TRT, the system of paper pulp liner at refrigerated conditions

has the highest % TRT at 58.2% and the system of PE foam liner at tropical

67

conditions has the lowest % TRT at 34.3%. It is also evident that the relaxation
of the container-closure system is time dependent and it is enhanced by storage
conditions especially at tropical conditions (104i4°F, 85i5% RH). The time
dependent properties are characteristic of long chain structures and can be
explained by the polymer structures. For instance, an entangled linear polymer
is held at constant elongation. The force applied instantly to obtain the given
elongation is that needed to uncoil the chains; it is equivalent to the elastic
restoring force. But as the system is held at the given elongation, the chains will
have time to flow past each other, allowing them to recoil and relax the stress.

After a long enough time, no load will be required to maintain the deformation.

 

100

 

90-

80 ~~

%FRT

 

 

20.

104

 

 

 

0 1440 2880 4320 5760 7200
Time, min

 

 

 

Figure 31 Plot of % FRT as a Function of Time for All Treatments

68

 

100

 

 

 

%TRT

 

20a

10-

 

 

 

0 1440 2880 4320 5760 7200
Time, min

 

 

 

Figure 32 Plot of % TRT as a Function of Time for All Treatments

5.4 Effect of Environmental Conditions on the % FRT and % TRT

In order to analyze the effect of temperature and relative humidity on the
% FRT and % TRT of container-closure systems (PE foam and paper pulp liner),
a plot of the % FRT and % TRT for each liner system in test conditions was
generated. From the plots of the % FRT (Figures 33 and 34), the % FRT of PE
foam systems in the three test conditions was distributed over the narrow range
from 40% to 44% after 5-day relaxation. The environmental conditions did not
have a significant effect on the % FRT of PE foam systems. The effect on the %
FRT of paper pulp systems was similarly limited except for the system at tropical
conditions in which it was subjected to high temperature of 104°F and high

relative humidity of 85%. The % FRT of the paper pulp system at this conditions

69

was significantly lower (10%) than the other two conditions. This is because high
temperature and high relative humidity in storage conditions. Paper is a
hygroscopic material; the mechanical properties especially the elasticity that is
associated with the % FRT varies as a function of the moisture content of the
material. As the moisture content increases, the elasticity of the paper pulp will
decrease; as a result decreasing the % FRT over time. In addition, since the
moisture content in paper is also related to the amount of moisture in the air, a
psychrometric chart can be used to provide supportive information to the
explanation. The amount of moisture in the air at refrigerated, standard and
tropical conditions was 32.1, 61.2 and 287.5 grains/ lb of dry air respectively.
Apparently, the tropical conditions show the highest moisture content in the air.
Therefore it may conclude that the highest temperature and highest moisture
content in the air at tropical conditions leads to the lowest % FRT of the paper

pulp system.

70

 

 

 

100

 

804

%FRT

 

 

 

20 -«

1o-

 

 

O r , fl

0 1440 2880 4320 5760 7200
Time, min

 

 

 

Figure 33 Plot of % FRT as a Function of Time for PE Foam Liner

 

 

100

 

%FRT
8 8 8

POW-std
”Wm
// ......

-—-\ V_._‘
"——_q ‘-. ___fi

20«

1O«

 

 

 

0 1440 2880 4320 5760 7200
Time, min

 

 

Figure 34 Plot of % FRT as a Function of Time for Paper Pulp Liner

71

 

 

100

 

801

70 .

'-.-

. . '--~.-
~ .—
.- .

...
.0
.....
...............
.....................

"'o-o..o--o- -' .- .......

96HRT
I

 

‘°~
--~--..
‘..
-'-—-o—oo
——.._.._
~—.o__
"~-.—
‘0‘.-

20

10 .

 

 

 

0 1440 2880 4320 5760 7200
Thne,nfin

 

 

 

Figure 35 Plot of % TRT as a Function of Time for PE Foam Liner

 

100

 

 

 

%nrrr

 

20 .

10 a

 

 

 

0 1440 2880 4320 5760 7200
Thne,nfin

 

 

Figure 36 Plot of % TRT as a Function of Time for Paper Pulp Liner

72

In contrast to the % FRT, the % TRT of both systems in Figures 35 and 36
shows fluctuations overtime due to the nature of measurement of removal torque
and the significant effect of the environmental conditions on the % TRT of all test
conditions is noticeable. The PE foam and paper pulp systems responded to the
test conditions in the same way; the % TRT ranged from high to the low are the
systems at refrigerated, standard, and tropical conditions. The systems stored at
tropical conditions always have the lowest % TRT and % FRT. This is exactly
the sort of behavior that could occur if a container-closure system was stored at
tropical conditions. The mechanical properties of polymers are generally very
sensitive to high temperature. The modulus of polymer decreases with
increasing temperature. In this case, the storage temperatures are higher than
the glass transition temperatures (T g) of PP, HDPE and PE foam which induce
some form of molecular motion causing a relaxation process. In general, as the
temperature is increased, the modulus decreases and the polymer becomes
more ductile as a result in increasing the relaxation process. Therefore, the
lowest % TRT and % FRT were found in storage at tropical conditions. Besides,
it must be realized that the coefficients of friction at thread interface and liner
interface play a significant role in the torque retention of the container-closure
systems. These coefficient values are greatly decreased when a lubricant
(moisture) is present in between the interface layers. The reason for this may be
related to the amount of moisture in the air. It is believed that this factor may be
used to explain the significant effect of environmental conditions on the % TRT.

This is because the moisture in the air behaves like a lubricant. However, the

73

experimental data is not available to support this statement yet. The observation
on the systems stored at tropical conditions found that they showed tiny water
drops around the container neck at the end of day 5. The higher the amount of
moisture in the air, the higher the lubricating effect which causes a lower % TRT.
This explanation supports the results that the highest temperature and amount of
moisture in the air (using psychrometric chart) yield the lowest % TRT and vice
versa.
5.5 Characteristics of the % FRT and % TRT

As discussed earlier, the removal torque or % TRT is generally used as
the mechanical seal indicator for the container-closure systems throughout the
industry. However, there has been dissatisfaction with accuracy and precision of
this indicator. The % FRT was proposed in this research as an alternative
indicator. In this part, Figure 37 was deduced from the experimental results in
order to investigate the characteristics of the % F RT and % TRT. The curves of
% TRT were higher than the curves of % F RT except for the PE foam system at
tropical conditions; this indicated that the % TRT is always higher than the %
FRT indicating less relaxation of torque than of force. The difference between
these two parameters becomes smaller when the temperature and amount of
moisture in the air increase. The % TRT curves dropped down more when either
the PE foam system or paper pulp system was subjected to storage conditions
having the higher temperature and amount of moisture in the air. This indicates
that the % TRT is more sensitive to the change of temperature and moisture in

the air than the % FRT if the system is in the same storage conditions. The

74

correlation between both indicators is also of interest since the theory points out
that the removal torque is proportional to the sealing force. In other words,
theoretically, the TRT is equal to the %FRT. The results show that the average
of this ratio for five days distributed from 1 to 1.44 which disagree with the theory.
The systems at refrigerated conditions show the highest ratio of TRT to FRT,
whereas the lowest ratio was obtained from the systems at tropical conditions.
This is because of the effect of time dependent properties and temperature on
the relaxation of viscoelastic materials. The theory derived from the assumption
of a rigid body cannot completely describe these complicated properties of
viscoelastic materials. Although the correlation between the % TRT and the %

F RT seems to be linear, the linear regression was not employed in this analysis.
The % TRT data over time were too crude in comparison to the % FRT data,
which contributed to the large error when using the linear regression. Thus, the
average ratio of % TRT to % FRT was chosen to describe this correlation. The
application of both parameters in describing the seal integrity must be considered
carefully because the result from one parameter might conflict with the result

from another.

