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Frictional Coefficients
Between Plug and Sheet
[Problems with Theories,
Experiments in Plug Assist]
James L. Throne
Sherwood Technologies, Inc.
Dunedin Florida 34698-3347
Paper presented at
2004 Thermoforming Conference
Indianapolis IN
TF Conference 2004 – Throne
Frictional Coefficients Between Plug and Sheet
Objective
To better understand the problems
with theories and experiments in plug
assist thermoforming
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Frictional Coefficients Between Plug and Sheet
Caveat
It is my intent to raise concerns about
the ways in which we view the
interaction between the plug and the
sheet
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Frictional Coefficients Between Plug and Sheet
Caveat
It is my intent to raise concerns about
the ways in which we view the
interaction between the plug and the
sheet
It is NOT my intent to provide
answers to the questions about the
interfacial conditions between the
plug and the sheet
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Frictional Coefficients Between Plug and Sheet
Think about this Question!
In plug-assist thermoforming,
what is sliding against what?
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Frictional Coefficients Between Plug and Sheet
Outline
I.
A discussion of the coefficient of
friction issue
II. A sliding experiment
III.Some prototypical plug
experiments
IV. Conclusions
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I. Some thoughts on the
coefficient of friction
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Coefficient of Friction
• Frictional characteristics considered part
of tribology
• Tribology is study of friction, lubrication
and wear
• Traditional view is that all three are
extant in thermoforming
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Historical views of coefficient of friction-I
“The relation that the power required to
move a body bears to the weight or
pressure on the body is known as the
coefficient of friction.”
W.M. Davis, Friction and Lubrication, A Handbook
For Engineers, Mechanics, Superintendents and
Managers, The Lubrication Publishing Co.,
Pittsburgh PA, 1903.
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Historical Views of coefficient of friction-II
“The coefficient of friction is the ratio
between the resistance to motion and the
perpendicular pressure.”
W.M. Davis, Friction and Lubrication, A Handbook
For Engineers, Mechanics, Superintendents and
Managers, The Lubrication Publishing Co.,
Pittsburgh PA, 1903.
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Historical Views of coefficient of friction-III
“There is no other element in connection
with… lubrication… that has received so
much consideration as that of the
coefficient of friction, and yet there is
no other that is in so indeterminable a
state…”
Mr. Hall, Car Lubrication, ca. 1900 - cited in
W.M. Davis,Friction and Lubrication, A Handbook
For Engineers, Mechanics, Superintendents and
Managers, The Lubrication Publishing Co.,
Pittsburgh PA, 1903.
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Historical views of coefficient of friction-IV
“While the coefficient of friction must
always be taken into consideration when
designing and constructing machinery, it is
not always practicable to calculate it with
any degree of accuracy, [and] in fact it
can only be determined absolutely by
experiment.”
W.M. Davis,Friction and Lubrication, A Handbook
For Engineers, Mechanics, Superintendents and
Managers, The Lubrication Publishing Co.,
Pittsburgh PA, 1903.
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Coefficient of Friction
Following discussion assumes that
frictional effects are extant in
plug-assisted thermoforming
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Blunt-nose plug moving into sheet
Contact may involve some sheet sliding
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•
•
•
•
Frictional Conditions
Between Plug* And Sheet
Static CoF, no sliding (coefficient max)
Sliding CoF, no static (coefficient zero)
Some static, some sliding
Slip-stick behavior
*or mold wall
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Frictional Conditions
Between Plug* And Sheet
• Static CoF, no sliding (coefficient max)
• Sliding CoF, no static (coefficient zero)
• Some static, some sliding
• Slip-stick behavior
*or mold wall
Which of these are relevant when plastic
stretches against plug surface?
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Coefficient of Friction
• Static CoF - Initiation of sliding between
plug (and mold wall) and sheet
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Coefficient of Friction
• Static CoF - Initiation of sliding between
plug (and mold wall) and sheet
• Sliding CoF- Continuation of sliding
between plug (and mold wall) and sheet
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Coefficient of Friction
• Static CoF - Initiation of sliding between
plug (and mold wall) and sheet
• Sliding CoF - Continuation of sliding
between plug (and mold wall) and sheet
• Static friction value usually 100s to
1000s greater than sliding friction value,
but not always!
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Sliding Coefficient of Friction
• Contact area increases with increasing load
Plastic sheet
Plug
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Sliding Coefficient of Friction
• Contact area increases with increasing load
• Ergo, coefficient independent of load
Plastic sheet
Plug
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• Are there other factors influencing the
interaction between the plug and the
sheet?
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• Are there other factors influencing the
interaction between the plug and the
sheet?
