James L. Throne Sherwood Technologies, Inc. Dunedin Florida 34698-3347
description
Transcript of James L. Throne Sherwood Technologies, Inc. Dunedin Florida 34698-3347
Frictional Coefficients Between Plug and
Sheet
[Problems with Theories, Experiments in Plug Assist]
James L. ThroneSherwood Technologies, Inc.Dunedin Florida 34698-3347
Paper presented at
2004 Thermoforming Conference
Indianapolis IN
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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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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Think about this Question!
In plug-assist thermoforming,In plug-assist thermoforming,what is sliding against what?what is sliding against what?
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Outline
I. A discussion of the coefficient of friction issue
II. A sliding experimentIII. Some prototypical plug
experimentsIV. Conclusions
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I. Some thoughts on the coefficient of friction
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Coefficient of FrictionCoefficient 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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“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-I
“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-II
“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-III
“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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Historical views of coefficient of friction-IV
Coefficient of FrictionCoefficient of Friction
Following discussion assumes that frictional effects are extant in plug-assisted thermoforming
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Blunt-nose plug moving into sheetContact 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 wallWhich of these are relevant when plastic
stretches against plug surface?
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Coefficient of FrictionCoefficient of Friction• Static CoF - Initiation of sliding
between plug (and mold wall) and sheet
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Coefficient of FrictionCoefficient 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 FrictionCoefficient 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 FrictionSliding Coefficient of Friction• Contact area increases with increasing
load
Plastic sheet
Plug
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Sliding Coefficient of FrictionSliding 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 FrictionSliding Coefficient of FrictionWear v. sliding friction
Friction maximum in polymer transition region
Wear minimum in polymer transition region
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Sliding Coefficient of FrictionSliding 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” slidingDry v. “wet” sliding• Dry sliding assumes no lube between
surfaces
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Dry v. “wet” slidingDry 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” slidingDry 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” slidingDry 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” slidingDry 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 slidingSheet does not move far under plug
force
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Measuring Frictional Coefficients
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Traditional methods ofmeasuring coefficient of friction
• Weight sliding on inclined surface
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Traditional methods ofmeasuring coefficient of friction
• Tabor “Abrasor” – stylus rubbing on rotating disk
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Traditional…• Other
methods• No methods
entirely applicable to measuring plug-sheet friction…
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Observations• Frictional resistance is a complex
issue:o Static v. slidingo Dry v. weto The extent of slidingo Boundary v. hydrodynamic effects
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Observations• Frictional resistance is a complex
issue:o Static v. slidingo Dry v. weto The extent of slidingo 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,In plug-assist thermoforming,
what is sliding against what?what is sliding against what?
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II. A sliding experiment
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Traditional…• Other methods• No methods
entirely applicable to measuring plug-sheet 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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ParametersFixed
Sheet, heater temperatureSliding length, times
MeasuredForceBlock 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 time-
dependent force
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Observations• Hot plate experiments yield time-
dependent 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, bullet- or bull-nosed
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Plug design characteristics - Plug typesTapered, bullet- or bull-nosed
ApplicationsVery deep drawsWhere thinning of sidewall is
criticalWhere wall thickness is criticalWhere polymer chills rapidly
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Blunt-nose plug moving into sheetContact 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: = (2-1/)(2C1+2C2/)
For plane strain:(l
2-1)1/2(1-1/l2)=(F/2r)(2C1-2C2)/to
Where 1/l= h = t/to
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Plane strain stretchingForce F required to stretch sheet to a
depth with a flat plug:
F = 2E(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 PlugsInto Circular Sheets
• 0.015-inch natural rubber sheet, 6.75-inch diameter
• Two wooden sphere diametersSmall ball diameter = 0.75 inchLarge ball diameter = 3 inch
• Force and penetration measured with scales
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Schematic of Plug Experiment
Left Half-Initial Plug Position
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Schematic of Plug Experiment
Right Half-Plug Position During Sheet Stretching
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Large Sphere Surface Treatment1. As-is [rough-grained exterior pine]2. Sanded w/200 grit paper3. Wood-putty-filled, sanded w/320 grit
paper4. Filled, sanded, and polished5. Filled, sanded, polished and talc-
coated6. 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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ExperimentDraw a circle on the free portion of the
sheet…
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ExperimentDraw a circle on the free portion of the
sheet…Press the plug into the sheet to a given
depth…
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ExperimentDraw 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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ExperimentDraw 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 of Theory and ExperimentPenetration No Frict Max Frict
Exptl*2.0 in 0.832 0.813 0.8052.4 in 0.778 0.738 0.744
* Average of 9-10 experiments
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Solid Circles – Measured Red Tk
Sheet ThicknessWhat about the relationship between
stretching force and sheet thickness?
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Sheet ThicknessWhat 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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ObservationsThe nature of the dry plug surface
does not substantially affect the amount of force needed to stretch the membrane
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ObservationsThe 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 InterfaceSo far, all experiments have been
with a presumed dry interface…
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Lubed InterfaceSo far, all experiments have been
with a presumed dry interface…
Remember the discussion on wet v. dry sliding?
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Lubed InterfaceSo 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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ObservationsSo, what happened when the
interface is lubricated?
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ObservationsSo, what happened when the
interface is lubricated?If it’s oil-lubed, essentially nothing..
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ObservationsSo, 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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ObservationsSo, 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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ConclusionsFrom 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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ConclusionsFrom 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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ConclusionsSimple measurements show applied
force increases with increasing sheet thickness
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ConclusionsSimple 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 water-based?
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ConclusionsFurthermore, 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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ConclusionsFurthermore, 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 In plug-assist thermoforming,thermoforming,
what is sliding against what?what is sliding against what?
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Questions?
THANK YOU THANK YOU FOR YOUR FOR YOUR ATTENTIONATTENTION!!