75

 

 

—o—%FRT I
---I---%TRT
'. ----- ‘- """" l ----- .' .._!

 

 

 

 

 

 

 

 

 

100

 

 

 

 

 

 

 

 

 

20 Avg of TRT/FRT= 1.35
0 I T j T T
0 1440 2880 4320 5760 7200}
Time g
Foam refri
l .0. 7
I 80 +%FRT

---I---%TRT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20 , Avg of TRT/FRT: 1.15
0 T T T T
0 1440 2880 4320 5760 7200
Tlme
Foam std
100
80 —+—%FRT
we .. %TRT
60
°\°
4O ' ' - - - I . flffl ...... —
2° Avg of TRT/FRT: 1
0 I T T Ti T
l 0 1440 2880 4320 5760 7200
I
L Time
Foam trop

 

80 +%FRT
~- -I ------ .., --I-- %TRT
60 . . ' - ------ - .....
°\° \
40 - 7+ c c
20 ~
Avg of TRT/FRT= 1.44
o T T 1 I
0 1440 2880 4320 5760 7200
Time
Paper refri
100
80 +%FRT
60 ---I-- %TRT
---- I....., .
o\° \ . I ..... - """ -
4o . v c e c
20 «
Avg of TRT/FRT: 1.25
o I T T I
0 1440 2880 4320 5760 7200
Time
Paper std
100
80 —O—%FRT

 

 

---l---%TRT

 

 

 

2° * Avg of TRT/FRT= 1.13
0 I if T l
o 1440 2880 4320 5760 7200
Time
Paper trop

Figure 37 Comparing % FRT and % TRT of Systems at Test Conditions

76

 

 

The practical application: at standard conditions, after relaxation for 15
min which corresponds to the conditions for measuring the immediate removal
torque, was chosen as the example. A comparison of seal integrity between the
paper pulp system and the PE foam system is shown in Figure 38. Note that 1a
and 1b are the % TRT of the paper pulp system and of the PE foam system, and
2a and 2b are the % FRT of the paper pulp system and of the PE foam system.
It shows that % TRT-1a of the paper pulp is higher than % TRT-1b of the PE
foam. Using % TRT as the indicator, one might conclude that the paper pulp
system is better than the PE foam system. This is incorrect because the sealing
force retained in the paper pulp system (% FRT-2a) is actually lower than the PE
foam liner (% FRT-2b). Therefore, using the % TRT as the indicator may be
misleading interpretation of the seal integrity. The results disagree with each
other because the removal torque is a complex indicator; other factors not related
to the seal integrity can affect the removal torque. This finding would be one
reason that in some cases; the container-closure systems having high removal

torque still shows leakage problem.

77

 

 

80

67.6

7° ‘ 63.3 61.5

 

60~

404

% Retention

304

PE Foam liner
PE Foam liner

20—
104

 

 

 

 

 

 

 

 

%TRT %FRT

 

 

 

Figure 38 % FRT and % TRT of Systems at Standard Conditions
at the End of 15 Minutes

5.6 Modeling the Relaxation Behavior of Container-Closure Systems
Determination of the seal integrity of container-closure systems during
required shelf life is, in many cases, an essential part of packaging evaluations.
Running actual storage tests (keeping the container-closure systems under
actual or simulated environmental conditions) is an expensive and time
consuming process. Often it is impossible to perform complete storage tests
since the shelf life of packaged products is often more than a year. To reduce
time and the amount of experimentation necessary to finish the long-term storage
test, mathematical modeling is commonly used. Principally, the entire history of
the stress relaxation of the polymer can be reconstructed by adding the stress
histories that correspond to individual bits of a strain history (Matsuoka, 1992).

Modeling the % FRT and % TRT of the systems is then based on the assumption

78

that if the model fits very well with the experimental data during 5-day relaxation,
the reasonably predicted results beyond the experimental data can be obtained
by extrapolating the model. In building the theoretical models, the effect of
environmental conditions was excluded from the independent variable because
there is no simple theory to explain this effect on the relaxation. It was found
that the theoretical models derived from mechanical model using spring and
dashpot are unsuccessful to describe the relaxation characteristics of the
container-closure systems. The relaxation behavior obtained from the theoretical
model levels off overtime. In fact, the actual behavior of the systems continues
to relax indefinitely. This is because the strain energy is continuously dissipated
through the rearrangement of molecules into a lower free energy state causing
the relaxation behavior to approach a nearly constant strain rate. Thus, the
relaxation behavior is a continuous process. The spring and dashpot can mimic
material behavior only under limited sets of conditions because the relaxation
rate is only formulated by a first-order equation. In addition, if a model derived
from spring and dashpot is made to fit a set of real relaxation data, it cannot fit
the creep data for the same material. This shows that a model of springs and
dashpots has a serious deficiency because a valid mathematical model must fit
all experimental data without changing the values of the parameters. More
complicated models can be derived from combinations of numbers of springs and
dashpots but none of those can satisfy this simple requirement.

The relaxation of the container-closure systems is so far very complex

behavior; more sophisticated theory is needed to model this behavior which may

79

not promise a success in modeling the relaxation behavior of the system and
also may reduce simplicity of use in the application. In considering practical
applications, an alternative approach using curve fitting techniques on the
empirical model was then introduced to fit the experimental data of % FRT and %
TRT as a function of one variable: time. The reason for choosing only one
variable is the limitation of the experimental design which did not include the
study of temperature and % relative humidity factors individually. Therefore, the
effect of environmental conditions on the % FRT and % TRT cannot isolate the
effect of temperature and % relative humidity from each other because they are
confounded with each other. It may be that both temperature and % relative
humidity contributed to a combined effect on the relaxation in this study. In this
research, the form of the empirical model was decided according to these
criteria:

a. Low error between the experimental and predicted values.

b. Simplicity of the model from a computational point of view.

c. The model should satisfy conditions at the extreme of independent variable.
d. The model should have no discontinuities in the range of practical values of

the independent variable.

The coefficients of empirical models were then determined by using the

curve fitting techniques presented in Chapter 4 and they are listed in Table 5. In

addition, the predicted values of the % FRT and % TRT during storage over time

80

at three test conditions were calculated according to the coefficients of the

models and plotted in comparison with the experimental data in Figures 39 to 50.