• Wear
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Sliding Coefficient of Friction
Wear v. sliding friction
Friction maximum in polymer transition region
Wear minimum in polymer transition region
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Sliding Coefficient of Friction
Friction
maximum,
wear minimum
in polymer
transition
region
Glass Transition
Region
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• Are there other factors influencing the
interaction between the plug and the
sheet?
• Wear
• Dry v. wet sliding
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Dry v. “wet” sliding
• Dry sliding assumes no lube between surfaces
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Dry v. “wet” sliding
• Dry sliding assumes no lube between surfaces
• Plastics exude small molecules (low MW
polymers, additives, processing aids)
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Dry v. “wet” sliding
• Dry sliding assumes no lube between surfaces
• Plastics exude small molecules (low MW
polymers, additives, processing aids)
• Small molecules reside between plug and sheet
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•
•
•
•
Dry v. “wet” sliding
Dry sliding assumes no lube between surfaces
Plastics exude small molecules (low MW
polymers, additives, processing aids)
Small molecules reside between plug and sheet
Small molecules transfer from sheet to plug
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•
•
•
•
•
Dry v. “wet” sliding
Dry sliding assumes no lube between surfaces
Plastics exude small molecules (low MW
polymers, additives, processing aids)
Small molecules reside between plug and sheet
Small molecules transfer from sheet to plug
Interface may go from dry to wet (or wet to
dry!) as plug advances into sheet
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• Are there other factors influencing the
interaction between the plug and the
sheet?
• Wear
• Dry v. wet sliding
– More than one type of wet sliding
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Two types of wet sliding
• Boundary lubrication – low sliding velocity, low
interfacial viscosity, high loading
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Two types of wet sliding
• Boundary lubrication – low sliding velocity, low
interfacial viscosity, high loading
• Hydraulic or hydrodynamic lubrication – high
sliding velocity, high viscosity, low loading
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Two types of wet sliding
• Boundary lubrication – low sliding velocity, low
interfacial viscosity, high loading
• Hydraulic or hydrodynamic lubrication – high
sliding velocity, high viscosity, low loading
• Boundary lubrication occurs during start/top
activities [as might be the case with plugs in
contact with sheet]
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•
•
•
•
Two types of wet sliding
Boundary lubrication – low sliding velocity, low
interfacial viscosity, high loading
Hydraulic or hydrodynamic lubrication – high
sliding velocity, high viscosity, low loading
Boundary lubrication occurs during start/top
activities [as might be the case with plugs in
contact with sheet]
Boundary lube friction 100s greater than
hydraulic lube friction
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Two types of wet sliding
Sheet does not move far under plug force
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Measuring Frictional Coefficients
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Traditional methods of
measuring coefficient of friction
• Weight sliding on inclined surface
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Traditional methods of
measuring coefficient of friction
• Tabor “Abrasor” – stylus rubbing on
rotating disk
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Between Plug and Sheet
Traditional…
• Other methods
• No methods
entirely
applicable to
measuring plugsheet friction…
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Observations
• Frictional resistance is a complex issue:
o
o
o
o
Static v. sliding
Dry v. wet
The extent of sliding
Boundary v. hydrodynamic effects
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Observations
• Frictional resistance is a complex issue:
o
o
o
o
Static v. sliding
Dry v. wet
The extent of sliding
Boundary v. hydrodynamic effects
• Standard frictional devices may not give
reliable results
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Are We Answering the Question?
In plug-assist thermoforming,
what is sliding against what?
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II. A sliding experiment
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Between Plug and Sheet
Traditional…
• Other methods
• No methods
entirely
applicable to
measuring plugsheet friction
(except g but
modified)
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Plug-sheet friction – experiment
• Consider figure below…
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Plug-sheet friction – experiment
• Consider figure below…
– A is plug material, B is plastic sheet, p is
applied load
– Plug material moved against sheet…
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Plug-sheet friction – experiment
• Consider figure below…
– First, plug, sheet surfaces examined optically
(100X or SEM)
– Plug mounted in fixture, load similar to applied
plug force applied…
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Plug-sheet friction – experiment
• Consider figure below…
– Sheet placed on hot plate, heated to forming
temperature
– Plug heated to 20C of the sheet temperature…
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Plug-sheet friction – experiment
• Consider figure below…
– Plug pressed against sheet
– Moved at slow rate (~ 1 mm/sec, say) against
sheet, then stopped…
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Plug-sheet friction – experiment
• Consider figure below…
– Plug then lifted and indexed to new place on