Table 5 Empirical Models for % FRT and % TRT of Container-Closure Systems

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model System Relaxation Parameters Adequacy
Indicator of Fit
Model C Foam-refri % FRT a=37.74, b=62.26, Max error
a + b k=0.89, p=0.28 = 1.40%
(1 + k.x P) % TRT a=-7.28, b=107.28, Max error
k=0.33, p=0.079 = 3.12%
Foam-std % FRT a=37.62, b=62.38, Max error
k=0.72, p=0.28 = 1.16%
% TRT a=32.79, b=67.21, Max error
k=0.73, p=0.16 = 0.90%
Foam-trop % FRT =34.99, b=65.01, Max error
k=0.94, p=0.29 = 1.30%
% TRT =-391.56, b=491.56, Max error
k=0.069, p=0.088 = 0.54%
Paper-refri % F RT a=35.14, b=64.86, Max error
k=0.91, p=0.32 = 1.40%
% TRT a=-1458.33, Max error
b=1558.33, k=0.01, = 6.12%
p=0.1 1
Paper-std % FRT a=35.15, b=64.85, Max error
k=0.86, p=0.30 = 1.63%
% TRT =-319.95, b=419.95, Max error
k=0.051, p=0.088 = 2.59%
Paper-trop % FRT a=19.54, b=80.46, Max error
k=0.85, p=0.23 = 1.97%
% TRT a=30.86, b=69.14, Max error
k=0.35, p=0.42 = 0.71%
Model D Foam-refri % FRT k=-2.76, c=66.41 r = 0.9911
y = k. lnx + c % TRT =-1.13, c=68.70 r = 0.8586
Foam-std % F RT k=-3.03, 0:69.90 r = 0.9949
% TRT k=-2.28, p=69.59 r = 0.9941
Foam-trop % FRT k=—2.70, p=63.07 r = 0.9874
%TRT =-4.14, p=71.55 r = 0.9989
Paper-refri % FRT k=-2.73, c=62.34 r = 0.9749
% TRT k=-2.19, c=80.60 r = 0.7602
Paper-std % FRT k=-2.70, c=63.60 r = 0.9824
% TRT k=-2.46, p=74.88 r = 0.9674
Paper-trop % FRT k=-3.13, p=57.78 r = 0.9912
% TRT k=-4.77, p=75.85 r = 0.9908

 

81

 

Table 5 (cont’d).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model System Relaxation Parameters Adequacy
Indicator of Fit
Model E Foam-refri % F RT k=-2.55, yn=43, r = 0.9865
x xn=7200
y =y, ”ML J % TRT k=-1.69, y,,=56, r = 0.4880
" xn=7200
Foam-std % F RT k=-2.84, yn=44, r = 0.9342
xn=7200
% TRT k=-2.28, y..=49, r = 0.9941
xn=7200
Foam-trop % FRT k=-2.53, yn=40, r = 0.9844
xn=7200
% TRT k=-4.25, yn=34, r = 0.6524
xn=7200
Paper-refri % F RT k=-2.56, yn=39, r = 0.9865
xn=7200
% TRT k=-2.86, yn=58, r = 0.6524
xn=7200
Paper-std % FRT k=-2.63, yn=40, r = 0.9819
xn=7200
% TRT k=~2.99, y..=51, r = 0.9016
xn=7200
Paper-trop % FRT k=-3.13, yn=30, r = 0.9912
xn=7200
% TRT k=-4.39, yn=35, r = 0.9106
xn=7200

 

 

 

 

 

Notes: y = % F RT or % TRT and x = Time (min)

82

 

 

 

 

Exp data-foam-refn'
7o - ------ Model C

60 )
50 a

20 i Max error = 1.40%

%FRT

 

 

 

o l I 7 l
O 1440 2880 4320 5760 ~7200

Tlme, min

 

 

 

 

9° ‘ —Exp data-foam-refri
70 - ------ Model D

23 lg

20 ~ r = 0.9911

0 1 r T r
O 1440 2880 4320 5760 7200

Tlme, min

%F RT

 

 

 

 

 

 

 

 

 

90 - -——Exp data-foam-refri
70 . ------ Model E

60 -
50 k

%FRT

 

20 ‘ r = 0.9865

0 T T T r
0 1440 2880 4320 5760 7200

Time, min

 

 

 

 

 

 

Figure 39 Comparison of Experimental and Predicted % FRT of PE Foam Liner
at Refrigerated Conditions (Short-Term Prediction 5 Days)

83

 

A

%FRT
88883883888

 

 

Exp data-foam-std
------ Model C

3L

 

Max error= 1.16%

 

 

 

0 1440 2880 4320 5760 7200
Time, min

 

 

 

 

 

9° “ ——Exp data-foam-std
70 - ------ Model D

%FRT
on
o

 

20 . r =0.9949

 

 

 

‘

0 1440 2880 4320 5760 7200
Tlme, min

 

 

 

90 i —-—Exp data-foam-std
70 « ------ Model E

60 1

50 ~

20 . r=0.9919

o I T T T

0 1440 2880 4320 5760 7200
Tlma, min

%FRT

 

 

 

 

 

 

 

 

Figure 40 Comparison of Experimental and Predicted % FRT of PE Foam Liner
at Standard Conditions (Short-Term Prediction 5 Days)

84

 

 

90 4 —Exp data-foam-trop
7o - ------ Model C

60 -
50 L

20 : Max error = 1.30%

o I I r
O 1440 2880 4320 5760 7200

Tlme, min

 

%F RT

 

 

 

 

 

 

 

 

90 ~ —— Exp data-foam-trop
7o - ------ Model D

28 :l

20 4 r = 0.9874

%FRT

 

 

 

 

T T

0 1440 2880 4320 5760 7200
Time, min

 

 

90 . —— Exp data-foam-trop
7o . ------ Model E

33 3g

20 ‘ r = 0.9844

%F RT

 

 

 

0 1440 2880 4320 5760 7200
Time, min

 

 

 

Figure 41 Comparison of Experimental and Predicted % FRT of PE Foam Liner
at Tropical Conditions (short-term prediction 5 Days)

85

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100
:3 ‘ Exp data-paper—refri
70 ~ ------ Model C
l— 60 -
E 50 L
89 40 ~
30 ~
20 — Max error= 1.39%
10 .
O T T T T
0 1440 2880 4320 5760 7200
Tlme, min
100
80 —— Exp data-paper-refri
j ------ Model D
l- 60
m L
IL
83 40 ~
20 ‘ r = 0.9749
0 . . .
0 1440 2880 4320 5760 7200
Time, min
100
:3 ‘ —Exp data-paper-refri
70 . ------ Model E
I— 60 «
E 50 L
33 40 .
30 -
20 ‘ r = 0.9722
10 .
0 . . . .
0 1440 2880 4320 5760 7200
Time, min

 

 

 

Figure 42 Comparison of Experimental and Predicted % FRT of Paper Pulp Liner
at Refrigerated Conditions (Short-Term Prediction 5 Days)

86

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100
:3 ‘ Exp data-paper-std
70 « ------ Model C
l- 50 ‘
E 50 «
32 4o -
30 a
20 ~ Max error = 1.63%
10 —
0 . . , ,
0 1440 2880 4320 5760 7200
L Time. min
100
:8 ‘ — Exp data-paper-std
70 ~ ------ Model D
l- 60 -
E 50 ”L
83 40 .
30 .
20 2 r =0.9824
10 «
o T If T 7
0 1440 2880 4320 5760 7200
Tlme, min
fi
100
:8 ‘ —— Exp data-paper-std
70 ~ ------ Model E
I- 60 +
E 50 k
o\° 40 —
30 -
20 - ..
10 q r -0.9819
0 r T T T
0 1440 2880 4320 5760 7200
Tlme, min

 

 

 

Figure 43 Comparison of Experimental and Predicted % FRT of Paper Pulp Liner
at Standard Conditions (Short-Term Prediction 5 Days)

87

 

 

9° ‘ —Exp data-paper-trop
70 1 ------ Model C

4. .L

10 Max error = 1.97%

o I T T T
O 1440 2880 4320 5760 7200

Tlme, min

%FRT
01
o

 

 

 

 

 

 

 

9° ‘ —Exp data-paper-tmp
70 ~ ------ Model D

40 1L

10 a l' = 0.9912
0 1 l . .
0 1440 2880 4320 5760 7200

Tlme, min

%F RT
or
o

 

N
O

 

 

 

 

 

 

90 ~ —Exp data-paper-trop
7o _ ------ Model E

40 L

10 . r= 0.9914
0 . T .

. 0 1440 2880 4320 5760 7200
L Time, min

Figure 44 Comparison of Experimental and Predicted % FRT of Paper Pulp Liner
at Tropical Conditions (Short-Term Prediction 5 Days)

%F RT
01
o

 

 

 

 

 

 

88

 

 

9° 4 — Exp data-foam-refri
70 ‘ll ----- Model C

'
.Iouo-oucnoouu-ou—_

 

 

%TRT
or
o

20 “ Max error = 3.12%

0 T I T T
0 1440 2880 4320 5760 7200

Tlme, min

 

 

 

 

 

 

 

90 ‘ — Em data-foam-refn'
70 i ------ Model D

60 .“ -......-.-.---_ _ ......

%TRT
a:
o

20 ‘ r = 0.8586

0 I f T I
0 1440 2880 4320 5760 7200

Time, min

 

 

 

 

 

 

9° ‘ —— Em data-foam-refri

%TRT
01
o

20 1 r = 0.4880

 

 

 

o T T fir T

0 1440 2880 4320 5760 7200
Tlme, min

 

 

 

Figure 45 Comparison between Experimental and Predicted % TRT of PE
Foam Liner at Refrigerated Conditions (Short-Term Prediction
5 Days)

89

 

 

9° : — Exp data-foam-std

 

‘A----

 

%TRT
or
c:

20 . Max error = 0.90%

0 . . . l
0 1440 2880 4320 5760 7200

Tlme, min

 

 

 

 

 

 

9° ‘ — Em data-foam-std

%TRT
on
o

20 1 r = 0.9941

 

 

 

0 1440 2880 4320 5760 7200
Tlme, min

 

 

 

 

9° i —— Em data-foam-std
70 a """ Model E

20 ‘ r = 0.9941

 

 

 

0 1440 2880 4320 5760 7200
Tlme, min

 

 

 

 

 

Figure 46 Comparison between Experimental and Predicted % TRT of PE
Foam Liner at Standard Conditions (Short-Term Prediction 5 Days)

90

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100
:3 ‘ —Em data-foam-trop
70 ~ ------ Model C
l— 60 —
E 50 4\g
3’3 40 ~ --------------- _ _ _ _
30 .
$3 ‘ Max error = 0.54%
0 ~ I T l
0 1440 2880 4320 5760 7200
Time, min
100
:3 ‘ ——Em data-foam-trop
70 . ------ Model 0
I- 60 - .
E 50 4k
o\° 40 .
30 .
20 i r = 0.9989
10 .
o T I I T
0 1440 2880 4320 5760 7200
‘l'lme, min
100
:8 7 —-Exp data-foam-trop
7O 4 ------ Model E
I- 60 . ..
E 50 d\
s 40 ~ - -
30 1
2° ‘ r = 0.9978
10 I
o l r 1 7
O 1440 2880 4320 5760 7200
Time, min

 

 

 

Figure 47 Comparison between Experimental and Predicted % TRT of PE
Foam Liner at Tropical Conditions (Short-Term Prediction 5 Days)

91

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100 .
go 4 —Exp data-paper-refn
80 ------ Model C
)—
0:
)—
°\° -
30 4
fig : Max error = 6.12%
o T I T T
0 1440 2880 4320 5760 7200
Time, min
100
90 « Exp data-paper-refri
80 ~_ ------ Model D
'- .
a:
j.
32
20 : r = 0.7602
10 -
0 i T T T
0 1440 2880 4320 5760 7200
Time, min
100
90 . ——Em data-paper-refri
80 ------ Model E
70 «*4
'_ 60 H ".m‘ - _ -
E 50 ~
32 40 «
30 ~
20 ~ r = 0.6524
10 —
o T T T T
0 1440 2880 4320 5760 7200
Tlme, min

 

Figure 48 Comparison between Experimental and Predicted % TRT of Paper Pulp
Liner at Refrigerated Conditions (Short-Term Prediction 5 Days)

92

 

 

 

Exp data-paper-std
80 ~ ------ Model C

%TRT
8‘
):

20 ‘ Max error = 2.63%

o T T T T
0 1440 2880 4320 5760 7200

Time, min

 

 

 

 

 

 

 

90 ~ — Exp data-paper-std
80 1 ------ Model D

20 : r = 0.9674

0 T T T T
O 1440 2880 4320 5760 7200

Time, min

 

 

 

 

 

 

 

Em data-paper-std
80 . ------ Model E

70 « ..

60 "\W

-C.-..-..--.----“

%TRT
a:
o

20 - r = 0.9816

0 7 T T T
0 1440 2880 4320 5760 7200

Tlme, min

 

 

 

 

 

 

Figure 49 Comparison between Experimental and Predicted % TRT of Paper Pulp
Liner at Standard Conditions (Short-Term Prediction 5 Days)

93

 

 

 

Em data-paper-trop
------ Model C

%TRT
b.0100
c>c>c>

20 ‘ Max error = 0.71%

 

 

 

0 1440 2880 4320 5760 7200
Time, min

 

 

 

90 ~ — Exp data-paper-trop
80 7 ------ Model D

%TRT
or
o

20 1 r = 0.9908

0 T T 1 T7
0 1440 2880 4320 5760 7200

Tlma, min

 

 

 

 

 

 

90 — ——Em data-paper—trop
80 “ ------ Model E

 

2° : r = 0.9016

 

 

 

T T

0 1440 2880 4320 5760 7200
Tlrne, min

 

 

 

Figure 50 Comparison between Experimental and Predicted % TRT of Paper Pulp
Liner at Tropical Conditions (Short-Term Prediction 5 Days)