sheet
– Plug held away from sheet for period of time
(10 sec, say)…
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Plug-sheet friction – experiment
• Consider figure below…
– Plug then placed against sheet and moved
other direction at (~ 1 mm/sec, say)
– After 10 (say) to-and-fro motions, plug
removed from fixture and examined…
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Plug-sheet friction – experiment
• Consider figure below…
– Plug surface examined optically (100X or SEM)
– Scrapings from plug surface chemically
analyzed (FTIR) to determine mat’l transfer…
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Plug-sheet friction – experiment
• Consider figure below…
– New plug examined, then heated and brought
in contact with fresh sheet surface
– Plug moved to-and-fro 100 times, then
examined optically and chemically…
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Plug-sheet friction – experiment
• Consider figure below…
– Only after material transfer level reaches
constant value…
– is resistance to sliding measured, using strain
gauge or load cell…
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•
•
•
•
•
•
•
Experiment #1
E&C Syntactic Foam, sanded w/180 grit, blown
with oil-free air
Normal stress= 3 lb/in2
Hot plate temp setting = 162+/-2oF
0.120 inch black GP-PS sheet
Block held on sheet 10 s, moved 10 cm in 10
sec, then removed and cooled 15 s
Force measured once block moved
Concluded after 10 contacts
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•
•
•
•
•
•
•
Experiment #2
E&C Syntactic Foam, sanded w/180 grit, blown
with oil-free air
Normal stress= 3 lb/in2
Hot plate temp setting = 162+/-2oF
0.120 inch black GP-PS sheet
Block immediately moved 10 cm in 10 s, then
removed and cooled 15 s
Force measured once block moved
Concluded after 40 contacts
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Parameters
Fixed
Sheet, heater temperature
Sliding length, times
Measured
Force
Block surface temperature
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Visual Observations
• After 10 contacts in Expt #1, plug
surface is smoother and grayer
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Visual Observations
• After 10 contacts in Expt #1, plug
surface is smoother and grayer
• After 40 contacts in Expt #2, plug
surface is gray, with small <1 micron
specks in surface
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Mea Culpa
• Syntactic foam blocks were sent to local
university for FTIR reflectance and
ESCA measurements in August 2001
• Blocks mysteriously disappeared (!)
• Retesting to obtain new samples has not
yet begun
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Observations
• Hot plate experiments yield timedependent force
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Observations
• Hot plate experiments yield timedependent force
• Force is dependent on plug surface
temperature
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III. Some prototypical plug
experiments
[Focus on ball or spherical plugs]
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Plug design
characteristics Plug types
Tapered, bulletor bull-nosed
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Plug design characteristics - Plug types
Tapered, bullet- or bull-nosed
Applications
 Very deep draws
 Where thinning of sidewall is critical
 Where wall thickness is critical
 Where polymer chills rapidly
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Blunt-nose plug moving into sheet
Contact may involve some sheet sliding
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Load Creep
• Rough acrylic under
load – increasing
time or increasing
temperature
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Load Creep
• Rough acrylic under
load
• Red – low temp
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Load Creep
• Rough acrylic under
load
• Red – low temp
• Yellow – medium
temp
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•
•
•
•
Load Creep
Rough acrylic under
load
Red – low temp
Yellow – medium
temp
Blue – high temp
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•
•
•
•
•
Load Creep
Rough acrylic under
load
Red – low temp
Yellow – medium
temp
Blue – high temp
Note increasing
contact area with
increasing
temperature
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Sheet stretching characteristics
• Sheet stretched in uniaxial, biaxial, equibiaxial
and plane strain modes
• Mathematical models include
 Ogden doubly-infinite power-law
 Mooney form of Rivlin strain energy function
 Plane strain linear law
 K-BKZ viscoelastic model
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Sheet stretching characteristics
• Sheet stretched in uniaxial, biaxial, equibiaxial
and plane strain modes
• Mathematical models include
 Ogden doubly-infinite power-law
 Mooney form of Rivlin strain energy function
 Plane strain linear law
 K-BKZ viscoelastic model
• Plugs stretch sheet in plane strain
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Plane strain
stretching, cont.
Top and side view of
plug-assisted
stretching
[Circles appear as
circles from top…]
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Plane strain
stretching, cont.
Top and side view of
plug-assisted
stretching
[Circles appear as
circles from top, are
actually distorted]
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Plane strain stretching, cont.
Mooney-Rivlin equation:
sl = (l2-1/l)(2C1+2C2/l)
For plane strain:
(ll2-1)1/2(1-1/ll2)=(F/2pr)(2C1-2C2)/to
Where
1/l l= lh = t/to
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Plane strain stretching
Force F required to stretch sheet to a
depth d with a flat plug:
F = 2pdE(T)to/ln (a/b)
Where E(T) is temperature-dependent
modulus, to is initial sheet thickness, a is
plug diameter, b is sheet diameter
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Plane strain
stretching,
cont.