94

“wiry

 

In comparing the experimental and predicted values of % FRT and % TRT
over time at test conditions, it can be seen that generally, the predicted results of
% FRT obtained from all three models are in excellent agreement with those
determined experimentally. Even so, the models show a poorer fit when used to
predict the % TRT over time especially for the systems stored at refrigerated
conditions. This is because the % TRT data from one point to the next point
fluctuated during the first 3 days and dropped down quickly later. A possible
explanation is that the amount of moisture in the air at refrigerated conditions is
low which will take a longer time for the moisture passing through the container-
closure systems to reach equilibrium stage compared with other conditions. This
moisture affects the static coefficients of friction of the systems which contribute
to the removal torque. Hence, during the first 3 days, the amount of moisture in
the systems might not reach the equilibrium yet, thus causing the fluctuations of
the measuring results. In addition, regarding the limitation of the measuring
technique, the removal torque was measured on different container-closure
systems every time; this would contribute to high variability as well. However,
based on the adequacy of fit, the models proposed are still acceptable for
predicting the % TRT over time. Overall, the comparisons suggest that the
empirical model provides the best fit for modeling the relaxation behavior of the
container-closure systems.

It is important to note that the empirical models of % FRT and % TRT are
proposed for predicting long term response; thus, it makes sense to focus on the

last data point which is least sensitive to the error made at the beginning such as

95

experimental error. This can be done by forcing fit through the last data point
and these forced fit models are expected to provide a better extrapolated long
term response. This is the philosophy behind model C and E. It is also
worthwhile to continue a discussion on model D and E which are semi-log
models. These were primarily initiated from examination of the relaxation curves
of the container-closure systems which indicated that the % FRT and the % TRT
decrease rapidly during the first fifteen minutes and then continue to drop down
at slower rate indefinitely. Thus, it is logical to formulate a simple linear model by
using a logarithmic time scale which is the basis for model D and E. Plots of the
% FRT and % TRT on a logarithmic time scale in Figures 51 and 52 substantiate
this concept. A linear relationship is observed from Figure 51; the container-
closure systems response at all test conditions is simple linear regression,
therefore. It is also obvious that these % FRT curves have almost similar shape
to each other, which is theoretically possible to apply a superposition principle for
developing a master curve of the container—closure systems at test conditions.
This would be an interesting area for future researches. There was a possible
source of error that lies in using the linear regression for modeling the systems.
The rate of % FRT change in log of time is averaged out of the set of data as
indicated in the slope of the equation, whereas the actual curves show that the
actual rate of % FRT change slowly changes overtime. This may introduce an

error in long term prediction of the % FRT and % TRT.

96

 

%FRT

 

100

 

90~

80~

70 —«

60~

50~

40-

304

20-

10—

0

/ foam-std
':- foam-refri

     
 

T/ paper-std

\. x ..
\. ‘-
. \.
\\

.
C .
~‘ ‘~.

—~ ‘.~

~
~
.
n‘ ‘‘‘‘‘
~‘ '~.
-0 ..Q
~ .....
.‘ .....
-.

paper-refri “We.
paper-trop

L LJJ

J 1 AAAIAAA A | 111111

 

 

0.1

 

11 L 1 AAA ' A A ILLALJ
T 7 T 1

1 10 100 1000 10000
Time, min

Figure 51 % Experimental FRT as a Function of Logarithmic Time

 

%TRT

 

 

 

 

 

 

 

100
a r-refri
90 _ P P9
paper-std
80 foam-refri
// foam-std
70 .
60 .
50 »
4o . foam-trop
30 - paper-trop
20 -
10 -
o “, 4.....1) . W.
10 100 1000 10000
Time, min

 

Figure 52 % Experimental TRT as a Function of Logarithmic Time

97

 

 

Regarding to the excellent short-term prediction results from the models, it

is confident to use the models developed for long-term prediction of % FRT and

% TRT. The predicted results of 3-year prediction were tabulated in Table 6 and

plotted in Figures 53 to 56.

Table 6 Predicted Values of % FRT and % TRT for Long-term Prediction

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Relaxation System Model Predicted Value

indicator 15 min. 5 daLs 30 days 1 year 2 years 3years

% F RT Foam-refri C 59.1 43.0 41.0 39.4 39.1 39.0

D 58.9 41.9 36.9 30.0 28.1 27.0

E 58.8 43.0 38.4 32.1 30.3 29.3

Paper-refri C 55.6 39.0 37.4 36.2 36.0 35.9

D 55.0 38.1 33.2 26.4 24.5 23.4

E 54.8 39.0 34.4 28.0 26.2 25.2

Foam-std C 62.2 44.0 41.7 39.7 39.3 39.2

D 61.7 43.0 37.6 30.0 27.9 26.7

E 61.5 44.0 38.9 31.8 29.8 28.7

Paper-std C 57.3 40.0 38.1 36.6 36.3 36.2

D 56.3 39.6 34.7 28.0 26.1 25.0

E 56.2 40.0 35.3 28.7 26.9 25.8

Foam-trop C 56.4 40.0 38.1 36.5 36.3 36.1

D 55.8 39.1 34.2 27.5 25.6 24.5

E 55.6 40.0 35.5 29.1 27.4 26.4

Paper-trop C 50.7 30.2 26.9 23.9 23.3 23.0

D 49.3 30.0 24.4 16.6 14.4 13.1

E 49.3 30.0 24.4 16.6 14.4 13.1

% TRT Foam-refri C 68.9 57.2 53.5 48.3 46.8 46.0

D 65.6 58.6 56.6 53.7 53.0 52.5

E 66.4 56.0 53.0 48.7 47.6 46.9

Paper-refri C 78.8 58.2 49.2 33.5 28.3 25.2

D 74.7 61.1 57.2 51.7 50.2 49.3

E 75.7 58.0 52.9 45.7 43.7 42.6

Foam-std C 64.4 49.7 46.3 42.6 41.7 41.2

D 63.4 49.4 45.3 39.6 38.0 37.1

E 63.1 49.0 44.9 39.2 37.6 36.7

Paper-std C 71.1 52.1 45.0 34.0 30.7 28.8

D 68.2 53.0 48.6 42.5 40.8 39.8

E 69.5 51.0 45.6 38.2 36.1 34.9

Foam-trop C 60.4 35.5 26.1 11.2 6.7 3.9

D 60.3 34.8 27.4 17.0 14.2 12.5

E 60.3 34.0 26.4 15.8 12.8 11.1

Paper-trop C 64.1 35.5 33.1 31.7 31.5 31.4

D 62.9 33.5 24.9 13.0 9.7 7.7

E 62.1 35.0 27.1 16.2 13.1 11.4

 

 

 

 

 

 

 

 

 

98

 

 

 

 

 

 

 

70 1
l Foam-refri ' Model C
6° +Model o
50 - +M0del E
l- 40 : cf 6
0:
IL
=2 so ~ :g: :.
20 ~
10 .
1 yr 2 yrs 3 yrs
0 T T fl
0 525600 1051200 1576800
Time, min

 

 

 

70
Foam-std + Model 0
6° + Model D
+ Model E

 

 

 

 

 

 

 

 

l: a 4
‘6
° :.: :I‘
20 .
10 ~
1 yr 2 yrs 3 yrs
0 r r fl
0 525600 1051200 1576800
Time, min
60
l Foam-trap I Model C
50 . +Model D
—-e— Model E

 
    

 

A
v

 

 

 

 

 

'—
E 30 .
83
20 .
10 ..
1 yr 2 yrs 3 yrs
0 T T 1
0 525600 1051200 1576800
Time, min

 

Figure 53 Long-Term Prediction of % FRT Values for PE Foam Liner

99

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

60
l Paper-refri ' Model c
50 - + Model D
E
Ll.
32
10 .
1 yr 2 yrs 3 yrs
0 4 r .
0 525600 1051200 1576800
Time, min
70
Paper-std M odel C
6° +Model o
50 . + Model E
IE ; -
IL —_V
33
fii‘ _.
10 -
1 yr 2 yrs 3 yrs
0 T T I
0 525600 1051200 1576800
Tlme, min
60
Paper-trop ' Model C
50 + Model D
+ Model E
40 ~
E
LL
32

 

 

1yr 2yrs 3yrs

 

 

T Tl fl

525600 1051200 1576800
Time, min

 

 

Figure 54 Long-Term Prediction of % FRT Values for Paper Pulp Liner

100

 

ll

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

80
Foam-refri I Model C
70
+Model D
60 +Model E
50 « _ I, -.
E V V
l- 40 .
32
30 '1
20 -
10 —
1 yr 2 yrs 3 yrs
0 T T T
0 525600 1051200 1576800
Time, min
70
} Foam—std Model C
60 +Model D
50 & +Model E
E 40 1 VI fi
32 30 a
20 1
10 -
1 yr 2 yrs 3 yrs
0 ~ . .
0 525600 1051200 1576800
Time, min
70
l F°am"'°P —0— Model 0
6° +Model e g
50 . +Modelf i
’12 ‘°‘
6° 30 -
20 - 1 yr 2 yrs 3 yrs
10 .
0 r T I
0 525600 1051200 1576800
Time, mil

 

 

 

Figure 55 Long-Term Prediction of % TRT Values for PE Foam Liner

101

 

 

   
  
   
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  
   
    

90

80 Paper-refri + Model C

70 +Model D
—aFJWmMflE

60

E:50~ «——l—— __.

£3 40 « '
30~
201
1° ‘ 1 yr 2 yrs 3 yrs

0 fl T I
0 525600 1051200 1576800
Time, min
80
Paper-std I Model C
70
+ Model D
6° +Model E
50

'—

E 40 - + I
304 c -
20.

10—
1 yr 2 yrs 3 yrs
0 T . 4444
0 525600 1051200 1576800
Time, min
70
Pape'ml’ + Model 6
5° + Model 0
50 + Model E
E 40
33 30 ¢

 

 

1yr 3)ns
o T T T T

0 525600 1051200 1576800
Time, min

 

 

 

 

Figure 56 Long-Term Prediction of % TRT Values for Paper Pulp Liner

102

 

The predicted results in Table 6 (page 97) show that the % FRT obtained
from models C, D and E agree with each other. There is no significant difference
of predicted % FRT values among the systems at test conditions except for the
paper pulp system at tropical conditions which shows a significantly lower value;
the results agree with the experimental results of 5—day relaxation which indicates
the consistency of the predictive models. It was found that the models (C, D and
E) show excellent agreement of the results for short time prediction (less than 30
days). Then, as the prediction period is longer, the algorithms of models C, D
and E appear to show the effect on the predicted % FRT values. This is because
the accumulation of deviation of the predicted results among the models over
time. The predicted results from model C tend to be higher than the semi-log
models (D and E) around 10% at the end of year 3. The predicted result is still in
the acceptable range for agreement among the models. However, the
experimental data to support the predicted results for long-term prediction is not
available. The validity of the long-term prediction must be conducted in the
future research.

The quality of the input data from relaxation experiment affects the
accuracy and agreement of the predicted results obtained from models C, D and
E. This can be noticed in the predicted % TRT values in Table 6. The predicted
values show fairly high variation from model to model up to 24% especially
between model C and models D and E. This is the result of fluctuations of input
% TRT data which can be explained by the nature of removal torque

measurement. A general conclusion can be drawn from the predicted values that

103

at 3-year relaxation, the systems stored at refrigerated conditions have the
highest % TRT value whereas the systems stored at tropical conditions retain the
lowest % TRT value. This conclusion also corresponds to the experimental
results of 5-day relaxation (short-term prediction).

The analysis of predicted values from models C, D and E was performed
further to compare between the % F RT and % TRT at 3-year relaxation. The F-
results of each model were plotted as bar graphs as shown in Figures 57, 58 and
59. The predicted values obtained from model C indicate that there is not much

difference between the predicted % FRT and % TRT values except for the PE

 

foam system at tropical conditions. On the other hand, the predicted values ’9'
obtained from models D and E show that overall, the % TRT is higher than the %

FRT except for the systems at tropical conditions. Therefore, it can be concluded

that for long-term storage at standard conditions, for the same container-closure

system the % TRT tends to be higher than the % FRT. There is not much

difference when comparing between the % FRT of PE foam liner and % F RT of

paper pulp liner. The same result also found when comparing between the %

TRT of PE foam liner and %TRT of paper pulp liner.

104

 

 

100.0

9°'°‘ I%FRT
,80'0” D%TRT

70.0 .
.2
36.2 36.1 31.4
28.8 23.0
3.9

60.0 .

50.0 -
Foam- Paper- Foam- Paper- Foam- Paper-
refri reli'i std std trop trop

40.0 4
Figure 57 Comparison of Predicted % FRT and % TRT at 3 years using Model C

 

 

 

 

% Retention

30.0 4
20.0 -
10.0 +

0.0 -

 

 

 

 

 

 

 

 

 

 

100.0

9°'° ‘ I %FRT

30.0 r o
70.0 . 1:1 /oTRT

50-0 ‘ 52.5
50.0 -
40.0 ~
30.0 - 27-
20.0 -
10.0 —

0.0 J

 

 

 

 

% Retention

 

 

 

 

 

Foam- Paper- Foam- Paper- Foam- Paper-
refn' refri std std trop trop

Figure 58 Comparison of Predicted % FRT and % TRT at 3 years using Model D

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100.0
33‘ I%FRT
' d o
70.0 . El /oTRT
5 60.0 +
‘c‘ -
g 50'0 “'9 42.6
m 40.0 4 34-9
32 30.0 . 29' 25. 25. 26.4
- 13.1
20'0 11.1 11.4
10.0 —
0.0 " I r r T
Foam- Paper- Foam- Paper- Foam~ Paper-
refn' refri std std trop trop

 

 

 

Figure 59 Comparison of Predicted % FRT and % TRT at 3 years using Model E

105

Modeling of relaxation behavior of container-closure systems was then
extended to improve the torque-friction model (Equations 2 and 3). The idea of
improvement is to combine this theoretical model based on the equations of
equilibrium which is inadequate to describe the relaxation behavior with the
empirical model of the coefficients of friction at thread interface and liner
interface. According to the torque-friction model (Equations (2) and (3), the time
dependent and nonlinear terms are not included in the original equation. These
terms were planned to impose on the coefficients of friction terms in Equations
(2) and (3). To do this, it is necessary to acquire and check the data of both
coefficients over time from the experimental results before modifying the model.
Data for coefficient of friction at the thread interface were deduced from the
torque-friction model by using the input data of sealing force during storage over
time from the measuring device and removal torque over time during storage
from the actual system as shown in Figure 60. It was found that the coefficient
increased over time from 0.33 at 15 min to 0.431 at day 5 and the coefficient
obtained from this method is a lot higher than using the method developed from a

previous study (Pisuchpen, 2000).