Comparison of
theories and
flat plug
experimental
data –
JLT, 1986
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2004 Experiments on Spherical Plugs
Into Circular Sheets
• 0.015-inch natural rubber sheet, 6.75inch diameter
• Two wooden sphere diameters
Small ball diameter = 0.75 inch
Large ball diameter = 3 inch
• Force and penetration measured with
scales
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Schematic
of Plug
Experiment
Left HalfInitial Plug
Position
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Schematic
of Plug
Experiment
Right HalfPlug
Position
During
Sheet
Stretching
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1.
2.
3.
4.
5.
6.
Large Sphere Surface Treatment
As-is [rough-grained exterior pine]
Sanded w/200 grit paper
Wood-putty-filled, sanded w/320 grit
paper
Filled, sanded, and polished
Filled, sanded, polished and talc-coated
Filled, sanded, polished and coated with
lube
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•
•
•
•
•
•
Measurements
Height of plug into sheet
Force
Diameter of spherical cap
Calculations
Area of spherical cap
Area of truncated cone
Thickness of sheet
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Thickness of free portion of membrane
Two extremes shown in next figure
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Thickness of free portion of membrane
Two extremes shown in next figure
• If sheet slides on surface (friction
coeff=0), thickness is uniform
everywhere
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Thickness of free portion of membrane
Two extremes shown in next figure
• If sheet slides on surface (friction
coeff=0), thickness is uniform
everywhere
• If sheet sticks to surface (friction
coeff=1), sheet on cap is original
thickness
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Experiment
Draw a circle on the free portion of the
sheet…
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Experiment
Draw a circle on the free portion of the
sheet…
Press the plug into the sheet to a given
depth…
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Experiment
Draw a circle on the free portion of the
sheet…
Press the plug into the sheet to a given
depth…
Measure the major and minor axes of the
ellipse (a and b)…
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Experiment
Draw a circle on the free portion of the
sheet…
Press the plug into the sheet to a given
depth…
Measure the major and minor axes of the
ellipse (a and b)…
Use the relative areal draw ratio equation
Rarel = r2/ab
to calculate reduced thickness, 1/ Rarel
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Comparison
Penetration
2.0 in
2.4 in
of Theory
No Frict
0.832
0.778
and Experiment
Max Frict Exptl*
0.813
0.805
0.738
0.744
* Average of 9-10 experiments
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Solid Circles –
Measured Red Tk
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Sheet Thickness
What about the relationship between
stretching force and sheet thickness?
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Sheet Thickness
What about the relationship between
stretching force and sheet thickness?
According to plane strain theory, the force
increases in proportion to the thickness.
Does this hold true for this experiment?
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Observations
The nature of the dry plug surface does
not substantially affect the amount of
force needed to stretch the membrane
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Observations
The nature of the dry plug surface does
not substantially affect the amount of
force needed to stretch the membrane
It appears that from simple
measurements, the sheet adheres to
rather than slides on the dry plug
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Lubed Interface
So far, all experiments have been with a
presumed dry interface…
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Lubed Interface
So far, all experiments have been with a
presumed dry interface…
Remember the discussion on wet v. dry
sliding?
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Lubed Interface
So far, all experiments have been with a
presumed dry interface…
Remember the discussion on wet v. dry
sliding? What happens if the interface is
lubricated?
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Lubed Interface
Large plug coated with…
• Heavy grease [oil-based]
• Glycerin [water-based]
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Observations
So, what happened when the interface is
lubricated?
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Observations
So, what happened when the interface is
lubricated?
If it’s oil-lubed, essentially nothing..
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Observations
So, what happened when the interface is
lubricated?
If it’s oil-lubed, essentially nothing..
But if it’s water-lubed, stretching force is
reduced…
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Observations
So, what happened when the interface is
lubricated?
If it’s oil-lubed, essentially nothing..
But if it’s water-lubed, stretching force is
reduced…
[This obviously needs more study!]
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IV. Conclusions
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Conclusions
 From simple plug experiments, it is
apparent (at least to me) that the
interaction between the plug and the
sheet is not clearly defined
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Conclusions
 From simple plug experiments, it is
apparent (at least to me) that the
interaction between the plug and the
sheet is not clearly defined
 It is not apparent (again, at least to me)
that coefficient of friction is an
appropriate measure of this interaction
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Conclusions
 Simple measurements show applied force
increases with increasing sheet thickness
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Conclusions
 Simple measurements show applied force
increases with increasing sheet thickness
 Something is going on when the interface
is lubricated. But why is the force
reduced only when the lube is waterbased?
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Conclusions
 Furthermore, one might anticipate that
with thick-gauge sheet, compression and
shear might also be important - in
addition to (or instead of) sliding.
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Conclusions
 Furthermore, one might anticipate that
with thick-gauge sheet, compression and
shear might also be important - in
addition to (or instead of) sliding.
 But the question remains…
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In plug-assist thermoforming,
what is sliding against what?
Questions?
THANK YOU
FOR YOUR
ATTENTION!
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