 

 

Fv T'
Sealing force from Removal torque
measuring device from actual system

\ ./

u,
Coefficient of friction
at thread interface

 

 

 

 

 

 

 

 

 

 

Figure 60 Coefficient of Friction at Thread Interface determined from Sealing
Force Measuring Device and Actual System

106

 

Data of the coefficient of friction at liner interface were also deduced from
the torque-friction model but using the input data of removal torque overtime
from the actual system and coefficient of friction at thread interface and sealing
force over time from the measuring device as shown in Figure 61. Verification of
the data shows that negative values of coefficient of friction at the liner interface

were found.

 

Coefficient of
friction at thread
interface from
measuring device

 

 

 

 

 

Fv T'
Sealing force from Removal torque
measuring device from actual system

\. ./

u,
Coefficient of friction
at liner interface

 

 

 

 

 

 

 

 

 

 

 

Figure 61 Coefficient of Friction at Liner Interface determined from Sealing Force
Measuring Device and Actual System

In doing this, we tried to add every part of the input energy applied in the
torque-friction model to end up as friction loss. This is because the equations
have only the coefficients of friction term that contributes to the loss of input
energy. The negative values of the coefficient were attributed to the error from
either the method to deduce the data or the torque-friction model itself. This
suggests that the simple modification as described on the torque-friction model is

unable to provide a satisfactory. Elaboration on the time dependent properties of

107

the torque-friction model with other approaches is needed in order to make the

model showed relaxation behavior.

108

6. CONCLUSIONS, RECOMMENDATIONS AND FUTURE WORKS

This new technique for measuring sealing force of container-closure
systems using a strain gage based transducer offers an alternative way to
measure and verify the mechanical seal integrity of the systems. Although the
removal torque is widely used through out the industry, it sometimes provides
high variation results in some container-closure systems. On the other hand, the
sealing force shows the consistent results and is considered as a direct indicator
compared to the removal torque. The technique developed in this research can
be applied to other types of container-closure systems; in addition, the test
fixtures were also proposed as a simple technique for study of the relaxation
behavior of container-closure systems. The sealing force measuring device in
combination with a torque meter was employed in this research to study the
effect of environmental conditions on the relaxation behavior of container-closure
systems. The responses overtime from both devices transformed to the % force
retention (FRT) and % torque retention (TRT) were used to analyze the effect of
environmental conditions.

The results of this investigation show that only the relaxation (% FRT and
% TRT) of the systems stored at tropical conditions especially the paper pulp
system was significantly higher than the relaxation of other conditions. The high
temperature and high relative humidity of the environment play a significant role
in the relaxation behavior of the systems. The % TRT data were less consistent
than the % FRT data. Comparing between the % FRT and % TRT, the relaxation

results obtained from the % TRT were less than the % FRT which disagrees with

109

 

the theory based on the equations of equilibrium (Pisuchpen, 2000). Therefore,
using the removal torque or % TRT may be misleading in the interpretation of the
seal integrity of the container-closure systems. This finding may explain in some
cases, the leakage problem found in container-closure systems having high
removal torque.

In attempting to predict a long-term relaxation of container-closure
systems based on mathematical models, it was found that the theoretical models
derived from spring and dashpot are not applicable. The empirical models using
curve fitting techniques were then suggested for modeling the relaxation behavior
of the systems. Excellent fits were obtained from % FRT and % TRT of short-
terrn prediction (5 days). The results were extended to long-term prediction by
extrapolating the same models to 3 years. The predicted results were found in
the acceptable range. However, the experimental data to support the long-term
prediction from the models is not available. Future research must be done in
order to verify the predicted results. From simplicity of the mathematical
operation, the semi-log model: model D was suggested to use in general
applications to the relaxation behavior of the systems. Despite the benefit of
modeling in long-term prediction, it must be realized that accuracy of the
predicted results relies on the accuracy of the input data of the models. Thus,
the errors from experimentation and human should be minimized and controlled.
The concept of modeling in this research can be applied to other cases which

undergo the relaxation behavior.

110

Recommendations and Future Works

Implication of the technique developed in this research is immense since it
introduces a new concept in monitoring the mechanical seal integrity of the
container-closure systems. The concept of this technique can be applied to
develop the sealing force measuring device for other types of closure-container
system. It is important to note that the sealing force measuring device is
designed only to measure the sum of all forces acting at the thread and liner
interface. Hence, uniformity of the distributed sealing forces around the contact
area should be measured additionally by other techniques in order to have
complete information about seal integrity of the systems. It should be
emphasized that the present investigation was based on limited data sets and
types of container-closure system; more research is needed to check the validity
of the models and to investigate their precision. More input data overtime would
probably increase the precision and make the models suitable for a large range
of prediction. The future growth expected in this area will be the combination of
this technique with other analytical methods such as permeation test and
package leak detection in which the results can be used to correlate the physical
parameter (% FRT) and the product-package parameters (permeability and leak
rate). Further refinement on the modeling of long-term relaxation behavior will be
also needed. Appropriate solutions to combine the theoretical model with the
empirical model are needed in order to develop standard parameters for material
used in the container-closure systems. Another crucial area that will demand

attention is to generate master curves of relaxation behavior of container-closure

111

systems which will provide useful information for estimating the seal integrity of

the container-closure systems during service time.

112

APPENDIX

113

THE COMPUTER PROGRAM FOR MODEL C

10 REM: FITS Y=A+Bl(1+K*X"P) TO N (X,Y)'s

20 REM: CREEP/RELAXATION MODEL: Y goes from 100 to F as X goes from O
to infinity

30 READ N,F : DIM X(N),Y(N) 'open arrays X and Y for data

40 FOR l=1 TO N : READ X(l),Y(I) : NEXT I 'read N data

50 DATA N, F ‘number of data (N), value of the last data point (F%) for fit

60 DATA X, Y ‘user inputs data: x = time, y = %FRT or %TRT, for example x, y is
0, 100

70 MIN=10000 'search for fit with smallest maximum error for all P,K

80 FOR K=.703 TO .705 STEP .0001 : FOR P=.172 TO .174 STEP .0001 ‘user
varies K and P in desired step in order to minimize the error between actual
value of y and calculated value of y.

90 BIG=0 : FOR l=1 TO N 'BIG is largest error for a given K,P

100 A=F-(100-F)/(K*X(N)"P) : B=100-A

110 ER=ABS(Y(I)-A-B/(1+K*X(I)"P)) 'error at lth data point

120 IF ER>BIG THEN BIG=ER 'call "BIG" the largest error for given K,P

130 NEXT l

140 IF BIG>=MIN THEN 160 'compare BlG's for every possible K,P

150 MIN=BIG : K0=K : P0=P 'remember the K and P with smallest BIG

160 NEXT P : NEXT K

170 PRINT " k=";K0;" p=";P0;" max error=";MlN

180 'LIST 80

114

190 GOTO 280

200 FOR J=1 TO N/20 : INPUT Z 'meaningless input to slow down printout
210 PRINT " l X given Y fitted Y error"
220 FOR l=20*(J-1)+1 TO 20*J

230 A=F-(100-F)/(K*X(N)"P) : B=100-A

240 YI=A+B/(1+K0*X(I)"P0)

250 PRINT l,X(I),Y(I),YI,Yl-Y(I)

260 NEXT I

270 NEXT J

280 PRINT "A=";A"; B=";B;" KO*X(N)"P=";K0*X(N)"PO
290 INPUT "give a time in days";XX

300 XX=XX*24*60 : YI=A+B/(1+KO*XX"P0) : PRINT "Y=";Y|

310 GOTO 290

115

THE COMPUTER PROGRAM FOR MODEL D

10 REM: FITS Y=K*LNX+C, TO N (X,Y)'s

20 REM: user makes changes to line 60

30 READ N : DIM X(N),Y(N) 'open arrays X and Y for data

40 FOR l=1 TO N : READ X(l),Y(I) : NEXT I 'read N data

50 DATA N ‘ user inputs number of data

60 DATA X, Y ‘user inputs data: x = time, y = %FRT or %TRT, for example x, y
is 0, 100

70 SX=0 : SY=0 : SXX=0 : SXY=0 : SYY=0 : SSE=0 'initialize sums

80 FOR l=1 TO N 'form sums

90 SX=SX+LOG(X(I))IN : SY=SY+Y(I)IN : SXY=SXY+LOG(X(I))*Y(l)/N
100 SXX=SXX+LOG(X(l))*LOG(X(I))/N : SYY=SYY+Y(I)*Y(l)/N

110 NEXT l

120 K=(SXY-SX*SY)/(SXX-SX*SX) : C=SY-M*SX 'slope, y-intercept

130 R=ABS(M)*SQR((SXX-SX*SX)/(SYY-SY*SY)) 'correlation coefficient
140 FOR l=1 TO N : SSE=SSE+(Y(|)-M*LOG(X(I))-B)"2 : NEXT l 'sum of
squares of errors

150 PRINT " y=k*Inx+c fit to";N;"data"

160 PRINT: PRINT " k=";K;" c=";C

170 PRINT : PRINT “ x given y predicted y=k*Inx+c"

180 FOR l=1 TO N : PRINT X(l),Y(I),K*LOG(X(I))+C : NEXT I

190 PRINT : PRINT " correlation coefficient R=";R

200 PRINT " sum of squares of errors SSE=";SSE

116

 

210 PRINT " rrns error = sqr(SSElN)=";SQR(SSEIN)

220 END

 

117

THE COMPUTER PROGRAM FOR MODEL E

10 REM: FITS Y=Yn+K*LN(X/Xn) TO N (X,Y)‘s
20 N=6 : DIM X(N),Y(N) 'open arrays X and Y for data
30 FOR l=1 TO N : READ X(l),Y(I) : NEXT |

40 DATA X, Y “user inputs data: x = time, y = %FRT or %TRT, for example x, y is
0, 100

50 S1=0 : $2=0 : FOR l=1 TO N

60 S1=S1+(Y(l)-Y(N))*LOG(X(l)/X(N))

70 $2=SZ+LOG(X(I)IX(N))"2

80 NEXT l

90 K=S1/82

100 PRINT“ fit y=yN+k*ln(xlxN) to";N;"data"
110 PRINT : PRINT " k=";K

120 PRINT: PRINT " x given y fitted y"
130 S3=0 : S4=0 : S5=0

140 FOR l=1 TO N

150 S3=S3+Y(I)

160 YI=Y(N)+K*LOG(X(I)IX(N))

170 85=SS+(Y(l)-YI)"2

180 PRINT USING" W.###";X(I),Y(l),¥l

190 NEXT I

200 M=S3IN

210 FOR I =1 TO N

118

 

220 S4=S4+(Y(|)-M)"2 : NEXT I

230 R=SQR(1-35/S4) : PRINT " correlation coeff=";R
240 ‘PRINT : INPUT "time in days";T

250 'T=T*24*60 : YI=Y(N)+K*LOG(T/X(N)) : PRINT "y=";Yl
260 'GOTO 240

119

 

REFERENCES

120

 

REFERENCES

. Aklonis, John J., MacKnight William J.,and Shen, Mitchel (1972), Introduction
to Polvmer Viscoelastic'fiy.

. Arridge, R.G.C. (1985), An lntrod_uction to Polvmer Mechanics. Taylor &
Francis.

. ASM Metals Handbook Vol 2 (1990), ASM lntemational, Ohio.

 

. Closure Guides (1993), Closure Manufacturers Association.

. Dally, James W., Riley, William F., McConnell, Kenneth G. (1993),
lnstrgmentajon for Engineering Measurements, John Wiley & Sons.

. Dowling, Norman E. (1993), Mechanical Behavior of Materials, Prentice Hall.

. Ferry, John D. (1970), Viscoelastic Properties of Polymers, John Willey &
Sons.

. Greenway, Gerald, A_§hort-Term Study of Cap Torgue Decay, Packaging
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. Lai, Ching-Sung and Greenway, Gerald, The Effect of Time on Cap Removal
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10. Lockhart, Hugh, Detennigtion of Torgue Loss for a 28 mm Metal Closure on

Plastic Bottle, School of Packaging, Michigan State University, Unpublished,
August 1992.

11.Matsuoka, Shiro (1992), Relaxation Phenomena in Pglvme_r§_, Oxford

 

University Press.

12. McCarthy, Robert V. (1956), Performance of Plastic Screw Thrga_d

Attachment. MS. Thesis, Franklin and Marshall College, Lancaster,
Pennsylvania.

121

 

13. Pisuchpen, Supachai (2000), Model for Pre_dicting Application Torgue and
Removal Torgue of a Continuous Thread Closure, MS. Thesis, School of
Packaging, Michigan State University.

14. Rosan, Stephen L. (1993), Fundamenjil Principles of Polvmeric Mgteriafi,
John Wiley & Sons.

15. Sobotka, Z. (1992), Bh_eologv of Materials and Engineering Structures,
Elsevier Science Publishers.

 

16.Window, AL. (1989), Strain Gauge Technology, Elsevier Science Publishers.

122